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From first principles to machine intelligence: explaining charge carrier behavior in inorganic materials

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From first principles to machine intelligence: explaining charge carrier behavior in inorganic materials

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Content From First Principles to Machine Intelligence:
Explaining Charge Carrier Behavior in Inorganic Materials
By
Jingyi Ran
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMISTRY)
May 2024
Copyright 2024 Jingyi Ran

ii
We are all in the gutter, but some of us are looking at the stars.
- Oscar Wilde, “Lady Windermere’s Fan”

iii
Acknowledgements
The research included in this thesis would not have been achievable without the constant
guidance, valuable insights, and enduring patience of my thesis and research advisor, Prof. Oleg
Prezhdo. His clear direction on my projects, constructive feedback, and unwavering support
through every challenge were central. More than just shaping my research and academic
development, Oleg fostered an environment of open communication and actively championed my
interests - actions that will undoubtedly have a profound impact on my future. Under his guidance,
I transitioned from a graduate student to a researcher at the PhD level. He granted me the freedom
to pursue projects that not only interest me but also aligned with my career aspirations,
significantly boosting my motivation, engagement, and prospects for future success.
My deep gratitude extends to Prof. Curt Wittig, whose trust in me became a beacon of light
during the most challenging times of my PhD journey. Curt was not just a mentor in the academic
sense; he is a wise and experienced guide who generously shared his knowledge and insights with
me. His wisdom, distilled from years of experience, has been guiding me and will continue to
illuminate my path as I navigate the complexities of life.
I am immensely grateful to my colleagues within the Prezhdo group and our collaborators
beyond it. Their significant contributions to my research, along with consistent support and
insightful feedback, were valuable. The solidarity among PhD students is unique, and it was this
community that truly understood the journey. A special word of thanks goes to Carlos, whose
mentorship was incomparable. His recommendation to join the group and his generous guidance
were critical in my research projects. My gratitude extends to Dongyu, Sraddha, and Shriya, whose

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daily support was consistent, and to all members of the Prezhdo group who were always ready to
assist whenever I sought their help. I am also thankful for the opportunity to collaborate with
Christina and Linjie, with whom working on projects was a rewarding experience.
My gratitude towards my family is boundless, for their tenacious understanding,
encouragement, and support throughout my academic journey. Despite the vast distance across the
Pacific Ocean, my parents have consistently been a source of strength, frequently checking in on
me. Their encouragement and trust, especially during the most challenging times, have been a
cornerstone of my perseverance. The parents of my fiancé have also been a source of joy, showing
genuine interest and cheerfulness towards my projects. And most importantly, my fiancé Ryan has
been a strong partner since the beginning of the PhD program. He has been by my side through
both triumphs and trials, always ready to embrace my vulnerabilities and provide support. The
depth of their support is deeply felt and has been instrumental in my journey.
Reflecting on my time in the PhD program in Chemistry at the University of Southern
California, I consider myself incredibly lucky. The opportunity to engage in cutting-edge research
at such a prestigious institution was a remarkable privilege. Beyond the chance to pursue my
academic interests, the program provided me with comprehensive financial support.
Finally, my heartfelt thanks once again go to the members of my thesis committee. Their
time, feedback, and expertise are critical to the refinement of my research. Thank you.
Jingyi Ran, March 2024

TABLE OF CONTENTS
Epigraph .............................................................................................................................................................. ii
Acknowledgements .......................................................................................................................................... iii
List of Tables ...................................................................................................................................................... v
List of Figures .................................................................................................................................................... vi
Abstract ............................................................................................................................................................. vii
Chapter 1: Introduction and Background...................................................................................................... 1
Overview ....................................................................................................................................... 1
Metal Halide Perovskites ............................................................................................................ 1
Defects in Solids .......................................................................................................................... 3
Midgap Trap States in Perovskite Materials ............................................................................ 4
Ion Migration in Perovskite Materials ...................................................................................... 5
Van der Waals (vdW) Interactions in Solids ........................................................................... 6
References ......................................................................................................................................8
Chapter 2: Thesis Objectives......................................................................................................................... 13
Chapter 3: Theory and Computational Methods........................................................................................ 15
The Schrödinger Equation ....................................................................................................... 15
Density Functional Theory (DFT) ......................................................................................... 19
Perdew-Burke-Ernzerhof (PBE) Functionals ....................................................................... 26
Molecular Dynamics (MD) ...................................................................................................... 27
Force Field .................................................................................................................................. 30
VASP ........................................................................................................................................... 30
A Brief Summary of the Adiabatic Dynamics ....................................................................... 31
Nonadiabatic Coupling and Nonadiabatic Molecular Dynamics ....................................... 33

Nonadiabatic Coupling Time v.s. Carrier Lifetime .............................................................. 38
References ....................................................................................................................................39
Chapter 4: Machine Learning Basics............................................................................................................. 42
Machine Learning in Materials Studies .................................................................................. 42
Machine Learning Force Field ................................................................................................. 43
DeePMD-kit ................................................................................................................................44
References ....................................................................................................................................51
Chapter 5: The Electronic Property Studies of the CsPbBr3 Quantum Dot with Halide Vacancies
.................................................................................................................................................................. 53
Chapter 6: The Vacancy Migration Studies in CsPbBr3 Quantum Dot.................................................... 77
Chapter 7: Study on van der Waals Interactions in Perovskite Materials with Point Defects............... 99
Chapter 8: Conclusions and Future Directions.......................................................................................... 117
Conclusions ............................................................................................................................... 117
Ongoing Projects ..................................................................................................................... 118
Bibliography ................................................................................................................................................... 119

v
List of Tables
Table 1. Contributions of p-Orbitals of the Two Pb Atoms .......................................................... 60
Table 2. Pb-Pb distances and Br-Br distances ............................................................................... 98

vi
List of Figures
Figure 1. Overview of the DeePMD-kit Workflow in a TensorFlow graph................................. 48
Figure 2. Optimized structure of CsPbBr3 .................................................................................... 56
Figure 3. Correlation between the energy gap from LUMO to LUMO+
and the Pb-Pb distance in CsPbBr3 with the Br vacancy in the bulk .............................. 58
Figure 4. Projected DOS of CsPbBr3 with Br vacancy in the bulk................................................ 59
Figure 5. Charge densities of the four midgap trap states in CsPbBr3
with the Br vacancy in the bulk ...................................................................................... 60
Figure 6. Relationship between the energy gap from LUMO to LUMO+1
and the displacement of the Pb atom under the Br vacancy on the CsPbBr3 surface ... 61
Figure 7. DOS of CsPbBr3 with the Br vacancy on the surface .................................................. 63
Figure 9. Optimized structure of CsPbBr3.................................................................................... 78
Figure 10. The energy of the optimized structure and the Pb-Pb distances ................................. 79
Figure 11. Calculated energy profiles for the vacancy migration in the interlayer ..................... 81
Figure 12. Calculated energy profiles for the vacancy migration in the intralayer ..................... 83
Figure 13. Schematic illustration ................................................................................................. 85
Figure 14. Optimized geometric structure of orthorhombic CsPbBr3 .......................................... 97
Figure 15. Total energies ............................................................................................................. 99
Figure 16. Electronic density of states ....................................................................................... 100
Figure 17. Fluctuation of the midgap state energy relative to HOMO
in CsPbBr3 with a neutral Br vacancy ...................................................................... 103
Figure 18. Fourier transforms of fluctuations ............................................................................ 105

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Abstract
This thesis explores the applications of computational chemistry and machine learning to
study the behaviors and properties of inorganic materials, with a focus on metal halide perovskites
and 2D materials. It centers the impact of defects in these materials on their performance, including
vacancies, interstitials, and grain boundaries, and their effects on ionic conductivity and charge
carrier mobility. The work also includes the examinations of the midgap trap states and ion
migration in perovskites, highlighting the critical influence of van der Waals interactions. Through
the application of machine learning techniques, this thesis develops predictive models for material
properties, aiming to advance the understanding of metal halide perovskites for photovoltaic
applications and improve the efficiency and stability of devices. This research not only leads the
frontier of knowledge in computational chemistry and materials science but also sets the
groundwork for significant technological advancements in renewable energy and electronics. By
providing deeper insights into the atomic-level interactions within metal halide perovskites and
2D materials, this work paves the way for the development of more efficient, stable, and costeffective photovoltaic devices and electronic applications. Ultimately, the predictive models and
fundamental understanding gained through this thesis have the potential to revolutionize the design
and optimization of materials for a wide range of critical applications, contributing to the global
efforts in sustainable energy and environmental preservation.

Chapter 1
Introduction and Background
1.0 Overview
This chapter underscores the importance of using computational chemistry methods to study
the behaviors and properties of inorganic materials such as perovskites and 2D materials, by
discussing the structures, history, applications, etc. of these materials. This chapter also delves into
the roles of defects in solids, specifically in perovskites, and their impact on material performance.
It examines intrinsic and extrinsic point defects, such as vacancies and interstitials, alongside
extended defects like grain boundaries, detailing their influence on ionic conductivity and overall
material efficacy. Furthermore, the phenomenon of midgap trap states and ion migration in
perovskites are introduced. Additionally, the chapter highlights the critical role of van der Waals
interactions in defining the structural, electronic, and dynamic behaviors of MHPs. The
foundational knowledge is crucial for advancing the studies of inorganic materials.
1.1 Metal Halide Perovskites
Metal halide perovskites (MHPs) are a highly promising class of materials for photovoltaic
applications, primarily stemming from their low manufacturing costs and exceptional electronic
and optical characteristics.
1-3 These include a tunable band gap, which allows for the absorption of
1

a broad spectrum of light,4, 5 long charge carrier diffusion lengths that facilitate efficient charge
transport,6, 7 and strong light absorption capabilities.8, 9 Such attributes enable MHPs to achieve
impressive solar-to-electricity conversion efficiencies of over 25%, surpasses the performance of
traditional semiconductors such as silicon.10 The versatility of the perovskite structure is another
significant advantage, offering a wide array of compositions and dimensionalities. This diversity
means MHPs can be tailored for a variety of applications beyond solar cells, including lightemitting diodes (LEDs), photodetectors, and lasers.11-13
Perovskites are named after the mineral discovered by Gustav Rose in 1839,14 named in honor
of Russian mineralogist Lev Perovski.15 The perovskite structure is characterized by its ABX3
formula, where 'A' and 'B' are cations of different sizes, and 'X' is an anion that bonds to both.
16 In
metal halide perovskites, 'B' is typically a metal cation (such as lead or tin), 'A' is an inorganic or
organic cation (such as cesium or methylammonium), and 'X' is a halide (chlorine, bromine, or
iodine).17 This structure is key to the material's tunable band gap and the ability to absorb a wide
range of the solar spectrum. Over the years, research into MHPs has evolved from curiosity about
their structure and theoretical potential to practical applications, demonstrating their efficacy in
converting sunlight to electricity with high efficiency and exploring their use in other technologies.
CsPbBr3, a specific type of MHP, has got particular interest as a representative material for
studying the broader class of perovskites.18-20 Its importance lies in its stability, high efficiency in
photovoltaic applications, and ease of fabrication, making it an excellent model for understanding
the behavior of MHPs in practical applications.21-24 The applications of CsPbBr3 extend beyond
solar cells - it is also explored in LEDs, photodetectors, and even in creating lasers, highlighting
2

the material's versatility.25-27 The study of CsPbBr3 and other MHPs is crucial not just for
improving solar cell technologies but also for advancing a range of optoelectronic devices.28-31 The
development of atomistic models that can accurately predict the behavior of MHPs over time
scales relevant to device operation is essential. Such models can help in understanding the
structural fluctuations MHPs undergo and their impact on electronic energy levels and defect
properties.32, 33 This understanding is vital for pushing the boundaries of what's possible with MHP
technology, potentially leading to more efficient, cost-effective, and versatile photovoltaic and
optoelectronic devices.
1.2 Defects in Solids
Generally there are two different kinds of defects in solids, point defects such as vacancies and
extended defects such as grain boundaries. Point defects fall into two main categories, intrinsic
defects, and extrinsic defects. Additionally, there are two common kinds of intrinsic defects -
Schottky defects and Frenkel defects. Schottky defects consist of vacancies while Frenkel defects
consist of interstitials – both are common and important defects in perovskite materials.34, 35 In this
thesis, Br vacancies and interstitials in perovskite material CsPbBr3 and grain boundary in 2D
material MoS2 are studied.
Vacancies play an important role in ionic conductivity because the vacancies enable ions to
move through the lattice by lowering the activation energy required for ions to migrate from one
site to another.36 In contrast, interstitial defects, where atoms occupy spaces between the lattice
points that are not normally occupied, can also influence ionic conductivity by providing
alternative paths for ion migration, though their effect is complex and depends on the specific
lattice structure and ion size.37, 38 Grain boundaries are a type of extended defect in materials,
3

unlike point defects such as vacancies. They are interfaces of a 2D plane where the different
orientations of the crystalline meet.39 The most common extrinsic defect, although not discussed
in this thesis, is doping. Doping can create extrinsic defects. Most common doping in perovskite
materials is A site and B site doping.40
1.3 Midgap Trap States in Perovskite Materials
Midgap trap states are generally not ideal for materials like perovskites, particularly in
applications such as solar cells or light-emitting diodes, as the presence of midgap trap states can
increase the frequency and duration of blinking (the phenomenon where the emission of light from
quantum dots intermittently turns on and off), negatively affecting the performance and reliability
of quantum dot-based devices.41-46 Additionally, midgap trap states can capture charge carriers,
hindering their free movement through the material. This leads to a decrease in the charge carrier
mobility, which is crucial for efficient solar energy conversion and light emission.28, 42, 47-49
Furthermore, In LEDs, midgap trap states can also reduce efficiency, because they can capture
electrons or holes, preventing them from recombining radiatively (emitting light). This leads to
less light output for a given amount of electrical input.50, 51 In solar cells, the presence of midgap
trap states can reduce the efficiency of converting sunlight into electricity. Trapped charge carriers
recombine non-radiatively (without emitting light), wasting the energy that could have been
converted to electricity.50
4

1.4 Ion Migration in Perovskite Materials
In perovskite materials and perovskite solar cells, current-voltage hysteresis remains an
important and widely studied phenomenon as it is a key performance measurement and is closely
related to the structures and properties of the perovskite materials.52-54
Current-voltage hysteresis is a phenomenon where the current response of a device to an
applied voltage depends on the history of the voltage – the current measured during the voltage
sweep in one direction (such as increasing voltage) differs from during the sweep in the opposite
direction (decreasing voltage). This phenomenon creates a loop-like feature in the current-voltage
curve, instead of a single, consistent line (in an ideal scenario without hysteresis, the currentvoltage curve during both forward and reverse sweeps should overlap, thus producing a single
line).
The relationship between current and voltage in an ideal solar cell under light can be
described as:
! = !!" − !# %&
$%
&'( − 1( − )
*)
where ! is the current through the solar cell, !!" is the photocurrent generated by the absorbed
light, !# is the dark saturation current, ) is the voltage across the solar cell, + is the charge of an
electron, , is the ideality factor, - is the Boltzmann constant, . is the temperature in Kelvin, and
*) is the series resistance.
In ideal conditions, where series resistance and shunt resistances are negligible, the
relationship between current and voltage is exponential as dominated by the diode equation
5

(!# /&
!"
#$% − 10). The ideal situation indicates the cell's output is stable and predictable under many
conditions. Hysteresis, on the other hand, suggests that there are transient effects such as ion
migration or charge trapping that cause the current at a given voltage to change based on the history
of the applied voltage, which is undesirable for the reasons previously mentioned.
Ion migration in perovskite materials can lead to current-voltage hysteresis for several possible
reasons: (1) Ion accumulation at interfaces: When ions migrate within the perovskite layer under
an electric field (like during the I-V sweep), they can accumulate at interfaces, such as the
perovskite/electron or hole transport layers. This accumulation can create internal electric fields
that oppose the external applied voltage, altering the charge carrier dynamics and leading to
hysteresis.55 (2) Changing the internal electric field: migrating ions can change the internal electric
field in a way that affects the transport and recombination of charge carriers. As the electric field
changes during the I-V sweep, it can alter the rate at which charge carriers are generated, separated,
and collected, which may vary between the forward and reverse sweeps, hence causing
hysteresis.56 (3) Charge trapping and de-trapping: ions that have migrated can also act as trap states
for charge carriers. These traps can capture and release carriers at different rates depending on the
direction and speed of the voltage sweep, leading to a time-dependent effect that contributes to
hysteresis.57
1.5 Van der Waals (vdW) Interactions in Solids
Van der Waals interactions play a crucial role in the properties of materials including metal
halide perovskites. These weak, non-covalent forces significantly influence the structural,
6

electronic, and dynamic behaviors of perovskites. Structurally, vdW interactions help stabilize the
crystal lattice, affecting the material's tolerance to strain and its thermal expansion
characteristics.58 Electronically, they modulate the band structure and electronic states at the edges,
which are critical for the material's optical properties and charge transport capabilities.59
Dynamically, vdW forces impact ion migration within the perovskite lattice, influencing ionic
conductivity and, consequently, the efficiency and stability of perovskite-based devices.60 By
affecting these fundamental properties, vdW interactions are pivotal in optimizing the performance
and durability of metal halide perovskites for a range of applications.61
In the context of CsPbBr3, vdW interactions have a specific and nuanced role in modifying Br
vacancies and interstitials, which are critical defects affecting the material's efficiency and
stability. These interactions can influence the formation energy and migration barriers of Br
defects, thereby determining their concentration and mobility within the crystal lattice. For Br
vacancies, vdW forces can stabilize the local structure around the vacancy, affecting the material's
optical properties by altering the local electronic structure. For Br interstitials, vdW interactions
can modulate the ease with which these defects move, impacting ionic conductivity and the nonradiative recombination of charge carriers. Understanding the role of vdW interactions in these
defect processes is crucial for tailoring defect engineering strategies to improve the photophysical
properties and operational stability of CsPbBr3-based devices. Through careful manipulation of
vdW interactions, it is possible to enhance the material's performance, making CsPbBr3 and related
perovskites more viable for high-efficiency, stable photovoltaic and optoelectronic applications.
7

References
(1) Stranks, S. D.; Snaith, H. J. Metal-Halide Perovskites for Photovoltaic and Light-Emitting Devices.
Nature Nanotechnology 2015, 10 (5), 391-402.
(2) Zhang, W.; Eperon, G. E.; Snaith, H. J. Metal Halide Perovskites for Energy Applications. Nature
Energy 2016, 1 (6), 1-8.
(3) Jena, A. K.; Kulkarni, A.; Miyasaka, T. Halide Perovskite Photovoltaics: Background, Status, and
Future Prospects. Chemical Reviews 2019, 119 (5), 3036-3103.
(4) Filip, M. R.; Eperon, G. E.; Snaith, H. J.; Giustino, F. Steric Engineering of Metal-Halide Perovskites
with Tunable Optical Band Gaps. Nature Communications 2014, 5 (1), 5757.
(5) Unger, E.; Kegelmann, L.; Suchan, K.; Sörell, D.; Korte, L.; Albrecht, S. Roadmap and Roadblocks for
the Band Gap Tunability of Metal Halide Perovskites. Journal of Materials Chemistry A 2017, 5 (23),
11401-11409.
(6) Herz, L. M. Charge-Carrier Mobilities in Metal Halide Perovskites: Fundamental Mechanisms and
Limits. ACS Energy Letters 2017, 2 (7), 1539-1548.
(7) Seitz, M.; Magdaleno, A. J.; Alcázar-Cano, N.; Meléndez, M.; Lubbers, T. J.; Walraven, S. W.; Pakdel,
S.; Prada, E.; Delgado-Buscalioni, R.; Prins, F. Exciton Diffusion in Two-Dimensional Metal-Halide
Perovskites. Nature Communications 2020, 11 (1), 2035.
(8) Manser, J. S.; Christians, J. A.; Kamat, P. V. Intriguing Optoelectronic Properties of Metal Halide
Perovskites. Chemical Reviews 2016, 116 (21), 12956-13008.
(9) Zhao, X.-G.; Yang, J.-H.; Fu, Y.; Yang, D.; Xu, Q.; Yu, L.; Wei, S.-H.; Zhang, L. Design of Lead-Free
Inorganic Halide Perovskites for Solar Cells via Cation-Transmutation. Journal of the American Chemical
Society 2017, 139 (7), 2630-2638.
(10) Chen, J.; Dong, C.; Idriss, H.; Mohammed, O. F.; Bakr, O. M. Metal Halide Perovskites for Solar‐to‐
Chemical Fuel Conversion. Advanced Energy Materials 2020, 10 (13), 1902433.
(11) Fu, Y.; Zhu, H.; Chen, J.; Hautzinger, M. P.; Zhu, X.-Y.; Jin, S. Metal Halide Perovskite
Nanostructures for Optoelectronic Applications and the Study of Physical Properties. Nature Reviews
Materials 2019, 4 (3), 169-188.
(12) Snaith, H. J. Present Status and Future Prospects of Perovskite Photovoltaics. Nature Materials 2018,
17 (5), 372-376.
(13) Green, M. A.; Ho-Baillie, A.; Snaith, H. J. The Emergence of Perovskite Solar Cells. Nature Photonics
2014, 8 (7), 506-514.
(14) Navrotsky, A.; Weidner, D. J. Perovskite: A structure of Great Interest to Geophysics and Materials
Science. Geophysical Monograph Series 1989, 45.
8

(15) Katz, E. A. Perovskite: Name Puzzle and German‐Russian Odyssey of Discovery. Helvetica Chimica
Acta 2020, 103 (6), e2000061.
(16) Glazer, A. Simple Ways of Determining Perovskite Structures. Acta Crystallographica Section A:
Crystal Physics, Diffraction, Theoretical and General Crystallography 1975, 31 (6), 756-762.
(17) Bhalla, A. S.; Guo, R.; Roy, R. The Perovskite Structure—A Review of Its Role in Ceramic Science
and Technology. Materials Research Innovations 2000, 4 (1), 3-26.
(18) Stoumpos, C. C.; Malliakas, C. D.; Peters, J. A.; Liu, Z.; Sebastian, M.; Im, J.; Chasapis, T. C.;
Wibowo, A. C.; Chung, D. Y.; Freeman, A. J. Crystal Growth of the Perovskite Semiconductor CsPbBr3:
A New Material for High-Energy Radiation Detection. Crystal Growth & Design 2013, 13 (7), 2722-2727.
(19) Swarnkar, A.; Chulliyil, R.; Ravi, V. K.; Irfanullah, M.; Chowdhury, A.; Nag, A. Colloidal CsPbBr3
Perovskite Nanocrystals: Luminescence Beyond Traditional Quantum Dots. Angewandte Chemie 2015, 127
(51), 15644-15648.
(20) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
(21) Yu, J.; Liu, G.; Chen, C.; Li, Y.; Xu, M.; Wang, T.; Zhao, G.; Zhang, L. Perovskite CsPbBr3 Crystals:
Growth and Applications. Journal of Materials Chemistry C 2020, 8 (19), 6326-6341.
(22) Zhang, H.; Liu, X.; Dong, J.; Yu, H.; Zhou, C.; Zhang, B.; Xu, Y.; Jie, W. Centimeter-Sized Inorganic
Lead Halide Perovskite CsPbBr3 Crystals Grown by An Improved Solution Method. Crystal Growth &
Design 2017, 17 (12), 6426-6431.
(23) Zhang, M.; Zheng, Z.; Fu, Q.; Chen, Z.; He, J.; Zhang, S.; Yan, L.; Hu, Y.; Luo, W. Growth and
Characterization of All-Inorganic Lead Halide Perovskite Semiconductor CsPbBr3 Single Crystals.
CrystEngComm 2017, 19 (45), 6797-6803.
(24) Rakita, Y.; Kedem, N.; Gupta, S.; Sadhanala, A.; Kalchenko, V.; Böhm, M. L.; Kulbak, M.; Friend,
R. H.; Cahen, D.; Hodes, G. Low-Temperature Solution-Grown CsPbBr3 Single Crystals and Their
Characterization. Crystal Growth & Design 2016, 16 (10), 5717-5725.
(25) Zhang, C.; Wang, S.; Li, X.; Yuan, M.; Turyanska, L.; Yang, X. Core/Shell Perovskite Nanocrystals:
Synthesis of Highly Efficient and Environmentally Stable FAPbBr3/CsPbBr3 for LED applications.
Advanced Functional Materials 2020, 30 (31), 1910582.
(26) Kang, C. H.; Dursun, I.; Liu, G.; Sinatra, L.; Sun, X.; Kong, M.; Pan, J.; Maity, P.; Ooi, E.-N.; Ng, T.
K. High-Speed Colour-Converting Photodetector with All-Inorganic CsPbBr3 Perovskite Nanocrystals for
Ultraviolet Light Communication. Light: Science & Applications 2019, 8 (1), 94.
(27) Huang, C.-Y.; Zou, C.; Mao, C.; Corp, K. L.; Yao, Y.-C.; Lee, Y.-J.; Schlenker, C. W.; Jen, A. K.;
Lin, L. Y. CsPbBr3 Perovskite Quantum Dot Vertical Cavity Lasers with Low Threshold and High Stability.
Acs Photonics 2017, 4 (9), 2281-2289.
9

(28) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on A
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(29) Li, W.; Vasenko, A. S.; Tang, J.; Prezhdo, O. V. Anharmonicity Extends Carrier Lifetimes in Lead
Halide Perovskites at Elevated Temperatures. The Journal of Physical Chemistry Letters 2019, 10 (20),
6219-6226.
(30) Strandell, D.; Mora Perez, C.; Wu, Y.; Prezhdo, O. V.; Kambhampati, P. Excitonic Quantum
Coherence in Light Emission from CsPbBr3 Metal-Halide Perovskite Nanocrystals. Nano Letters 2023, 24
(1), 61-66.
(31) Ran, J.; Wang, B.; Wu, Y.; Liu, D.; Mora Perez, C.; Vasenko, A. S.; Prezhdo, O. V. Halide Vacancies
Create No Charge Traps on Lead Halide Perovskite Surfaces but Can Generate Deep Traps in the Bulk. The
Journal of Physical Chemistry Letters 2023, 14 (26), 6028-6036.
(32) Baker, H.; Perez, C. M.; Sonnichsen, C.; Strandell, D.; Prezhdo, O. V.; Kambhampati, P. Breaking
Phonon Bottlenecks Through Efficient Auger Processes in Perovskite Nanocrystals. ACS Nano 2023, 17
(4), 3913-3920.
(33) Wu, Y.; Liu, D.; Chu, W.; Wang, B.; Vasenko, A. S.; Prezhdo, O. V. Fluctuations at Metal Halide
Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis.
ACS Applied Materials & Interfaces 2022, 14 (50), 55753-55761.
(34) Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C. G.
First-Principles Calculations for Point Defects in Solids. Reviews of modern physics 2014, 86 (1), 253.
(35) Stoneham, A. M. Theory of Defects in Solids: Electronic Etructure of Defects in Insulators and
Semiconductors; Oxford University Press, 2001.
(36) Ai, M.; Zhang, J. W.; Wu, Y. W.; Pan, L.; Shi, C.; Zou, J. J. Role of Vacancies in Photocatalysis: A
Review of Recent Progress. Chemistry–An Asian Journal 2020, 15 (22), 3599-3619.
(37) Yuan, Y.; Huang, J. Ion Migration in Organometal Trihalide Perovskite and Its Impact on Photovoltaic
Efficiency and Stability. Accounts of Chemical Research 2016, 49 (2), 286-293.
(38) Liu, Z.; Qin, L.; Cao, X.; Zhou, J.; Pan, A.; Fang, G.; Wang, S.; Liang, S. Ion Migration and Defect
Effect of Electrode Materials in Multivalent-Ion Batteries. Progress in Materials Science 2022, 125,
100911.
(39) Amelinckx, S.; Dekeyser, W. The Structure and Properties of Grain Boundaries. In Solid state physics,
Vol. 8; Elsevier, 1959; pp 325-499.
(40) Wang, J. T.-W.; Wang, Z.; Pathak, S.; Zhang, W.; deQuilettes, D. W.; Wisnivesky-Rocca-Rivarola,
F.; Huang, J.; Nayak, P. K.; Patel, J. B.; Yusof, H. A. M. Efficient Perovskite Solar Cells by Metal Ion
Doping. Energy & Environmental Science 2016, 9 (9), 2892-2901.
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(41) Jin, H.; Debroye, E.; Keshavarz, M.; Scheblykin, I. G.; Roeffaers, M. B.; Hofkens, J.; Steele, J. A. It's
A Trap! On the Nature of Localised States and Charge Trapping in Lead Halide Perovskites. Materials
Horizons 2020, 7 (2), 397-410.
(42) Wu, Y.; Chu, W.; Vasenko, A. S.; Prezhdo, O. V. Common Defects Accelerate Charge Carrier
Recombination in CsSnI3 without Creating Mid-Gap States. The Journal of Physical Chemistry Letters
2021, 12 (36), 8699-8705.
(43) Wu, X.; Trinh, M. T.; Niesner, D.; Zhu, H.; Norman, Z.; Owen, J. S.; Yaffe, O.; Kudisch, B. J.; Zhu,
X.-Y. Trap States in Lead Iodide Perovskites. Journal of the American Chemical Society 2015, 137 (5),
2089-2096.
(44) Levine, I.; Vera, O. G.; Kulbak, M.; Ceratti, D.-R.; Rehermann, C.; Marquez, J. A.; Levcenko, S.;
Unold, T.; Hodes, G.; Balberg, I. Deep Defect States in Wide-Band-Gap ABX3 Halide Perovskites. ACS
Energy Letters 2019, 4 (5), 1150-1157.
(45) Staub, F.; Rau, U.; Kirchartz, T. Statistics of the Auger Recombination of Electrons and Holes via
Defect Levels in the Band Gap—Application to Lead-Halide Perovskites. ACS omega 2018, 3 (7), 8009-
8016.
(46) Zhou, Y.; Poli, I.; Meggiolaro, D.; De Angelis, F.; Petrozza, A. Defect Activity in Metal Halide
Perovskites with Wide and Narrow Bandgap. Nature Reviews Materials 2021, 6 (11), 986-1002.
(47) Li, L.; Lin, M.-F.; Zhang, X.; Britz, A.; Krishnamoorthy, A.; Ma, R.; Kalia, R. K.; Nakano, A.;
Vashishta, P.; Ajayan, P. Phonon-Suppressed Auger Scattering of Charge Carriers in Defective TwoDimensional Transition Metal Dichalcogenides. Nano Letters 2019, 19 (9), 6078-6086.
(48) Wang, B.; Chu, W.; Wu, Y.; Casanova, D.; Saidi, W. A.; Prezhdo, O. V. Electron-Volt Fluctuation of
Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale. The Journal of Physical Chemistry
Letters 2022, 13 (25), 5946-5952.
(49) Qiao, L.; Fang, W. H.; Long, R.; Prezhdo, O. V. Extending Carrier Lifetimes in Lead Halide
Perovskites with Alkali Metals by Passivating and Eliminating Halide Interstitial Defects. Angewandte
Chemie 2020, 132 (12), 4714-4720.
(50) Sandberg, O. J.; Kaiser, C.; Zeiske, S.; Zarrabi, N.; Gielen, S.; Maes, W.; Vandewal, K.; Meredith, P.;
Armin, A. Mid-Gap Trap State-Mediated Dark Current in Organic Photodiodes. Nature Photonics 2023,
17 (4), 368-374.
(51) Polyakov, A.; Smirnov, N.; Yakimov, E.; Tarelkin, S.; Turutin, A.; Shemerov, I.; Pearton, S.; Bae, K.-
B.; Lee, I.-H. Deep Traps Determining the Non-Radiative Lifetime and Defect Band Yellow Luminescence
in N-GaN. Journal of Alloys and Compounds 2016, 686, 1044-1052.
(52) Meloni, S.; Moehl, T.; Tress, W.; Franckevičius, M.; Saliba, M.; Lee, Y. H.; Gao, P.; Nazeeruddin, M.
K.; Zakeeruddin, S. M.; Rothlisberger, U. Ionic Polarization-Induced Current–Voltage Hysteresis in
CH3NH3PbX3 Perovskite Solar Cells. Nature Communications 2016, 7 (1), 10334.
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(53) Unger, E. L.; Hoke, E. T.; Bailie, C. D.; Nguyen, W. H.; Bowring, A. R.; Heumüller, T.; Christoforo,
M. G.; McGehee, M. D. Hysteresis and Transient Behavior in Current–Voltage Measurements of HybridPerovskite Absorber Solar Cells. Energy & Environmental Science 2014, 7 (11), 3690-3698.
(54) Snaith, H. J.; Abate, A.; Ball, J. M.; Eperon, G. E.; Leijtens, T.; Noel, N. K.; Stranks, S. D.; Wang, J.
T.-W.; Wojciechowski, K.; Zhang, W. Anomalous Hysteresis in Perovskite Solar Cells. The Journal of
Physical Chemistry Letters 2014, 5 (9), 1511-1515.
(55) Jacobs, D. A.; Wu, Y.; Shen, H.; Barugkin, C.; Beck, F. J.; White, T. P.; Weber, K.; Catchpole, K. R.
Hysteresis Phenomena in Perovskite Solar Cells: the Many and Varied Effects of Ionic Accumulation.
Physical Chemistry Chemical Physics 2017, 19 (4), 3094-3103.
(56) Weber, S. A.; Hermes, I. M.; Turren-Cruz, S.-H.; Gort, C.; Bergmann, V. W.; Gilson, L.; Hagfeldt,
A.; Graetzel, M.; Tress, W.; Berger, R. How the Formation of Interfacial Charge Causes Hysteresis in
Perovskite Solar Cells. Energy & Environmental Science 2018, 11 (9), 2404-2413.
(57) Kalon, G.; Jun Shin, Y.; Giang Truong, V.; Kalitsov, A.; Yang, H. The Role of Charge Traps in
Inducing Hysteresis: Capacitance–Voltage Measurements on Top Gated Bilayer Graphene. Applied Physics
Letters 2011, 99 (8).
(58) Stöhr, M.; Van Voorhis, T.; Tkatchenko, A. Theory and Practice of Modeling van der Waals
Interactions in Electronic-Structure Calculations. Chemical Society Reviews 2019, 48 (15), 4118-4154.
(59) Ferri, N.; DiStasio Jr, R. A.; Ambrosetti, A.; Car, R.; Tkatchenko, A. Electronic Properties of
Molecules and Surfaces with A Self-Consistent Interatomic van der Waals Density Functional. Physical
Review Letters 2015, 114 (17), 176802.
(60) Wang, Y.; Gould, T.; Dobson, J. F.; Zhang, H.; Yang, H.; Yao, X.; Zhao, H. Density Functional Theory
Analysis of Structural and Electronic Properties of Orthorhombic Perovskite CH3NH3PbI3. Physical
Chemistry Chemical Physics 2014, 16 (4), 1424-1429.
(61) Hermann, J.; DiStasio Jr, R. A.; Tkatchenko, A. First-Principles Models for van der Waals Interactions
in Molecules and Materials: Concepts, Theory, and Applications. Chemical Reviews 2017, 117 (6), 4714-
4758.
12

Chapter 2
Thesis Objectives
1. Exploring the Importance and Applications of Computational Chemistry and
Machine Learning in Material Science: This thesis highlights the significance of using
computational methods to study the behaviors and properties of inorganic materials, with
a focus on perovskites and 2D materials. It probes the impact of defects in solids on
material performance and introduces the role of midgap trap states and ion migration in
perovskites. Furthermore, it underscores the critical role of van der Waals interactions in
these materials.
2. Leading Machine Learning Applications in Material Science: The thesis sets out to
apply machine learning techniques to develop predictive models that can understand and
predict a material's physical and chemical properties based on its composition and structure
using the CsPbBr3 perovskite prototype. This involves using machine learning force fields
for molecular dynamics simulations and ab initio methods to model the interactions of
atoms and molecule over time.
3. Researching Nonadiabatic Dynamics for Material Properties: The thesis aims to
investigate the nonadiabatic dynamics in material simulations, acknowledging the dynamic
interplay between electronic and nuclear motions. This involves understanding how
13

electronic states change with nuclear motion, which is crucial for modeling chemical
reactions involving excited states or the influence of external electromagnetic fields.
4. Examining Metal Halide Perovskites for Photovoltaic Applications: This thesis aims
to investigate the promising attributes of metal halide perovskites for solar energy
conversion by understanding the complicated structure-property relationships inherent to
materials, leveraging machine learning algorithms for predictive modeling.
5. Understanding the Role of Defects in Solids: This thesis explores the impact of point and
extended defects, such as vacancies, interstitials and grain boundaries, on the properties
and performance of inorganic materials. It focuses on Br vacancies and interstitials in
CsPbBr3 and grain boundaries in MoS2, analyzing their effects on ionic conductivity,
charge carrier mobility, and device efficiency.
6. Investigating the Influence of Van der Waals Interactions: This thesis emphasizes the
significance of van der Waals forces in determining the structural, electronic, and dynamic
properties of materials. It discusses how these non-covalent interactions affect the crystal
lattice stability, band structure, ion migration, and overall material performance,
particularly in the prototype metal halide perovskite CsPbBr3.
14

Chapter 3
Theory and Computational Methods
3.1 The Schrödinger Equation
Quantum mechanics depends on finding solutions to the Schrödinger equation. The equation
tells a lot about the systems such as the kinetic and the potential energies, the most stable
geometries and the vibrational electronic energy levels.1
12Ψ = 4Ψ
which is the non-relativistic, time-independent Schrödinger equation. Where 12 is the Hamiltonian
operator and Ψ is the wave function - a set of solutions (eigenstates) of the Hamiltonian. The
Hamiltonian is a differential operator that represents the total energy of the system – the sum of
the kinetic and potential energies. The wave function is a set of eigen functions that are solutions
of the Hamiltonian. These solutions are referred to as eigenstates and each eigenstate Ψ& has a
corresponding eigenvalue En, which is a real number. En is the energy of eigenstate Ψ&.
The detailed definition of the Hamiltonian depends on the physical system we wish to
describe using the Schrödinger equation. Several well-known examples include the particle in a
box and the simple harmonic oscillator. The examples have the simple form of Hamiltonian.
However, the type of systems involved in this thesis, specifically materials, molecules, and
surfaces, are much more complicated, as there are many electrons interacting with multiple nuclei
15

in these systems. Here is a Hamiltonian operator for a system consisting of M nuclei and N
electrons in the absence of external magnetic or electric fields.
It is extremely complicated to find a solution for this system as all the contribution
interaction of every single electron in nucleus simultaneously.
Thus, ways to simplify this problem were studied. An important simplification for this
complex problem can be obtained from the following observation. The mass of an electron and a
given nucleus differ by at least three orders of magnitude. A consequence of this observation is
given the same amount of kinetic energy, the electrons will travel at least three orders of magnitude
faster than the nucleus (5&6789:; = <*+&'
,-)) ). In other words, to the electrons it appears as if the
nuclei are fixed in place, while to the nuclei the electrons appear to instantaneously respond to
their every move. Hence, the problem can be simplified by splitting it into two different parts – (1)
the electronic part and (2) the nuclear part. Then, the two parts can be solved separately. The
electronic part can be first solved by treating the nuclei as fixed with respect to the electrons and
16

the nuclei part can be solved using the potential energy surface (PES) calculated from the
electronic part.2-4 The electronic part is solved repeatedly as the nuclei positions are changed in
small steps, so the electronic energy can be mapped out as a function of the nuclei coordinates to
produce a PES.
The separation of the problem into electronic and nuclear parts is known as the BornOppenheimer approximation (The B.O. Approx.).
5, 6 The B.O. Approx. simplifies the
Hamiltonian by making the kinetic energy of the nuclei zero and the nuclei-nuclei repulsion a
constant, thus the molecular system interested can be described almost entirely by the “electronic
Hamiltonian”.
The solution to the Schrödinger equation with an electronic Hamiltonian is the electronic
wave function Ψ./.0 with the eigenvalues 4./.0. The electronic wave function depends only on the
17

electrons’ spatial coordinates, although a complete description must include the electron spin (up
or down). The electronic wave function depends on the nuclei coordinates only parametrically, so
the nuclei coordinates do not explicitly in Ψ./.0. The wave function solution of the system that
gives the lowest energy is called the ground state. The eigen value of the ground state wave
function is call ed the ground state energy. However, beyond trivial systems, it is impossible to
exactly determine the electronic wave function, as the last term in the electronic Hamiltonian is
difficult to solve (∑ ∑ 1
2()
3
4 61
3
781 ). This is because each electron simultaneously experiences an
electrostatic repulsion through the presence of every other electron. As a result, this is a manybody problem. To get past this rather major roadblock, an approximation to the true wave function
is needed.
1
>./.0?Ψ./.0(A⃑1, … , A⃑3) = 4./.0Ψ./.0(A⃑1, … , A⃑3)
where A⃑7 is the electron position.
In developing this approximation, it is worth remembering the wave function itself cannot
be directly measured. Instead, something that in principle can be measured is the probability that
there are N electrons at some particular set of coordinates A⃑1 through A⃑3. The probability is given
by
|Ψ(A⃑1, … , A⃑3)|* = Ψ ∗ (A⃑1, … , A⃑3)?(A⃑1, … , A⃑3)
(The square of the electron wave function equals to Ψ ∗ time Ψ, where the asterisk the star denotes
a complex conjugate.)
?(A⃑1, … , A⃑3) can be approximated as a product of individual electron wave functions as known by
a Hartree product.
7-9
18

Ψ(A⃑1, … , A⃑3) ≅ Ψ1(A⃑)?*(A⃑) … Ψ3(A⃑)
Another point to make here is in experiments electrons are indistinguishable, so they cannot
be labeled as electron1, electron2, etc. Hence, what we can measure is the probability that any
order of a set of N electrons are the coordinates A⃑1 through A⃑3.
Something closely related is the density of electrons at a particular position in space and as
a function of position. The electron density can be calculated by how many electrons will on
average we found at this position. By summing over all the probabilities that an electron in the
individual electron wave function ?7 as a function of r is located at the position r, the factor of two
before the summation comes from the electrons having spin, because of this according to the Pauli
exclusion principle, each individual electronic wave function can be occupied by two separate
electrons if they have opposite spins. It is important to note that the electron density contains a lot
of information that is observable from the full wave function, but it is a much simpler quantity to
handle as it is a function of only three spatial coordinates rather than 3N coordinates.
,(A⃑) = 2J?7
∗
7
(A⃑)?7(A⃑)
How can the electron density be used to obtain a solution to the Schrödinger equation? The
answer is the use of density functional theory (DFT), which is a way of simplifying the process
of finding solutions to the Schrödinger equation using the electron density.
3.1 Density Functional Theory (DFT)
Density functional theory (DFT) is particularly useful and well-suited for a wide range of
electronic and static properties of molecules and materials. The properties include band structure,
19

density of states, molecular orbital energies, electron density distribution, magnetic properties and
even redox potentials.
The entire field of DFT is based on two fundamental mathematical theorems proved by Kohn
and Hohenberg as well as on the later derivation of a set of equations by Kohn and Sham.10-12 The
first of the Kohn-Hohenberg theorem states the ground state energy E from the Schrödinger’s
equation is a unique functional of the electron density n(A⃑). The second theorem states the electron
density that minimizes the energy of the overall functional is the true electron density,
corresponding to the full solution of the Schrödinger equation.
Functionals mentioned earlier are defined as – a functional takes a function as its input and
outputs a single number. For example, K[M(N)] = ∫ M(N)QN 1
:1 where M(N) = N* + 1, after
evaluating this functional gives K[M(N)] = 8/3.
Using the definition of functional, we can return to the Kohn-Hohenberg theorem and restate
the result as there existing a one-to-one mapping between the ground state wave function and the
ground state electron density E[n(A⃑)] = E - the ground state energy of a system can be expressed
as a functional of the electron density, which is known as the density functional theory.
Thus, by taking advantage of the Kohn-Hohenberg theorems the problem of solving the
Schrödinger equation can be reduced from finding a function of 3N variables (the wave function
defining in a function) to just three variables (the electron density). The complete energy functional
described by the Kohn-Hohenberg theorems in terms of single electron wave functions is E[{Ψ7}]
20

and the wave functions collectively define the electron density. The terms of the energy functional
can be split into two major parts. The first part, 4'&<& , a function of Ψ, is a collection of the
terms that can be written down in a simple analytic form. Everything else is a part of EXC.
4[{Ψ7}] = 4'&<& [{Ψ7}] + 4=>[{Ψ7}]
The 4'&<& include four contributions: (1) the electron kinetic energies, (2) the Coulomb
interactions between electrons and nuclei, (3) the Coulomb interactions between pairs of electrons
and (4) the Coulomb interactions between pairs of nuclei.
4'&<& [{Ψ7}] = JX Ψ7
∗
∇*?7Q?A + X )(A⃑),(A⃑)Q?A
7
+
1
2Z,(A⃑),(A⃑@
)
|A⃑ − A⃑@| Q?AQ?A′ + 47;&
While 4=>[{Ψ7}] is the exchange correlation functional, which includes all the quantum
mechanical effects not included in the 4'&<& [{Ψ7}] terms.
The way to finding the minimum energy solutions to the total energy functional is given
by Kohn and Sham – they showed the task of finding the right electron density can be expressed
in a way that involves solving a set of equations in which each equation involves only a single
electron. The equations are superficially similar to the electronic Hamiltonian though the main
difference is the Kohn-Sham equations are missing the summations that appear inside the full
Schrödinger equation, because the solutions of the Kohn-Sham equations are single electron wave
functions that depend only on the three spatial variables instead of 3N.
\
1
2 ∇* + )(A⃑) + )A(A⃑) + )=>(A⃑)] Ψ7(A⃑) = ^7Ψ7(A⃑)
21

The first of these terms (1
*
∇*) represents the kinetic energy of the electron while the latter
three terms ()(A⃑), )A(A⃑), )=>(A⃑)) are potentials. )(A⃑) is the potential from the interaction between
an electron and a collection of atomic nuclei. )A(A⃑) is the Hartree potential which describes the
Coulomb repulsion between the electron being considered in one of the Kohn-Sham orbitals and
the total electron density defined by all electrons in the problem ()A(A⃑) = ∫ &B2⃑*D
|2⃑: 2⃑*|
Q?A′). As a
result, the Hartree potential includes a self-interaction contribution because the electron describing
the Kohn-Sham equations is also a part of the total electron density. Part of the Hartree potential
includes a Coulomb interaction between the electron and itself which is an unphysical result. The
correction for this self-interaction is )=>(A⃑). )=>(A⃑) is the potential that defines the exchange and
correlation contributions to the single-electron equations. It can be defined as a functional
derivative of the exchange correlation energy with respect to the electron density ()=>(A⃑) =
F++,(2⃑)
F&(2⃑) ).
The transformation from the Schrödinger equation to the Kohn-Sham equations in DFT is
a fascinating process as it makes it feasible computationally. The Schrödinger equation involves a
many-electron system, which makes it incredibly complex due to the electron-electron
interactions. Luckily, the Kohn-Sham equations of DFT provide an accurate way to approximate
the solutions to the many-body problem by transforming it into a non-interacting electrons
problem, where the non-interacting electrons (electrons do not exert electrostatic forces on each
other, but the non-interacting system still interact with the nuclei) moving in an effective potential.
The equation of the Kohn-Sham approach looks like this:
_− ℎ*
2a
∇* + ).II(A)bc7(A) = ^7c7(A)
22

where c7(A) are the Kohn-Sham orbitals for the non-interacting system, ^7 is the orbital energies,
and ).II(A) is the effective potential including the external potential, the Hartree potential
(electron-electron repulsion potential) and the exchange-correlation potential.
).II(A) , the effective potential, is a key concept as it allows for the simplification of the manybody problem of interacting electrons. The equation for the effective potential is:
).II(A) = ).JK(A) + )A(A) + )J0(A)
where ).JK(A) is the external potential, which is from the nuclei and any external fields. So the
electron feels the positively charged nuclei in the system. )A(A) is the Hartree potential, which
accounts for the classical electrostatic interaction between the electrons. It represents the electronelectron repulsion and is calculated as the electrostatic potential due to the charge distribution of
all the electrons. )J0(A) is a functional of the electron density, which is a potential depends on the
position and is determined by the entire electron density distribution.
In summary, Kohn-Sham equations consider an auxiliary system which simplifies the DFT
calculations in three ways: (1) effective potential: The Kohn-Sham DFT reduces the complexity
of electron-electron interactions by incorporating them into an effective potential, ).II(A), which
avoids the need to calculate the interactions directly. (2) Exchange-correlation functional: the
exchange-correlation potential accounts for the complex many-body interactions in a functional
form, which is easier to compute than the individual interactions. (3) Single-particle equations: the
Kohn-Sham equations are a set of single-particle equations, which are significantly easier to solve
than the many-particle Schrödinger equation.
23

However, there might be a circular about the Kohn-Sham equations: to solve the KohnSham equations, it is required to define the Hartree potential. To define the Hartree potential
requires knowing the electron density. To find the electron density requires knowing the single
electron wave functions. To know the wave functions requires soling the Kohn-Sham equations.
To break the circle, the problem is usually treated in an iterative fashion. The brief steps
are shown below:
Step 1. Define an initial, trial electron density, ,(A⃑).
Step 2. Solve the Kohn-Sham equations defined using the trial electron density to find the singleparticle wave functions, ?7(A⃑).
Step 3. Calculate the electron density defined by the Kohn-Sham single-particle wavefunctions
from step two, ,LM(A⃑) = 2 ∑ ?7
∗ 7 (A⃑)?7(A⃑).
Step 4. Compare the calculated electron density, ,LM(A⃑), with the trial electron density used to
solve the Kohn-Sham equations, ,(A⃑). If these densities are the same, this is the ground-state
electron density. Otherwise update the trial electron density somehow and begin again at Step 2.
The useful way to classify quantum chemistry calculations is according to the types of functions
used to represent the solutions. Broadly speaking the types of functions used are either spatially
localized such as for cluster calculations or spatially extended such as for bulk calculations.
24

If calculations based on the bulk materials are the main interest, periodic functions are often
used to describe them. The methods based on the spatially periodic functions are known as planewave methods.
13-17
Additionally, there is still a small holdup when it comes to solving the Kohn-Sham
equations – to solve them requires specifying the exact exchange correlation functional )=>(A⃑).
However, finding this exchange correlation functional is very difficult as the true form of the
exchange correlation functional is not known. Fortunately, there is one case where this functional
can be exactly derived: the uniform electron gas. In this case, the electron density is constant at all
points in space although this might not seem extremely useful since in any real material it is the
variation in electron density that makes things interesting. On the other hand, some approximations
are used.
One of the most common approximations is the local density approximation. The uniform
electron gas provides a practical way to use the Kohn-Sham equations. To achieve this, the
exchange correlation potential at each position should be set as the known exchange correlation
potential from a uniform electron gas at the electron density observed at that position. This
approximation uses only the local density to define the approximate exchange correlation
functional. Thus, it is called the local density approximation (LDA).
11
)=>(A⃑) = )=>
./.0K2;& N-)[,(A⃑)]
25

The LDA provides a way to completely define the Kohn-Sham equations although the
results from these equations do not solve the Schrödinger equation exactly as there are a few
approximations involved.
Another commonly used approximation is the generalized gradient approximation (GGA),
which uses information about the local electron density and the local gradient in the electron
density.18 There are many ways the information from the gradient of the electron density can be
included in a GGA functional. The most used GGA functionals for solids are the Perdew-Wang
(PW91)19 or Perdew-Burke-Ernzerhof (PBE)18, 20 functionals. Since different functional give
different results for any particular configuration of atoms, it is necessary to specify the functional
used in a particular calculation.
3.2 Perdew-Burke-Ernzerhof (PBE) Functionals
The use of different DFT functionals, such as PBE (Perdew-Burke-Ernzerhof), 20(PBE with
Grimme's D3 dispersion correction),21 and PBE+TS (PBE with Tkatchenko-Scheffler dispersion
correction),22, 23 reflects attempts to accurately account for these interactions. The PBE functional,
while widely used for its efficiency and general applicability, often underestimates vdW forces
due to its inherent limitations in capturing long-range electron correlation effects. The addition of
dispersion corrections, as in PBE+D3 and PBE+TS, enhances the ability of DFT calculations to
model the subtle yet significant vdW interactions. These corrections are crucial for predicting the
correct lattice parameters, band structures, and defect properties in metal halide perovskites. By
improving the representation of vdW interactions, these enhanced DFT approaches enable more
accurate simulations of the material's properties, aiding in the design and optimization of
perovskite-based devices.
26

3.3 Molecular Dynamics (MD)
Molecular dynamics (MD) is a complimentary method to DFT. DFT provides detailed
information about the electronic structure and static properties of a system, MD provides insights
into the dynamic behavior.
24, 25 MD first allows for the simulation of the time evolution of atomic
and molecular systems, which provides insights into how the system evolves, interact and respond
to various conditions over time. MD is also essential for the study of diffusion and phase transitions
as temperature, pressure and external forces are involved.26-28 Additionally, MD is well-suited for
larger systems such as biological macromolecules and polymers and nanomaterials and complex
environments such as solutions and interfaces.
29, 30 Furthermore, MD can help explore pathways
and barriers of chemical reactions.31, 32 The underlying physics of MD relies on Newtonian
mechanics, while the DFT stems from the quantum nature in solving the Schrödinger equation. As
a result, MD approach focuses on the macroscopic picture – the atomic movements, whereas the
DFT method focuses on the electronic structure and property changes, being a quantum
mechanical method.
MD and DFT are sometimes combined in simulations, known as the ab initio, where DFT
calculates the forces acting on the atoms at each timestep of an MD simulation.33
Traditional MD simulations treat atoms as classical particles and use Newton’s equations of
motion to predict the trajectory of atoms and molecules over time. The essence of MD simulations
is how atomic positions and velocities evolve over time from forces derived from a potential
energy surface. The equation can be derived as:
A(:) + 5(:)d: = A(: + d:)
27

r(t) – all the atom positions at time t
v(t) – velocity at time t
d: – the change in time
A(: + d:) – the positions of the atoms at time t plus d:
5(: + d:) = 5(:) + e(:)d:
The velocity of : + d: comes from adding the initial velocity (5(:)) to the acceleration at time t
times d: (e(:)d:).
e(:) = K(:)
a
Newton’s equations of motion.
F(t) – force
m – mass
K = − Q
QA )(A)
Force itself comes from the negative derivative of the potential energy ()(A)), especially
when discussing ab initio molecular dynamics (AIMD). The potential energy )(A) is calculated
using quantum mechanics, typically through methods like DFT.
V(r) is the key as it is the interatomic potentials, which is also closely related to force field.
The following figure shows the equation of )(A).
28

The equation of )(A) defines: (1) the energy based on the bonds between atoms (harmonic
band), (2) the energy based on the angles between three atoms (harmonic angle), (3) the energy
based on dihedral angles between four atoms and a rotation about the central bond, (4) through
space energy Van der Waals, and (5) through space energy electrostatic.
With this equation the molecular dynamics trajectories can be stepped through time.
Additionally, the potential energy is the sum over all the bonds, angles, dihedrals, Van der Waals
and electrostatic energies for all the atoms in the trajectory.
From here, the force can be calculated based on the negative gradient of this potential
function V (see equation below):
K = −∇)
29

Newton’s equations of motions are based on the force calculated from the equation above.
Then the position (R(t)) of all the atoms in the system at any point in time can be calculated.
a
Q*N
Q:* = K(:) − fa
QN
Q: + *(:)
3.4 Force Field
A force field in this context is a set of mathematical functions and parameters used to calculate
the forces acting on each atom in the system.34, 35 Specifically, it provides a mathematical
description of the potential energy )(A) as a function of the positions of the atoms A in the system.
Essentially, it describes how atoms interact with each other. Force field usually includes terms for
bonded interactions such as bonds, angle, dihedrals, and non-bonded interactions such as van der
Waals forces and electrostatic interactions. As mentioned above, force field determines the values
of the Vbond, Vangle, Vdihedral, VvdW and Velec to in turn determine the potential energy )(A).
In MD simulations, force field is critical, yet it is not derived from MD itself. Instead, the force
field is an input to MD simulations to provide the necessary information to calculate the forces on
each atom at each step in the simulation based on their positions. Thus, force field directly impacts
the dynamics of the system, and consequently affects the predictions of structural and
thermodynamics properties.
3.5 VASP
Five different input files must be prepared, and they are the INCAR, KPOINTS, POSCAR,
POTCAR, and job submission files:
15, 36
30

- INCAR: contains all the tags used to define the calculation parameters; "what to do and
how to do it".
- KPOINTS: specifies the Bloch vectors (k-points) that will be used to sample the Brillouin
zone.
- POSCAR: defines the supercell dimensions and all atomic positions.
- POTCAR: contains the pseudopotential for each atomic species used in the calculation.
- The job submission file: contains instructions required for the computer to run the VASP
calculations.
3.6 A Brief Summary of the Adiabatic Dynamics and A Short Intro to the Nonadiabatic
Dynamics
The key difference between the traditional molecular dynamics and nonadiabatic molecular
dynamics largely lies in how the potential energy V(r) is treated. A simplification often used in
conventional molecular dynamics simulations. In traditional molecular dynamics simulations, the
electronic states of the molecules or materials being simulated are considered to be fixed or
unchanging during the course of the simulation. This is often referred to as the "Born-Oppenheimer
Approximation." The assumption is that the motion of the nuclei (the atoms' cores) and the
electrons can be separated. The electrons are assumed to instantly adjust to any changes in the
positions of the nuclei, maintaining a constant electronic state. The nuclei move on a static
potential energy surface that is determined by these fixed electronic states. This surface describes
how the potential energy of the system varies with the positions of the nuclei. This approach is
generally suitable for systems where electronic transitions are not significant to the process being
studied, such as many ground-state reactions or physical transformations. However, this static
31

approach does not capture the effects of electronic excitations or the coupling between electronic
and nuclear motions, which can be critical in processes like photochemical reactions, nonradiative
transitions, and other phenomena where the electronic state of the system changes over time.
In contrast, nonadiabatic molecular dynamics simulations do not make this simplification.
They consider the dynamic interplay between electronic and nuclear motions, allowing for the
study of processes where the electronic states can change, such as during chemical reactions
involving excited states or under the influence of external electromagnetic fields.
Up till now the theory discussed is all about the adiabatic dynamics and they have three
special features. (1) The electronics states are solved under the assumption that the nuclei are
stationary. The assumption is based on the Born-Oppenheimer approximation, which is valid
since nuclei are much heavier thus move much slower than electrons. (2) Based on the assumption
of the first point, the motions of electrons and nuclei are considered separable. The electrons are
assumed to change positions with the nuclei instantaneously – essentially “sensing” a static
potential energy landscape created by the nuclei. (3) Electrons are considered to move on a fixed
potential energy surface (PES) corresponding to their electronic state.
However, when the electrons make transitions between potential energy surfaces (states), it is
not typically considered as adiabatic dynamics. Instead, we will discuss nonadiabatic dynamics
from the next section, and the main distinctions can be summarized as three points. (1) In
nonadiabatic dynamics, the motions of electrons and nuclei are coupled – the change in the
positions of the nuclei can change the electronic states, and vice versa. (2) Nonadiabatic effects
32

become significant when then the system goes through transitions between different electronic
states – when the PESs of two states come close to each other (no crossings) or intersect (conical
(cone-shaped) intersections). (3) Thus, nonadiabatic dynamics go beyond the Born-Oppenheimer
approximation.
In conclusion, in adiabatic dynamics, “slow nuclei, fast electrons”, and electronic states do not
change as nuclei move. However, in nonadiabatic dynamics, “interactive nuclei and electrons”,
and electronic states change with the nuclear motion.
3.7 Nonadiabatic Coupling and Nonadiabatic Molecular Dynamics
Nonadiabatic molecular dynamics (NAMD)37-47 simultaneously simulates the dynamics of
electrons and atomic nuclei (the atom’s core), unlike traditional molecular dynamics that treat
electronic states as static. In MD simulations usually the electronic states being simulated are fixed
– Born-Oppenheimer Approximation. (The assumption/approximation is that the motion of the
nuclei and the electrons can be separated, and the electrons are assumed to instantly adjust to any
changes in the positions of the nuclei, so a constant electronic state can be maintained. The fixed
electronic states also determine a static potential energy surface for the nuclei to move on. The
details of the traditional MD simulations are explained in earlier sections.) Thus NAMD can be
used to accurately describe the electronic states during chemical reactions in a time-dependent
fashion. Hence, NAMD is great help in understanding and predicting properties of materials –
especially those sensitive to electronic state changes.
33

NAMD ignores the photon emission or absorption in the coupling process – which is a valid
approach here because the internal molecular transitions are the primary interest, instead of the
external electromagnetic fields. Additionally, neglecting the photon release makes the simulations
more computationally feasible, which allows the studies of larger systems or timescales.
However, the simplification means NAMD is less suitable for systems where light-matter
interactions are the primary consideration, as the interaction of light (photons) with matter is a key
aspect of their function or behavior. For example, these systems include OLED materials,
photosynthetic systems, spectroscopy studies, etc.
To derive the NAC vector, the time-dependent Schrödinger equation (TDSE) is a good place
to start:
9ℏ
hΨ(A, *,:)
h: = 1(A, *,:)Ψ(A, *,:)
where 9ℏ is the imaginary unit times the reduced Planck’s constant (1.054571817×10−34 J.s). This
prefactor ensures the units on both sides of the equation are constant and 9 indicates the wave-like
nature of the wavefunction’s evolution. Ψ(A, *,:) is the total wavefuntion of the system – the
wavefunction depends on the electronic coordinates A, nuclear coordinates * and time :. It denotes
how the wavefunction changes over time. 1(A, *,:) is the Hamiltonian operator, representing the
total energy of the system (kinetic + potential energies).
The equation essentially states the partial derivative of Ψ(A, *,:) with respect to time times
9ℏ is the product of the Hamiltonian and the wavefunction, and more importantly, the time
evolution of the quantum state (the wavefunction) is governed by the Hamiltonian of the system.
34

The Hamiltonian includes all the kinetic and potential energies of the particles in the system and
dictates how these energies interact to generate the dynamic behavior of the system according to
quantum mechanics.
To solve the electronic structure problem, we can expand the wavefunction in adiabatic
Kohn-Sham orbitals,
Ψ(A, *,:) = J 84(:)?4iA; *(:)k
4
where 84(:) is the time-dependent coefficients and ?4iA; *(:)k is the l-th adiabatic Kohn-Sham
orbitals – which are solutions to the stationary Kohn-Sham equations at a particular nuclear
configuration *(:). In ?4iA; *(:)k, the “;” in the notation distinguishes between the different types
of variables and their roles - A represents the coordinates of the electrons, which is the set of
variables that the orbital depends on directly and primarily. Yet *(:) are the nuclear coordinates
at time :. These nuclear coordinates are treated as parameters that the electronic orbitals depend
upon (the “;” indicates *(:) is not a variable of the wavefunction in the same way as A, but instead
it sets the context or conditions under which the orbital ?4 is defined). The separation of the
notations A and *(:) shows the different considerations of the adiabatic and nonadiabatic
considerations.
Essentially, the orbital ?4 is a function of the electronic coordinates A with the nuclear
configuration *(:) influencing its shape and properties.
35

In summary, the adiabatic Kohn-Sham orbitals provide a manageable representation of the
electronic structure of a system.
The coefficients, 84(:), evolves over time, and can be described by a set of coupled firstorder differential equations derived from the TDSE:
9ℏ
h84(:)
h: = J 8'(:)[md4' − 9ℏQ4' ∙ *̇
]
'
where O0)(K)
OK is the time derivative of the coefficient for state l – indicating how 84(:) changes over
time. 8'(:) is the coefficient of other states at time :, and the sum over - shows the evolution of
84(:) can be influenced by all other states. m is the energy eigenvalue for the adiabatic state. d4' is
the Kronecker delta, meaning if l = -, d4' = 1, and otherwise 0 (which ensures the energy term m
only contributes when l = -). Q4' is the nonadiabatic coupling vector elements, describing the
coupling between the electronic states l and - with nuclear motion. *̇ is the nuclear velocity vector,
describing how the positions of the nuclei change over time.
There are two parts in the equation, the adiabatic term md4' and the nonadiabatic term
− 9ℏQ4' ∙ *̇
. The adiabatic term represents the energy associated with each adiabatic state. The
nonadiabatic term represents the effect of the nuclear motion on the electronic states and this term
causes the coefficients 84(:) to mix over time, allowing transitions between different electronic
states.
The evolution of 84(:) is important because it determines how the probabilities of the
system being in different electronic states change over time in the nonadiabatic dynamics. In
36

summary, the evolution of 84(:) describes the time-dependent behavior of the electronic
wavefunction in response to the nuclear motions. This supports the simulation of nonadiabatic
effects because electronic transitions and nuclear motions are combined, which is crucial for more
accurate modeling in chemical and physical processes.
From the equations above, the nonadiabatic coupling (NAC) vector can be expressed as
Q4' ∙ *̇ = p?4q∇Pq?'r ∙ *̇ = p?4q∇P12q?'r
m' − m4
∙ *̇
where Q4' is the NAC vector element between states l and -. ∇P12 is the gradient of the
Hamiltonian with respect to the nuclear coordinates. m' and m4 are the eigenvalues for states - and
l respectively, and the eigenvalues correspond to the allowed energy levels of the system.
The matrix element p?4q∇P12q?'r represents the overlap between the gradient of the
Hamiltonian with respect to nuclear coordinates (on the wavefunction ?') and the wavefunction
?4.
The term m' − m4, which is the difference in the eigenvalues in the denominator shows the
coupling strength is inversely related to the energy gap between the two states – when the gap is
small, the coupling is stronger, making the transitions between the states more likely.
In the context of NAC, the “coupling” refers to the interaction between different electronic
states, which also implies the electronic states are not independent. The NAC vector Q4' represents
the coupling between different electronic states from the motion of the nuclei.
37

3.8 Nonadiabatic Coupling Time v.s. Carrier Lifetime
Nonadiabatic coupling time refers to the time scale over which nonadiabatic transitions
occur between different electronic states in a system yet carrier lifetime is a measure of the
average time an electron or hole remains in a free or excited state before recombining. While
nonadiabatic coupling time deals with the speed of transitions between electronic states often on a
molecular level, carrier lifetime is more about how long charge carriers (electrons/holes) in a
semiconductor can exist before recombination.
The relationship between the two is usually inversed - generally, if nonradiative coupling
is efficient and happens quickly (short coupling time), it can reduce the carrier lifetime because it
provides a fast pathway for carriers to return to the ground state without emitting light.
38

References
(1) Berezin, F. A.; Shubin, M. The Schrödinger Equation; Springer Science & Business Media, 2012.
(2) Lang, N.; Kohn, W. Theory of Metal Surfaces: Charge Density and Surface Energy. Physical Review B
1970, 1 (12), 4555.
(3) Lewars, E. G.; Lewars, E. G. The Concept of the Potential Energy Surface. Computational Chemistry:
Introduction to the Theory and Applications of Molecular and Quantum Mechanics 2016, 9-49.
(4) Batzill, M.; Diebold, U. The Surface and Materials Science of Tin Oxide. Progress in Surface Science
2005, 79 (2-4), 47-154.
(5) Born, M. Born-oppenheimer Approximation. Ann. Phys 1927, 84, 457-484.
(6) Kantorovich, L. V.; Krylov, V. I.; Benster, C. D.; Weiss, G. Approximate Methods of Higher Analysis.
Physics Today 1960, 13 (1), 74-76.
(7) Lykos, P.; Pratt, G. Discussion on the Hartree-Fock Approximation. Reviews of Modern Physics 1963,
35 (3), 496.
(8) Löwdin, P.-O. Quantum Theory of Many-Particle Systems. II. Study of the Ordinary Hartree-Fock
Approximation. Physical Review 1955, 97 (6), 1490.
(9) Valeev, E. F.; Sherrill, C. D. The Diagonal Born–Oppenheimer Correction Beyond the Hartree–Fock
Approximation. The Journal of Chemical Physics 2003, 118 (9), 3921-3927.
(10) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Physical Review 1964, 136 (3B), B864.
(11) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Physical
Review 1965, 140 (4A), A1133.
(12) Sham, L. J.; Kohn, W. One-Particle Properties of An Inhomogeneous Interacting Electron Gas.
Physical Review 1966, 145 (2), 561.
(13) Car, R.; Parrinello, M. Unified Approach for Molecular Dynamics and Density-Functional Theory.
Physical Review Letters 1985, 55 (22), 2471.
(14) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T.; Joannopoulos, a. J. Iterative Minimization
Techniques for Ab Initio Total-Energy Calculations: Molecular Dynamics and Conjugate Gradients.
Reviews of Modern Physics 1992, 64 (4), 1045.
(15) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using
A Plane-Wave Basis Set. Physical Review B 1996, 54 (16), 11169.
(16) Marx, D.; Hutter, J. Ab Initio Molecular Dynamics: Theory and Implementation. Modern Methods and
Algorithms of Quantum Chemistry 2000, 1 (301-449), 141.
(17) Martin, R. M. Electronic Structure: Basic Theory and Practical Methods; Cambridge University Press,
2020.
39

(18) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical
Review Letters 1996, 77 (18), 3865.
(19) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation
Energy. Physical Review B 1992, 45 (23), 13244.
(20) Perdew, J. P.; Burke, K.; Ernzerhof, M. Perdew, Burke, and Ernzerhof reply. Physical Review Letters
1998, 80 (4), 891.
(21) Grimme, S. Density Functional Theory with London Dispersion Corrections. Wiley Interdisciplinary
Reviews: Computational Molecular Science 2011, 1 (2), 211-228.
(22) Tkatchenko, A.; Scheffler, M. Accurate Molecular van der Waals Interactions from Ground-State
Electron Density and Free-Atom Reference Data. Physical Review Letters 2009, 102 (7), 073005.
(23) Anatole von Lilienfeld, O.; Tkatchenko, A. Two-and Three-Body Interatomic Dispersion Energy
Contributions to Binding in Molecules and Solids. The Journal of Chemical Physics 2010, 132 (23).
(24) Frenkel, D.; Smit, B. Understanding Molecular Simulation: from Algorithms to Applications; Elsevier,
2023.
(25) Van Gunsteren, W. F.; Berendsen, H. J. Computer Simulation of Molecular Dynamics: Methodology,
Applications, and Perspectives in Chemistry. Angewandte Chemie International Edition in English 1990,
29 (9), 992-1023.
(26) Schneider, T.; Stoll, E. Molecular-Dynamics Study of a Three-Dimensional One-Component Model
for Distortive Phase Transitions. Physical Review B 1978, 17 (3), 1302.
(27) Tycko, R.; Dabbagh, G.; Fleming, R.; Haddon, R.; Makhija, A.; Zahurak, S. Molecular Dynamics and
the Phase Transition in Solid C60. Physical Review Letters 1991, 67 (14), 1886.
(28) Tsuneyuki, S.; Aoki, H.; Tsukada, M.; Matsui, Y. Molecular-Dynamics Study of the α to β Structural
Phase Transition of Quartz. Physical Review Letters 1990, 64 (7), 776.
(29) Karplus, M.; McCammon, J. A. Molecular Dynamics Simulations of Biomolecules. Nature Structural
Biology 2002, 9 (9), 646-652.
(30) Binder, K. Monte Carlo and Molecular Dynamics Simulations in Polymer Science; Oxford University
Press, 1995.
(31) Hénin, J.; Chipot, C. Overcoming Free Energy Barriers Using Unconstrained Molecular Dynamics
Simulations. The Journal of Chemical Physics 2004, 121 (7), 2904-2914.
(32) Claeyssens, F.; Harvey, J. N.; Manby, F. R.; Mata, R. A.; Mulholland, A. J.; Ranaghan, K. E.; Schutz,
M.; Thiel, S.; Thiel, W.; Werner, H.-J. High-Accuracy Computation of Reaction Barriers in Enzymes.
ANGEWANDTE CHEMIE-INTERNATIONAL EDITION IN ENGLISH- 2006, 45 (41), 6856.
(33) Carsky, P.; Urban, M. Ab Initio Calculations: Methods and Applications in Chemistry; Springer
Science & Business Media, 2012.
(34) González, M. A. Force Fields and Molecular Dynamics Simulations. École Thématique de la Société
Française de la Neutronique 2011, 12, 169-200.
40

(35) Unke, O. T.; Koner, D.; Patra, S.; Käser, S.; Meuwly, M. High-Dimensional Potential Energy Surfaces
for Molecular Simulations: from Empiricism to Machine Learning. Machine Learning: Science and
Technology 2020, 1 (1), 013001.
(36) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and
Semiconductors Using a Plane-Wave Basis Set. Computational Materials Science 1996, 6 (1), 15-50.
(37) Tully, J. Mixed Quantum–Classical Dynamics. Faraday Discussions 1998, 110, 407-419.
(38) Nikitin, E. Nonadiabatic Transitions: What We Learned from Old Masters and How Much We Owe
Them. Annual Review of Physical Chemistry 1999, 50 (1), 1-21.
(39) Worth, G. A.; Cederbaum, L. S. Beyond Born-Oppenheimer: Molecular Dynamics Through A Conical
Intersection. Annu. Rev. Phys. Chem. 2004, 55, 127-158.
(40) Jasper, A. W.; Nangia, S.; Zhu, C.; Truhlar, D. G. Non-Born−Oppenheimer Molecular Dynamics.
Accounts of Chemical Research 2006, 39 (2), 101-108.
(41) Prezhdo, O. V. Quantized Hamilton Dynamics. Theoretical Chemistry Accounts 2006, 116, 206-218.
(42) Nelson, T.; Fernandez-Alberti, S.; Roitberg, A. E.; Tretiak, S. Nonadiabatic Excited-State Molecular
Dynamics: Modeling Photophysics in Organic Conjugated Materials. Accounts of Chemical Research 2014,
47 (4), 1155-1164.
(43) Wang, L.; Akimov, A.; Prezhdo, O. V. Recent Progress in Surface Hopping: 2011–2015. The Journal
of Physical Chemistry Letters 2016, 7 (11), 2100-2112.
(44) Crespo-Otero, R.; Barbatti, M. Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–
Classical Dynamics. Chemical Reviews 2018, 118 (15), 7026-7068.
(45) Curchod, B. F.; Martínez, T. J. Ab Initio Nonadiabatic Quantum Molecular Dynamics. Chemical
Reviews 2018, 118 (7), 3305-3336.
(46) Zheng, Q.; Chu, W.; Zhao, C.; Zhang, L.; Guo, H.; Wang, Y.; Jiang, X.; Zhao, J. Ab Initio Nonadiabatic
Molecular Dynamics Investigations on the Excited Carriers in Condensed Matter Systems. Wiley
Interdisciplinary Reviews: Computational Molecular Science 2019, 9 (6), e1411.
(47) Prezhdo, O. V. Modeling Non-Adiabatic Dynamics in Nanoscale and Condensed Matter Systems.
Accounts of Chemical Research 2021, 54 (23), 4239-4249.
41

Chapter 4
Machine Learning Basics
4.1 Machine Learning in Materials Studies
Machine learning (ML) is and becomes even more of a critical tool for discovering knowledge
and introducing innovation in materials science.
1-4 Predominantly, ML has great capability to
develop predictive models to understand and manipulate the complicated structure-property
relationships inherent to materials.5-11 By leveraging existing datasets, ML algorithms enable the
prediction of a material's physical, chemical, and mechanical properties based on its composition
and structure with satisfying accuracy, thereby bypassing the reliance on labor-intensive
experimental methodologies. Additionally, the predictive excellence can be extended to highthroughput screening processes, where ML helps the rapidly identify materials with optimal
properties from an expansive library, significantly streamlining the materials discovery phase.
Thus, ML-driven design strategies empower researchers to tailor new materials with desired
properties and with specific application requirements, such as enhanced energy efficiency or
superior mechanical strength. Beyond discovery and design, ML also excels in refining materials
processing techniques.12, 13 By analyzing real-time data, ML algorithms optimize manufacturing
parameters to maximize yield, reduce waste, and enhance material quality. Collectively, ML
makes a strong impact in materials science, providing more nuanced understandings of material
42

behavior, expediting the development of innovative materials, and optimizing manufacturing
processes for the technological advancements.
4.2 Machine Learning Force Field
Machine learning force fields (MLFFs)14-17 are primarily designed for predicting the forces
acting on atoms and the potential energy of a system based on atomic configurations. As will be
shown in the following sections and published papers, MLFFs are primarily used in MD
simulations to model how atoms and molecules move and interact over time. It cannot directly
predict electronic properties; however, the electronic properties of the extended systems can be
obtained by ab initio methods.
Previous studies include DeePMD18-20 (used in the studies in this thesis) and E(3)-equivariant
methods21-23 - they are at the forefront of computational chemistry, leveraging deep learning to
revolutionize molecular dynamics simulations. DeePMD, developed to scale with the accuracy of
quantum mechanics, employs deep neural networks to predict interatomic forces and potential
energies from ab initio data, enabling efficient and accurate simulations across various systems.
Meanwhile, a newer method, E(3)-equivariant graph neural networks, introduced in NequIP,21
enhance data efficiency and accuracy by utilizing symmetries in physical systems through E(3)-
equivariant convolutions. The NequIP approach requires fewer training data to achieve high
fidelity, paving the way for simulations that closely mirror quantum chemical accuracy. Together,
these methods signify significant advances in accurately modeling complex molecular behaviors
with computational efficiency.
43

4.3 DeePMD-kit
DeePMD is an established package in MLFF that facilitates molecular dynamics simulations
using neural network potentials. This method uses a many-body potential and interatomic forces
generated by a deep neural network trained with ab initio data, maintaining natural symmetries of
the problem.
The Deep Potential (DP) model s, which is the overall model that maps the input features to
the predicted properties, is represented as
;7 = s(N7,tN4u
4∈&(7)
; v) = K(w /N7,tN4u
4∈&(7)
; vR0 ; vI)
where ;7 is the propertiesthat are trying to be predicted for atom 9 (the properties could be energies,
forces, etc.). N7 is the degrees of freedom of the atom i (N7 = (A7, x7), A7 is the Cartesian coordinates
and x7 is the chemical species). N4 is the degrees of freedom of the neighboring atoms and the set
,(9) contains the indices of atoms that are neighbors of atom i within a specified cut-off radius.
The network parameters are v = {vR , vI}, which are learned during training. These parameters
are what the network adjusts to make more accurate predictions. vR and vI the subsets of v
specifically for the descriptor and the fitting network, respectively.
w is the descriptor, which is a function that takes N7 and N4 and computes a set of descriptors that
input into the fitting network K. The descriptor captures the local environment of an atom and is a
important part of the model as it determines how the information about the atomic environment is
encoded.
44

K is the fitting network, and it takes the output of the descriptor and produces the final property
prediction. It is the function that fits the computed descriptors to the desired properties (like forces
or energies).
So to further clarify things, the input data for the DP model are the positions A7 and the
types x7 of the atoms in the system. The inputs are essentially the degrees of freedom of each atom
– representing the atoms’ location in space and their chemical nature. The descriptor function
takes the input data and computes a set of descriptors. Note: descriptors are not raw input data but
instead they are features engineered from the input data to capture the relevant information needed
for the model to make predictions. The fitting network is the neural network component of the
DP model. Once the descriptors are computed, they are input into the fitting network. The
network's role is to fit or map the computed descriptors to the desired output properties. It is the
"function approximator" within the DP model. The parameters v = {vR , vI} are what the neural
network learns during training. The training process involves using known data (such as from
molecular dynamics simulations) to adjust these parameters so that the network's predictions match
the known data as closely as possible.
In summary, the DP model s is using information about each atom and its local
environment (its neighbors within a certain radius) to predict properties relevant to molecular
dynamics. The model does this by first transforming the raw atomic positions and types into a
descriptor w, which is then fed into a neural network K to predict the properties ;7. The parameters
of this model v are learned from data (such as molecular dynamics simulations or experimental
measurements), to ensure that the predictions are as accurate as possible. In a word, s is a
45

combination of the descriptor function w and the fitting network K, along with any other
preprocessing or postprocessing steps involved in the model pipeline.
The neural network function y is the composition of multiple layers z(7)
,
y = z(&) ∘ z(&:1) ∘ … ∘ z(1)
which means the output of one layer is passed as the input to the next layer.
A layer L may be one of the following forms – depending on whether a residual network
(ResNet) is used and the number of nodes it contains:
; = z(N; |, }) = ~
|⨀c(N(| + }) + N, *&Åy&: e,Q y* = y1
|⨀c(N(| + }) + {N, N}, *&Åy&: e,Q y* = 2y1
|⨀c(N(| + }), 7:ℎ&A|9Å&
For example, if ResNet is used and y* = y1 (the number of nodes in the subsequent layer
is the same), the output is a combination of a transformation of the input vector N through weights
|, bias }, and activation function c, plus the input vector itself N.
ResNet, short for Residual Network, is a type of neural network architecture that was
designed to enable the training of very deep networks, which typically refers to networks that have
a very large number of layers, often significantly more than what was traditionally used. While
there is no strict threshold, networks with over 100 layers are often considered very deep.
The activation function c can be any function. The ones used here are tanh, ReLU, ReLU6
and others. The variables | and } represent the weights and biases of the neural network,
respectively, which are trainable parameters. The paper includes an equation that represents the
46

layer function ; = z(N; |, }), indicating how the input vector N, weights |, and biases } interact
to produce the output vector ;.
The DeePMD package works great for machine learning force field because if the atom’s
position and type are known, the potential energy can be predicted using the neutral network
discussed previously, and the force K acting on an atom can be calculated as the negative gradient
of the potential energy 4 with respect to its position *:
K = −∇4(*)
A configuration file (JSON script) for setting up the DP model can look like this:
47

where a few parts are specified – the types of atoms, the descriptors, the fitting net, the learning
rate, the loss function and the training and validation datasets.
To tweak the neural network for improved performance, the following parameters can be
adjusted:
48

1. Neurons in layers: the numbers in the neuron arrays under both descriptor and fitting net
can be changed. Adding more neurons can increase the model's capacity to learn complex
features but may also increase the risk of overfitting and require more computational
resources.
2. Learning rate: Modifying start_lr can have a significant impact. A higher starting learning
rate can speed up learning but might overshoot minima, while a lower starting rate can
make learning more stable but slower.
3. Loss function weights: the start_pref_e, limit_pref_e, start_pref_f, limit_pref_f,
start_pref_v, and limit_pref_v parameters control the contribution of different components
to the loss function. Adjusting these can change how the network prioritizes learning
different aspects of the data like energy or forces.
4. Batch size: under training_data and validation_data, the batch_size can be adjusted. A
batch is each iteration's sample of training data. A larger batch size can lead to faster
training but might require more memory. A smaller batch size can provide a regularizing
effect and better generalize but might slow down training.
49

Figure 1. Overview of the DeePMD-kit Workflow in a TensorFlow graph: this schematic figure
shows the data flow and computational processes involved in the DeePMD-kit framework. The
'Inference' block includes the model's core while the 'Trainer' block contains the optimization loop.
The 'Inference' block consists of the 'Descriptor' module for encoding the coordinates and atomic
types into a rotationally, translationally, and permutationally invariant representation, and the
'Fitting network' module for predicting the system's potential energy and forces. 'Type embedding'
enhances the model by embedding atomic type information before passing it to the Descriptor.
Post-processing 'Modifiers' such as Deep Potential Smoothing Layer (DPSL) or interpolation are
applied to the raw output of the fitting network to refine the predicted properties. In the 'Trainer'
block, the 'Optimizer' updates model parameters by minimizing the 'Loss', which quantifies the
difference between the model's predictions and 'Reference fitting properties' from quantum
mechanical calculations or experimental data.
50

References
(1) Schleder, G. R.; Padilha, A. C.; Acosta, C. M.; Costa, M.; Fazzio, A. From DFT to Machine Learning:
Recent Approaches to Materials Science–A Review. Journal of Physics: Materials 2019, 2 (3), 032001.
(2) Gu, G. H.; Noh, J.; Kim, I.; Jung, Y. Machine Learning for Renewable Energy Materials. Journal of
Materials Chemistry A 2019, 7 (29), 17096-17117.
(3) Huan, T. D.; Batra, R.; Chapman, J.; Krishnan, S.; Chen, L.; Ramprasad, R. A Universal Strategy for
the Creation of Machine Learning-Based Atomistic Force Fields. NPJ Computational Materials 2017, 3
(1), 37.
(4) Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine Learning for Molecular
and Materials Science. Nature 2018, 559 (7715), 547-555.
(5) Ouyang, Y.; Yu, C.; He, J.; Jiang, P.; Ren, W.; Chen, J. Accurate Description of High-Order Phonon
Anharmonicity and Lattice Thermal Conductivity from Molecular Dynamics Simulations with Machine
Learning Potential. Physical Review B 2022, 105 (11), 115202.
(6) Mortazavi, B.; Podryabinkin, E. V.; Novikov, I. S.; Rabczuk, T.; Zhuang, X.; Shapeev, A. V.
Accelerating First-Principles Estimation of Thermal Conductivity by Machine-Learning Interatomic
Potentials: A MTP/ShengBTE Solution. Computer Physics Communications 2021, 258, 107583.
(7) Zong, H.; Pilania, G.; Ding, X.; Ackland, G. J.; Lookman, T. Developing An Interatomic Potential for
Martensitic Phase Transformations in Zirconium by Machine Learning. NPJ Computational Materials
2018, 4 (1), 48.
(8) Li, L.; Yang, Y.; Zhang, D.; Ye, Z.-G.; Jesse, S.; Kalinin, S. V.; Vasudevan, R. K. Machine Learning–
Enabled Identification of Material Phase Transitions Based on Experimental Data: Exploring Collective
Dynamics in Ferroelectric Relaxors. Science Advances 2018, 4 (3), eaap8672.
(9) Meuwly, M. Machine Learning for Chemical Reactions. Chemical Reviews 2021, 121 (16), 10218-
10239.
(10) Westermayr, J.; Gastegger, M.; Marquetand, P. Combining SchNet and SHARC: The SchNarc
Machine Learning Approach for Excited-State Dynamics. The Journal of Physical Chemistry Letters 2020,
11 (10), 3828-3834.
(11) Kim, C.; Pilania, G.; Ramprasad, R. From Organized High-Throughput Data to Phenomenological
Theory Using Machine Learning: the Example of Dielectric Breakdown. Chemistry of Materials 2016, 28
(5), 1304-1311.
(12) Szymanski, N. J.; Rendy, B.; Fei, Y.; Kumar, R. E.; He, T.; Milsted, D.; McDermott, M. J.; Gallant,
M.; Cubuk, E. D.; Merchant, A. An Autonomous Laboratory for the Accelerated Synthesis of Novel
Materials. Nature 2023, 624 (7990), 86-91.
(13) Raccuglia, P.; Elbert, K. C.; Adler, P. D.; Falk, C.; Wenny, M. B.; Mollo, A.; Zeller, M.; Friedler, S.
A.; Schrier, J.; Norquist, A. J. Machine-Learning-Assisted Materials Discovery Using Failed Experiments.
Nature 2016, 533 (7601), 73-76.
51

(14) Unke, O. T.; Chmiela, S.; Sauceda, H. E.; Gastegger, M.; Poltavsky, I.; Schütt, K. T.; Tkatchenko, A.;
Müller, K.-R. Machine Learning Force Fields. Chemical Reviews 2021, 121 (16), 10142-10186.
(15) Botu, V.; Batra, R.; Chapman, J.; Ramprasad, R. Machine Learning Force Fields: Construction,
Aalidation, and Outlook. The Journal of Physical Chemistry C 2017, 121 (1), 511-522.
(16) Jinnouchi, R.; Karsai, F.; Kresse, G. On-the-Fly Machine Learning Force Field Generation:
Application to Melting Points. Physical Review B 2019, 100 (1), 014105.
(17) Chmiela, S.; Tkatchenko, A.; Sauceda, H. E.; Poltavsky, I.; Schütt, K. T.; Müller, K.-R. Machine
Learning of Accurate Energy-Conserving Molecular Force Fields. Science Advances 2017, 3 (5), e1603015.
(18) Wang, H.; Zhang, L.; Han, J.; Weinan, E. DeePMD-kit: A Deep Learning Package for Many-Body
Potential Energy Representation and Molecular Dynamics. Computer Physics Communications 2018, 228,
178-184.
(19) Zhang, L.; Han, J.; Wang, H.; Car, R.; Weinan, E. Deep Potential Molecular Dynamics: A Scalable
Model with the Accuracy of Quantum Mechanics. Physical Review Letters 2018, 120 (14), 143001.
(20) Zeng, J.; Zhang, D.; Lu, D.; Mo, P.; Li, Z.; Chen, Y.; Rynik, M.; Huang, L. a.; Li, Z.; Shi, S. DeePMDKit V2: A Software Package for Deep Potential Models. The Journal of Chemical Physics 2023, 159 (5).
(21) Batzner, S.; Musaelian, A.; Sun, L.; Geiger, M.; Mailoa, J. P.; Kornbluth, M.; Molinari, N.; Smidt, T.
E.; Kozinsky, B. E (3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic
Potentials. Nature Communications 2022, 13 (1), 2453.
(22) Batatia, I.; Batzner, S.; Kovács, D. P.; Musaelian, A.; Simm, G. N.; Drautz, R.; Ortner, C.; Kozinsky,
B.; Csányi, G. The Design Space of E (3)-Equivariant Atom-Centered Interatomic Potentials. arXiv preprint
arXiv:2205.06643 2022.
(23) Brandstetter, J.; Hesselink, R.; van der Pol, E.; Bekkers, E. J.; Welling, M. Geometric and Physical
Quantities Improve E (3) Equivariant Message Passing. arXiv preprint arXiv:2110.02905 2021.
52

Chapter 5
The Electronic Property Studies of the CsPbBr3 Quantum
Dot with Halide Vacancies
Overview
Metal halide perovskites (MHP) have attracted strong attention for their high
optoelectronic performance that is fundamentally rooted in the unusual properties of MHP defects.
By developing an ab initio-based machine-learning force-field, we sample structural dynamics of
MHPs on a nanosecond timescale and show that halide vacancies create midgap trap states in MHP
bulk but not on a surface. Deep traps result from formation of Pb-Pb dimers across the vacancy,
and the dimers can only form in the bulk. The dimer formation requires shortening of the Pb-Pb
distance by nearly 3 Å, which is facilitated either by charge trapping or thermal fluctuations that
occur on a 50 ps timescale. The large-scale structural deformations are possible because the MHP
lattice is soft. Halide vacancies on MHP surface create no deep traps, while they separate electrons
from holes, keeping the charges mobile and decreasing nonradiative charge trapping and
recombination. This situation is particularly favorable for MHP quantum dots, which do not
require sophisticated surface passivation to emit light and blink much less than quantum dots
formed from traditional inorganic semiconductors.
53

Author List
Jingyi Ran, Bipeng Wang, Yifan Wu, Dongyu Liu, Carlos Mora Perez, Andrey S. Vasenko, Oleg
V. Prezhdo
Metal halide perovskites (MHPs) have garnered significant attention as solar cell
candidates due to their low manufacturing cost, and versatile electronic and optical properties,
1, 2
including a tunable band gap, 3-5 long charge carrier diffusion,6-9 and strong light absorption.10-12
With these exceptional characteristics, MHPs can achieve solar-to-electricity conversion
efficiencies for over 25%,13 approaching or even surpassing those of traditional semiconductors
such as silicon. Furthermore, MHPs exhibit much greater diversity than the traditional
semiconductors, owing to the versatile perovskite structure that allows a broad range of
compositions and dimensionalities.
14-19 MHPs are softer than the inorganic semiconductors and
undergo significant structural fluctuations that can lead to large fluctuations of electronic energy
levels, particularly those associated with defects.20-23 During the fluctuations, midgap trap states
can appear, reducing the energy gap between the highest occupied molecular orbital (HOMO) and
the lowest unoccupied molecular orbital (LUMO). The HOMO and LUMO can split off the
valence and conduction bands and form midgap trap states that can capture charge carriers,
affecting their transport and recombination.24-29 The energy level fluctuations in MHPs are much
more significant than those in the traditional inorganic semiconductors,20 and such fluctuations
contribute to the unusual defect properties of MHPs.28-34 Defects in MHPs and their fluctuations
have been extensively studied at the ab initio level. However, ab initio calculations are typically
54

limited to picoseconds, while MHP undergo much slower structural oscillations and
rearrangements.21-23 To gain a thorough understanding of the MHP properties, it is essential to
develop atomistic models that can sample MHP conformations on timescales similar to charge
carrier lifetimes. Extending the studies to hundreds of picoseconds already reveals new dynamic
regimes and phenomena.21-23, 35
Machine learning (ML) techniques allow one to train force fields (FFs) models utilizing
data from ab initio methods, and then apply MLFFs to sample a broad range of atomic geometries
and long timescales. MLFF algorithms offer high accuracy while reducing computational cost
compared to calculations relying solely on ab initio methods.36-39 MLFFs allow one to address
many problems, such as anharmonic lattice dynamics,40, 41 phase transitions,42, 43 chemical
dynamics,44, 45 etc.
22, 23, 46-48 Structural motifs in condensed matter systems enable generation of
global and local descriptors. These mathematical representations capture essential features of a
system and can be used to create physically motivated FF models that approximate accurately
interactions between particles.49 As a result, cost-effective MLFFs can facilitate molecular
dynamics (MD) simulations for larger MHP systems with longer trajectories compared to ab initio
MD simulations. MLFF-assisted studies can provide insights into structural evolution of MHPs on
nanosecond timescales, comparable to those of charge carrier trapping and recombination. Then,
ab initio methods can be used to sample electronic structure and electron-vibrational interactions,
providing important insights into how slow geometry fluctuations influence excited state dynamics
that govern material properties and determine device efficiencies.
In this letter, we demonstrate that a halide vacancy, one of the most common defects in
MHPs,50, 51 exhibits different behavior on the surface and in the bulk. Focusing on the Br vacancy
in CsPbBr3, we develop a MLFF that allows us to sample MHP structural dynamics on a
nanosecond timescale and identify changes in the electronic properties induced by such dynamics.
At 0 K neither bulk nor surface vacancy exhibit midgap levels. However, at ambient temperature,
up to four midgap trap states can emerge on a timescale of tens of picoseconds in the bulk but not
on the surface. Similarly, charging the vacancy can create deep traps only in the bulk. The defect
level properties correlate well with the distance between the two Pb atoms surrounding the bulk
vacancy. In contrast, for the surface vacancy, no correlations are observed between the movement
of the Pb atom directly beneath the vacancy and the energy of the vacancy electronic state. Rather
55

than trapping charges, the surface halide vacancy facilitates electron-hole separation, while
keeping charges mobile. The deep traps appear in the bulk only transiently and infrequently, and
therefore, they are not detrimental to the optoelectronic performance. However, once charged, the
traps become stable and can cause performance deterioration, e.g., at high carrier density. The
absence of charge traps due to halide vacancies on MHP surface rationalizes the excellent
optoelectronic properties of perovskite quantum dots (QDs), which emit well and blink little, in
comparison to QDs composed of traditional inorganic semiconductors that blink due to surface
charge trapping.
Density functional theory (DFT) calculations are performed using the Vienna Ab-initio
Simulation Package (VASP).
52 The electron-ion interactions are characterized by employing the
Perdew-Burke-Ernzerhof (PBE) functional53 and the projected-augmented wave (PAW) method.54
The structures are visualized using the VESTA software.55 Two CsPbBr3 models with Br
vacancies on the surface and in the bulk are constructed by considering a CsPbBr3 slab composed
of 2×2×5 unit cells, Figure 1. A 20 Å vacuum layer is added to the z-direction containing 5-unit
cells. Periodic boundary conditions are employed in all directions. Br vacancies are introduced by
removing one Br atom from the top (surface) and middle (bulk) layers. The locations of these
vacancies are highlighted by the dotted green circles in Figure 1a,d. The electronic structure
calculations are performed at the Γ k-point, since the structure already includes 20-unit cells, and
because the CsPbBr3 bandgap is located at the Γ-point. The CsPbBr3 models with Br vacancies
contain 87 atoms each.
To investigate the defect properties on a nanosecond timescale, which is comparable to the
duration of charge carrier trapping and recombination, and to circumvent the high computational
cost of direct ab initio calculations, a MLFF model is trained for the vacancy systems. For the
collection of training and validation datasets, the CsPbBr3 systems with the Br vacancies are heated
from 0 K to 1600 K in increments of 100 K using the ab initio method described above. The wide
range of temperatures provides a diverse set of configurations that the systems may explore on a
long timescale at ambient temperature. At each temperature up to 1200 K, 4000 data points are
collected, while 2000 data points are gathered at the higher temperatures. The output of the ab
initio calculations is processed by a data preparation algorithm embedded in the DeepMD
package56 to extract information for the MLFF model's input data. The input data is randomly
56

partitioned into training and validation sets at an approximate ratio of 80% and 20%. The quality
of MLFF is assessed by comparing the potential energies obtained ab initio and from the ML
model. The ML and ab initio potential energies show good agreement, as demonstrated in Figure
S1 of Supporting Information. The root-mean-square errors are 1.74 meV per atom for the surface
vacancy system and 2.18 meV per atom for the bulk vacancy system.
Once a reliable MLFF model is established, the systems are heated to 300 K, and 1 ns MD
trajectories are generated for each system in the microcanonical ensemble, using the Large-scale
Atomic/Molecular Massively Parallel Simulator (LAMMPS).57 During the 1 ns MD trajectories,
the Br vacancies are observed to migrate between layers, indicating that the MLFF method can be
used to perform a detailed atomistic study of defect migration that plays important roles in MHPs,
causing phase separation, current-voltage hysteresis and chemical instabilities.58-62 For the present
purpose, we select parts of the trajectories in which the vacancies remain in the selected locations.
Once the MLFF trajectories are generated, the electronic properties are investigated every 1 ps by
ab initio DFT. The electronic properties for selected parts of trajectories are investigated every 100
fs.
Figure 1 presents geometric and electronic structure of the defective CsPbBr3 systems in
the optimized geometries, corresponding to 0 K. The Pb-Pb distance surrounding the vacancy in
the bulk is 6.19 Å, similar to that in the pristine region without vacancies. Despite the presence of
the defects, no midgap trap states are observed in either structure. The charge densities of the
valence band maximum (VBM) and conduction band minimum (CBM) for both surface and bulk
vacancies are delocalized. The densities of states (DOS) for the two structures demonstrate that
the CBM and VBM are formed primarily by Pb and Br atomic orbitals, respectively.
57

Figure 1. (a) Optimized structure of CsPbBr3 with the Br vacancy on the surface. The vacancy is
highlighted by the green circle. (b, c) Corresponding VBM and CBM charge densities. (d) Optimized
structure of CsPbBr3 with the Br vacancy in the bulk. (e, f) Corresponding VBM and CBM charge densities.
(g, h) Projected DOS of CsPbBr3 with the Br vacancy on the surface and in the bulk, respectively, at 0 K.
In the optimized structures, the vacancies create no midgap trap states, and the frontier orbitals are
delocalized.
At an ambient temperature, MHPs undergo significant structural fluctuations that can
modulate their electronic properties. Defects levels, that are either shallow or hidden inside bands
at 0 K, can become deep, while levels that are deep at 0 K can approach band edges. In particular,
a halide vacancy defect that creates no midgap states in the optimized geometry can create a level
as deep as 1 eV below the CBM at room temperature.20, 21 In the present study, we observe a
58

qualitative difference in the fluctuation of the defect energy levels for the Br vacancy on the surface
and in the bulk. While both structures undergo significant geometric distortions at the ambient
temperature, only the bulk Br vacancy creates deep midgap trap levels. The Br vacancy on the
CsPbBr3 surface creates no deep trap levels, though the band edges still undergo fluctuations,
Figure S2.
Figure 2 presents evolution of the energy gap between the lowest unoccupied molecular
orbital (LUMO) and LUMO+1 for CsPbBr3 with the Br vacancy in the bulk. The figure also shows
the distance between the two Pb atoms across the vacancy. There are several times over the 200
ps trajectory, during which the LUMO/LUMO+1 energy gap reaches nearly 1 eV, similarly to the
iodine vacancy in bulk MAPbI3.
21 Focusing on one such event, Figure 2a, we observe that the deep
trap exists for about 3 ps, also similarly to MAPbI3 with an iodine vacancy.21 The
LUMO/LUMO+1 energy gap exhibits a strong correlation with the Pb-Pb distance: the shorter the
distance, the deeper the trap state. The Pb-Pb distance across the Br vacancy measures 6.19 Å in
the optimized structure, while it fluctuates from 3.80 Å to 6.45 Å at 300 K. The 2.65 Å fluctuation
of the defect structure, giving rise to the 1 eV fluctuation of the defect energy level is possible
because MHPs are soft, much softer than the traditional inorganic semiconductors, such as Si,
CdSe and TiO2. When the Pb-Pb distance is at its shortest, up to 4 midgap states can appear.
59

Figure 2. Correlation between the energy gap from LUMO to LUMO+1 (blue) and the Pb-Pb distance
(orange) in CsPbBr3 with the Br vacancy in the bulk for (a) a 7 ps region with deep trap, and (b) the long
trajectory. A strong correlation is observed. The Pb-Pb distance refers to the two Pb atoms across the
vacancy. The LUMO to LUMO+1 gap demonstrates that the deepest midgap trap state fluctuates by 1 eV
down from the CsPbBr3 CBM, as illustrated further in Figure S2.
Figure 3 demonstrates projected DOS for four representative CsPbBr3 structures with the
Br vacancy in the bulk, exhibiting 1, 2, 3 and 4 midgap states. The corresponding charge densities
can be found in Figures 4 and S3. Generally, the shorter the Pb-Pb distance, the greater the number
of midgap states. When the Pb-Pb distance exceeds 4.7 Å, no trap states are observed, as shown in
Figure S4. As the Pb-Pb distance decrease, midgap trap states begin to emerge. Figure 3 illustrates
a single trap appearing when the Pb-Pb distance reaches 4.68 Å, and two traps emerging when the
distance is reduced to 3.91 Å. Subsequently, three traps appear when the Pb-Pb distance reaches
3.87 Å, and four traps appear when the distance is at 3.80 Å. A maximum of three trap states was
observed in the previous study of the halide vacancy in MAPbI3,
21 in comparison to the four states
seen here. Most likely, this is because the CsPbBr3 structure is more compact than the MAPbI3
structure, because Br is smaller than I, and Cs is smaller than MA. Thus, shorter Pb-Pb distances
60

are possible across the halide vacancy in CsPbBr3 than MAPbI3. All-inorganic perovskites, such
as CsPbBr3, differ from mixed organic-inorganic perovskites, such as MAPbI3, in the shape of the
inert cation, Cs+ vs MA+. Cs+ and other inorganic cations are spherically symmetric, while MA+
and other organic cations have an asymmetric charge distribution and can form hydrogen bonds
with the inorganic lattice.63 These factors can create additional structural disorder in hybrid
organic-inorganic perovskites compared to all-organic perovskites, increasing charge
localization.64-66 In both CsPbBr3 and MAPbI3 studied thus far, only one of the trap states arising
from a halide vacancy is very deep, while the other states are relatively shallow, Figures 3 and
ref.21
Figure 3. (a-d) Projected DOS of CsPbBr3 with Br vacancy in the bulk at four representative MD
timepoints. Midgap trap states emerge as the Pb-Pb distance varies from 4.68 Å to 3.80 Å. A greater number
of midgap trap states are observed as the Pb-Pb distance shortens. When the Pb-Pb distance reaches 3.80
Å, four trap states are detected.
Analysis of the defect state charge densities indicates that deeper traps are more localized,
Figures 4 and S3. Shallower traps couple strongly with CsPbBr3 conduction band states and extend
onto multiple neighboring atoms of the pristine structure. The missing Br atom leaves unsaturated
valencies in the two surrounding Pb atoms, and the charge densities of the trap states are localized
61

on the corresponding Pb orbitals. Table 1 presents contributions of p-orbitals from the two Pb
atoms to the four traps seen in Figure 3d, with the charge densities shown in Figure 4. The deepest
trap 1 is localized on the pz-orbitals of the two Pb atoms and is oriented perpendicular to the slab.
Trap 2 is oriented in the plane of the slab. It originates from the px-orbital of a single Pb atom and
spreads onto the neighboring Pb atoms in the x-direction. Both trap 3 and trap 4 have charge
densities supported by the py-orbitals of the two Pb atoms across the vacancy. They delocalize
significantly onto many neighboring Pb atoms. Trap 1 is a deep state, because it is supported by a
s-bond formed by the two Pb p-orbitals pointing towards each other across the vacancy. The other
states are formed by Pb p-orbitals pointing perpendicular to the Pb-Pb vacancy dimer direction,
and therefore, can only form p-bonds, and are higher in energy.
Figure 4. (a-d) Charge densities of the four midgap trap states in CsPbBr3 with the Br vacancy in the bulk,
corresponding to Figure 3d. All midgap states are localized around the vacancy. Trap 1 is supported by the
s-bond formed by two p-orbitals of the Pb atoms across the vacancy. It has the lowest energy and is most
localized. The other trap states are supported by p-orbitals perpendicular to the Pb-Pb dimer direction,
forming p-bonds. They are higher in energy and delocalize onto neighboring pristine Pb atoms.
Table 1. Contributions of p-Orbitals of the Two Pb Atoms Across the Vacancy Site in CsPbBr3 with the Br
Vacancy in the Bulk, Corresponding to the Four Trap Charge Densities Shown in Figure 4.
px py pz
Trap 1 Pb (above) 0.000 0.000 0.139
Pb (below) 0.000 0.000 0.025
Trap 2 Pb (above) 0.007 0.000 0.001
Pb (below) 0.259 0.000 0.000
Trap 3 Pb (above) 0.000 0.013 0.001
Pb (below) 0.000 0.163 0.002
Trap 4 Pb (above) 0.000 0.026 0.001
Pb (below) 0.000 0.088 0.001
62

In contrast to the bulk vacancy, the Br vacancy on the CsPbBr3 surface does not exhibit
deep traps. The LUMO/LUMO+1 energy gap fluctuates within 0.15 eV, Figure 5, compared to the
1 eV fluctuation for the bulk vacancy, Figure 2. The HOMO/LUMO energy gap can decrease
significantly, Figure S2c,e; however, this decrease is not associated with formation of deep trap
states separated from the bands. Rather, the whole set of valence and conduction band states
fluctuate in energy, decreasing the fundamental bandgap. It should be noted that, while the
properties of defect states can be modeled with small models, such as the current simulation cell,
because the defect states are localized, the extent of fluctuation of energies of delocalized band
states may depend on simulation cell size, since typically, stated delocalized over more atoms
fluctuate less.
Figure 5. Relationship between the energy gap from LUMO to LUMO+1 and the displacement of the Pb
atom under the Br vacancy on the CsPbBr3 surface for (a) a selected 7 ps region and (b) the long trajectory.
The Pb atom displacement refers to the position normal to the surface, and 0 refers to average position of
all Pb atoms in the surface layer. In contrast to the Br vacancy in the bulk, Figure 2, the trap state separates
from the CBM by only 0.15 eV, as illustrated further in Figure S2. No significant correlation between the
energy gap fluctuation and the Pb movement is observed.
63

Halide vacancies on lead halide perovskite surfaces do not form deep trap states because
there is only one Pb next to the vacancy, and there is no opportunity to form a Pb-Pb dimer, as in
the bulk. We did not find a simple structural feature that would correlate with the
LUMO/LUMO+1 energy gap for the surface vacancy system. For example, considering the
displacement of the Pb atom below the vacancy in the vertical direction perpendicular to the slab,
an analogue of the Pb-Pb dimer distance for a single Pb atom, we observe no correlation with the
LUMO/LUMO+1 gap. Such a correlation should not be expected, because defect states
energetically close to band edges are coupled to band states and delocalize, and therefore, their
properties are determined by collective motions of multiple atoms.
Figure 6 shows a representative CsPbBr3 structure with the surface Br vacancy, its DOS,
and charge densities of HOMO, LUMO and LUMO+1. Since there are no states inside the bandgap
separated energetically from the bands, the HOMO can be regarded as the VBM, and the LUMO
as the CBM. All states are delocalized in the plane of the slab, however, the symmetry of the slab
is broken by the vacancy, such that the CBM and VBM are localized on the opposite sides. Such
scenario leads to separation of electrons and holes, which nevertheless, remain mobile because the
HOMO and LUMO are delocalized and not separated from the bands energetically. Such situation
favors material performance in solar cells and other applications that require charge separation,
Localization of the CBM and VBM on the opposite surfaces is not maintained continuously.
However, it assists in solar energy applications even if it happens only in a fraction of
conformations. Such electron-hole symmetry breaking has been detected in other MHP systems,
with and without defects.67-72 The reduced probability of formation of deep trap states on MHP
surfaces, and the electron-hole separation facilitated by surfaces, interfaces and grain boundaries
minimize nonradiative charge recombination that constitutes the primary loss channel in
photovoltaic applications.
64

Figure 6. (a) DOS of CsPbBr3 with the Br vacancy on the surface for a representative geometry at room
temperature. (b-d) Charge densities of VBM, CBM and CBM+1. There are no midgap states. The VBM
and CBM are spatially separated and remain largely delocalized. Such condition favors long-lived excited
states.
Calculations show that halide vacancies create midgap trap states associated with Pb-Pb
bonding when the vacancies are charged.24, 73 more A negative charge replacing a halide ion
attracts the Pb2+ cations across the vacancy, creating a Pb-Pb species that is stable at both low and
ambient temperatures. This mechanism of the deep midgap trap formation cannot operate on
perovskite surfaces because there is no second Pb atom to create a dimer. This is confirmed by the
results in Figure 7, demonstrating three midgap trap states for the bulk vacancy with the -2 charge,
and only one shallow state for the surface vacancy with the -2 charge. The trap states can be
distinguished by localization in the periodic direction of the slab. Because generation of deep trap
levels requires capture of two electrons, the bulk vacancy defects should be detrimental at high
charge carrier density and benign at low carrier density. Thus, the surface halide vacancy
demonstrates absence of deep midgap trap states, while the same vacancy in the bulk exhibits
multiple deep trap states that can arise from thermal fluctuations and are stabilized by trapped
charges.
65

`
Figure 7. Densities of states of a Br vacancy (a,b) on the CsPbBr3 surface and (c,d) in the CsPbBr3 bulk
with added (a,c) -1 and (b,d) -2 charges, in the optimized geometries. The inserts show charge densities of
the key states. In the -1 state, the vacancies create no midgap trap states at 0 K. The surface vacancy breaks
the slab symmetry and results in electron-hole charge separation, similarly to the neutral vacancy at room
temperature, Figure 6b,c. Note that there is no electron-hole separation in the neutral surface vacancy at 0
K, Figure 1e,f. In the -2 state at 0 K, the surface vacancy creates as shall electron trap, part b. However, the
bulk vacancy creates three deep midgap traps, part d, similarly to the neutral vacancy at room temperature,
Figures 3, 4 and S3. The negative charge attracts the Pb2+ cations across the bulk vacancy, creating a stable
species.
The absence of deep trap states associated with halide vacancies, a very common point
defect, on lead halide surfaces contributes to bright emission of MHP QDs.19, 74-76 Colloidal QDs
made from the traditional inorganic semiconductors, such as CdSe, PbS or Si,77-79 blink, and the
blinking is typically associated with formation of charged trap states on QD surfaces.80-82 The
surface vacancy defects do not form deep traps, reducing the blinking.76 It remains to be seen
66

whether the favorable difference in the properties of point defects in MHP bulk vs. surface persist
for other point defects, motivating further investigations. It is important to emphasize that one
needs to consider not only optimized structures but also structures sampled at an appropriate
temperature, and that proper structure sampling may require long trajectories to capture the slow
structural rearrangements of MHPs.21-23
Slow anharmonic motions play many important roles in MHPs. They induce partial charge
carrier localization67, 83-88 that rationalizes the unconventional temperature dependence of radiative
and nonradiative charge carrier lifetimes, i.e., the lifetimes increase rather than decrease with
temperature.84, 85, 89, 90 Geometric distortions of the soft MHP structure give rise to temperature
induced changes in the MHP bandgap.16, 89, 91, 92 Anharmonicity relaxes electron-phonon coupling
selection rules and allows additional vibrations to couple to the electronic subsystem at higher
temperatures.89 This accelerates loss of coherence in the electronic subsystem, and typically short
coherence times favor long excited state lifetimes,93-96 a valuable feature for solar energy and
optoelectronic applications.97-99 However, at low temperature, when anharmonicity is
insignificant, coherence times can be very long,74 an important condition for quantum information
processing.
In summary, we have demonstrated that halide vacancies can create deep trap states in the
bulk of lead halide perovskites, however, no analogous states arise on lead halide perovskite
surfaces. Appearance of deep traps requires formation of a bond between the two Pb atoms across
the vacancy, and no such bond can form on the surface. The conclusion applies to both neutral and
charged vacancies. Negatively charged vacancies can form stable Pb-Pb dimer species, while
neutral vacancies can create the dimers transiently, due to large amplitude thermal fluctuations of
the MHP lattice. The transient neutral defects are benign; however, stable charged vacancy defects
can be detrimental in the bulk. Because generation of deep trap states requires capture of two
electrons, the bulk vacancy defects should be detrimental at high charge carrier density and benign
at low carrier density. The relevant lattice fluctuations occur on a 50-100 ps timescale, and in order
to sample such fluctuations we have developed a ML FF, trained based on ab initio DFT. As the
length of the Pb-Pb bond across the Br vacancy shortens, up to four trap states can appear inside
the CsPbBr3 bandgap. The deepest trap state is formed by p-orbitals of the Pb atoms overlapping
to make a s-bond. The shallow trap states arise from p-orbitals of the Pb atoms forming p-bonds.
67

A halide vacancy on a lead halide perovskite surface breaks the symmetry in the distribution of
electron and hole charge densities, with the electron localizing at the vacancy on the surface and
hole localizing in the bulk. Although the electron state is supported by the surface vacancy, it is
not a trap state, because it is not separated energetically from the conduction band, and since it is
delocalized along the surface. The electron-hole separation facilitated by the surface halide
vacancies extend nonradiative and radiative excited state lifetimes. The formation of the multiple
deep midgap levels in lead halide perovskite bulk by halide vacancies is possible due to the flexible
nature of the lattice that allows large scale thermal fluctuations and strong structural response to
injected charges. This behavior makes MHPs qualitatively different from the traditional inorganic
semiconductors that are stiff and undergo minimal structural fluctuations. Halide vacancies are
among the most common point defects in MHPs. The absence of the vacancy generated trap states
on MHP surfaces, combined with the vacancy induced electron-hole separation, contributes to the
excellent optoelectronic properties of MHP QDs that exhibit bright luminescence and slow
nonradiative excited state decay, without the need for a thorough surface passivation. The absence
of charge traps on MHP QD surfaces decreases blinking that is common in QDs formed from the
traditional inorganic semiconductors. The insights provided by the present study contribute to the
fundamental understanding of MHP properties and help in development of efficient solar energy
and optoelectronic devices.
68

References
(1) Zhang, W.; Eperon, G. E.; Snaith, H. J. Metal Halide Perovskites for Energy Applications. Nature
Energy 2016, 1 (6), 1-8.
(2) Shalan, A. E.; Akman, E.; Sadegh, F.; Akin, S. Efficient and Stable Perovskite Solar Cells Enabled by
Dicarboxylic Acid-Supported Perovskite Crystallization. Journal of Physical Chemistry Letters 2021, 12
(3), 997-1004. DOI: 10.1021/acs.jpclett.0c03566.
(3) Lao, X.; Li, X.; Ågren, H.; Chen, G. Highly Controllable Synthesis and DFT Calculations of
Double/Triple-Halide CsPbX3 (X= Cl, Br, I) Perovskite Quantum Dots: Application to Light-Emitting
Diodes. Nanomaterials 2019, 9 (2), 172.
(4) Kulkarni, S. A.; Baikie, T.; Boix, P. P.; Yantara, N.; Mathews, N.; Mhaisalkar, S. Band-Gap Tuning of
Lead Halide Perovskites Using a Sequential Deposition Process. Journal of Materials Chemistry A 2014, 2
(24), 9221-9225.
(5) Unger, E.; Kegelmann, L.; Suchan, K.; Sörell, D.; Korte, L.; Albrecht, S. Roadmap and Roadblocks for
the Band Gap Tunability of Metal Halide Perovskites. Journal of Materials Chemistry A 2017, 5 (23),
11401-11409.
(6) McGovern, L.; Koschany, I.; Grimaldi, G.; Muscarella, L. A.; Ehrler, B. Grain Size Influences
Activation Energy and Migration Pathways in MAPbBr3 Perovskite Solar Cells. Journal of Physical
Chemistry Letters 2021, 12 (9), 2423-2428. DOI: 10.1021/acs.jpclett.1c00205.
(7) Gutiérrez Álvarez, S.; Lin, W.; Abdellah, M.; Meng, J.; Zidek, K.; Pullerits, T. n.; Zheng, K. Charge
Carrier Diffusion Dynamics in Multisized Quaternary Alkylammonium-Capped CsPbBr3 Perovskite
Nanocrystal Solids. ACS Applied Materials & Interfaces 2021, 13 (37), 44742-44750.
(8) Herz, L. M. Charge-Carrier Mobilities in Metal Halide Perovskites: Fundamental Mechanisms and
Limits. ACS Energy Letters 2017, 2 (7), 1539-1548.
(9) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J.; Leijtens, T.; Herz, L. M.;
Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in An Organometal
Trihalide Perovskite Absorber. Science 2013, 342 (6156), 341-344.
(10) Noh, J. H.; Im, S. H.; Heo, J. H.; Mandal, T. N.; Seok, S. I. Chemical Management for Colorful,
Efficient, and Stable Inorganic–Organic Hybrid Nanostructured Solar Cells. Nano Letters 2013, 13 (4),
1764-1769.
(11) Saliba, M.; Matsui, T.; Domanski, K.; Seo, J.-Y.; Ummadisingu, A.; Zakeeruddin, S. M.; CorreaBaena, J.-P.; Tress, W. R.; Abate, A.; Hagfeldt, A. Incorporation of Rubidium Cations into Perovskite Solar
Cells Improves Photovoltaic Performance. Science 2016, 354 (6309), 206-209.
(12) Zhang, J. B.; Yin, C. Y.; Yang, F.; Yao, Y.; Yuan, F. L.; Chen, H. T.; Wang, R. W.; Bai, S.; Tu, G. L.;
Hou, L. T. Highly Luminescent and Stable CsPbI3 Perovskite Nanocrystals with Sodium Dodecyl Sulfate
Ligand Passivation for Red-Light-Emitting Diodes. Journal of Physical Chemistry Letters 2021, 12 (9),
2437-2443. DOI: 10.1021/acs.jpclett.1c00008.
69

(13) Kim, M.; Jeong, J.; Lu, H. Z.; Lee, T. K.; Eickemeyer, F. T.; Liu, Y. H.; Choi, I. W.; Choi, S. J.; Jo,
Y.; Kim, H. B.; et al. Conformal Quantum Dot-SnO2 Layers as Electron Transporters for Efficient
Perovskite Solar Cells. Science 2022, 375 (6578), 302-306, Article. DOI: 10.1126/science.abh1885.
(14) Jiang, Y. Z.; Wei, J. L.; Yuan, M. J. Energy-Funneling Process in Quasi-2D Perovskite Light-Emitting
Diodes. Journal of Physical Chemistry Letters 2021, 12 (10), 2593-2606. DOI:
10.1021/acs.jpclett.1c00072.
(15) Cheng, S. J.; Zhong, H. Z. What Happens When Halide Perovskites Meet with Water? Journal of
Physical Chemistry Letters 2022, 13 (10), 2281-2290. DOI: 10.1021/acs.jpclett.2c00166.
(16) Marronnier, A.; Roma, G.; Boyer-Richard, S.; Pedesseau, L.; Jancu, J.-M.; Bonnassieux, Y.; Katan,
C.; Stoumpos, C. C.; Kanatzidis, M. G.; Even, J. Anharmonicity and Disorder in the Black Phases of Cesium
Lead Iodide Used for Stable Inorganic Perovskite Solar Cells. ACS Nano 2018, 12 (4), 3477-3486.
(17) Jeon, N. J.; Noh, J. H.; Yang, W. S.; Kim, Y. C.; Ryu, S.; Seo, J.; Seok, S. I. Compositional Engineering
of Perovskite Materials for High-Performance Solar Cells. Nature 2015, 517 (7535), 476. DOI:
10.1038/nature14133.
(18) Cao, D. H.; Stoumpos, C. C.; Farha, O. K.; Hupp, J. T.; Kanatzidis, M. G. 2D Homologous Perovskites
as Light-Absorbing Materials for Solar Cell Applications. Journal of the American Chemical Society 2015,
137 (24), 7843-7850. DOI: 10.1021/jacs.5b03796.
(19) Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.;
Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, and
I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano Letters 2015,
15 (6), 3692-3696. DOI: 10.1021/nl5048779.
(20) Cohen, A. V.; Egger, D. A.; Rappe, A. M.; Kronik, L. Breakdown of the Static Picture of Defect
Energetics in Halide Perovskites: the Case of the Br Vacancy in CsPbBr3. The Journal of Physical
Chemistry Letters 2019, 10 (16), 4490-4498.
(21) Wang, B.; Chu, W.; Wu, Y.; Casanova, D.; Saidi, W. A.; Prezhdo, O. V. Electron-Volt Fluctuation of
Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale. The Journal of Physical Chemistry
Letters 2022, 13 (25), 5946-5952.
(22) Wu, Y.; Liu, D.; Chu, W.; Wang, B.; Vasenko, A. S.; Prezhdo, O. V. Fluctuations at Metal Halide
Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis.
ACS Applied Materials & Interfaces 2022, 14, 55753–55761.
(23) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on A
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(24) Li, W.; Liu, J.; Bai, F.-Q.; Zhang, H.-X.; Prezhdo, O. V. Hole Trapping by Iodine Interstitial Defects
Decreases Free Carrier Losses in Perovskite Solar Cells: A Time-Domain Ab Initio Study. ACS Energy
Letters 2017, 2 (6), 1270-1278.
70

(25) Li, W.; Sun, Y.-Y.; Li, L.; Zhou, Z.; Tang, J.; Prezhdo, O. V. Control of Charge Recombination in
Perovskites by Oxidation State of Halide Vacancy. Journal of the American Chemical Society 2018, 140
(46), 15753-15763.
(26) Chu, W.; Saidi, W. A.; Zhao, J.; Prezhdo, O. V. Soft Lattice and Defect Covalency Rationalize
Tolerance of β‐CsPbI3 Perovskite Solar Cells to Native Defects. Angewandte Chemie International Edition
2020, 59 (16), 6435-6441.
(27) Chu, W.; Zheng, Q.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Low-Frequency Lattice Phonons in Halide
Perovskites Explain High Defect Tolerance Toward Electron-Hole Recombination. Science Advances 2020,
6 (7), eaaw7453.
(28) Li, W.; Long, R.; Tang, J.; Prezhdo, O. V. Influence of Defects on Excited-State Dynamics in Lead
Halide Perovskites: Time-Domain Ab Initio Studies. The Journal of Physical Chemistry Letters 2019, 10
(13), 3788-3804.
(29) Li, W.; She, Y.; Vasenko, A. S.; Prezhdo, O. V. Ab Initio Nonadiabatic Molecular Dynamics of Charge
Carriers in Metal Halide Perovskites. Nanoscale 2021, 13 (23), 10239-10265.
(30) Yin, W. J.; Shi, T. T.; Yan, Y. F. Unusual Defect Physics in CH3NH3PbI3 Perovskite Solar Cell
Absorber. Applied Physics Letters 2014, 104 (6). DOI: 10.1063/1.4864778.
(31) Chang, T.; Wei, Q. L.; Zeng, R. S.; Cao, S.; Zhao, J. L.; Zou, B. S. Efficient Energy Transfer in Te4+-
Doped Cs2ZrCl6 Vacancy-Ordered Perovskites and Ultrahigh Moisture Stability via A-Site Rb-Alloying
Strategy. Journal of Physical Chemistry Letters 2021, 12 (7), 1829-1837. DOI:
10.1021/acs.jpclett.1c00255.
(32) Wright, A. D.; Buizza, L. R. V.; Savill, K. J.; Longo, G.; Snaith, H. J.; Johnston, M. B.; Herz, L. M.
Ultrafast Excited-State Localization in Cs2AgBiBr6 Double Perovskite. Journal of Physical Chemistry
Letters 2021, 12 (13), 3352-3360. DOI: 10.1021/acs.jpclett.1c00653.
(33) Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic
Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Letters 2014, 14 (5), 2584-
2590. DOI: 10.1021/nl500390f.
(34) Liu, D. Y.; Perez, C. M.; Vasenko, A. S.; Prezhdo, O. V. Ag-Bi Charge Redistribution Creates Deep
Traps in Defective Cs2AgBiBr6: Machine Learning Analysis of Density Functional Theory. Journal of
Physical Chemistry Letters 2022, 13 (16), 3645-3651. DOI: 10.1021/acs.jpclett.2c00869.
(35) Chu, W. B.; Saidi, W. A.; Prezhdo, O. V. Long-Lived Hot Electron in a Metallic Particle for
Plasmonics and Catalysis: Ab Initio Nonadiabatic Molecular Dynamics with Machine Learning. Acs Nano
2020, 14 (8), 10608-10615. DOI: 10.1021/acsnano.0c04736.
(36) Schleder, G. R.; Padilha, A. C.; Acosta, C. M.; Costa, M.; Fazzio, A. From DFT to Machine Learning:
Recent Approaches to Materials Science–A Review. Journal of Physics: Materials 2019, 2 (3), 032001.
(37) Gu, G. H.; Noh, J.; Kim, I.; Jung, Y. Machine Learning for Renewable Energy Materials. Journal of
Materials Chemistry A 2019, 7 (29), 17096-17117.
71

(38) Huan, T. D.; Batra, R.; Chapman, J.; Krishnan, S.; Chen, L.; Ramprasad, R. A Universal Strategy for
the Creation of Machine Learning-Based Atomistic Force Fields. NPJ Computational Materials 2017, 3
(1), 37.
(39) Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine Learning for Molecular
and Materials Science. Nature 2018, 559 (7715), 547-555.
(40) Ouyang, Y.; Yu, C.; He, J.; Jiang, P.; Ren, W.; Chen, J. Accurate Description of High-Order Phonon
Anharmonicity and Lattice Thermal Conductivity from Molecular Dynamics Simulations with Machine
Learning Potential. Physical Review B 2022, 105 (11), 115202.
(41) Mortazavi, B.; Podryabinkin, E. V.; Novikov, I. S.; Rabczuk, T.; Zhuang, X.; Shapeev, A. V.
Accelerating First-Principles Estimation of Thermal Conductivity by Machine-Learning Interatomic
Potentials: A MTP/ShengBTE Solution. Computer Physics Communications 2021, 258, 107583.
(42) Zong, H.; Pilania, G.; Ding, X.; Ackland, G. J.; Lookman, T. Developing An Interatomic Potential for
Martensitic Phase Transformations in Zirconium by Machine Learning. NPJ Computational Materials
2018, 4 (1), 48.
(43) Li, L.; Yang, Y.; Zhang, D.; Ye, Z.-G.; Jesse, S.; Kalinin, S. V.; Vasudevan, R. K. Machine Learning–
Enabled Identification of Material Phase Transitions Based on Experimental Data: Exploring Collective
Dynamics in Ferroelectric Relaxors. Science Advances 2018, 4 (3), eaap8672.
(44) Meuwly, M. Machine Learning for Chemical Reactions. Chemical Reviews 2021, 121 (16), 10218-
10239.
(45) Westermayr, J.; Gastegger, M.; Marquetand, P. Combining SchNet and SHARC: The SchNarc
Machine Learning Approach for Excited-State Dynamics. The Journal of Physical Chemistry Letters 2020,
11 (10), 3828-3834.
(46) Lee, J.; Seko, A.; Shitara, K.; Nakayama, K.; Tanaka, I. Prediction Model of Band Gap for Inorganic
Compounds by Combination of Density Functional Theory Calculations and Machine Learning
Techniques. Physical Review B 2016, 93 (11), 115104.
(47) Kim, C.; Pilania, G.; Ramprasad, R. From Organized High-Throughput Data to Phenomenological
Theory Using Machine Learning: the Example of Dielectric Breakdown. Chemistry of Materials 2016, 28
(5), 1304-1311.
(48) Gastegger, M.; Behler, J.; Marquetand, P. Machine Learning Molecular Dynamics for the Simulation
of Infrared Spectra. Chemical Science 2017, 8 (10), 6924-6935.
(49) Poltavsky, I.; Tkatchenko, A. Machine Learning Force Fields: Recent Advances and Remaining
Challenges. The Journal of Physical Chemistry Letters 2021, 12 (28), 6551-6564.
(50) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
72

(51) Yin, J.; Yang, H.; Song, K.; El-Zohry, A. M.; Han, Y.; Bakr, O. M.; Brédas, J.-L.; Mohammed, O. F.
Point Defects and Green Emission in Zero-Dimensional Perovskites. The Journal of Physical Chemistry
Letters 2018, 9 (18), 5490-5495.
(52) Kresse, G.; Furthmuller, J. VASP the Guide (Vienna University of Technology, Vienna, 2001); G.
Kresse and J. Hafner. Phys. Rev. B 1993, 47, 558.
(53) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical
Review Letters 1996, 77 (18), 3865.
(54) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.
Physical Review b 1999, 59 (3), 1758.
(55) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and
Morphology Data. Journal of Applied Crystallography 2011, 44 (6), 1272-1276.
(56) Wang, H.; Zhang, L.; Han, J.; Weinan, E. DeePMD-kit: A Deep Learning Package for Many-Body
Potential Energy Representation and Molecular Dynamics. Computer Physics Communications 2018, 228,
178-184.
(57) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of Computational
Physics 1995, 117 (1), 1-19.
(58) Yuan, Y. B.; Huang, J. S. Ion Migration in Organometal Trihalide Perovskite and Its Impact on
Photovoltaic Efficiency and Stability. Accounts of Chemical Research 2016, 49 (2), 286-293. DOI:
10.1021/acs.accounts.5b00420.
(59) Bischak, C. G.; Hetherington, C. L.; Wu, H.; Aloni, S.; Ogletree, D. F.; Limmer, D. T.; Ginsberg, N.
S. Origin of Reversible Photoinduced Phase Separation in Hybrid Perovskites. Nano Letters 2017, 17 (2),
1028-1033. DOI: 10.1021/acs.nanolett.6b04453.
(60) Jokar, E.; Chuang, H. S.; Kuan, C. H.; Wu, H. P.; Hou, C. H.; Shyue, J. J.; Diau, E. W. G. Slow
Passivation and Inverted Hysteresis for Hybrid Tin Perovskite Solar Cells Attaining 13.5% via Sequential
Deposition. Journal of Physical Chemistry Letters 2021, 12 (41), 10106-10111. DOI:
10.1021/acs.jpclett.1c03107.
(61) Tong, C. J.; Geng, W.; Prezhdo, O. V.; Liu, L. M. Role of Methylammonium Orientation in Ion
Diffusion and Current Voltage Hysteresis in the CH3NH3PbI3 Perovskite. Acs Energy Letters 2017, 2 (9),
1997-2004. DOI: 10.1021/acsenergylett.7b00659.
(62) Tong, C. J.; Li, L. Q.; Liu, L. M.; Prezhdo, O. V. Synergy between Ion Migration and Charge Carrier
Recombination in Metal-Halide Perovskites. Journal of the American Chemical Society 2020, 142 (6),
3060-3068. DOI: 10.1021/jacs.9b12391.
(63) Shi, R.; Fang, W. H.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Efficient Passivation of DY Center in
CH3NH3PbBr3 by Chlorine: Quantum Molecular Dynamics. Nano Research 2022, 15 (3), 2112-2122. DOI:
10.1007/s12274-021-3840-y.
73

(64) Neutzner, S.; Thouin, F.; Cortecchia, D.; Petrozza, A.; Silva, C.; Kandada, A. R. S. Exciton-Polaron
Spectral Structures in Two-Dimensional Hybrid Lead-Halide Perovskites. Physical Review Materials 2018,
2 (6), 064605.
(65) Lang, F.; Shargaieva, O.; Brus, V. V.; Neitzert, H. C.; Rappich, J.; Nickel, N. H. Influence of Radiation
on the Properties and the Stability of Hybrid Perovskites. Advanced Materials 2018, 30 (3), 1702905.
(66) Straus, D. B.; Kagan, C. R. Electrons, Excitons, and Phonons in Two-Dimensional Hybrid Perovskites:
Connecting Structural, Optical, and Electronic Properties. The Journal of Physical Chemistry Letters 2018,
9 (6), 1434-1447.
(67) Zhang, Z.; Fang, W.-H.; Long, R.; Prezhdo, O. V. Exciton Dissociation and Suppressed Charge
Recombination at 2D Perovskite Edges: Key Roles of Unsaturated Halide Bonds and Thermal Disorder.
Journal of the American Chemical Society 2019, 141 (39), 15557-15566.
(68) Shi, R.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Edge Influence on Charge Carrier Localization and
Lifetime in CH3NH3PbBr3 Perovskite: Ab Initio Quantum Dynamics Simulation. Journal of Physical
Chemistry Letters 2020, 11 (21), 9100-9109. DOI: 10.1021/acs.jpclett.0c02800.
(69) He, J. L.; Fang, W. H.; Long, R.; Prezhdo, O. V. Bidentate Lewis Bases Are Preferred for Passivation
of MAPbI3 Surfaces: A Time-Domain Ab Initio Analysis. Nano Energy 2021, 79. DOI:
10.1016/j.nanoen.2020.105491.
(70) Zhao, X.; Vasenko, A. S.; Prezhdo, O. V.; Long, R. Anion Doping Delays Nonradiative Electron-Hole
Recombination in Cs-Based All-Inorganic Perovskites: Time Domain ab Initio Analysis. Journal of
Physical Chemistry Letters 2022, 13 (49), 11375-11382. DOI: 10.1021/acs.jpclett.2c03072.
(71) Shi, R.; Long, R.; Fang, W. H.; Prezhdo, O. V. Rapid Interlayer Charge Separation and Extended
Carrier Lifetimes due to Spontaneous Symmetry Breaking in Organic and Mixed Organic-Inorganic DionJacobson Perovskites. Journal of the American Chemical Society 2023, 145, 5297–5309. DOI:
10.1021/jacs.2c12903.
(72) Liu, L. H.; Fang, W. H.; Long, R.; Prezhdo, O. V. Lewis Base Passivation of Hybrid Halide Perovskites
Slows Electron-Hole Recombination: Time-Domain Ab lnitio Analysis. Journal of Physical Chemistry
Letters 2018, 9 (5), 1164-1171. DOI: 10.1021/acs.jpclett.8b00177.
(73) Agiorgousis, M. L.; Sun, Y. Y.; Zeng, H.; Zhang, S. B. Strong Covalency-Induced Recombination
Centers in Perovskite Solar Cell Material CH3NH3Pbl3. Journal of the American Chemical Society 2014,
136 (41), 14570-14575. DOI: 10.1021/ja5079305.
(74) Utzat, H.; Sun, W. W.; Kaplan, A. E. K.; Krieg, F.; Ginterseder, M.; Spokoyny, B.; Klein, N. D.;
Shulenberger, K. E.; Perkinson, C. F.; Kovalenko, M. V.; Bawendi, M. G. Coherent Single-Photon
Emission from Colloidal Lead Halide Perovskite Quantum Dots. Science 2019, 363 (6431), 1068. DOI:
10.1126/science.aau7392.
(75) Akkerman, Q. A.; Raino, G.; Kovalenko, M. V.; Manna, L. Genesis, Challenges and Opportunities for
Colloidal Lead Halide Perovskite Nanocrystals. Nature Materials 2018, 17 (5), 394-405. DOI:
10.1038/s41563-018-0018-4.
74

(76) Swarnkar, A.; Chulliyil, R.; Ravi, V. K.; Irfanullah, M.; Chowdhury, A.; Nag, A. Colloidal CsPbBr3
Perovskite Nanocrystals: Luminescence beyond Traditional Quantum Dots. Angewandte ChemieInternational Edition 2015, 54 (51), 15424-15428. DOI: 10.1002/anie.201508276.
(77) Alivisatos, A. P. Semiconductor Clusters, Nanocrystals, and Quantum Dots. Science 1996, 271 (5251),
933-937. DOI: 10.1126/science.271.5251.933.
(78) Prezhdo, O. V. Multiple Excitons and the Electron-Phonon Bottleneck in Semiconductor Quantum
Dots: An Ab Initio Perspective. Chemical Physics Letters 2008, 460 (1-3), 1-9. DOI:
10.1016/j.cplett.2008.03.099.
(79) Hyeon-Deuk, K.; Prezhdo, O. V. Multiple Exciton Generation and Recombination Dynamics in Small
Si and CdSe Quantum Dots: An Ab Initio Time-Domain Study. Acs Nano 2012, 6 (2), 1239-1250. DOI:
10.1021/nn2038884.
(80) Chen, O.; Zhao, J.; Chauhan, V. P.; Cui, J.; Wong, C.; Harris, D. K.; Wei, H.; Han, H. S.; Fukumura,
D.; Jain, R. K.; Bawendi, M. G. Compact High-Quality CdSe-CdS Core-Shell Nanocrystals with Narrow
Emission Linewidths and Suppressed Blinking. Nature Materials 2013, 12 (5), 445-451. DOI:
10.1038/nmat3539.
(81) Houtepen, A. J.; Hens, Z.; Owen, J. S.; Infante, I. On the Origin of Surface Traps in Colloidal II-VI
Semiconductor Nanocrystals. Chemistry of Materials 2017, 29 (2), 752-761. DOI:
10.1021/acs.chemmater.6b04648.
(82) Trivedi, D. J.; Wang, L. J.; Prezhdo, O. V. Auger-Mediated Electron Relaxation Is Robust to Deep
Hole Traps: Time-Domain Ab Initio Study of CdSe Quantum Dots. Nano Letters 2015, 15 (3), 2086-2091.
DOI: 10.1021/nl504982k.
(83) Li, W.; Vasenko, A. S.; Tang, J.; Prezhdo, O. V. Anharmonicity Extends Carrier Lifetimes in Lead
Halide Perovskites at Elevated Temperatures. The Journal of Physical Chemistry Letters 2019, 10 (20),
6219-6226.
(84) Zhou, G.; Chu, W.; Prezhdo, O. V. Structural Deformation Controls Charge Losses in MAPbI3:
Unsupervised Machine Learning of Nonadiabatic Molecular Dynamics. ACS Energy Letters 2020, 5 (6),
1930-1938.
(85) Mangan, S. M.; Zhou, G.; Chu, W.; Prezhdo, O. V. Dependence Between Structural and Electronic
Properties of CsPbI3: Unsupervised Machine Learning of Nonadiabatic Molecular Dynamics. The Journal
of Physical Chemistry Letters 2021, 12 (35), 8672-8678.
(86) Aristidou, N.; Eames, C.; Sanchez-Molina, I.; Bu, X.; Kosco, J.; Islam, M. S.; Haque, S. A. Fast
Oxygen Diffusion and Iodide Defects Mediate Oxygen-Induced Degradation of Perovskite Solar Cells.
Nature Communications 2017, 8 (1), 15218.
(87) He, J.; Fang, W.-H.; Long, R.; Prezhdo, O. V. Superoxide/Peroxide Chemistry Extends Charge
Carriers’ Lifetime but Undermines Chemical Stability of CH3NH3PbI3 Exposed to Oxygen: Time-Domain
Ab Initio Analysis. Journal of the American Chemical Society 2019, 141 (14), 5798-5807.
75

(88) Zhang, Z.; Fang, W.-H.; Tokina, M. V.; Long, R.; Prezhdo, O. V. Rapid Decoherence Suppresses
Charge Recombination in Multi-Layer 2D Halide Perovskites: Time-Domain Ab Initio Analysis. Nano
Letters 2018, 18 (4), 2459-2466.
(89) Li, W.; Tang, J.; Casanova, D.; Prezhdo, O. V. Time-Domain Ab Initio Analysis Rationalizes the
Unusual Temperature Dependence of Charge Carrier Relaxation in Lead Halide Perovskite. ACS Energy
Letters 2018, 3 (11), 2713-2720.
(90) Li, W.; Chen, Z.; Tang, J.; Prezhdo, O. V. Anti-Correlation between Band Gap and Carrier Lifetime
in Lead Halide Perovskites under Compression Rationalized by Ab Initio Quantum Dynamics. Chemistry
of Materials 2020, 32 (11), 4707-4715.
(91) Patrick, C. E.; Jacobsen, K. W.; Thygesen, K. S. Anharmonic Stabilization and Band Gap
Renormalization in the Perovskite CsSnI3. Physical Review B 2015, 92 (20), 201205.
(92) Long, R.; Fang, Q.; Vasenko, A. S.; Shi, R.; Fang, W. H.; Prezhdo, O. V. Structural Disorder in HigherTemperature Phases Increases Charge Carrier Lifetimes in Metal Halide Perovskites. Journal of the
American Chemical Society 2022, 144 (41), 19137-19149. DOI: 10.1021/jacs.2c08627.
(93) Akimov, A. V.; Prezhdo, O. V. Persistent Electronic Coherence Despite Rapid Loss of ElectronNuclear Correlation. Journal of Physical Chemistry Letters 2013, 4 (22), 3857-3864. DOI:
10.1021/jz402035z.
(94) Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.; Prezhdo, O. V. Quantum Zeno Effect
Rationalizes the Phonon Bottleneck in Semiconductor Quantum Dots. Physical Review Letters 2013, 110
(18). DOI: 10.1103/PhysRevLett.110.180404.
(95) Itano, W. M.; Heinzen, D. J.; Bollinger, J. J.; Wineland, D. J. Quantum Zeno Effect. Physical Review
A 1990, 41 (5), 2295-2300. DOI: 10.1103/PhysRevA.41.2295.
(96) Kamisaka, H.; Kilina, S. V.; Yamashita, K.; Prezhdo, O. V. Ultrafast Vibrationally-Induced Dephasing
of Electronic Excitations in PbSe Quantum Dot. Nano Letters 2006, 6 (10), 2295-2300. DOI:
10.1021/nl0617383.
(97) Li, X.; Cao, F.; Yu, D.; Chen, J.; Sun, Z.; Shen, Y.; Zhu, Y.; Wang, L.; Wei, Y.; Wu, Y. All Inorganic
Halide Perovskites Nanosystem: Synthesis, Structural Features, Optical Properties and Optoelectronic
Applications. Small 2017, 13 (9), 1603996.
(98) Fu, Y.; Zhu, H.; Chen, J.; Hautzinger, M. P.; Zhu, X.-Y.; Jin, S. Metal Halide Perovskite
Nanostructures for Optoelectronic Applications and the Study of Physical Properties. Nature Reviews
Materials 2019, 4 (3), 169-188.
(99) Zhao, Y.; Zhu, K. Organic–Inorganic Hybrid Lead Halide Perovskites for Optoelectronic and
Electronic Applications. Chemical Society Reviews 2016, 45 (3), 655-689.
76

Chapter 6
The Vacancy Migration Studies in CsPbBr3 Quantum Dot
Overview
Quantum dots of metal halide perovskites (MHPs) have cumulated substantial interest for
advanced optoelectronic applications, but their efficacy can be hindered by ionic defects, notably
vacancies, which induce phase separation, hysteresis, and instability, presenting unique challenges
and opportunities at the nanoscale. This study presents a comprehensive analysis of Br migration
within the prototype MHP quantum dot, CsPbBr3, utilizing the nudge elastic band (NEB) method
to elucidate the energy profiles associated with interlayer and intralayer vacancy migration
pathways. Our investigation reveals that intralayer vacancy migrations exhibit much higher energy
barriers compared to interlayer migrations, with the surface layer displaying anomalous behavior.
Crucially, the challenge in the in-plane tilting of octahedra restricts intralayer pathways, leading
to elevated energy barriers, unlike those observed in interlayer migration. The NEB calculations,
supported by structural scrutiny, disclose that surface vacancies are stabilized by undercoordinated atoms, resulting in distinct migration energy profiles compared to the bulk layer
vacancies. Furthermore, the energy profiles for vacancy migration in CsPbBr3 quantum dots show
clear correlations with electronic structural changes we observed in our previous studies. This
study enhances the understanding of defect dynamics in perovskite quantum dots, highlighting the
significant effects of quantum confinement and surface phenomena on vacancy behaviors. The
insights gained are pivotal for the design of more stable and efficient perovskite-based devices.
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Author List
Jingyi Ran, Carlos Mora Perez, Oleg V. Prezhdo
Metal halide perovskites (MHPs) have attracted remarkable attention in scientific research
through their outstanding photovoltaic and optoelectronic characteristics.1, 2 The unique features
of these materials arise from their narrow full width at half-maximum (FWHM) emission lines,3-5
tunable band gaps,6-9 high photoluminescence quantum yields (PLQYs),10-13 and long carrier
diffusion lengths.14-16 In parallel with the advances in MHP bulk materials, MHP quantum dots
have gained significant attention, emerging as a novel class of nanomaterials with distinct and
enhanced properties.17-20 The inherent surface strain within these quantum dots not only retain the
perovskite phase under a broader range of conditions but also introduce considerable tunability
over optoelectronic characteristics.21-23 By altering the quantum dot sizes, the absorption and
emission spectra can be controlled, enabling tailored wavelength selection for targeted
applications.24-27 Moreover, these nanoscale materials exhibit efficient multiple exciton
generation, where a single photon can induce the formation of multiple electron-hole pairs, thus
promising a substantial boost in device performance.28-30 The intricate surface properties of MHP
quantum dots further improve their interaction with the environment, which can be leveraged to
design highly sensitive sensors and novel catalytic systems.31-33
However, the functionality and operational stability of MHP quantum dots are intrinsically
influenced by various considerations including vacancy migrations.34-36 These vacancies,
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primarily of the halide and lead species, are known to induce phase segregation and contribute to
current-voltage hysteresis.
37-45 Such phenomena can markedly deteriorate device performance,
leading to reduced efficiency and shortened lifetimes.46-48 Thus, a comprehensive understanding
of vacancy migration mechanisms and their impact on the structural and electronic integrity of
MHP quantum dots is crucial. The understanding can unlock strategies for defect management and
the design of MHP quantum dot-based devices that combine high performance with robust
stability—a pivotal step towards their successful commercial deployment.
In this study, we focus on the halide vacancy migration behavior in the prototype MHP
quantum dot - CsPbBr3 quantum dot to elucidate the possible mechanisms of interlayer and
intralayer migrations. The ab initio calculations, particularly nudge elastic band (NEB) method,49
are used to determine the energy profiles and barriers of Br vacancy migrations under various
scenarios. Our simulations reveal layer-dependent halide vacancy migration processes in quantum
dots, in contrast to the 3D bulk counterparts, with notable distinct surface layer behaviors.
Generally, energy barriers in interlayer migrations are lower than in intralayer ones. Vacancies
tend to migrate from the surface towards the bulk, as suggested by the general decrease of energy
barriers during the interlayer migrations. Conversely, the intralayer migration energy increases
when moving from the surface layers to the bulk, further echoing that vacancy migration becomes
increasingly challenging as the vacancy moves deeper into the material. This pattern emphasizes
the preference for vacancies to migrate between layers rather than within the same layer in MHP
quantum dots. Remarkably, the surface layer stands out in the trends by exhibiting a higher than
usual interlayer migration energy barrier and a much lower intralayer migration energy. This can
be explained by the unique surface environment of quantum dots, where surface atoms are not
fully coordinated, resulting in a more distorted local environment and lattice tension.50-53 The
significant role of quantum confinement, structural limitations, surface phenomena and vacancy
dynamics in MHP quantum dots are enhanced by the results of the study. The insights gained in
this study can inform better design of more stable and efficient perovskite quantum dot-based
devices.
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In the investigation of ion migration mechanisms, density functional theory (DFT)
simulations are conducted utilizing the Vienna Ab-initio Simulation Package (VASP).54 The
electron-ion interaction dynamics are described through the Perdew–Burke–Ernzerhof (PBE)55
exchange-correlation functional with the projector-augmented-wave (PAW) method.56 An energy
cutoff for the plane-wave basis set is at 350 eV. Structural visualization is facilitated by the VESTA
software.57 For the examination of Br ion migration, five distinct CsPbBr3 models are designed:
each featuring one Br vacancy at each layer of the slab from the first layer to the central layer
number five. These models originate from a supercell approach, structuring a slab consisting of 2
× 2 × 5 unit cells (Figure 1(a)). The termination of the slab surfaces with CsBr is selected based
on its thermodynamic stability, corroborated by both experimental58, 59 and theoretical evidence.60,
61 To mitigate spurious interactions, a 20 Å vacuum buffer is introduced perpendicular to the slab
layers. The implementation of periodic boundary conditions in three dimensions ensures the
accurate modeling of the crystal. Br vacancies are generated by the deliberate omission of a Br
atom from the layers, with their positions demarcated by dotted beige circles in Figure 1. Given
the extensive unit cell incorporation in the model, electronic structure calculations are confined to
the Γ k-point, aligning with the known CsPbBr3 band gap.62 Each of the vacancy-containing
CsPbBr3 models is composed of 87 atoms, facilitating a comprehensive study of the vacancyinduced alterations in ion migration pathways.
To determine the minimum energy path between two stable end points, the NEB method
is used. The NEB method is a computational algorithm used to determine the most favorable path
for transitional states in a system.49, 63 It is thus valuable for studying the dynamic behavior of
vacancy migrations in perovskite quantum dots, providing insights into the diffusion
mechanisms.29, 64, 65 All migration paths contain seven images. Two different kinds of paths are
studied – interlayer and intralayer paths. Four interlayer paths are considered, namely from each
layer to the layer underneath (for example, from layer 1 to 2, 2 to 3, etc.) NEB is also used to
calculate the energy barriers in each distinct layer so five intralayer paths are obtained. Each image
was constructed by doing geometry optimization after removing Br atom from the perfect crystal.
The energy barrier values are calculated as the difference between the 4,-J and 4,7&.
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Figure 1 illustrates the optimized geometries of defective CsPbBr3 slabs, displaying the (a)
side view and top views of (b) odd and (c) even layers at 0 K. In each layer, potential vacancies
are identified as dotted beige circles. The focus on Br vacancies is vital, considering their
significant influence on the electronic and optical properties of CsPbBr3. Halide vacancies,
particularly Br vacancies in CsPbBr3, have relatively low formation energies.66 Once formed, they
introduce midgap trap states that can impact charge transport and recombination rates, leading to
potential losses in device efficiency.28, 67-72 Additionally, these vacancies may alter the absorption
and emission spectra of the perovskite quantum dots, potentially resulting in the quenching of
photoluminescence, which further affects the optical performance of these materials.35, 73-77
Building upon previous studies that have investigated similar defect structures in perovskites,67, 68,
73 our work further elucidates the defect dynamics by introducing two critical migration scenarios:
interlayer and intralayer migration. These scenarios are essential for understanding the mobility of
vacancies and their impact on the overall performance of the material. The detailed representations
of both side and top views enable a comprehensive understanding of the geometric structure
variations between the odd and even layers, which is crucial for grasping the complex 3D
architecture of the perovskite quantum dot.
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Figure 1. (a) The side view of the optimized structure of CsPbBr3 with the possible Br defect vacancies. A
20 Å vacuum layer is added to the z-direction. Cs, Pb and Br atoms are represented by large dark green,
medium grey and small dark orange spheres, respectively. The vacancies are highlighted by the dotted light
orange circles. The Br vacancies locate at different layers from surface to bulk of the slab and the atomic
layers are marked from 1 to 5 correspondingly. (b) The top view of the odd layers (1, 3 and 5) with Br
vacancy of the structure. (c) The top view of the even layers (2 and 4) with Br vacancy of the structure. The
side view enhances the visualization of interlayer ion migration, whereas the top views facilitate a clearer
representation of intralayer ion migration.
Figure 2 illustrates the relationship between the energies and Pb-Pb distances of different
layers in the optimized structures of CsPbBr3 quantum dots with vacancies. The observed
variations in energies and Pb-Pb distances within different layers suggest a clear layer-dependent
lattice distortion. Energies are observed to be higher for vacancies in odd layers as opposed to even
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layers, a variation attributable to asymmetrical crystal field effects near the surface that modify the
electronic states of vacancies. Such differences are linked to Pb-Pb distances, where even layers
show a shorter bond length, indicative of a denser and potentially more stable lattice side by side,
correlating with lower energies. In contrast, the elongated Pb-Pb distances in odd layers suggest a
more relaxed lattice structure, leading to higher energies potentially due to weaker bonding. As
vacancies move from the surface into the bulk, the lattice strain diminishes, resulting in a decrease
in energy when the even and odd layers are considered separately. The position of a vacancy within
the layered structure of a quantum dot perovskite can lead to complex changes in the local charge
environment. These changes, in turn, affect the material’s properties and behaviors. Moreover, the
energy variance aligns with quantum confinement effects that are more pronounced near the
surface and diminish as the vacancy transitions deeper into the bulk, further shaping the energy
landscape. This complexity in vacancy behavior, distinct from the uniformity expected in bulk
CsPbBr3, underlines the unique properties of quantum dots. It emphasizes an individualized
consideration of each layer when analyzing the structural and electronic properties, thereby
highlighting the intricate interplay between quantum confinement, lattice structure, and energy
within these nanoscale materials.
Figure 2. (a) The energy of the optimized structure and the Pb-Pb distances are shown in the same plot
when the vacancy lies in layer 1 to 5. The energy is shown in red dots and the Pb-Pb distances are shown
in blue dots. The Pb-Pb distance measurement is not applicable to vacancies in layer 1, as there is only one
Pb atom below the vacancy. (b) The two different Br vacancy scenarios are demonstrated, namely the
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vacancy between two Pb atoms parallel to the surface plane (in even layers) and perpendicular to surface
plane (in odd layers). Generally, the energy is lower in even layers than in odd layers. This distinction in
energies is also consistent with the differences in the Pb-Pb distances. The complex vacancy behaviors of
the CsPbBr3 quantum dot indicate an individualized consideration of each layer when analyzing the
structural and electronic properties, while highlight the elaborate interplay between quantum confinement,
lattice structure, and energy within these nanoscale materials.
While the analysis of energy in the individual layers provides valuable insight into the static
structural properties of the CsPbBr3 quantum dot, understanding the dynamic process of the
vacancy migrations requires the energy barriers information. The energy landscapes associated
with interlayer vacancy migration are described in Figure 3. The partial structures of the initial,
saddle point (where the energy at the highest in the calculations) and final configurations are
inserted as well. Specifically, the transitions from odd to even-numbered layers (Figure 3(a)) and
from even to odd layers (Figure 3(b)) are depicted independently. As discussed in the previous
paragraphs, the initial energy state is higher in the former scenario, whereas the latter has a higher
final energy state. Relative to interlayer vacancy migrations observed within the bulk layers, the
substantial increase in the energy barrier of a vacancy transitioning from the surface layer to the
subsurface layer (from layer 1 to 2) can be attributed to the distinct structural characteristics of
surface atoms and their environmental context. At the quantum dot surface, atoms exhibit lower
coordination compared to their bulk material counterparts, leading to potential stabilization of
surface vacancies through the adaptive rearrangement of adjacent atoms. In particular, this
rearrangement is markedly pronounced in the row of octahedra tilting containing the vacancy, as
illustrated in Figure S1(a). Such reconfiguration may result in an energy barrier that exceeds the
typical threshold required for a vacancy to descend into layers characterized by higher atomic
coordination. Comparative analysis of the energy barriers for vacancy transition between layers 2
to 3 and 4 to 5 reveals analogous tendencies, with a reduced energy barrier observed in the layer 4
to 5 migration. This discrepancy is principally ascribed to the difference in the octahedral tilting
during vacancy transit. Initial configurations with vacancies in layers 2 or 4 both have octahedral
tilting to allow lower energy. At the saddle points, this tilting persists in transitions from layer 4 to
5 (Figure S1(d)), in contrast to a straignten of tilting from layers 2 to 3 (Figure S1(b)), thus
constricting the migration pathway more significantly in the latter, which leads to higher energy
84

barrier. Although the information is limited, the findings from the differences in Figure 3(a) and
(b) suggest a systematically lower energy barrier for vacancies migrating from odd to even layers.
This phenomenon may be attributed to the inherent structural nuances of the quantum dot, which
is amplified when a vacancy is present. In this context, the proximity between vacancies and the
nearest Cs atoms—considering the substantial atomic radius of Cs—is particularly pivotal during
layer transitions. The vacancy-Cs distance becomes closer in parts of the migration pathway,
relative to a when the vacancy sits at a Br position, is critical. Given the difficulty of measuring
the direct vacancy-Cs distances, an inferential reverse deduction methodology is employed. For
instance, a vacancy migrating from layer 3 to 4 correlates with a Br migration from layer 4 to 3,
and so on. The saddle point Br-Cs distances during Br migration from layer 5 to 4 (vacancy
migration from 4 to 5) and from layer 4 to 3 (vacancy migration from 3 to 4) 5.217 Å and 5.344
Å, respectively. A larger Br-Cs distance facilitates the migration of the Br ion, evidently due to
reduced electrostatic repulsion and a more favorable alignment within the lattice structure,
therefore implying a lower energy at the saddle point. Consequently, when the vacancy migrates
from layer 3 to 4, the energy barrier is lower. This suggests that vacancy migrating from an odd to
an even layer have a lower energy barrier in general.
Figure 3. Calculated energy profiles using NEB methods for the vacancy migration in the inter-layer
(between different layers) situations from (a) the odd layers to the next even layers and (b) the even layers
to the next odd layers. Five images (excluding the initial and final points) are calculated for each migration
path. All the energies are relative energies referenced to the initial structures. The zoom-in structures of the
initial, saddle point (where the energy at the highest in the calculations) and final configurations are inserted.
The estimated vacancies in the migration trajectory are highlighted with a light blue circle. The saddle point
85

in the process of vacancy moving from layer 1 to 2 is especially high (1.9054 eV) compared to any other
process shows relative stability of the vacancy defect on the surface. The higher than usual energy barrier
can be attributed to the distinct structural characteristics of surface atoms and their coordination
environment. Yet, after overcoming the first hurdle, the remaining of the vacancy migration process coasts
and the vacancy migrates into the bulk. The lower barriers for transitions from odd to even layers are from
the structural adaptability of the quantum dot and the critical role of the Cs – vacancy proximity is
highlighted.
The intralayer vacancy migration energy profiles for layers 1 to 5, along with potential
migration pathways, are illustrated in Figure 4. Overall, the intralayer vacancy migrations are
characterized by significantly higher energy barriers—ranging from double to triple—compared
to their interlayer counterparts. Notably, the surface layer, layer 1, presents an anomaly with the
lowest energy barrier for intralayer migration. This reduced barrier can be attributed to the surface
atoms’ lower coordination, which allows for greater relaxation and movement to alleviate stress,
thus enhancing their mobility within the layer. In stark contrast, the intralayer migration within the
bulk layers is heavily constrained by the crystal lattice. This limitation hinders the atoms’ ability
to reposition and provide a spacious pathway for the migrating vacancy. Beyond the surface layer,
the even and odd layers within the CsPbBr3 quantum dots have much higher energy barriers for
the vacancy migrations with different energy pathways. In even layers, vacancies face steep energy
ascents early in the migration, yet in the odd layers, the energy increase through the pathways are
flatter. The vacancy migration trajectory for the even layers is semi-circular, potentially due to the
disruption of stronger Pb-Pb bonds. In odd layers, however, the migration trajectory is more direct
and may interact less with surrounding lattice structures. The discrepancy in the energy profiles
might also come from the distinct Cs atom positions in relation to the migrating vacancy.
Particularly in odd layers, where the vacancy’s path is within the same plane as the Cs atoms, the
electrostatic interactions between the neighboring atoms can also play a part. Despite the distinct
structurers and thus migration pathways in the even and odd layers, the energy barriers are similar
in both cases. This could be attributed to the interplay of various compensating energy contributes
within the lattice. The initial energy ascent may be steep in even layers, the energy barrier can be
counterbalanced by a less convoluted migration pathway. Conversely, the odd layers present a
more straightforward pathway, but the cumbersome appearance of Cs atom along the way can also
86

contribute to the energy barrier. Furthermore, the inherent symmetry of the lattice and the local
strain energy around the vacancy may contribute to equalize the migration barrier across different
layers.
Figure 4. (a) Calculated energy profiles using NEB methods for the vacancy migration in the intralayer
(within the layer) cases of layers 1 to 5. Five images are calculated for each migration path as mentioned in
Figure 4. The i’ indicates a different location in the same layer. In layer 1, the energy barrier associated
with vacancy migration is significantly lower compared to subsequent layers. This can be attributed to its
surface location, which precludes any interference from additional Cs atoms along the migration pathway.
The top view of the structures of the initial, saddle point and final configurations are shown for the (b) even
87

and (c) odd layers. The predicted vacancies in the migration trajectory are highlighted with a light blue
circle. The higher barriers compared to interlayer migration, with the exception of the surface layer show
decreased atomic coordination and enhanced atomic mobility.
The comparative analysis of the interlayer and intralayer migration paths in CsPbBr3
quantum dots reveals distinct energetic trends influenced by their respective lattice environments.
Figure 5(a) and (b) show the side view interlayer migration paths and Figure 5(c) and (d) show the
top view of the intralayer migration paths. Interlayer migration is notably impacted by the lattice
structure due to the transition of vacancies across different layers, where the crystal field varies
significantly. To compare the energy barriers of all the computed results in this study, they are
depicted on the same plot as illustrated in Figure 5(e). The surface layer, or the first layer, exhibits
unique migration characteristics due to its lower coordination and more distorted structure, which
is a stamp of the quantum dot's significant surface behavior. This results in energy profiles where
vacancies exhibit a tendency to migrate towards the bulk, as indicated by the generally decreasing
energy barriers encountered during interlayer migration from the surface to the bulk. Opposite, the
intralayer migration energy trend increases when moving from the surface layers to the bulk,
suggesting that vacancy migration becomes increasingly challenging as the vacancy moves deeper
into the material. This behavior underscores the preference for vacancies to migrate between layers
rather than within the same layer. The intrinsic structural flexibility of the perovskite's cornersharing octahedra, which tilt to accommodate vacancy migration across layers,78, 79 contributes to
the lower energy barriers in interlayer migrations. However, within the plane of a layer, such tilting
is significantly less pronounced, resulting in higher energy barriers for intralayer migration.
88

Figure 5. The inter-layer (between different layers) schematic illustration of the Br vacancy migration
mechanisms when the vacancies are in (a) odd, and (b) even layers. The intra-layer (within the layer)
schematic illustration of the Br vacancy migration mechanisms when the vacancies are in (c) odd, and (d)
even layers. The arrows show the migration directions and the Br atoms with different shades represent the
simulated migration paths. (e) Energy barrier comparisons of different inter-layer and intra-layer migration
scenarios are shown in yellow and purple dots, respectively. In intra-layer migration, energy barriers are
higher than those in inter-layer migration, suggesting that ion migration is more favored between layers.
Additionally, for odd-numbered layers, intra-layer energy barriers are generally larger (with the exception
of the first layer). This can be attributed to the tilting preferences of the octahedral of the quantum dot.
89

The energy profiles for vacancy migration in CsPbBr3 quantum dots show clear
correlations with electronic structural changes we observed in our previous studies.28, 30, 80-83 It was
found that while Br vacancies do not create persistent midgap trap states on the surface, they do
lead to the formation of deep traps within the bulk.67 This distinction is reflected in the energy
barriers during the migration: on the surface, the absence of stable trap states allows for relatively
unimpeded vacancy movement within the layer, resulting in lower energy barriers. In contrast, the
appearance of deep traps in the bulk leads to high-energy regions, which contribute to the higher
energy barriers for intralayer migration. Additionally, navigating through these traps within the
bulk layers is energetically costly, further hindering the vacancy movement. This also aligns with
the observed preference for vacancies to migrate between layers rather than within them. Interlayer
migration, bypassing the deep trap states in the bulk, provides a more energetically favorable route,
underscoring the intricate interplay between the structural defects and charge carrier dynamics in
perovskite quantum dots.
In summary, we have demonstrated the distinct energy profiles associated with both the
interlayer and intralayer Br vacancy migrations in CsPbBr3 quantum dot through NEB
calculations, underscoring the unique surface properties of quantum dot materials. Contrary to the
uniform characteristics of their 3D bulk MHP analogs, the vacancy migrations show strong layer
dependency in quantum dots. Specifically, the odd layers have higher energies and longer Pb-Pb
distances, a consequence of the asymmetrical crystal field effects. In contrast, the even layers
present lower energies and shorter Pb-Pb distances, indicative of a denser and potentially more
stable crystalline lattice. As vacancies navigate through the lattice, the interlayer migration is
preferred, evidenced by the comparatively reduced energy barriers in such transitions. This
preference is likely facilitated by the intrinsic structural flexibility of the octahedra of the
perovskite, which exhibit tilting to accommodate the transit of vacancies across the layered
interface. However, within a layer, such tilting is well less noticeable, leading to higher energy
barriers for intralayer migration. Notably, the surface layer shows difference from the norm by
displaying a higher than usual energy barrier for interlayer migration, and a much lower barrier for
intralayer movement. This anomaly can be attributed to the unique surface properties of quantum
90

dots, where atoms are not fully coordinated, thus lattice strain and a more distorted local
environment. In this context, the energy profiles for vacancy migration are intricately connected
to the electronic structures previously observed in our research. On the surface, Br vacancies do
not create midgap trap states; conversely, deep traps are observed within the bulk, causing regions
of high energy that elevate the energy barriers for intralayer migration. Accordingly, to bypass the
energetically costly deep traps, the vacancy migrates in the interlayer fashion. With an emphasis
on optimizing stability and efficiency by leveraging the nuanced understanding of vacancy
behaviors at nanoscale, the perception achieved herein hold considerable promise for informing
the strategic design of quantum dot-based devices.
91

References
(1) Stranks, S. D.; Snaith, H. J. Metal-Halide Perovskites for Photovoltaic and Light-Emitting Devices.
Nature Nanotechnology 2015, 10 (5), 391-402.
(2) Eperon, G. E.; Paternò, G. M.; Sutton, R. J.; Zampetti, A.; Haghighirad, A. A.; Cacialli, F.; Snaith, H.
J. Inorganic Caesium Lead Iodide Perovskite Solar Cells. Journal of Materials Chemistry A 2015, 3 (39),
19688-19695.
(3) Swarnkar, A.; Chulliyil, R.; Ravi, V. K.; Irfanullah, M.; Chowdhury, A.; Nag, A. Colloidal CsPbBr3
Perovskite Nanocrystals: Luminescence Beyond Traditional Quantum Dots. Angewandte Chemie 2015, 127
(51), 15644-15648.
(4) Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.;
Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X= Cl, Br, and
I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano letters 2015,
15 (6), 3692-3696.
(5) Li, Z.; Kong, L.; Huang, S.; Li, L. Highly Luminescent and Ultrastable CsPbBr3 Perovskite Quantum
Dots Incorporated into a Silica/Alumina Monolith. Angewandte Chemie 2017, 129 (28), 8246-8250.
(6) Song, J.; Li, J.; Li, X.; Xu, L.; Dong, Y.; Zeng, H. Quantum Dot Light‐Emitting Diodes Based on
Inorganic Perovskite Cesium Lead Halides (CsPbX3). Advanced materials 2015, 27 (44), 7162-7167.
(7) Du, X.; Wu, G.; Cheng, J.; Dang, H.; Ma, K.; Zhang, Y.-W.; Tan, P.-F.; Chen, S. High-Quality CsPbBr3
Perovskite Nanocrystals for Quantum Dot Light-emitting Diodes. RSC Advances 2017, 7 (17), 10391-
10396.
(8) Kulkarni, S. A.; Baikie, T.; Boix, P. P.; Yantara, N.; Mathews, N.; Mhaisalkar, S. Band-Gap Tuning of
Lead Halide Perovskites Using a Sequential Deposition Process. Journal of Materials Chemistry A 2014, 2
(24), 9221-9225.
(9) Unger, E.; Kegelmann, L.; Suchan, K.; Sörell, D.; Korte, L.; Albrecht, S. Roadmap and Roadblocks for
the Band Gap Tunability of Metal Halide Perovskites. Journal of Materials Chemistry A 2017, 5 (23),
11401-11409.
(10) Chiba, T.; Hayashi, Y.; Ebe, H.; Hoshi, K.; Sato, J.; Sato, S.; Pu, Y.-J.; Ohisa, S.; Kido, J. AnionExchange Red Perovskite Quantum Dots with Ammonium Iodine Salts for Highly Efficient Light-Emitting
Devices. Nature Photonics 2018, 12 (11), 681-687.
(11) Cho, H.; Jeong, S.-H.; Park, M.-H.; Kim, Y.-H.; Wolf, C.; Lee, C.-L.; Heo, J. H.; Sadhanala, A.;
Myoung, N.; Yoo, S. Overcoming the Electroluminescence Efficiency Limitations of Perovskite LightEmitting Diodes. Science 2015, 350 (6265), 1222-1225.
(12) Cao, Y.; Wang, N.; Tian, H.; Guo, J.; Wei, Y.; Chen, H.; Miao, Y.; Zou, W.; Pan, K.; He, Y. Perovskite
Light-Emitting Diodes Based on Spontaneously Formed Submicrometre-Scale Structures. Nature 2018,
562 (7726), 249-253.
92

(13) Lin, K.; Xing, J.; Quan, L. N.; de Arquer, F. P. G.; Gong, X.; Lu, J.; Xie, L.; Zhao, W.; Zhang, D.;
Yan, C. Perovskite Light-Emitting Diodes with External Quantum Efficiency Exceeding 20 Per Cent.
Nature 2018, 562 (7726), 245-248.
(14) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J.; Leijtens, T.; Herz, L. M.;
Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal
Trihalide Perovskite Absorber. Science 2013, 342 (6156), 341-344.
(15) Herz, L. M. Charge-Carrier Mobilities in Metal Halide Perovskites: Fundamental Mechanisms and
Limits. ACS Energy Letters 2017, 2 (7), 1539-1548.
(16) McGovern, L.; Futscher, M. H.; Muscarella, L. A.; Ehrler, B. Understanding the Stability of MAPbBr3
Versus MAPbI3: Suppression of Methylammonium Migration and Reduction of Halide Migration. The
Journal of Physical Chemistry Letters 2020, 11 (17), 7127-7132.
(17) Sanehira, E. M.; Marshall, A. R.; Christians, J. A.; Harvey, S. P.; Ciesielski, P. N.; Wheeler, L. M.;
Schulz, P.; Lin, L. Y.; Beard, M. C.; Luther, J. M. Enhanced Mobility CsPbI3 Quantum Dot Arrays for
Record-Efficiency, High-Voltage Photovoltaic Cells. Science Advances 2017, 3 (10), eaao4204.
(18) Akkerman, Q. A.; Rainò, G.; Kovalenko, M. V.; Manna, L. Genesis, Challenges and Opportunities for
Colloidal Lead Halide Perovskite Nanocrystals. Nature materials 2018, 17 (5), 394-405.
(19) Kovalenko, M. V.; Protesescu, L.; Bodnarchuk, M. I. Properties and Potential Optoelectronic
Applications of Lead Halide Perovskite Nanocrystals. Science 2017, 358 (6364), 745-750.
(20) Perez, C. M.; Ghosh, D.; Prezhdo, O.; Tretiak, S.; Neukirch, A. J. Excited-State Properties of Defected
Halide Perovskite Quantum Dots: Insights from Computation. The Journal of Physical Chemistry Letters
2021, 12 (3), 1005-1011.
(21) Chen, D.; Yuan, S.; Chen, J.; Zhong, J.; Xu, X. Robust CsPbX3 (X= Cl, Br, and I) Perovskite Quantum
Dot Embedded Glasses: Nanocrystallization, Improved Stability and Visible Full-Spectral Tunable
Emissions. Journal of Materials Chemistry C 2018, 6 (47), 12864-12870.
(22) Lin, J.; Lu, Y.; Li, X.; Huang, F.; Yang, C.; Liu, M.; Jiang, N.; Chen, D. Perovskite Quantum Dots
Glasses Based Backlit Displays. ACS Energy Letters 2021, 6 (2), 519-528.
(23) Su, Y.; Chen, X.; Ji, W.; Zeng, Q.; Ren, Z.; Su, Z.; Liu, L. Highly Controllable and Efficient Synthesis
of Mixed-Halide CsPbX3 (X= Cl, Br, I) Perovskite QDs toward the Tunability of Entire Visible Light. ACS
applied materials & interfaces 2017, 9 (38), 33020-33028.
(24) Wei, Y.; Cheng, Z.; Lin, J. An Overview on Enhancing the Stability of Lead Halide Perovskite
Quantum Dots and Their Applications in Phosphor-Converted LEDs. Chemical Society Reviews 2019, 48
(1), 310-350.
(25) Wei, Y.; Cheng, Z.; Lin, J. Correction: An Overview on Enhancing the Stability of Lead Halide
Perovskite Quantum Dots and Their Applications in Phosphor-Converted LEDs. Chemical Society Reviews
2019, 48 (1), 405-405.
93

(26) Wang, X.; Bao, Z.; Chang, Y.-C.; Liu, R.-S. Perovskite Quantum Dots for Application in High Color
Gamut Backlighting Display of Light-Emitting Diodes. ACS Energy Letters 2020, 5 (11), 3374-3396.
(27) Li, X.; Cao, F.; Yu, D.; Chen, J.; Sun, Z.; Shen, Y.; Zhu, Y.; Wang, L.; Wei, Y.; Wu, Y. All Inorganic
Halide Perovskites Nanosystem: Synthesis, Structural Features, Optical Properties and Optoelectronic
Applications. Small 2017, 13 (9), 1603996.
(28) He, J.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Halide Composition Controls Electron–Hole
Recombination in Cesium–Lead Halide Perovskite Quantum Dots: A Time Domain Ab Initio Study. The
Journal of Physical Chemistry Letters 2018, 9 (8), 1872-1879.
(29) Li, W.; She, Y.; Vasenko, A. S.; Prezhdo, O. V. Ab Initio Nonadiabatic Molecular Dynamics of Charge
Carriers in Metal Halide Perovskites. Nanoscale 2021, 13 (23), 10239-10265.
(30) Shi, R.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Edge Influence on Charge Carrier Localization and
Lifetime in CH3NH3PbBr3 perovskite: Ab Initio Quantum Dynamics Simulation. The Journal of Physical
Chemistry Letters 2020, 11 (21), 9100-9109.
(31) Gao, G.; Xi, Q.; Zhou, H.; Zhao, Y.; Wu, C.; Wang, L.; Guo, P.; Xu, J. Novel Inorganic Perovskite
Quantum Dots for Photocatalysis. Nanoscale 2017, 9 (33), 12032-12038.
(32) Li, P.; Lu, Y.; Duan, Y.; Xu, S.; Zhang, J. Potential Application of Perovskite Glass Material in
Photocatalysis Field. The Journal of Physical Chemistry C 2021, 125 (4), 2382-2392.
(33) Gao, F.; Yang, W.; Liu, X.; Li, Y.; Liu, W.; Xu, H.; Liu, Y. Highly Stable and Luminescent SilicaCoated Perovskite Quantum Dots at Nanoscale-Particle Level via Nonpolar Solvent Synthesis. Chemical
Engineering Journal 2021, 407, 128001.
(34) Yuan, Y.; Huang, J. Ion Migration in Organometal Trihalide Perovskite and Its Impact on Photovoltaic
Efficiency and Stability. Accounts of Chemical Research 2016, 49 (2), 286-293.
(35) Azpiroz, J. M.; Mosconi, E.; Bisquert, J.; De Angelis, F. Defect Migration in Methylammonium Lead
Iodide and Its Role in Perovskite Solar Cell Operation. Energy & Environmental Science 2015, 8 (7), 2118-
2127.
(36) Eames, C.; Frost, J. M.; Barnes, P. R.; O’regan, B. C.; Walsh, A.; Islam, M. S. Ionic Transport in
Hybrid Lead Iodide Perovskite Solar Cells. Nature Communications 2015, 6 (1), 7497.
(37) Son, D.-Y.; Kim, S.-G.; Seo, J.-Y.; Lee, S.-H.; Shin, H.; Lee, D.; Park, N.-G. Universal Approach
toward Hysteresis-Free Perovskite Solar Cell via Defect Engineering. Journal of the American Chemical
Society 2018, 140 (4), 1358-1364.
(38) Mosconi, E.; De Angelis, F. Mobile Ions in Organohalide Perovskites: Interplay of Electronic Structure
and Dynamics. ACS Energy Letters 2016, 1 (1), 182-188.
(39) Yoon, S. J.; Draguta, S.; Manser, J. S.; Sharia, O.; Schneider, W. F.; Kuno, M.; Kamat, P. V. Tracking
Iodide and Bromide Ion Segregation in Mixed Halide Lead Perovskites during Photoirradiation. ACS
Energy Letters 2016, 1 (1), 290-296.
94

(40) Samu, G. F.; Balog, Á.; De Angelis, F.; Meggiolaro, D.; Kamat, P. V.; Janáky, C. Electrochemical
Hole Injection Selectively Expels Iodide from Mixed Halide Perovskite Films. Journal of the American
Chemical Society 2019, 141 (27), 10812-10820.
(41) Van Reenen, S.; Kemerink, M.; Snaith, H. J. Modeling Anomalous Hysteresis in Perovskite Solar
Cells. The Journal of Physical Chemistry Letters 2015, 6 (19), 3808-3814.
(42) Richardson, G.; O'Kane, S. E.; Niemann, R. G.; Peltola, T. A.; Foster, J. M.; Cameron, P. J.; Walker,
A. B. Can Slow-Moving Ions Explain Hysteresis in the Current–Voltage Curves of Perovskite Solar Cells?
Energy & Environmental Science 2016, 9 (4), 1476-1485.
(43) Chen, R.; Cao, J.; Duan, Y.; Hui, Y.; Chuong, T. T.; Ou, D.; Han, F.; Cheng, F.; Huang, X.; Wu, B.
High-Efficiency, Hysteresis-Less, UV-Stable Perovskite Solar Cells with Cascade ZnO–ZnS Electron
Transport Layer. Journal of the American Chemical Society 2018, 141 (1), 541-547.
(44) Tong, C.-J.; Geng, W.; Prezhdo, O. V.; Liu, L.-M. Role of Methylammonium Orientation in Ion
Diffusion and Current–Voltage Hysteresis in the CH3NH3PbI3 Perovskite. ACS Energy Letters 2017, 2 (9),
1997-2004.
(45) Tong, C.-J.; Li, L.; Liu, L.-M.; Prezhdo, O. V. Synergy Between Ion Migration and Charge Carrier
Recombination in Metal-Halide Perovskites. Journal of the American Chemical Society 2020, 142 (6),
3060-3068.
(46) Li, W.; Long, R.; Tang, J.; Prezhdo, O. V. Influence of Defects on Excited-State Dynamics in Lead
Halide Perovskites: Time-Domain Ab Initio Studies. The Journal of Physical Chemistry Letters 2019, 10
(13), 3788-3804.
(47) Yoon, S. J.; Kuno, M.; Kamat, P. V. Shift happens. How Halide Ion Defects Influence Photoinduced
Segregation in Mixed Halide Perovskites. ACS Energy Letters 2017, 2 (7), 1507-1514.
(48) Landi, G.; Neitzert, H. C.; Barone, C.; Mauro, C.; Lang, F.; Albrecht, S.; Rech, B.; Pagano, S.
Correlation Between Electronic Defect States Distribution and Device Performance of Perovskite Solar
Cells. Advanced Science 2017, 4 (10), 1700183.
(49) Jónsson, H.; Mills, G.; Jacobsen, K. W. Nudged Elastic Band Method for Finding Minimum Energy
Paths of Transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations, World
Scientific, 1998; pp 385-404.
(50) Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.; Prezhdo, O. V. Quantum Zeno Effect
Rationalizes the Phonon Bottleneck in Semiconductor Quantum Dots. Physical Review Letters 2013, 110
(18), 180404.
(51) Kamisaka, H.; Kilina, S. V.; Yamashita, K.; Prezhdo, O. V. Ultrafast Vibrationally-Induced Dephasing
of Electronic Excitations in PbSe Quantum Dots. Nano letters 2006, 6 (10), 2295-2300.
(52) Prezhdo, O. V. Photoinduced Dynamics in Semiconductor Quantum Dots: Insights from Time-Domain
Ab Initio Studies. Accounts of Chemical Research 2009, 42 (12), 2005-2016.
95

(53) Wei, H. H.-Y.; Evans, C. M.; Swartz, B. D.; Neukirch, A. J.; Young, J.; Prezhdo, O. V.; Krauss, T. D.
Colloidal Semiconductor Quantum Dots with Tunable Surface Composition. Nano letters 2012, 12 (9),
4465-4471.
(54) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Physical Review B 1993, 47
(1), 558.
(55) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical
Review Letters 1996, 77 (18), 3865.
(56) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.
Physical Review B 1999, 59 (3), 1758.
(57) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and
Morphology Data. Journal of Applied Crystallography 2011, 44 (6), 1272-1276.
(58) Oksenberg, E.; Sanders, E.; Popovitz-Biro, R.; Houben, L.; Joselevich, E. Surface-Guided CsPbBr3
Perovskite Nanowires on Flat and Faceted Sapphire with Size-Dependent Photoluminescence and Fast
Photoconductive Response. Nano Letters 2018, 18 (1), 424-433.
(59) Ma, S.; Kim, S. H.; Jeong, B.; Kwon, H. C.; Yun, S. C.; Jang, G.; Yang, H.; Park, C.; Lee, D.; Moon,
J. Strain‐Mediated Phase Stabilization: A New Strategy for Ultrastable α‐CsPbI3 Perovskite by
Nanoconfined Growth. Small 2019, 15 (21), 1900219.
(60) Ezzeldien, M.; Al-Qaisi, S.; Alrowaili, Z.; Alzaid, M.; Maskar, E.; Es-Smairi, A.; Vu, T. V.; Rai, D.
Electronic and Optical Properties of Bulk and Surface of CsPbBr3 Inorganic Halide Perovskite A First
Principles DFT 1/2 Approach. Scientific Reports 2021, 11 (1), 20622.
(61) Yang, Y.; Hou, C.; Liang, T.-X. Energetic and Electronic Properties of CsPbBr3 Surfaces: A FirstPrinciples Study. Physical Chemistry Chemical Physics 2021, 23 (12), 7145-7152.
(62) Lanigan-Atkins, T.; He, X.; Krogstad, M.; Pajerowski, D.; Abernathy, D.; Xu, G. N.; Xu, Z.; Chung,
D.-Y.; Kanatzidis, M.; Rosenkranz, S. Two-Dimensional Overdamped Fluctuations of the Soft Perovskite
Lattice in CsPbBr3. Nature materials 2021, 20 (7), 977-983.
(63) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for
Finding Saddle Points and Minimum Energy Paths. The Journal of Chemical Physics 2000, 113 (22), 9901-
9904.
(64) Xu, X.; Wu, Z.; Zhao, Z.; Lu, Z.; Gao, Y.; Huang, X.; Huang, J.; Zhang, Z.; Cai, Y.; Qu, Y. FirstPrinciples Study of Detrimental Iodine Vacancy in Lead Halide Perovskite Under Strain and Electron
Injection. Applied Physics Letters 2022, 121 (9).
(65) Shi, Y.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Iodine and Sulfur Vacancy Cooperation Promotes
Ultrafast Charge Extraction at MAPbI3/MoS2 Interface. ACS Energy Letters 2020, 5 (5), 1346-1354.
(66) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
96

(67) Ran, J.; Wang, B.; Wu, Y.; Liu, D.; Mora Perez, C.; Vasenko, A. S.; Prezhdo, O. V. Halide Vacancies
Create No Charge Traps on Lead Halide Perovskite Surfaces but Can Generate Deep Traps in the Bulk. The
Journal of Physical Chemistry Letters 2023, 14, 6028-6036.
(68) Li, W.; Vasenko, A. S.; Tang, J.; Prezhdo, O. V. Anharmonicity Extends Carrier Lifetimes in Lead
Halide Perovskites at Elevated Temperatures. The Journal of Physical Chemistry Letters 2019, 10 (20),
6219-6226.
(69) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on A
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(70) Strandell, D.; Mora Perez, C.; Wu, Y.; Prezhdo, O. V.; Kambhampati, P. Excitonic Quantum
Coherence in Light Emission from CsPbBr3 Metal-Halide Perovskite Nanocrystals. Nano Letters 2023.
(71) Chu, W.; Saidi, W. A.; Zhao, J.; Prezhdo, O. V. Soft Lattice and Defect Covalency Rationalize
Tolerance of β‐CsPbI3 Perovskite Solar Cells to Native Defects. Angewandte Chemie International Edition
2020, 59 (16), 6435-6441.
(72) Chu, W.; Zheng, Q.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Low-Frequency Lattice Phonons in Halide
Perovskites Explain High Defect Tolerance toward Electron-Hole Recombination. Science advances 2020,
6 (7), eaaw7453.
(73) Li, W.; Sun, Y.-Y.; Li, L.; Zhou, Z.; Tang, J.; Prezhdo, O. V. Control of Charge Recombination in
Perovskites by Oxidation State of Halide Vacancy. Journal of the American Chemical Society 2018, 140
(46), 15753-15763.
(74) Qiao, L.; Fang, W.-H.; Long, R.; Prezhdo, O. V. Elimination of Charge Recombination Centers in
Metal Halide Perovskites by Strain. Journal of the American Chemical Society 2021, 143 (26), 9982-9990.
(75) Zhang, Z.; Long, R.; Tokina, M. V.; Prezhdo, O. V. Interplay Between Localized and Free Charge
Carriers Can Explain Hot Fluorescence in the CH3NH3PbBr3 Perovskite: Time-Domain Ab Initio Analysis.
Journal of the American Chemical Society 2017, 139 (48), 17327-17333.
(76) Zhang, Z.-Y.; Wang, H.-Y.; Zhang, Y.-X.; Hao, Y.-W.; Sun, C.; Zhang, Y.; Gao, B.-R.; Chen, Q.-D.;
Sun, H.-B. The Role of Trap-Assisted Recombination in Luminescent Properties of Organometal Halide
CH3NH3PbBr3 Perovskite Films and Quantum Dots. Scientific Reports 2016, 6 (1), 27286.
(77) Wetzelaer, G. J. A.; Scheepers, M.; Sempere, A. M.; Momblona, C.; Ávila, J.; Bolink, H. J. Trap‐
Assisted Non‐Radiative Recombination in Organic–Inorganic Perovskite Solar Cells. Advanced Materials
2015, 27 (11), 1837-1841.
(78) Glazer, A. M. The Classification of Tilted Octahedra in Perovskites. Acta Crystallographica Section
B: Structural Crystallography and Crystal Chemistry 1972, 28 (11), 3384-3392.
(79) Woodward, P. M. Octahedral Tilting in Perovskites. I. Geometrical Considerations. Acta
Crystallographica Section B: Structural Science 1997, 53 (1), 32-43.
97

(80) Prezhdo, O. V. Multiple Excitons and the Electron–Phonon Bottleneck in Semiconductor Quantum
Dots: An Ab Initio Perspective. Chemical Physics Letters 2008, 460 (1-3), 1-9.
(81) Jankowska, J.; Long, R.; Prezhdo, O. V. Quantum Dynamics of Photogenerated Charge Carriers in
Hybrid Perovskites: Dopants, Grain Boundaries, Electric Order, and Other Realistic Aspects. ACS Energy
Letters 2017, 2 (7), 1588-1597.
(82) Chistyakov, A.; Zvaigzne, M.; Nikitenko, V.; Tameev, A.; Martynov, I.; Prezhdo, O. Optoelectronic
Properties of Semiconductor Quantum Dot Solids for Photovoltaic Applications. The Journal of Physical
Chemistry Letters 2017, 8 (17), 4129-4139.
(83) Wang, B.; Wu, Y.; Liu, D.; Vasenko, A. S.; Casanova, D.; Prezhdo, O. V. Efficient Modeling of
Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics. The
Journal of Physical Chemistry Letters 2023, 14 (37), 8289-8295.
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Chapter 7
Study on van der Waals Interactions in Perovskite Materials
with Point Defect
Overview
Weaker than ionic and covalent bonding, van der Waals (vdW) interactions can have a significant
impact on structure and function of molecules and materials, including stabilities of conformers
and phases, chemical reaction pathways, electro-optical response, electron-vibrational dynamics,
etc. Metal halide perovskites (MHPs) are widely investigated for their excellent optoelectronic
properties, stemming largely from high defect tolerance. Although MHPs are primarily ionic
compounds, we demonstrate that vdW interactions contribute ~5% to the total energy, and that
static, dynamics, electronic and optical properties of point defects in MHPs depend significantly
on the vdW interaction model used. Focusing on widely studied CsPbBr3 with the common Br
vacancy and interstitial defects, we compare the PBE, PBE+D3 and PBE+TS models and show
that vdW interactions strongly alter the global and local geometric structure, and change the
fundamental bandgap, midgap state energies and electron-vibrational coupling. The vdW
interaction sensitivity stems from involvement of heavy and highly polarizable chemical elements,
and soft MHP structure.
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Author List
Linjie Deng, Jingyi Ran, Bipeng Wang, Alexandre Tkatchenko, Jun Jiang, Oleg V. Prezhdo
Metal halide perovskites (MHPs) have gathered significant attention for their potential in
photovoltaic cells and other applications due to their cost-effective fabrication and high-power
conversion efficiency.1-3 They show exceptional optical properties for solar energy conversion4
and display promise as semiconductors for efficient, economical transistors,5 given their ease of
processing and high charge carrier mobility. CsPbBr3 is one of the most studied perovskite
materials, with applications in high-quality inkjet-printed films for LED technology6 and quantum
information processing.
7 A recent demonstration of phonon-driven intra-exciton Rabi oscillations
in the orthorhombic phase CsPbBr3 single crystals has opened new avenues for enhancing
optoelectronic properties.8 However, intrinsic defects, such as vacancies, interstitials and antisites,
are common and unavoidable in both low-dimensional and 3D bulk materials, influencing their
structural and electronic properties, as previously examined through first-principles calculations.7,
9 It is important to employ accurate methods for modeling defects in MHPs. MHPs are soft
materials10 undergoing large-scale structural rearrangements11 that influence the electronic
properties. The static and dynamic structure of MHPs are governed by a delicate interplay of ionic
interactions, and covalent and hydrogen bonding.12 Nuclear quantum effects of light hydrogens
can influence geometry of the heavy inorganic lattice,13 and van der Waals interactions play an
important role.14
Density functional theory (DFT) is the mainstream computational tool used extensively in
chemical and materials science due to its relatively high predictive ability, general applicability,
and computational efficiency.
15-18 The majority of commonly used DFT functionals are designed
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to describe short-range bonding interactions, and long-range van der Waals (vdW) interactions
require a special treatment in DFT. VdW interactions are a key ingredient of many systems and
processes, including organic, inorganic and biomaterials,14, 19 heterogenous and electrocatalysis,20
tribology,21 protein stability and function,22 etc. VdW interactions are included in DFT calculations
as an addition to the exchange-correlation functionals.
23, 24 Popular vdW interaction models
include D2,
25 D3,26 Tkatchenko-Scheffler (TS)27 and TS with many-body dispersion (TS-MBD).28
Proposed by Grimme and co-workers,25, 26, 29 DFT-D2 and DFT-D3 are simplest and most
commonly used approaches. To mitigate overestimation of vdW interactions in weakly bound
systems, DFT-D3 includes a damping function and is often preferred over DFT-D2.26, 30
Tkatchenko and Scheffler developed the TS model, calculating the vdW correction based on the
system's ground-state electron density. This advanced methodology accounts for environmental
and hybridization effects by computing the polarizability of a Hirshfeld volume.23, 31 In present,
we consider the PBE+D3 and PBE+TS models since they are used most and are computationally
efficient.
In this letter, we investigate the significance of an accurate treatment of vdW interactions on
structural and electronic properties of MHPs, by computing and comparing the structural
parameters and electronic properties of the commonly used bulk CsPbBr3 containing two typical
point defects, a Br vacancy (VBr) and a Br interstitial (IBr). We demonstrate that vdW interactions
change the properties of bulk by CsPbBr3 5-7%. The properties of point defects are much more
sensitive to the vdW interaction model because metastable defect structures depend on a delicate
balance of various factors and can undergo significant rearrangements and fluctuations. The
midgap electronic energy levels in optimized structures and level fluctuations at ambient
temperature can vary by nearly 1 eV depending on the description of vdW interactions. The
sensitivity stems from the soft nature of MHPs, shallow local energy minima of different MHP
structures, and involvement of large, highly polarizable chemical elements. Our findings affirm
that an accurate treatment of vdW interactions is essential for studying structural and electronic
properties of pristine and particularly defective MHPs.
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We focus on the orthorhombic phase of CsPbBr3, the stable phase under ambient
conditions.1, 32 The introduction of vdW interactions leads to notable changes in the CsPbBr3
structure and thermodynamic properties. Thermodynamic equations of state (EOS) are used for
understanding the behavior of crystalline solids under varying conditions of pressure, volume,
entropy, and temperature.
33-35 To determine the lattice constant parameters of the orthorhombic
(Pnma) CsPbBr3 perovskite unit cell (illustrated in Figure S1a-b, with the unit cell outlined as a
frame), the Birch-Murnaghan EOS was employed, in combination with different treatments of
vdW interactions for the unit cell optimization. The calculation details are provided in the
Supporting Information (SI). The total energy calculated by each method is plotted vs the
corresponding calculated volumes, as shown in Figure S1c. The lattice constants and volume of
the most stable structure, derived from the EOS fitting, are tabulated in Table S1. This comparison
highlights the influence of volume changes on energy: a reduction in energy corresponds to
enhanced lattice stability and a decrease in volume, attributable to increased vdW interactions.
These findings are in line with previous studies14, 23 which suggest that the attractive nature of vdW
interactions typically results in smaller lattice parameters. Having obtained the optimized unit
cells, we construct CsPbBr3 2x2x2 supercell bulk and introduce the bromine defects, which are the
main focus of our study. Additional details about computational methods are provided in the SI.
Figure 1a illustrated the structure of pristine CsPbBr3. The Br vacancy (VBr) and Br
interstitial (IBr) defects are introduced removing or adding a Br atom from/to the pristine system.
The optimized structures of the defect regions in different charge states are illustrated in Figure
1b-g. The presence of light, external electric field or chemical species can alter the charge of the
point defects, and the defect charge can have a strong influence on ionic and electronic
conductivity36 and charge carrier lifetime.37
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Figure 1. (a) Optimized geometric structure of orthorhombic CsPbBr3. Representation for the optimized
atomic structures of (b-d) bromine vacancies and (e-g) bromine interstitials in different charge states.
Green, gray, and purple spheres symbolize Cs, Pb, and Br atoms, respectively. Yellow dashed circles
specify the vacancies and interstitial atoms. The optimized structures and structural fluctuations at a finite
temperature depend significantly on the model for van der Waals interactions.
We consider the positive (+), neutral (0) and negative (-) charge states for both VBr and IBr.
The Pb-Pb distance between the nearest Pb atoms across the defect site is elongated in VBr+
compared to VBr0
. This change is attributed to the increased repulsion among the Pb2+ ions and the
positively charged Br vacancy. In contrast, the VBr- system exhibits a reduced Pb-Pb distance,
leading to the formation of a Pb dimer. This decrease occurs due to the presence of a negative
charge between two Pb2+ cations, which draws the neighboring Pb cations closer. Theoretical
studies corroborate the formation of stable Pb dimers in the presence of negatively charged halogen
vacancies.38, 39 The specific Pb-Pb distances for VBr0
, VBr+, and VBr- are detailed in Table 1. The
Pb-Pb dimer in the VBr- system remains stable under ambient conditions as well.38
The variation in the Pb-Pb distances across the Br vacancy obtained with the different vdW
interaction models demonstrates a strong impact of vdW interactions on the geometric structure of
CsPbBr3. For all charge states of the vacancy defect, the Pb-Pb distance is the greatest when PBE
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without a vdW correction is used. The Pb-Pb distance decreases when PBE+D3 and PBE+TS are
used. The difference between the PBE and PBE+TS results is over 2Å, indicating that the two
methods produce different chemical species.
The additional Br atom in the interstitial system either binds to the two Pb2+ cations, Figure
1e,g, or in the positive state forms a Br trimer, Figure 1f. The geometric structure of the Br
interstitial system is much less sensitive to the vdW interaction than that of the Br vacancy. The
bond distances change only by 0.05-0.1Å, Table 1. However, even such minor structural changes
can lead to notable changes in the electronic energy levels, up to 0.4 eV, Figure S3.
Table 1. Pb-Pb distances (Å) across Br vacancies and Br-Br distances for bromine interstitials optimized
by PBE, PBE+D3, and PBE+TS for the three charge states, Figure 1. Two distances are given for the IBr+
system: the average distances from the interstitial to the nearest top/bottom Br atoms (shorter distance) and
to the left/right Br atoms (longer distance), as illustrated in Figure 1f.
Pb-Pb distance for Br vacancy Br-Br distance for Br interstitial
method VBr0 VBr+ VBr- IBr0 IBr+ IBrPBE 5.91 6.43 3.74 3.54 2.567 3.916 3.55
PBE+D3 5.54 6.06 3.69 3.58 2.569 3.933 3.59
PBE+TS 3.85 5.64 3.57 3.55 2.555 3.804 3.60
Figure 2 presents a total energy comparison for the VBr and IBr systems. The comparison
highlights the impact of vdW interactions on the total energies of these systems. Notably, vdW
interactions universally stabilize all systems by reducing their total energy. Among the vdW
interaction models examined, the TS description predicts a more significant vdW interaction
energy more than the PBE model. Overall, vdW interactions contribute about 5% to the total
energy. However, even this relatively minor contribution can a significant influence on the
geometric structure and electronic properties of point defects, because MHPs are soft and respond
strongly to perturbations.10, 40, 41
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Figure 2. Total energies of (a) Br vacancy and (b) Br interstitial systems in different charge states,
calculated using PBE, PBE+D3, and PBE+TS. Van der Waals interactions contribute about 10% to the total
energy, with the TS model making a notably larger contribution than the D3 model. The charge has a
stronger effect on the total energy of the vacancy than the interstitial.
Comparing the different charge states of the defects, vdW interactions are slightly stronger
for the more positive charges, even though the number of electrons is smaller, and vdW
interactions generally increase with the number of electrons. Further, the weaker vdW interaction
in the negatively charged VBr- system causes more significant changes in the geometric properties
of compared to the neutral and positive vacancies, Figure 1 and Table 1.
To elucidate the impact of vdW interactions on the electronic properties of the CsPbBr3
systems with point defects, we calculated the density of states (DOS) and the electronic band
structure on both defective and pristine structures, as depicted in Figures 3 and S2-4. The results
indicate that vdW interactions can notably affect the fundamental bandgaps and midgap states.
Figure 3 illustrates the total DOS for all systems with a Br vacancy, evaluated with the three
methods in the corresponding optimized geometries. For VBr0
, Figure 3a, the PBE+TS model
predicts a prominent midgap trap state located 0.8 eV below the conduction band minimum
(CBM). In the case of VBr+, Figure 3b, the midgap trap state in the PBE+TS model shifts closer to
the CBM, and an additional peak appears near the band edge. In contrast, the PBE+D3 model
predicts shallow trap states for both VBr0 and VBr+, and PBE predicts no midgap states. In VBr-
(Figure 3c), midgap trap states are identified with all three calculations, a phenomenon that can be
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attributed to the formation of a dimer between the two Pb atoms across the vacancy, with PBE+TS
produces the deepest trap.
Figure 3. Electronic density of states of CsPbBr3 with (a) neutral, (b) positive, and (c) negative Br vacancy
in the optimized geometries, calculated using PBE, PBE+D3, and PBE+TS. The zero energy is set to the
VBM. The insets depict structures of the Br vacancy in the respective charge states. Gray, and purple
spheres represent Pb and Br atoms, respectively. Distinctly, a midgap trap state appears in both VBr
0 and
VBr+ systems at the PBE+TS level, but not the other two methods. Additionally, the fundamental bandgaps
are sensitive to the van der Waals interaction model.
The DOS results for bulk pristine CsPbBr3 and the IBr systems, Figures S3 and S4, exhibit
a weaker dependence on the vdW interaction model, while the trends are similar. The band gap is
the lowest in the PBE+D3 method. Only the IBr+ defect demonstrates midgap trap states at energies
that depend on the vdW interaction model, Figure S3b, suggesting that the trap state originates due
to electrostatic and covalent interactions resulting in formation of the I3 trimer, Figure 1f. At the
106

same time, the energy of the trap state varies 0.5 eV depending on the description of the vdW
interaction.
The band structure calculations further substantiate the fact that vdW interactions have a
pronounced impact on the electronic properties of the point defects in CsPbBr3. Focusing only on
the neutral defects, Figure S4 demonstrates that the valence band maximum (VBM) and CBM are
mainly contributed by Pb and Br atoms, respectively. VBr0 exhibits an unoccupied midgap state,
whose energy depends strongly on the vdW interaction model. Notably, the midgap state exhibits
no dependence on the k-point in the PBE+TS calculation, indicating that it is a localized state. In
contrast, the PBE and PBE+D3 methods show k-point dependence of the trap state energy between
R and G points. The dependence arises, because the midgap state is close to the CBM, mixes with
the band states, and is partially delocalized. While electrons trapped by the shallow midgap states
predicted by PBE and PBE+D3 can easily escape into the band, the trap state obtained by PBE+TS
is 1 eV below the CBM. The depth is much larger than the thermal energy, equal to 25 meV at
room temperature, suggesting that the midgap state can trap charge carriers permanently,
accelerating non-radiative recombination.42 This finding confirms earlier computational analyses
by Kang et al.7 and Shi et al.43
Most MHPs, including CsPbBr3, are soft and susceptible to significant structural
fluctuations at a finite temperature. These fluctuations particularly influence electronic energy
levels associated with defects, often resulting in an unusual behavior.
40, 41 To study influence of
the vdW interaction model on fluctuations of the defect energy levels we conducted ab initio
molecular dynamics (MD) simulations for the VBr0 and IBr0 systems, Figures 4 and S5-S6. In VBr0
,
midgap trap states emerge from Pb-Pb interactions during structural oscillations. These midgap
states, originating from the separation of the lowest unoccupied molecular orbital (LUMO) and
highest occupied molecular orbital (HOMO) from the conduction and valence bands, trap charge
carriers, thereby affecting their transport and recombination.10, 37, 44 The presence of deep midgap
trap states is highlighted by prolonged structural distortions. The occurrence of midgap states
induced by a halide vacancy defect is closely linked to the Pb-Pb distances between the adjacent
Pb atoms and ion coordination numbers during fluctuations.11 Figure S5 presents the energy levels
107

from HOMO-2 to LUMO+2 as functions of time along the MD trajectory for CsPbBr3 with VBr
and IBr. Midgap states are consistently observed in all VBr systems, Figure S5a-c, but not in the IBr
systems, Figure S5d-f, similar to the previous findings.45 As the treatment of vdW interactions
becomes more advanced, the defect states in CsPbBr3 with a Br vacancy become deeper, and the
amplitude of their energy fluctuation increases, Figure S5b-c. Figure S6 presents distributions of
the vacancy trap energies obtained by the three methods. Under the influence of vdW interactions,
the energy distribution becomes broader, indicating enhanced fluctuations. The corresponding
standard deviations increase from 0.08 eV to 0.14 eV and to 0.20 eV in the PBE, PBE+D3, and
PBE+TS calculations.
In all three methods, the Pb-Pb distances across the vacancy in the VBr0 system of CsPbBr3
show a clear correlation with the midgap trap state energy, Figure 4. Figure 4a compares the
evolution of the energy gap between the defect state and HOMO for the VBr0 system in CsPbBr3
bulk obtained with the PBE, PBE+D3 and PBE+TS methodologies. As the model for the vdW
interactions becomes more advanced, this energy gap reduces, and its oscillation intensifies. The
maximum detected energy gap between the HOMO and the midgap state increases from 0.57 eV
in PBE to 0.72 eV in PBE+D3 to 1.06 eV in PBE+TS. Cohen et al.9 previously identified that the
depth of the trap state has an inverse relationship with the Pb-Pb distance across the Br vacancy in
CsPbBr3. Our calculations corroborate this finding, revealing a strong correlation between the trap
state energy and the Pb-Pb distance: the shorter the Pb-Pb distance, the deeper the trap state. The
Pb-Pb distance fluctuates from 4.70 to 6.38 Å in the PBE calculation without a vdW correction,
and the trap state energy fluctuates between 2.19 and 1.69 eV, Figure S5a. When the D3 vdW
correction is included, the distance becomes shorter, fluctuating from 3.68 to 5.99 Å, and the trap
state energy levels vary from 1.95 to 1.26 eV, Figure S5b. The Pb-Pb distance decreases further in
the PBE+TS calculation, ranging from 3.25 to 4.83 Å, and the trap state becomes deeper, with the
energy level fluctuating between 1.88 and 0.84 eV, Figure S5c.
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Figure 4. (a) Fluctuation of the midgap state energy relative to HOMO in CsPbBr3 with a neutral Br
vacancy, calculated using PBE, PBE+D3 and PBE+TS along the 10 ps MD trajectories at 300 K. More
advanced treatments of van der Waals interactions both lower the trap state energy and increase its
fluctuation. Relationship between the midgap state energy and the Pb-Pb distance across the Br vacancy
calculated with (b) PBE, (c) PBE+D3, and (d) PBE+TS. In all methods, a clear correlation exists between
the energy gap and the Pb-Pb distance.
Figure 5 displays the charge density associated with the VBr0 defect state, as calculated by
three methods. The corresponding VBM and CBM charge densities are shown in Figure S7. The
LUMO charge density is localized around the Br vacancy, as it represents the defect state, while
the VBM and CBM charge densities remain delocalized. The PBE+TS method demonstrates
significantly more localized charge density around the vacancy compared to the other two
functionals. This increased localization correlates with the shorter Pb-Pb distance and the lower
defect level energy discussed above. The charge densities of the VBr0 defect state calculated with
PBE and PBE+D3 delocalize partially in the Pb-Pb direction, Figure 5a,b.
109

Figure 5. Charge densities of the defect state for a representative structure (at 5 ps) of CsPbBr3 with a
neutral Br vacancy, calculated with (a) PBE, (b) PBE+D3 and (c) PBE+TS method. The two Pb atoms
across the vacancy are highlighted in red. In contrast to the delocalized VBM and CBM, Figure S7, the
defect state is localized at the vacancy. As the vdW interaction model becomes more advanced, the Pb-Pb
distance shortens and the charge density becomes more localized.
Fourier transforms (FTs) of defect energy fluctuations characterize electron-vibrational
interactions, Figure 6. The frequencies detected in the FT spectra identify the phonon modes that
couple to the electronic subsystem, and the amplitude of the signal at a particular frequency
indicates the strength of the electron-phonon coupling for that phonon.
10, 11, 44, 46 MHPs are
composed of heavy elements and are soft. As a result, the spectra are dominated by low-frequency
signal, below 200 cm-1
, Figure 6. The FT amplitudes increase as the frequency decreases, with the
strongest peaks seen at 10 cm-1
. The electron-vibrational coupling is the strongest in for PBE+TS,
intermediate for PBE+D3, and weakest for PBE. Interestingly, the weak signals above 200 cm-1
are comparable across the three methods. The FTs indicate that vdW interactions strongly enhance
electron-vibrational interactions in MHPs. This is also true for the IBr system, Figure S8. Similar
to CsPbBr3 with a Br vacancy, the FT signal amplitudes are higher at lower frequencies, and they
intensify as the treatment of vdW interactions becomes more advanced. However, in the absence
110

of deep midgap trap states in the Br interstitial systems, the FT signals in the low-frequency regions
are considerably weaker compared to those in CsPbBr3 containing a Br vacancy.
Figure 6. Fourier transforms of fluctuations of the VBr
0 defect state energy over the 10 ps MD trajectories
obtained with the different van der Waals interaction models. The fluctuations predominantly occur at
frequencies of 200 cm-1 or lower, and the signal amplitude increases as the treatment of the vdW interactions
becomes more advanced, in agreement with Figure 4a. The signals associated with the Br vacancy, shown
here, are significantly stronger than those for the Br interstitial, Figure S8.
In summary, we have investigated the influence of the vdW interaction model on structural
and electronic properties and electron-vibrational interactions in CsPbBr3 bulk with the halide
vacancy VBr and interstitial IBr point defects in negative, neutral and positive charge states. We
have compared the results obtained with the commonly used PBE functional without a vdW
correction, with the commonly used D3 vdW correction, and with the more advanced TS vdW
interaction model. Inclusion of vdW interactions notably reduces the CsPbBr3 volume and lowers
its energy by 5-7%. The fundamental bandgap is reduced by a similar amount. The energies of
the midgap electronic states arising from structural defects depend much more significantly on the
vdW interaction model, because defect structures are less stable than pristine bulk and are more
111

sensitive to the delicate balance of ionic, covalent and vdW forces. The energy of the IBr interstitial
level changes by 0.4 eV in the optimized geometry depending on the vdW model. The VBr vacancy
is particularly sensitive to vdW interaction, because of the large, created void that allows
significant local structural deformations. The VBr energy level can shift by 1 eV depending on the
vdW interaction model and fluctuate by about the same amount at ambient temperature. vdW
forces can enhance the strength of electron-vibrational interactions three-fold. In practice, the TS
model is preferred to the D3 model, even though it is more computationally demanding and may
possibly overestimate the vdW interaction. The insights gained from this research underscore the
significance of accurate treatment of vdW in MHPs and other nanoscale systems, whose structure
and electronic properties depend on a delicate balance of many factors.
112

References
(1) Ezzeldien, M.; Al-Qaisi, S.; Alrowaili, Z.; Alzaid, M.; Maskar, E.; Es-Smairi, A.; Vu, T. V.; Rai, D.
Electronic and Optical Properties of Bulk and Surface of CsPbBr3 Inorganic Halide Perovskite A First
Principles DFT 1/2 Approach. Scientific Reports 2021, 11 (1), 20622.
(2) Yi, Z.; Ladi, N. H.; Shai, X.; Li, H.; Shen, Y.; Wang, M. Will Organic–Inorganic Hybrid Halide Lead
Perovskites Be Eliminated from Optoelectronic Applications? Nanoscale Advances 2019, 1 (4), 1276-1289.
(3) Maafa, I. M. All-Inorganic Perovskite Solar Cells: Recent Advancements and Challenges.
Nanomaterials 2022, 12 (10), 1651.
(4) Jiao, Y.; Qin, S.; Li, B.; Hao, W.; Wang, Y.; Li, H.; Yang, Z.; Dong, D.; Li, X.; Zhao, J. Ferroelasticity
Mediated Energy Conversion in Strained Perovskite Films. Advanced Electronic Materials 2022, 8 (11),
2200415.
(5) He, Y.; Hadar, I.; Kanatzidis, M. G. Detecting Ionizing Radiation Using Halide Perovskite
Semiconductors Processed Through Solution and Alternative Methods. Nature Photonics 2022, 16 (1), 14-
26.
(6) Vescio, G.; Frieiro, J. L.; Gualdrón‐Reyes, A. F.; Hernández, S.; Mora‐Seró, I.; Garrido, B.; Cirera, A.
High Quality Inkjet Printed‐Emissive Nanocrystalline Perovskite CsPbBr3 Layers for Color Conversion
Layer and LEDs Applications. Advanced Materials Technologies 2022, 7 (7), 2101525.
(7) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
(8) Nguyen, X. T.; Winte, K.; Timmer, D.; Rakita, Y.; Ceratti, D. R.; Aharon, S.; Ramzan, M. S.; Cocchi,
C.; Lorke, M.; Jahnke, F. Phonon-Driven Intra-Exciton Rabi Oscillations in CsPbBr3 Halide Perovskites.
Nature Communications 2023, 14 (1), 1047.
(9) Cohen, A. V.; Egger, D. A.; Rappe, A. M.; Kronik, L. Breakdown of the Static Picture of Defect
Energetics in Halide Perovskites: the Case of the Br Vacancy in CsPbBr3. The Journal of Physical
Chemistry Letters 2019, 10 (16), 4490-4498.
(10) Chu, W.; Saidi, W. A.; Zhao, J.; Prezhdo, O. V. Soft Lattice and Defect Covalency Rationalize
Tolerance of β‐CsPbI3 Perovskite Solar Cells to Native Defects. Angewandte Chemie International Edition
2020, 59 (16), 6435-6441.
(11) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on a
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(12) Walsh, A. Principles of Chemical Bonding and Band Gap Engineering in Hybrid Organic–Inorganic
Halide Perovskites. The Journal of Physical Chemistry C 2015, 119 (11), 5755-5760.
(13) Liu, Y.; Long, R.; Fang, W.-H.; Prezhdo, O. V. Nuclear Quantum Effects Prolong Charge Carrier
Lifetimes in Hybrid Organic–Inorganic Perovskites. Journal of the American Chemical Society 2023, 145
(25), 14112-14123.
113

(14) Pandech, N.; Kongnok, T.; Palakawong, N.; Limpijumnong, S.; Lambrecht, W. R.; Jungthawan, S.
Effects of the van der Waals Interactions on Structural and Electronic Properties of CH3NH (Pb, Sn)(I, Br,
Cl)3 Halide Perovskites. ACS Omega 2020, 5 (40), 25723-25732.
(15) Huang, B.; von Rudorff, G. F.; von Lilienfeld, O. A. The Central role of density functional theory in
the AI age. Science 2023, 381 (6654), 170-175.
(16) Song, S.; Vuckovic, S.; Kim, Y.; Yu, H.; Sim, E.; Burke, K. Extending Density Functional Theory
with Near Chemical Accuracy beyond Pure Water. Nature Communications 2023, 14 (1), 799.
(17) Liu, X.; Jiao, Y.; Zheng, Y.; Jaroniec, M.; Qiao, S.-Z. Mechanism of CN Bonds Formation in
Electrocatalytic Urea Production Revealed by Ab Initio Molecular Dynamics Simulation. Nature
Communications 2022, 13 (1), 5471.
(18) Araujo, R. B.; Rodrigues, G. L.; Dos Santos, E. C.; Pettersson, L. G. Adsorption Energies on Transition
Metal Surfaces: towards An Accurate and Balanced Description. Nature Communications 2022, 13 (1),
6853.
(19) Rabiee, N.; Ahmadi, S.; Rabiee, M.; Bagherzadeh, M.; Vahabi, H.; Jouyandeh, M.; Saeb, M. R. Green
Carbon-Based Nanocomposite Biomaterials through the Lens of Microscopes. Emergent Materials 2022,
5 (3), 665-671.
(20) Chen, B. W.; Xu, L.; Mavrikakis, M. Computational Methods in Heterogeneous Catalysis. Chemical
Reviews 2020, 121 (2), 1007-1048.
(21) Yuan, D.; Zhang, Y.; Ho, W.; Wu, R. Effects of van der Waals Dispersion Interactions in Density
Functional Studies of Adsorption, Catalysis, and Tribology on Metals. The Journal of Physical Chemistry
C 2020, 124 (31), 16926-16942.
(22) Stöhr, M.; Tkatchenko, A. Quantum Mechanics of Proteins in Explicit Water: The Role of PlasmonLike Solute-Solvent Interactions. Science Advances 2019, 5 (12), eaax0024.
(23) Freire, R. L.; Guedes-Sobrinho, D.; Kiejna, A.; Da Silva, J. L. Comparison of the Performance of van
der Waals Dispersion Functionals in the Description of Water and Ethanol on Transition Metal Surfaces.
The Journal of Physical Chemistry C 2018, 122 (3), 1577-1588.
(24) Shirali, K.; Shelton, W. A.; Vekhter, I. Importance of van der Waals Interactions for Ab Initio Studies
of Topological Insulators. Journal of Physics: Condensed Matter 2020, 33 (3), 035702.
(25) Grimme, S. Semiempirical GGA‐Type Density Functional Constructed with a Long‐Range Dispersion
Correction. Journal of Computational Chemistry 2006, 27 (15), 1787-1799.
(26) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of
Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. The Journal of Chemical
Physics 2010, 132 (15).
(27) Tkatchenko, A.; Scheffler, M. Accurate Molecular van der Waals Interactions from Ground-State
Electron Density and Free-Atom Reference Data. Physical Review Letters 2009, 102 (7), 073005.
114

(28) Tkatchenko, A.; DiStasio Jr, R. A.; Car, R.; Scheffler, M. Accurate and Efficient Method for ManyBody van der Waals Interactions. Physical Review Letters 2012, 108 (23), 236402.
(29) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density
Functional Theory. Journal of Computational Chemistry 2011, 32 (7), 1456-1465.
(30) Reckien, W.; Janetzko, F.; Peintinger, M. F.; Bredow, T. Implementation of Empirical Dispersion
Corrections to Density Functional Theory for Periodic Systems. Journal of Computational Chemistry 2012,
33 (25), 2023-2031.
(31) Hirshfeld, F. L. Bonded-Atom Fragments for Describing Molecular Charge Densities. Theoretica
Chimica Acta 1977, 44, 129-138.
(32) Becker, M. A.; Vaxenburg, R.; Nedelcu, G.; Sercel, P. C.; Shabaev, A.; Mehl, M. J.; Michopoulos, J.
G.; Lambrakos, S. G.; Bernstein, N.; Lyons, J. L. Bright Triplet Excitons in Caesium Lead Halide
Perovskites. Nature 2018, 553 (7687), 189-193.
(33) Beck, H.; Gehrmann, C.; Egger, D. A. Structure and Binding in Halide Perovskites: Analysis of Static
and Dynamic Effects from Dispersion-Corrected Density Functional Theory. APL Materials 2019, 7 (2).
(34) Latimer, K.; Dwaraknath, S.; Mathew, K.; Winston, D.; Persson, K. A. Evaluation of Thermodynamic
Equations of State across Chemistry and Structure in the Materials Project. NPJ Computational Materials
2018, 4 (1), 40.
(35) Ghaithan, H. M.; Alahmed, Z. A.; Qaid, S. M.; Hezam, M.; Aldwayyan, A. S. Density functional Study
of Cubic, Tetragonal, and Orthorhombic CsPbBr3 Perovskite. ACS Omega 2020, 5 (13), 7468-7480.
(36) Jiang, N.; Ma, G.; Song, D.; Qiao, B.; Liang, Z.; Xu, Z.; Wageh, S.; Al Ghamdi, A. A.; Zhao, S. Defects
in Lead Halide Perovskite Light-Emitting Diodes under Electric Field: from Behavior to Passivation
Strategies. Nanoscale 2024.
(37) Li, W.; She, Y.; Vasenko, A. S.; Prezhdo, O. V. Ab Initio Nonadiabatic Molecular Dynamics of Charge
Carriers in Metal Halide Perovskites. Nanoscale 2021, 13 (23), 10239-10265.
(38) Li, W.; Sun, Y.-Y.; Li, L.; Zhou, Z.; Tang, J.; Prezhdo, O. V. Control of Charge Recombination in
Perovskites by Oxidation State of Halide Vacancy. Journal of the American Chemical Society 2018, 140
(46), 15753-15763.
(39) Agiorgousis, M. L.; Sun, Y.-Y.; Zeng, H.; Zhang, S. Strong Covalency-Induced Recombination
Centers in Perovskite Solar Cell Material CH3NH3PbI3. Journal of the American Chemical Society 2014,
136 (41), 14570-14575.
(40) Ran, J.; Wang, B.; Wu, Y.; Liu, D.; Mora Perez, C.; Vasenko, A. S.; Prezhdo, O. V. Halide Vacancies
Create No Charge Traps on Lead Halide Perovskite Surfaces but Can Generate Deep Traps in the Bulk. The
Journal of Physical Chemistry Letters 2023, 14 (26), 6028-6036.
(41) Wu, Y.; Liu, D.; Chu, W.; Wang, B.; Vasenko, A. S.; Prezhdo, O. V. Fluctuations at Metal Halide
Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis.
ACS Applied Materials & Interfaces 2022, 14 (50), 55753-55761.
115

(42) Brenes, R.; Eames, C.; Bulović, V.; Islam, M. S.; Stranks, S. D. The Impact of Atmosphere on the
Local Luminescence Properties of Metal Halide Perovskite Grains. Advanced Materials 2018, 30 (15),
1706208.
(43) Shi, H.; Du, M.-H. Shallow Halogen Vacancies in Halide Optoelectronic Materials. Physical Review
B 2014, 90 (17), 174103.
(44) Chu, W.; Zheng, Q.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Low-Frequency Lattice Phonons in Halide
Perovskites Explain High Defect Tolerance toward Electron-Hole Recombination. Science Advances 2020,
6 (7), eaaw7453.
(45) Wang, B.; Chu, W.; Wu, Y.; Casanova, D.; Saidi, W. A.; Prezhdo, O. V. Electron-Volt Fluctuation of
Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale. The Journal of Physical Chemistry
Letters 2022, 13 (25), 5946-5952.
(46) Zheng, Q.; Chu, W.; Zhao, C.; Zhang, L.; Guo, H.; Wang, Y.; Jiang, X.; Zhao, J. Ab Initio Nonadiabatic
Molecular Dynamics Investigations on the Excited Carriers in Condensed Matter Systems. Wiley
Interdisciplinary Reviews: Computational Molecular Science 2019, 9 (6), e1411.
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Chapter 8
Conclusions and Future Directions
8.1 Conclusions
In this thesis, we have explored the intersection of computational chemistry and machine
learning to investigate the behavior and properties of charge carriers in inorganic materials, with a
specific focus on metal halide perovskites. The studies consider the impact of defects, including
vacancies and interstitials, on ionic conductivity and charge carrier mobility, as well as the role of
midgap trap states and ion migration in perovskites. Through rigorous computational methods and
the application of machine learning techniques, we have developed predictive models that enhance
our understanding of these materials and their potential applications in photovoltaic devices.
Our findings underscore the critical influence of defects on the performance of inorganic
materials. The detailed examination of vacancies and interstitials revealed their significant effects
on the electronic properties and stability of perovskites, highlighting the necessity of precise defect
engineering for optimizing device performance. Additionally, the study of van der Waals
interactions provided insights into their essential role in determining the material's structural,
electronic, and dynamic behaviors, thereby influencing the efficiency and durability of metal
halide perovskites in photovoltaic applications.
117

The integration of machine learning into our research approach has proven extremely
valuable. It has enabled the prediction of electronic properties with high accuracy, facilitating the
rapid screening of potential materials for photovoltaic applications. This combination of
computational chemistry and machine learning not only accelerates the discovery of new materials
but also contributes to the rational design of devices with improved efficiency and stability.
In conclusion, this thesis contributes to the advancement of knowledge in computational
chemistry and materials science, paving the way for significant technological developments in
renewable energy and electronics. The predictive models and fundamental understanding achieved
through this work hold the potential to revolutionize the design and optimization of materials for
a wide range of critical applications, contributing to global efforts in sustainable energy and
environmental preservation.
8.2 Ongoing Projects
Moving forward, I have broadened the scope of the studies in the ongoing projects in
several key areas. Initially, I have expanded the carrier lifetime investigations to encompass twodimensional materials, including MoS2. Furthermore, I have developed more complex models that
facilitate the comparison of various types of grain boundary defects. Lastly, I have endeavored to
connect theoretical studies with practical applications more closely, to enhance the relevance and
practical utility of our findings through experimental validation.
118

Bibliography
(1) Stranks, S. D.; Snaith, H. J. Metal-Halide Perovskites for Photovoltaic and Light-Emitting Devices.
Nature Nanotechnology 2015, 10 (5), 391-402.
(2) Zhang, W.; Eperon, G. E.; Snaith, H. J. Metal Halide Perovskites for Energy Applications. Nature
Energy 2016, 1 (6), 1-8.
(3) Jena, A. K.; Kulkarni, A.; Miyasaka, T. Halide Perovskite Photovoltaics: Background, Status, and
Future Prospects. Chemical Reviews 2019, 119 (5), 3036-3103.
(4) Filip, M. R.; Eperon, G. E.; Snaith, H. J.; Giustino, F. Steric Engineering of Metal-Halide Perovskites
with Tunable Optical Band Gaps. Nature Communications 2014, 5 (1), 5757.
(5) Unger, E.; Kegelmann, L.; Suchan, K.; Sörell, D.; Korte, L.; Albrecht, S. Roadmap and Roadblocks for
the Band Gap Tunability of Metal Halide Perovskites. Journal of Materials Chemistry A 2017, 5 (23),
11401-11409.
(6) Herz, L. M. Charge-Carrier Mobilities in Metal Halide Perovskites: Fundamental Mechanisms and
Limits. ACS Energy Letters 2017, 2 (7), 1539-1548.
(7) Seitz, M.; Magdaleno, A. J.; Alcázar-Cano, N.; Meléndez, M.; Lubbers, T. J.; Walraven, S. W.; Pakdel,
S.; Prada, E.; Delgado-Buscalioni, R.; Prins, F. Exciton Diffusion in Two-Dimensional Metal-Halide
Perovskites. Nature Communications 2020, 11 (1), 2035.
(8) Manser, J. S.; Christians, J. A.; Kamat, P. V. Intriguing Optoelectronic Properties of Metal Halide
Perovskites. Chemical Reviews 2016, 116 (21), 12956-13008.
(9) Zhao, X.-G.; Yang, J.-H.; Fu, Y.; Yang, D.; Xu, Q.; Yu, L.; Wei, S.-H.; Zhang, L. Design of Lead-Free
Inorganic Halide Perovskites for Solar Cells via Cation-Transmutation. Journal of the American Chemical
Society 2017, 139 (7), 2630-2638.
(10) Chen, J.; Dong, C.; Idriss, H.; Mohammed, O. F.; Bakr, O. M. Metal Halide Perovskites for Solar‐to‐
Chemical Fuel Conversion. Advanced Energy Materials 2020, 10 (13), 1902433.
(11) Fu, Y.; Zhu, H.; Chen, J.; Hautzinger, M. P.; Zhu, X.-Y.; Jin, S. Metal Halide Perovskite
Nanostructures for Optoelectronic Applications and the Study of Physical Properties. Nature Reviews
Materials 2019, 4 (3), 169-188.
(12) Snaith, H. J. Present Status and Future Prospects of Perovskite Photovoltaics. Nature Materials 2018,
17 (5), 372-376.
(13) Green, M. A.; Ho-Baillie, A.; Snaith, H. J. The Emergence of Perovskite Solar Cells. Nature Photonics
2014, 8 (7), 506-514.
(14) Navrotsky, A.; Weidner, D. J. Perovskite: A structure of Great Interest to Geophysics and Materials
Science. Geophysical Monograph Series 1989, 45.
119

(15) Katz, E. A. Perovskite: Name Puzzle and German‐Russian Odyssey of Discovery. Helvetica Chimica
Acta 2020, 103 (6), e2000061.
(16) Glazer, A. Simple Ways of Determining Perovskite Structures. Acta Crystallographica Section A:
Crystal Physics, Diffraction, Theoretical and General Crystallography 1975, 31 (6), 756-762.
(17) Bhalla, A. S.; Guo, R.; Roy, R. The Perovskite Structure—A Review of Its Role in Ceramic Science
and Technology. Materials Research Innovations 2000, 4 (1), 3-26.
(18) Stoumpos, C. C.; Malliakas, C. D.; Peters, J. A.; Liu, Z.; Sebastian, M.; Im, J.; Chasapis, T. C.;
Wibowo, A. C.; Chung, D. Y.; Freeman, A. J. Crystal Growth of the Perovskite Semiconductor CsPbBr3:
A New Material for High-Energy Radiation Detection. Crystal Growth & Design 2013, 13 (7), 2722-2727.
(19) Swarnkar, A.; Chulliyil, R.; Ravi, V. K.; Irfanullah, M.; Chowdhury, A.; Nag, A. Colloidal CsPbBr3
Perovskite Nanocrystals: Luminescence Beyond Traditional Quantum Dots. Angewandte Chemie 2015, 127
(51), 15644-15648.
(20) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
(21) Yu, J.; Liu, G.; Chen, C.; Li, Y.; Xu, M.; Wang, T.; Zhao, G.; Zhang, L. Perovskite CsPbBr3 Crystals:
Growth and Applications. Journal of Materials Chemistry C 2020, 8 (19), 6326-6341.
(22) Zhang, H.; Liu, X.; Dong, J.; Yu, H.; Zhou, C.; Zhang, B.; Xu, Y.; Jie, W. Centimeter-Sized Inorganic
Lead Halide Perovskite CsPbBr3 Crystals Grown by An Improved Solution Method. Crystal Growth &
Design 2017, 17 (12), 6426-6431.
(23) Zhang, M.; Zheng, Z.; Fu, Q.; Chen, Z.; He, J.; Zhang, S.; Yan, L.; Hu, Y.; Luo, W. Growth and
Characterization of All-Inorganic Lead Halide Perovskite Semiconductor CsPbBr3 Single Crystals.
CrystEngComm 2017, 19 (45), 6797-6803.
(24) Rakita, Y.; Kedem, N.; Gupta, S.; Sadhanala, A.; Kalchenko, V.; Böhm, M. L.; Kulbak, M.; Friend,
R. H.; Cahen, D.; Hodes, G. Low-Temperature Solution-Grown CsPbBr3 Single Crystals and Their
Characterization. Crystal Growth & Design 2016, 16 (10), 5717-5725.
(25) Zhang, C.; Wang, S.; Li, X.; Yuan, M.; Turyanska, L.; Yang, X. Core/Shell Perovskite Nanocrystals:
Synthesis of Highly Efficient and Environmentally Stable FAPbBr3/CsPbBr3 for LED applications.
Advanced Functional Materials 2020, 30 (31), 1910582.
(26) Kang, C. H.; Dursun, I.; Liu, G.; Sinatra, L.; Sun, X.; Kong, M.; Pan, J.; Maity, P.; Ooi, E.-N.; Ng, T.
K. High-Speed Colour-Converting Photodetector with All-Inorganic CsPbBr3 Perovskite Nanocrystals for
Ultraviolet Light Communication. Light: Science & Applications 2019, 8 (1), 94.
(27) Huang, C.-Y.; Zou, C.; Mao, C.; Corp, K. L.; Yao, Y.-C.; Lee, Y.-J.; Schlenker, C. W.; Jen, A. K.;
Lin, L. Y. CsPbBr3 Perovskite Quantum Dot Vertical Cavity Lasers with Low Threshold and High Stability.
Acs Photonics 2017, 4 (9), 2281-2289.
120

(28) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on A
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(29) Li, W.; Vasenko, A. S.; Tang, J.; Prezhdo, O. V. Anharmonicity Extends Carrier Lifetimes in Lead
Halide Perovskites at Elevated Temperatures. The Journal of Physical Chemistry Letters 2019, 10 (20),
6219-6226.
(30) Strandell, D.; Mora Perez, C.; Wu, Y.; Prezhdo, O. V.; Kambhampati, P. Excitonic Quantum
Coherence in Light Emission from CsPbBr3 Metal-Halide Perovskite Nanocrystals. Nano Letters 2023, 24
(1), 61-66.
(31) Ran, J.; Wang, B.; Wu, Y.; Liu, D.; Mora Perez, C.; Vasenko, A. S.; Prezhdo, O. V. Halide Vacancies
Create No Charge Traps on Lead Halide Perovskite Surfaces but Can Generate Deep Traps in the Bulk. The
Journal of Physical Chemistry Letters 2023, 14 (26), 6028-6036.
(32) Baker, H.; Perez, C. M.; Sonnichsen, C.; Strandell, D.; Prezhdo, O. V.; Kambhampati, P. Breaking
Phonon Bottlenecks Through Efficient Auger Processes in Perovskite Nanocrystals. ACS Nano 2023, 17
(4), 3913-3920.
(33) Wu, Y.; Liu, D.; Chu, W.; Wang, B.; Vasenko, A. S.; Prezhdo, O. V. Fluctuations at Metal Halide
Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis.
ACS Applied Materials & Interfaces 2022, 14 (50), 55753-55761.
(34) Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C. G.
First-Principles Calculations for Point Defects in Solids. Reviews of modern physics 2014, 86 (1), 253.
(35) Stoneham, A. M. Theory of Defects in Solids: Electronic Etructure of Defects in Insulators and
Semiconductors; Oxford University Press, 2001.
(36) Ai, M.; Zhang, J. W.; Wu, Y. W.; Pan, L.; Shi, C.; Zou, J. J. Role of Vacancies in Photocatalysis: A
Review of Recent Progress. Chemistry–An Asian Journal 2020, 15 (22), 3599-3619.
(37) Yuan, Y.; Huang, J. Ion Migration in Organometal Trihalide Perovskite and Its Impact on Photovoltaic
Efficiency and Stability. Accounts of Chemical Research 2016, 49 (2), 286-293.
(38) Liu, Z.; Qin, L.; Cao, X.; Zhou, J.; Pan, A.; Fang, G.; Wang, S.; Liang, S. Ion Migration and Defect
Effect of Electrode Materials in Multivalent-Ion Batteries. Progress in Materials Science 2022, 125,
100911.
(39) Amelinckx, S.; Dekeyser, W. The Structure and Properties of Grain Boundaries. In Solid state physics,
Vol. 8; Elsevier, 1959; pp 325-499.
(40) Wang, J. T.-W.; Wang, Z.; Pathak, S.; Zhang, W.; deQuilettes, D. W.; Wisnivesky-Rocca-Rivarola,
F.; Huang, J.; Nayak, P. K.; Patel, J. B.; Yusof, H. A. M. Efficient Perovskite Solar Cells by Metal Ion
Doping. Energy & Environmental Science 2016, 9 (9), 2892-2901.
121

(41) Jin, H.; Debroye, E.; Keshavarz, M.; Scheblykin, I. G.; Roeffaers, M. B.; Hofkens, J.; Steele, J. A. It's
A Trap! On the Nature of Localised States and Charge Trapping in Lead Halide Perovskites. Materials
Horizons 2020, 7 (2), 397-410.
(42) Wu, Y.; Chu, W.; Vasenko, A. S.; Prezhdo, O. V. Common Defects Accelerate Charge Carrier
Recombination in CsSnI3 without Creating Mid-Gap States. The Journal of Physical Chemistry Letters
2021, 12 (36), 8699-8705.
(43) Wu, X.; Trinh, M. T.; Niesner, D.; Zhu, H.; Norman, Z.; Owen, J. S.; Yaffe, O.; Kudisch, B. J.; Zhu,
X.-Y. Trap States in Lead Iodide Perovskites. Journal of the American Chemical Society 2015, 137 (5),
2089-2096.
(44) Levine, I.; Vera, O. G.; Kulbak, M.; Ceratti, D.-R.; Rehermann, C.; Marquez, J. A.; Levcenko, S.;
Unold, T.; Hodes, G.; Balberg, I. Deep Defect States in Wide-Band-Gap ABX3 Halide Perovskites. ACS
Energy Letters 2019, 4 (5), 1150-1157.
(45) Staub, F.; Rau, U.; Kirchartz, T. Statistics of the Auger Recombination of Electrons and Holes via
Defect Levels in the Band Gap—Application to Lead-Halide Perovskites. ACS omega 2018, 3 (7), 8009-
8016.
(46) Zhou, Y.; Poli, I.; Meggiolaro, D.; De Angelis, F.; Petrozza, A. Defect Activity in Metal Halide
Perovskites with Wide and Narrow Bandgap. Nature Reviews Materials 2021, 6 (11), 986-1002.
(47) Li, L.; Lin, M.-F.; Zhang, X.; Britz, A.; Krishnamoorthy, A.; Ma, R.; Kalia, R. K.; Nakano, A.;
Vashishta, P.; Ajayan, P. Phonon-Suppressed Auger Scattering of Charge Carriers in Defective TwoDimensional Transition Metal Dichalcogenides. Nano Letters 2019, 19 (9), 6078-6086.
(48) Wang, B.; Chu, W.; Wu, Y.; Casanova, D.; Saidi, W. A.; Prezhdo, O. V. Electron-Volt Fluctuation of
Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale. The Journal of Physical Chemistry
Letters 2022, 13 (25), 5946-5952.
(49) Qiao, L.; Fang, W. H.; Long, R.; Prezhdo, O. V. Extending Carrier Lifetimes in Lead Halide
Perovskites with Alkali Metals by Passivating and Eliminating Halide Interstitial Defects. Angewandte
Chemie 2020, 132 (12), 4714-4720.
(50) Sandberg, O. J.; Kaiser, C.; Zeiske, S.; Zarrabi, N.; Gielen, S.; Maes, W.; Vandewal, K.; Meredith, P.;
Armin, A. Mid-Gap Trap State-Mediated Dark Current in Organic Photodiodes. Nature Photonics 2023,
17 (4), 368-374.
(51) Polyakov, A.; Smirnov, N.; Yakimov, E.; Tarelkin, S.; Turutin, A.; Shemerov, I.; Pearton, S.; Bae, K.-
B.; Lee, I.-H. Deep Traps Determining the Non-Radiative Lifetime and Defect Band Yellow Luminescence
in N-GaN. Journal of Alloys and Compounds 2016, 686, 1044-1052.
(52) Meloni, S.; Moehl, T.; Tress, W.; Franckevičius, M.; Saliba, M.; Lee, Y. H.; Gao, P.; Nazeeruddin, M.
K.; Zakeeruddin, S. M.; Rothlisberger, U. Ionic Polarization-Induced Current–Voltage Hysteresis in
CH3NH3PbX3 Perovskite Solar Cells. Nature Communications 2016, 7 (1), 10334.
122

(53) Unger, E. L.; Hoke, E. T.; Bailie, C. D.; Nguyen, W. H.; Bowring, A. R.; Heumüller, T.; Christoforo,
M. G.; McGehee, M. D. Hysteresis and Transient Behavior in Current–Voltage Measurements of HybridPerovskite Absorber Solar Cells. Energy & Environmental Science 2014, 7 (11), 3690-3698.
(54) Snaith, H. J.; Abate, A.; Ball, J. M.; Eperon, G. E.; Leijtens, T.; Noel, N. K.; Stranks, S. D.; Wang, J.
T.-W.; Wojciechowski, K.; Zhang, W. Anomalous Hysteresis in Perovskite Solar Cells. The Journal of
Physical Chemistry Letters 2014, 5 (9), 1511-1515.
(55) Jacobs, D. A.; Wu, Y.; Shen, H.; Barugkin, C.; Beck, F. J.; White, T. P.; Weber, K.; Catchpole, K. R.
Hysteresis Phenomena in Perovskite Solar Cells: the Many and Varied Effects of Ionic Accumulation.
Physical Chemistry Chemical Physics 2017, 19 (4), 3094-3103.
(56) Weber, S. A.; Hermes, I. M.; Turren-Cruz, S.-H.; Gort, C.; Bergmann, V. W.; Gilson, L.; Hagfeldt,
A.; Graetzel, M.; Tress, W.; Berger, R. How the Formation of Interfacial Charge Causes Hysteresis in
Perovskite Solar Cells. Energy & Environmental Science 2018, 11 (9), 2404-2413.
(57) Kalon, G.; Jun Shin, Y.; Giang Truong, V.; Kalitsov, A.; Yang, H. The Role of Charge Traps in
Inducing Hysteresis: Capacitance–Voltage Measurements on Top Gated Bilayer Graphene. Applied Physics
Letters 2011, 99 (8).
(58) Stöhr, M.; Van Voorhis, T.; Tkatchenko, A. Theory and Practice of Modeling van der Waals
Interactions in Electronic-Structure Calculations. Chemical Society Reviews 2019, 48 (15), 4118-4154.
(59) Ferri, N.; DiStasio Jr, R. A.; Ambrosetti, A.; Car, R.; Tkatchenko, A. Electronic Properties of
Molecules and Surfaces with A Self-Consistent Interatomic van der Waals Density Functional. Physical
Review Letters 2015, 114 (17), 176802.
(60) Wang, Y.; Gould, T.; Dobson, J. F.; Zhang, H.; Yang, H.; Yao, X.; Zhao, H. Density Functional Theory
Analysis of Structural and Electronic Properties of Orthorhombic Perovskite CH3NH3PbI3. Physical
Chemistry Chemical Physics 2014, 16 (4), 1424-1429.
(61) Hermann, J.; DiStasio Jr, R. A.; Tkatchenko, A. First-Principles Models for van der Waals Interactions
in Molecules and Materials: Concepts, Theory, and Applications. Chemical Reviews 2017, 117 (6), 4714-
4758.
(1) Berezin, F. A.; Shubin, M. The Schrödinger Equation; Springer Science & Business Media, 2012.
(2) Lang, N.; Kohn, W. Theory of Metal Surfaces: Charge Density and Surface Energy. Physical Review B
1970, 1 (12), 4555.
(3) Lewars, E. G.; Lewars, E. G. The Concept of the Potential Energy Surface. Computational Chemistry:
Introduction to the Theory and Applications of Molecular and Quantum Mechanics 2016, 9-49.
(4) Batzill, M.; Diebold, U. The Surface and Materials Science of Tin Oxide. Progress in Surface Science
2005, 79 (2-4), 47-154.
(5) Born, M. Born-oppenheimer Approximation. Ann. Phys 1927, 84, 457-484.
123

(6) Kantorovich, L. V.; Krylov, V. I.; Benster, C. D.; Weiss, G. Approximate Methods of Higher Analysis.
Physics Today 1960, 13 (1), 74-76.
(7) Lykos, P.; Pratt, G. Discussion on the Hartree-Fock Approximation. Reviews of Modern Physics 1963,
35 (3), 496.
(8) Löwdin, P.-O. Quantum Theory of Many-Particle Systems. II. Study of the Ordinary Hartree-Fock
Approximation. Physical Review 1955, 97 (6), 1490.
(9) Valeev, E. F.; Sherrill, C. D. The Diagonal Born–Oppenheimer Correction Beyond the Hartree–Fock
Approximation. The Journal of Chemical Physics 2003, 118 (9), 3921-3927.
(10) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Physical Review 1964, 136 (3B), B864.
(11) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Physical
Review 1965, 140 (4A), A1133.
(12) Sham, L. J.; Kohn, W. One-Particle Properties of An Inhomogeneous Interacting Electron Gas.
Physical Review 1966, 145 (2), 561.
(13) Car, R.; Parrinello, M. Unified Approach for Molecular Dynamics and Density-Functional Theory.
Physical Review Letters 1985, 55 (22), 2471.
(14) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T.; Joannopoulos, a. J. Iterative Minimization
Techniques for Ab Initio Total-Energy Calculations: Molecular Dynamics and Conjugate Gradients.
Reviews of Modern Physics 1992, 64 (4), 1045.
(15) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using
A Plane-Wave Basis Set. Physical Review B 1996, 54 (16), 11169.
(16) Marx, D.; Hutter, J. Ab Initio Molecular Dynamics: Theory and Implementation. Modern Methods and
Algorithms of Quantum Chemistry 2000, 1 (301-449), 141.
(17) Martin, R. M. Electronic Structure: Basic Theory and Practical Methods; Cambridge University Press,
2020.
(18) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical
Review Letters 1996, 77 (18), 3865.
(19) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation
Energy. Physical Review B 1992, 45 (23), 13244.
(20) Perdew, J. P.; Burke, K.; Ernzerhof, M. Perdew, Burke, and Ernzerhof reply. Physical Review Letters
1998, 80 (4), 891.
(21) Grimme, S. Density Functional Theory with London Dispersion Corrections. Wiley Interdisciplinary
Reviews: Computational Molecular Science 2011, 1 (2), 211-228.
124

(22) Tkatchenko, A.; Scheffler, M. Accurate Molecular van der Waals Interactions from Ground-State
Electron Density and Free-Atom Reference Data. Physical Review Letters 2009, 102 (7), 073005.
(23) Anatole von Lilienfeld, O.; Tkatchenko, A. Two-and Three-Body Interatomic Dispersion Energy
Contributions to Binding in Molecules and Solids. The Journal of Chemical Physics 2010, 132 (23).
(24) Frenkel, D.; Smit, B. Understanding Molecular Simulation: from Algorithms to Applications; Elsevier,
2023.
(25) Van Gunsteren, W. F.; Berendsen, H. J. Computer Simulation of Molecular Dynamics: Methodology,
Applications, and Perspectives in Chemistry. Angewandte Chemie International Edition in English 1990,
29 (9), 992-1023.
(26) Schneider, T.; Stoll, E. Molecular-Dynamics Study of a Three-Dimensional One-Component Model
for Distortive Phase Transitions. Physical Review B 1978, 17 (3), 1302.
(27) Tycko, R.; Dabbagh, G.; Fleming, R.; Haddon, R.; Makhija, A.; Zahurak, S. Molecular Dynamics and
the Phase Transition in Solid C60. Physical Review Letters 1991, 67 (14), 1886.
(28) Tsuneyuki, S.; Aoki, H.; Tsukada, M.; Matsui, Y. Molecular-Dynamics Study of the α to β Structural
Phase Transition of Quartz. Physical Review Letters 1990, 64 (7), 776.
(29) Karplus, M.; McCammon, J. A. Molecular Dynamics Simulations of Biomolecules. Nature Structural
Biology 2002, 9 (9), 646-652.
(30) Binder, K. Monte Carlo and Molecular Dynamics Simulations in Polymer Science; Oxford University
Press, 1995.
(31) Hénin, J.; Chipot, C. Overcoming Free Energy Barriers Using Unconstrained Molecular Dynamics
Simulations. The Journal of Chemical Physics 2004, 121 (7), 2904-2914.
(32) Claeyssens, F.; Harvey, J. N.; Manby, F. R.; Mata, R. A.; Mulholland, A. J.; Ranaghan, K. E.; Schutz,
M.; Thiel, S.; Thiel, W.; Werner, H.-J. High-Accuracy Computation of Reaction Barriers in Enzymes.
ANGEWANDTE CHEMIE-INTERNATIONAL EDITION IN ENGLISH- 2006, 45 (41), 6856.
(33) Carsky, P.; Urban, M. Ab Initio Calculations: Methods and Applications in Chemistry; Springer
Science & Business Media, 2012.
(34) González, M. A. Force Fields and Molecular Dynamics Simulations. École Thématique de la Société
Française de la Neutronique 2011, 12, 169-200.
(35) Unke, O. T.; Koner, D.; Patra, S.; Käser, S.; Meuwly, M. High-Dimensional Potential Energy Surfaces
for Molecular Simulations: from Empiricism to Machine Learning. Machine Learning: Science and
Technology 2020, 1 (1), 013001.
(36) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and
Semiconductors Using a Plane-Wave Basis Set. Computational Materials Science 1996, 6 (1), 15-50.
(37) Tully, J. Mixed Quantum–Classical Dynamics. Faraday Discussions 1998, 110, 407-419.
125

(38) Nikitin, E. Nonadiabatic Transitions: What We Learned from Old Masters and How Much We Owe
Them. Annual Review of Physical Chemistry 1999, 50 (1), 1-21.
(39) Worth, G. A.; Cederbaum, L. S. Beyond Born-Oppenheimer: Molecular Dynamics Through A Conical
Intersection. Annu. Rev. Phys. Chem. 2004, 55, 127-158.
(40) Jasper, A. W.; Nangia, S.; Zhu, C.; Truhlar, D. G. Non-Born−Oppenheimer Molecular Dynamics.
Accounts of Chemical Research 2006, 39 (2), 101-108.
(41) Prezhdo, O. V. Quantized Hamilton Dynamics. Theoretical Chemistry Accounts 2006, 116, 206-218.
(42) Nelson, T.; Fernandez-Alberti, S.; Roitberg, A. E.; Tretiak, S. Nonadiabatic Excited-State Molecular
Dynamics: Modeling Photophysics in Organic Conjugated Materials. Accounts of Chemical Research 2014,
47 (4), 1155-1164.
(43) Wang, L.; Akimov, A.; Prezhdo, O. V. Recent Progress in Surface Hopping: 2011–2015. The Journal
of Physical Chemistry Letters 2016, 7 (11), 2100-2112.
(44) Crespo-Otero, R.; Barbatti, M. Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–
Classical Dynamics. Chemical Reviews 2018, 118 (15), 7026-7068.
(45) Curchod, B. F.; Martínez, T. J. Ab Initio Nonadiabatic Quantum Molecular Dynamics. Chemical
Reviews 2018, 118 (7), 3305-3336.
(46) Zheng, Q.; Chu, W.; Zhao, C.; Zhang, L.; Guo, H.; Wang, Y.; Jiang, X.; Zhao, J. Ab Initio Nonadiabatic
Molecular Dynamics Investigations on the Excited Carriers in Condensed Matter Systems. Wiley
Interdisciplinary Reviews: Computational Molecular Science 2019, 9 (6), e1411.
(47) Prezhdo, O. V. Modeling Non-Adiabatic Dynamics in Nanoscale and Condensed Matter Systems.
Accounts of Chemical Research 2021, 54 (23), 4239-4249.
(1) Schleder, G. R.; Padilha, A. C.; Acosta, C. M.; Costa, M.; Fazzio, A. From DFT to Machine Learning:
Recent Approaches to Materials Science–A Review. Journal of Physics: Materials 2019, 2 (3), 032001.
(2) Gu, G. H.; Noh, J.; Kim, I.; Jung, Y. Machine Learning for Renewable Energy Materials. Journal of
Materials Chemistry A 2019, 7 (29), 17096-17117.
(3) Huan, T. D.; Batra, R.; Chapman, J.; Krishnan, S.; Chen, L.; Ramprasad, R. A Universal Strategy for
the Creation of Machine Learning-Based Atomistic Force Fields. NPJ Computational Materials 2017, 3
(1), 37.
(4) Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine Learning for Molecular
and Materials Science. Nature 2018, 559 (7715), 547-555.
(5) Ouyang, Y.; Yu, C.; He, J.; Jiang, P.; Ren, W.; Chen, J. Accurate Description of High-Order Phonon
Anharmonicity and Lattice Thermal Conductivity from Molecular Dynamics Simulations with Machine
Learning Potential. Physical Review B 2022, 105 (11), 115202.
126

(6) Mortazavi, B.; Podryabinkin, E. V.; Novikov, I. S.; Rabczuk, T.; Zhuang, X.; Shapeev, A. V.
Accelerating First-Principles Estimation of Thermal Conductivity by Machine-Learning Interatomic
Potentials: A MTP/ShengBTE Solution. Computer Physics Communications 2021, 258, 107583.
(7) Zong, H.; Pilania, G.; Ding, X.; Ackland, G. J.; Lookman, T. Developing An Interatomic Potential for
Martensitic Phase Transformations in Zirconium by Machine Learning. NPJ Computational Materials
2018, 4 (1), 48.
(8) Li, L.; Yang, Y.; Zhang, D.; Ye, Z.-G.; Jesse, S.; Kalinin, S. V.; Vasudevan, R. K. Machine Learning–
Enabled Identification of Material Phase Transitions Based on Experimental Data: Exploring Collective
Dynamics in Ferroelectric Relaxors. Science Advances 2018, 4 (3), eaap8672.
(9) Meuwly, M. Machine Learning for Chemical Reactions. Chemical Reviews 2021, 121 (16), 10218-
10239.
(10) Westermayr, J.; Gastegger, M.; Marquetand, P. Combining SchNet and SHARC: The SchNarc
Machine Learning Approach for Excited-State Dynamics. The Journal of Physical Chemistry Letters 2020,
11 (10), 3828-3834.
(11) Kim, C.; Pilania, G.; Ramprasad, R. From Organized High-Throughput Data to Phenomenological
Theory Using Machine Learning: the Example of Dielectric Breakdown. Chemistry of Materials 2016, 28
(5), 1304-1311.
(12) Szymanski, N. J.; Rendy, B.; Fei, Y.; Kumar, R. E.; He, T.; Milsted, D.; McDermott, M. J.; Gallant,
M.; Cubuk, E. D.; Merchant, A. An Autonomous Laboratory for the Accelerated Synthesis of Novel
Materials. Nature 2023, 624 (7990), 86-91.
(13) Raccuglia, P.; Elbert, K. C.; Adler, P. D.; Falk, C.; Wenny, M. B.; Mollo, A.; Zeller, M.; Friedler, S.
A.; Schrier, J.; Norquist, A. J. Machine-Learning-Assisted Materials Discovery Using Failed Experiments.
Nature 2016, 533 (7601), 73-76.
(14) Unke, O. T.; Chmiela, S.; Sauceda, H. E.; Gastegger, M.; Poltavsky, I.; Schütt, K. T.; Tkatchenko, A.;
Müller, K.-R. Machine Learning Force Fields. Chemical Reviews 2021, 121 (16), 10142-10186.
(15) Botu, V.; Batra, R.; Chapman, J.; Ramprasad, R. Machine Learning Force Fields: Construction,
Aalidation, and Outlook. The Journal of Physical Chemistry C 2017, 121 (1), 511-522.
(16) Jinnouchi, R.; Karsai, F.; Kresse, G. On-the-Fly Machine Learning Force Field Generation:
Application to Melting Points. Physical Review B 2019, 100 (1), 014105.
(17) Chmiela, S.; Tkatchenko, A.; Sauceda, H. E.; Poltavsky, I.; Schütt, K. T.; Müller, K.-R. Machine
Learning of Accurate Energy-Conserving Molecular Force Fields. Science Advances 2017, 3 (5), e1603015.
(18) Wang, H.; Zhang, L.; Han, J.; Weinan, E. DeePMD-kit: A Deep Learning Package for Many-Body
Potential Energy Representation and Molecular Dynamics. Computer Physics Communications 2018, 228,
178-184.
(19) Zhang, L.; Han, J.; Wang, H.; Car, R.; Weinan, E. Deep Potential Molecular Dynamics: A Scalable
Model with the Accuracy of Quantum Mechanics. Physical Review Letters 2018, 120 (14), 143001.
127

(20) Zeng, J.; Zhang, D.; Lu, D.; Mo, P.; Li, Z.; Chen, Y.; Rynik, M.; Huang, L. a.; Li, Z.; Shi, S. DeePMDKit V2: A Software Package for Deep Potential Models. The Journal of Chemical Physics 2023, 159 (5).
(21) Batzner, S.; Musaelian, A.; Sun, L.; Geiger, M.; Mailoa, J. P.; Kornbluth, M.; Molinari, N.; Smidt, T.
E.; Kozinsky, B. E (3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic
Potentials. Nature Communications 2022, 13 (1), 2453.
(22) Batatia, I.; Batzner, S.; Kovács, D. P.; Musaelian, A.; Simm, G. N.; Drautz, R.; Ortner, C.; Kozinsky,
B.; Csányi, G. The Design Space of E (3)-Equivariant Atom-Centered Interatomic Potentials. arXiv preprint
arXiv:2205.06643 2022.
(23) Brandstetter, J.; Hesselink, R.; van der Pol, E.; Bekkers, E. J.; Welling, M. Geometric and Physical
Quantities Improve E (3) Equivariant Message Passing. arXiv preprint arXiv:2110.02905 2021.
(1) Zhang, W.; Eperon, G. E.; Snaith, H. J. Metal Halide Perovskites for Energy Applications. Nature
Energy 2016, 1 (6), 1-8.
(2) Shalan, A. E.; Akman, E.; Sadegh, F.; Akin, S. Efficient and Stable Perovskite Solar Cells Enabled by
Dicarboxylic Acid-Supported Perovskite Crystallization. Journal of Physical Chemistry Letters 2021, 12
(3), 997-1004. DOI: 10.1021/acs.jpclett.0c03566.
(3) Lao, X.; Li, X.; Ågren, H.; Chen, G. Highly Controllable Synthesis and DFT Calculations of
Double/Triple-Halide CsPbX3 (X= Cl, Br, I) Perovskite Quantum Dots: Application to Light-Emitting
Diodes. Nanomaterials 2019, 9 (2), 172.
(4) Kulkarni, S. A.; Baikie, T.; Boix, P. P.; Yantara, N.; Mathews, N.; Mhaisalkar, S. Band-Gap Tuning of
Lead Halide Perovskites Using a Sequential Deposition Process. Journal of Materials Chemistry A 2014, 2
(24), 9221-9225.
(5) Unger, E.; Kegelmann, L.; Suchan, K.; Sörell, D.; Korte, L.; Albrecht, S. Roadmap and Roadblocks for
the Band Gap Tunability of Metal Halide Perovskites. Journal of Materials Chemistry A 2017, 5 (23),
11401-11409.
(6) McGovern, L.; Koschany, I.; Grimaldi, G.; Muscarella, L. A.; Ehrler, B. Grain Size Influences
Activation Energy and Migration Pathways in MAPbBr3 Perovskite Solar Cells. Journal of Physical
Chemistry Letters 2021, 12 (9), 2423-2428. DOI: 10.1021/acs.jpclett.1c00205.
(7) Gutiérrez Álvarez, S.; Lin, W.; Abdellah, M.; Meng, J.; Zidek, K.; Pullerits, T. n.; Zheng, K. Charge
Carrier Diffusion Dynamics in Multisized Quaternary Alkylammonium-Capped CsPbBr3 Perovskite
Nanocrystal Solids. ACS Applied Materials & Interfaces 2021, 13 (37), 44742-44750.
(8) Herz, L. M. Charge-Carrier Mobilities in Metal Halide Perovskites: Fundamental Mechanisms and
Limits. ACS Energy Letters 2017, 2 (7), 1539-1548.
(9) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J.; Leijtens, T.; Herz, L. M.;
Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in An Organometal
Trihalide Perovskite Absorber. Science 2013, 342 (6156), 341-344.
128

(10) Noh, J. H.; Im, S. H.; Heo, J. H.; Mandal, T. N.; Seok, S. I. Chemical Management for Colorful,
Efficient, and Stable Inorganic–Organic Hybrid Nanostructured Solar Cells. Nano Letters 2013, 13 (4),
1764-1769.
(11) Saliba, M.; Matsui, T.; Domanski, K.; Seo, J.-Y.; Ummadisingu, A.; Zakeeruddin, S. M.; CorreaBaena, J.-P.; Tress, W. R.; Abate, A.; Hagfeldt, A. Incorporation of Rubidium Cations into Perovskite Solar
Cells Improves Photovoltaic Performance. Science 2016, 354 (6309), 206-209.
(12) Zhang, J. B.; Yin, C. Y.; Yang, F.; Yao, Y.; Yuan, F. L.; Chen, H. T.; Wang, R. W.; Bai, S.; Tu, G. L.;
Hou, L. T. Highly Luminescent and Stable CsPbI3 Perovskite Nanocrystals with Sodium Dodecyl Sulfate
Ligand Passivation for Red-Light-Emitting Diodes. Journal of Physical Chemistry Letters 2021, 12 (9),
2437-2443. DOI: 10.1021/acs.jpclett.1c00008.
(13) Kim, M.; Jeong, J.; Lu, H. Z.; Lee, T. K.; Eickemeyer, F. T.; Liu, Y. H.; Choi, I. W.; Choi, S. J.; Jo,
Y.; Kim, H. B.; et al. Conformal Quantum Dot-SnO2 Layers as Electron Transporters for Efficient
Perovskite Solar Cells. Science 2022, 375 (6578), 302-306, Article. DOI: 10.1126/science.abh1885.
(14) Jiang, Y. Z.; Wei, J. L.; Yuan, M. J. Energy-Funneling Process in Quasi-2D Perovskite Light-Emitting
Diodes. Journal of Physical Chemistry Letters 2021, 12 (10), 2593-2606. DOI:
10.1021/acs.jpclett.1c00072.
(15) Cheng, S. J.; Zhong, H. Z. What Happens When Halide Perovskites Meet with Water? Journal of
Physical Chemistry Letters 2022, 13 (10), 2281-2290. DOI: 10.1021/acs.jpclett.2c00166.
(16) Marronnier, A.; Roma, G.; Boyer-Richard, S.; Pedesseau, L.; Jancu, J.-M.; Bonnassieux, Y.; Katan,
C.; Stoumpos, C. C.; Kanatzidis, M. G.; Even, J. Anharmonicity and Disorder in the Black Phases of Cesium
Lead Iodide Used for Stable Inorganic Perovskite Solar Cells. ACS Nano 2018, 12 (4), 3477-3486.
(17) Jeon, N. J.; Noh, J. H.; Yang, W. S.; Kim, Y. C.; Ryu, S.; Seo, J.; Seok, S. I. Compositional Engineering
of Perovskite Materials for High-Performance Solar Cells. Nature 2015, 517 (7535), 476. DOI:
10.1038/nature14133.
(18) Cao, D. H.; Stoumpos, C. C.; Farha, O. K.; Hupp, J. T.; Kanatzidis, M. G. 2D Homologous Perovskites
as Light-Absorbing Materials for Solar Cell Applications. Journal of the American Chemical Society 2015,
137 (24), 7843-7850. DOI: 10.1021/jacs.5b03796.
(19) Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.;
Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, and
I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano Letters 2015,
15 (6), 3692-3696. DOI: 10.1021/nl5048779.
(20) Cohen, A. V.; Egger, D. A.; Rappe, A. M.; Kronik, L. Breakdown of the Static Picture of Defect
Energetics in Halide Perovskites: the Case of the Br Vacancy in CsPbBr3. The Journal of Physical
Chemistry Letters 2019, 10 (16), 4490-4498.
(21) Wang, B.; Chu, W.; Wu, Y.; Casanova, D.; Saidi, W. A.; Prezhdo, O. V. Electron-Volt Fluctuation of
Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale. The Journal of Physical Chemistry
Letters 2022, 13 (25), 5946-5952.
129

(22) Wu, Y.; Liu, D.; Chu, W.; Wang, B.; Vasenko, A. S.; Prezhdo, O. V. Fluctuations at Metal Halide
Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis.
ACS Applied Materials & Interfaces 2022, 14, 55753–55761.
(23) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on A
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(24) Li, W.; Liu, J.; Bai, F.-Q.; Zhang, H.-X.; Prezhdo, O. V. Hole Trapping by Iodine Interstitial Defects
Decreases Free Carrier Losses in Perovskite Solar Cells: A Time-Domain Ab Initio Study. ACS Energy
Letters 2017, 2 (6), 1270-1278.
(25) Li, W.; Sun, Y.-Y.; Li, L.; Zhou, Z.; Tang, J.; Prezhdo, O. V. Control of Charge Recombination in
Perovskites by Oxidation State of Halide Vacancy. Journal of the American Chemical Society 2018, 140
(46), 15753-15763.
(26) Chu, W.; Saidi, W. A.; Zhao, J.; Prezhdo, O. V. Soft Lattice and Defect Covalency Rationalize
Tolerance of β‐CsPbI3 Perovskite Solar Cells to Native Defects. Angewandte Chemie International Edition
2020, 59 (16), 6435-6441.
(27) Chu, W.; Zheng, Q.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Low-Frequency Lattice Phonons in Halide
Perovskites Explain High Defect Tolerance Toward Electron-Hole Recombination. Science Advances 2020,
6 (7), eaaw7453.
(28) Li, W.; Long, R.; Tang, J.; Prezhdo, O. V. Influence of Defects on Excited-State Dynamics in Lead
Halide Perovskites: Time-Domain Ab Initio Studies. The Journal of Physical Chemistry Letters 2019, 10
(13), 3788-3804.
(29) Li, W.; She, Y.; Vasenko, A. S.; Prezhdo, O. V. Ab Initio Nonadiabatic Molecular Dynamics of Charge
Carriers in Metal Halide Perovskites. Nanoscale 2021, 13 (23), 10239-10265.
(30) Yin, W. J.; Shi, T. T.; Yan, Y. F. Unusual Defect Physics in CH3NH3PbI3 Perovskite Solar Cell
Absorber. Applied Physics Letters 2014, 104 (6). DOI: 10.1063/1.4864778.
(31) Chang, T.; Wei, Q. L.; Zeng, R. S.; Cao, S.; Zhao, J. L.; Zou, B. S. Efficient Energy Transfer in Te4+-
Doped Cs2ZrCl6 Vacancy-Ordered Perovskites and Ultrahigh Moisture Stability via A-Site Rb-Alloying
Strategy. Journal of Physical Chemistry Letters 2021, 12 (7), 1829-1837. DOI:
10.1021/acs.jpclett.1c00255.
(32) Wright, A. D.; Buizza, L. R. V.; Savill, K. J.; Longo, G.; Snaith, H. J.; Johnston, M. B.; Herz, L. M.
Ultrafast Excited-State Localization in Cs2AgBiBr6 Double Perovskite. Journal of Physical Chemistry
Letters 2021, 12 (13), 3352-3360. DOI: 10.1021/acs.jpclett.1c00653.
(33) Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic
Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Letters 2014, 14 (5), 2584-
2590. DOI: 10.1021/nl500390f.
130

(34) Liu, D. Y.; Perez, C. M.; Vasenko, A. S.; Prezhdo, O. V. Ag-Bi Charge Redistribution Creates Deep
Traps in Defective Cs2AgBiBr6: Machine Learning Analysis of Density Functional Theory. Journal of
Physical Chemistry Letters 2022, 13 (16), 3645-3651. DOI: 10.1021/acs.jpclett.2c00869.
(35) Chu, W. B.; Saidi, W. A.; Prezhdo, O. V. Long-Lived Hot Electron in a Metallic Particle for
Plasmonics and Catalysis: Ab Initio Nonadiabatic Molecular Dynamics with Machine Learning. Acs Nano
2020, 14 (8), 10608-10615. DOI: 10.1021/acsnano.0c04736.
(36) Schleder, G. R.; Padilha, A. C.; Acosta, C. M.; Costa, M.; Fazzio, A. From DFT to Machine Learning:
Recent Approaches to Materials Science–A Review. Journal of Physics: Materials 2019, 2 (3), 032001.
(37) Gu, G. H.; Noh, J.; Kim, I.; Jung, Y. Machine Learning for Renewable Energy Materials. Journal of
Materials Chemistry A 2019, 7 (29), 17096-17117.
(38) Huan, T. D.; Batra, R.; Chapman, J.; Krishnan, S.; Chen, L.; Ramprasad, R. A Universal Strategy for
the Creation of Machine Learning-Based Atomistic Force Fields. NPJ Computational Materials 2017, 3
(1), 37.
(39) Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine Learning for Molecular
and Materials Science. Nature 2018, 559 (7715), 547-555.
(40) Ouyang, Y.; Yu, C.; He, J.; Jiang, P.; Ren, W.; Chen, J. Accurate Description of High-Order Phonon
Anharmonicity and Lattice Thermal Conductivity from Molecular Dynamics Simulations with Machine
Learning Potential. Physical Review B 2022, 105 (11), 115202.
(41) Mortazavi, B.; Podryabinkin, E. V.; Novikov, I. S.; Rabczuk, T.; Zhuang, X.; Shapeev, A. V.
Accelerating First-Principles Estimation of Thermal Conductivity by Machine-Learning Interatomic
Potentials: A MTP/ShengBTE Solution. Computer Physics Communications 2021, 258, 107583.
(42) Zong, H.; Pilania, G.; Ding, X.; Ackland, G. J.; Lookman, T. Developing An Interatomic Potential for
Martensitic Phase Transformations in Zirconium by Machine Learning. NPJ Computational Materials
2018, 4 (1), 48.
(43) Li, L.; Yang, Y.; Zhang, D.; Ye, Z.-G.; Jesse, S.; Kalinin, S. V.; Vasudevan, R. K. Machine Learning–
Enabled Identification of Material Phase Transitions Based on Experimental Data: Exploring Collective
Dynamics in Ferroelectric Relaxors. Science Advances 2018, 4 (3), eaap8672.
(44) Meuwly, M. Machine Learning for Chemical Reactions. Chemical Reviews 2021, 121 (16), 10218-
10239.
(45) Westermayr, J.; Gastegger, M.; Marquetand, P. Combining SchNet and SHARC: The SchNarc
Machine Learning Approach for Excited-State Dynamics. The Journal of Physical Chemistry Letters 2020,
11 (10), 3828-3834.
(46) Lee, J.; Seko, A.; Shitara, K.; Nakayama, K.; Tanaka, I. Prediction Model of Band Gap for Inorganic
Compounds by Combination of Density Functional Theory Calculations and Machine Learning
Techniques. Physical Review B 2016, 93 (11), 115104.
131

(47) Kim, C.; Pilania, G.; Ramprasad, R. From Organized High-Throughput Data to Phenomenological
Theory Using Machine Learning: the Example of Dielectric Breakdown. Chemistry of Materials 2016, 28
(5), 1304-1311.
(48) Gastegger, M.; Behler, J.; Marquetand, P. Machine Learning Molecular Dynamics for the Simulation
of Infrared Spectra. Chemical Science 2017, 8 (10), 6924-6935.
(49) Poltavsky, I.; Tkatchenko, A. Machine Learning Force Fields: Recent Advances and Remaining
Challenges. The Journal of Physical Chemistry Letters 2021, 12 (28), 6551-6564.
(50) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
(51) Yin, J.; Yang, H.; Song, K.; El-Zohry, A. M.; Han, Y.; Bakr, O. M.; Brédas, J.-L.; Mohammed, O. F.
Point Defects and Green Emission in Zero-Dimensional Perovskites. The Journal of Physical Chemistry
Letters 2018, 9 (18), 5490-5495.
(52) Kresse, G.; Furthmuller, J. VASP the Guide (Vienna University of Technology, Vienna, 2001); G.
Kresse and J. Hafner. Phys. Rev. B 1993, 47, 558.
(53) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical
Review Letters 1996, 77 (18), 3865.
(54) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.
Physical Review b 1999, 59 (3), 1758.
(55) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and
Morphology Data. Journal of Applied Crystallography 2011, 44 (6), 1272-1276.
(56) Wang, H.; Zhang, L.; Han, J.; Weinan, E. DeePMD-kit: A Deep Learning Package for Many-Body
Potential Energy Representation and Molecular Dynamics. Computer Physics Communications 2018, 228,
178-184.
(57) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of Computational
Physics 1995, 117 (1), 1-19.
(58) Yuan, Y. B.; Huang, J. S. Ion Migration in Organometal Trihalide Perovskite and Its Impact on
Photovoltaic Efficiency and Stability. Accounts of Chemical Research 2016, 49 (2), 286-293. DOI:
10.1021/acs.accounts.5b00420.
(59) Bischak, C. G.; Hetherington, C. L.; Wu, H.; Aloni, S.; Ogletree, D. F.; Limmer, D. T.; Ginsberg, N.
S. Origin of Reversible Photoinduced Phase Separation in Hybrid Perovskites. Nano Letters 2017, 17 (2),
1028-1033. DOI: 10.1021/acs.nanolett.6b04453.
(60) Jokar, E.; Chuang, H. S.; Kuan, C. H.; Wu, H. P.; Hou, C. H.; Shyue, J. J.; Diau, E. W. G. Slow
Passivation and Inverted Hysteresis for Hybrid Tin Perovskite Solar Cells Attaining 13.5% via Sequential
Deposition. Journal of Physical Chemistry Letters 2021, 12 (41), 10106-10111. DOI:
10.1021/acs.jpclett.1c03107.
132

(61) Tong, C. J.; Geng, W.; Prezhdo, O. V.; Liu, L. M. Role of Methylammonium Orientation in Ion
Diffusion and Current Voltage Hysteresis in the CH3NH3PbI3 Perovskite. Acs Energy Letters 2017, 2 (9),
1997-2004. DOI: 10.1021/acsenergylett.7b00659.
(62) Tong, C. J.; Li, L. Q.; Liu, L. M.; Prezhdo, O. V. Synergy between Ion Migration and Charge Carrier
Recombination in Metal-Halide Perovskites. Journal of the American Chemical Society 2020, 142 (6),
3060-3068. DOI: 10.1021/jacs.9b12391.
(63) Shi, R.; Fang, W. H.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Efficient Passivation of DY Center in
CH3NH3PbBr3 by Chlorine: Quantum Molecular Dynamics. Nano Research 2022, 15 (3), 2112-2122. DOI:
10.1007/s12274-021-3840-y.
(64) Neutzner, S.; Thouin, F.; Cortecchia, D.; Petrozza, A.; Silva, C.; Kandada, A. R. S. Exciton-Polaron
Spectral Structures in Two-Dimensional Hybrid Lead-Halide Perovskites. Physical Review Materials 2018,
2 (6), 064605.
(65) Lang, F.; Shargaieva, O.; Brus, V. V.; Neitzert, H. C.; Rappich, J.; Nickel, N. H. Influence of Radiation
on the Properties and the Stability of Hybrid Perovskites. Advanced Materials 2018, 30 (3), 1702905.
(66) Straus, D. B.; Kagan, C. R. Electrons, Excitons, and Phonons in Two-Dimensional Hybrid Perovskites:
Connecting Structural, Optical, and Electronic Properties. The Journal of Physical Chemistry Letters 2018,
9 (6), 1434-1447.
(67) Zhang, Z.; Fang, W.-H.; Long, R.; Prezhdo, O. V. Exciton Dissociation and Suppressed Charge
Recombination at 2D Perovskite Edges: Key Roles of Unsaturated Halide Bonds and Thermal Disorder.
Journal of the American Chemical Society 2019, 141 (39), 15557-15566.
(68) Shi, R.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Edge Influence on Charge Carrier Localization and
Lifetime in CH3NH3PbBr3 Perovskite: Ab Initio Quantum Dynamics Simulation. Journal of Physical
Chemistry Letters 2020, 11 (21), 9100-9109. DOI: 10.1021/acs.jpclett.0c02800.
(69) He, J. L.; Fang, W. H.; Long, R.; Prezhdo, O. V. Bidentate Lewis Bases Are Preferred for Passivation
of MAPbI3 Surfaces: A Time-Domain Ab Initio Analysis. Nano Energy 2021, 79. DOI:
10.1016/j.nanoen.2020.105491.
(70) Zhao, X.; Vasenko, A. S.; Prezhdo, O. V.; Long, R. Anion Doping Delays Nonradiative Electron-Hole
Recombination in Cs-Based All-Inorganic Perovskites: Time Domain ab Initio Analysis. Journal of
Physical Chemistry Letters 2022, 13 (49), 11375-11382. DOI: 10.1021/acs.jpclett.2c03072.
(71) Shi, R.; Long, R.; Fang, W. H.; Prezhdo, O. V. Rapid Interlayer Charge Separation and Extended
Carrier Lifetimes due to Spontaneous Symmetry Breaking in Organic and Mixed Organic-Inorganic DionJacobson Perovskites. Journal of the American Chemical Society 2023, 145, 5297–5309. DOI:
10.1021/jacs.2c12903.
(72) Liu, L. H.; Fang, W. H.; Long, R.; Prezhdo, O. V. Lewis Base Passivation of Hybrid Halide Perovskites
Slows Electron-Hole Recombination: Time-Domain Ab lnitio Analysis. Journal of Physical Chemistry
Letters 2018, 9 (5), 1164-1171. DOI: 10.1021/acs.jpclett.8b00177.
133

(73) Agiorgousis, M. L.; Sun, Y. Y.; Zeng, H.; Zhang, S. B. Strong Covalency-Induced Recombination
Centers in Perovskite Solar Cell Material CH3NH3Pbl3. Journal of the American Chemical Society 2014,
136 (41), 14570-14575. DOI: 10.1021/ja5079305.
(74) Utzat, H.; Sun, W. W.; Kaplan, A. E. K.; Krieg, F.; Ginterseder, M.; Spokoyny, B.; Klein, N. D.;
Shulenberger, K. E.; Perkinson, C. F.; Kovalenko, M. V.; Bawendi, M. G. Coherent Single-Photon
Emission from Colloidal Lead Halide Perovskite Quantum Dots. Science 2019, 363 (6431), 1068. DOI:
10.1126/science.aau7392.
(75) Akkerman, Q. A.; Raino, G.; Kovalenko, M. V.; Manna, L. Genesis, Challenges and Opportunities for
Colloidal Lead Halide Perovskite Nanocrystals. Nature Materials 2018, 17 (5), 394-405. DOI:
10.1038/s41563-018-0018-4.
(76) Swarnkar, A.; Chulliyil, R.; Ravi, V. K.; Irfanullah, M.; Chowdhury, A.; Nag, A. Colloidal CsPbBr3
Perovskite Nanocrystals: Luminescence beyond Traditional Quantum Dots. Angewandte ChemieInternational Edition 2015, 54 (51), 15424-15428. DOI: 10.1002/anie.201508276.
(77) Alivisatos, A. P. Semiconductor Clusters, Nanocrystals, and Quantum Dots. Science 1996, 271 (5251),
933-937. DOI: 10.1126/science.271.5251.933.
(78) Prezhdo, O. V. Multiple Excitons and the Electron-Phonon Bottleneck in Semiconductor Quantum
Dots: An Ab Initio Perspective. Chemical Physics Letters 2008, 460 (1-3), 1-9. DOI:
10.1016/j.cplett.2008.03.099.
(79) Hyeon-Deuk, K.; Prezhdo, O. V. Multiple Exciton Generation and Recombination Dynamics in Small
Si and CdSe Quantum Dots: An Ab Initio Time-Domain Study. Acs Nano 2012, 6 (2), 1239-1250. DOI:
10.1021/nn2038884.
(80) Chen, O.; Zhao, J.; Chauhan, V. P.; Cui, J.; Wong, C.; Harris, D. K.; Wei, H.; Han, H. S.; Fukumura,
D.; Jain, R. K.; Bawendi, M. G. Compact High-Quality CdSe-CdS Core-Shell Nanocrystals with Narrow
Emission Linewidths and Suppressed Blinking. Nature Materials 2013, 12 (5), 445-451. DOI:
10.1038/nmat3539.
(81) Houtepen, A. J.; Hens, Z.; Owen, J. S.; Infante, I. On the Origin of Surface Traps in Colloidal II-VI
Semiconductor Nanocrystals. Chemistry of Materials 2017, 29 (2), 752-761. DOI:
10.1021/acs.chemmater.6b04648.
(82) Trivedi, D. J.; Wang, L. J.; Prezhdo, O. V. Auger-Mediated Electron Relaxation Is Robust to Deep
Hole Traps: Time-Domain Ab Initio Study of CdSe Quantum Dots. Nano Letters 2015, 15 (3), 2086-2091.
DOI: 10.1021/nl504982k.
(83) Li, W.; Vasenko, A. S.; Tang, J.; Prezhdo, O. V. Anharmonicity Extends Carrier Lifetimes in Lead
Halide Perovskites at Elevated Temperatures. The Journal of Physical Chemistry Letters 2019, 10 (20),
6219-6226.
(84) Zhou, G.; Chu, W.; Prezhdo, O. V. Structural Deformation Controls Charge Losses in MAPbI3:
Unsupervised Machine Learning of Nonadiabatic Molecular Dynamics. ACS Energy Letters 2020, 5 (6),
1930-1938.
134

(85) Mangan, S. M.; Zhou, G.; Chu, W.; Prezhdo, O. V. Dependence Between Structural and Electronic
Properties of CsPbI3: Unsupervised Machine Learning of Nonadiabatic Molecular Dynamics. The Journal
of Physical Chemistry Letters 2021, 12 (35), 8672-8678.
(86) Aristidou, N.; Eames, C.; Sanchez-Molina, I.; Bu, X.; Kosco, J.; Islam, M. S.; Haque, S. A. Fast
Oxygen Diffusion and Iodide Defects Mediate Oxygen-Induced Degradation of Perovskite Solar Cells.
Nature Communications 2017, 8 (1), 15218.
(87) He, J.; Fang, W.-H.; Long, R.; Prezhdo, O. V. Superoxide/Peroxide Chemistry Extends Charge
Carriers’ Lifetime but Undermines Chemical Stability of CH3NH3PbI3 Exposed to Oxygen: Time-Domain
Ab Initio Analysis. Journal of the American Chemical Society 2019, 141 (14), 5798-5807.
(88) Zhang, Z.; Fang, W.-H.; Tokina, M. V.; Long, R.; Prezhdo, O. V. Rapid Decoherence Suppresses
Charge Recombination in Multi-Layer 2D Halide Perovskites: Time-Domain Ab Initio Analysis. Nano
Letters 2018, 18 (4), 2459-2466.
(89) Li, W.; Tang, J.; Casanova, D.; Prezhdo, O. V. Time-Domain Ab Initio Analysis Rationalizes the
Unusual Temperature Dependence of Charge Carrier Relaxation in Lead Halide Perovskite. ACS Energy
Letters 2018, 3 (11), 2713-2720.
(90) Li, W.; Chen, Z.; Tang, J.; Prezhdo, O. V. Anti-Correlation between Band Gap and Carrier Lifetime
in Lead Halide Perovskites under Compression Rationalized by Ab Initio Quantum Dynamics. Chemistry
of Materials 2020, 32 (11), 4707-4715.
(91) Patrick, C. E.; Jacobsen, K. W.; Thygesen, K. S. Anharmonic Stabilization and Band Gap
Renormalization in the Perovskite CsSnI3. Physical Review B 2015, 92 (20), 201205.
(92) Long, R.; Fang, Q.; Vasenko, A. S.; Shi, R.; Fang, W. H.; Prezhdo, O. V. Structural Disorder in HigherTemperature Phases Increases Charge Carrier Lifetimes in Metal Halide Perovskites. Journal of the
American Chemical Society 2022, 144 (41), 19137-19149. DOI: 10.1021/jacs.2c08627.
(93) Akimov, A. V.; Prezhdo, O. V. Persistent Electronic Coherence Despite Rapid Loss of ElectronNuclear Correlation. Journal of Physical Chemistry Letters 2013, 4 (22), 3857-3864. DOI:
10.1021/jz402035z.
(94) Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.; Prezhdo, O. V. Quantum Zeno Effect
Rationalizes the Phonon Bottleneck in Semiconductor Quantum Dots. Physical Review Letters 2013, 110
(18). DOI: 10.1103/PhysRevLett.110.180404.
(95) Itano, W. M.; Heinzen, D. J.; Bollinger, J. J.; Wineland, D. J. Quantum Zeno Effect. Physical Review
A 1990, 41 (5), 2295-2300. DOI: 10.1103/PhysRevA.41.2295.
(96) Kamisaka, H.; Kilina, S. V.; Yamashita, K.; Prezhdo, O. V. Ultrafast Vibrationally-Induced Dephasing
of Electronic Excitations in PbSe Quantum Dot. Nano Letters 2006, 6 (10), 2295-2300. DOI:
10.1021/nl0617383.
(97) Li, X.; Cao, F.; Yu, D.; Chen, J.; Sun, Z.; Shen, Y.; Zhu, Y.; Wang, L.; Wei, Y.; Wu, Y. All Inorganic
Halide Perovskites Nanosystem: Synthesis, Structural Features, Optical Properties and Optoelectronic
Applications. Small 2017, 13 (9), 1603996.
135

(98) Fu, Y.; Zhu, H.; Chen, J.; Hautzinger, M. P.; Zhu, X.-Y.; Jin, S. Metal Halide Perovskite
Nanostructures for Optoelectronic Applications and the Study of Physical Properties. Nature Reviews
Materials 2019, 4 (3), 169-188.
(99) Zhao, Y.; Zhu, K. Organic–Inorganic Hybrid Lead Halide Perovskites for Optoelectronic and
Electronic Applications. Chemical Society Reviews 2016, 45 (3), 655-689.
(1) Stranks, S. D.; Snaith, H. J. Metal-Halide Perovskites for Photovoltaic and Light-Emitting Devices.
Nature Nanotechnology 2015, 10 (5), 391-402.
(2) Eperon, G. E.; Paternò, G. M.; Sutton, R. J.; Zampetti, A.; Haghighirad, A. A.; Cacialli, F.; Snaith, H.
J. Inorganic Caesium Lead Iodide Perovskite Solar Cells. Journal of Materials Chemistry A 2015, 3 (39),
19688-19695.
(3) Swarnkar, A.; Chulliyil, R.; Ravi, V. K.; Irfanullah, M.; Chowdhury, A.; Nag, A. Colloidal CsPbBr3
Perovskite Nanocrystals: Luminescence Beyond Traditional Quantum Dots. Angewandte Chemie 2015, 127
(51), 15644-15648.
(4) Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.;
Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X= Cl, Br, and
I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano letters 2015,
15 (6), 3692-3696.
(5) Li, Z.; Kong, L.; Huang, S.; Li, L. Highly Luminescent and Ultrastable CsPbBr3 Perovskite Quantum
Dots Incorporated into a Silica/Alumina Monolith. Angewandte Chemie 2017, 129 (28), 8246-8250.
(6) Song, J.; Li, J.; Li, X.; Xu, L.; Dong, Y.; Zeng, H. Quantum Dot Light‐Emitting Diodes Based on
Inorganic Perovskite Cesium Lead Halides (CsPbX3). Advanced materials 2015, 27 (44), 7162-7167.
(7) Du, X.; Wu, G.; Cheng, J.; Dang, H.; Ma, K.; Zhang, Y.-W.; Tan, P.-F.; Chen, S. High-Quality CsPbBr3
Perovskite Nanocrystals for Quantum Dot Light-emitting Diodes. RSC Advances 2017, 7 (17), 10391-
10396.
(8) Kulkarni, S. A.; Baikie, T.; Boix, P. P.; Yantara, N.; Mathews, N.; Mhaisalkar, S. Band-Gap Tuning of
Lead Halide Perovskites Using a Sequential Deposition Process. Journal of Materials Chemistry A 2014, 2
(24), 9221-9225.
(9) Unger, E.; Kegelmann, L.; Suchan, K.; Sörell, D.; Korte, L.; Albrecht, S. Roadmap and Roadblocks for
the Band Gap Tunability of Metal Halide Perovskites. Journal of Materials Chemistry A 2017, 5 (23),
11401-11409.
(10) Chiba, T.; Hayashi, Y.; Ebe, H.; Hoshi, K.; Sato, J.; Sato, S.; Pu, Y.-J.; Ohisa, S.; Kido, J. AnionExchange Red Perovskite Quantum Dots with Ammonium Iodine Salts for Highly Efficient Light-Emitting
Devices. Nature Photonics 2018, 12 (11), 681-687.
(11) Cho, H.; Jeong, S.-H.; Park, M.-H.; Kim, Y.-H.; Wolf, C.; Lee, C.-L.; Heo, J. H.; Sadhanala, A.;
Myoung, N.; Yoo, S. Overcoming the Electroluminescence Efficiency Limitations of Perovskite LightEmitting Diodes. Science 2015, 350 (6265), 1222-1225.
136

(12) Cao, Y.; Wang, N.; Tian, H.; Guo, J.; Wei, Y.; Chen, H.; Miao, Y.; Zou, W.; Pan, K.; He, Y. Perovskite
Light-Emitting Diodes Based on Spontaneously Formed Submicrometre-Scale Structures. Nature 2018,
562 (7726), 249-253.
(13) Lin, K.; Xing, J.; Quan, L. N.; de Arquer, F. P. G.; Gong, X.; Lu, J.; Xie, L.; Zhao, W.; Zhang, D.;
Yan, C. Perovskite Light-Emitting Diodes with External Quantum Efficiency Exceeding 20 Per Cent.
Nature 2018, 562 (7726), 245-248.
(14) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J.; Leijtens, T.; Herz, L. M.;
Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal
Trihalide Perovskite Absorber. Science 2013, 342 (6156), 341-344.
(15) Herz, L. M. Charge-Carrier Mobilities in Metal Halide Perovskites: Fundamental Mechanisms and
Limits. ACS Energy Letters 2017, 2 (7), 1539-1548.
(16) McGovern, L.; Futscher, M. H.; Muscarella, L. A.; Ehrler, B. Understanding the Stability of MAPbBr3
Versus MAPbI3: Suppression of Methylammonium Migration and Reduction of Halide Migration. The
Journal of Physical Chemistry Letters 2020, 11 (17), 7127-7132.
(17) Sanehira, E. M.; Marshall, A. R.; Christians, J. A.; Harvey, S. P.; Ciesielski, P. N.; Wheeler, L. M.;
Schulz, P.; Lin, L. Y.; Beard, M. C.; Luther, J. M. Enhanced Mobility CsPbI3 Quantum Dot Arrays for
Record-Efficiency, High-Voltage Photovoltaic Cells. Science Advances 2017, 3 (10), eaao4204.
(18) Akkerman, Q. A.; Rainò, G.; Kovalenko, M. V.; Manna, L. Genesis, Challenges and Opportunities for
Colloidal Lead Halide Perovskite Nanocrystals. Nature materials 2018, 17 (5), 394-405.
(19) Kovalenko, M. V.; Protesescu, L.; Bodnarchuk, M. I. Properties and Potential Optoelectronic
Applications of Lead Halide Perovskite Nanocrystals. Science 2017, 358 (6364), 745-750.
(20) Perez, C. M.; Ghosh, D.; Prezhdo, O.; Tretiak, S.; Neukirch, A. J. Excited-State Properties of Defected
Halide Perovskite Quantum Dots: Insights from Computation. The Journal of Physical Chemistry Letters
2021, 12 (3), 1005-1011.
(21) Chen, D.; Yuan, S.; Chen, J.; Zhong, J.; Xu, X. Robust CsPbX3 (X= Cl, Br, and I) Perovskite Quantum
Dot Embedded Glasses: Nanocrystallization, Improved Stability and Visible Full-Spectral Tunable
Emissions. Journal of Materials Chemistry C 2018, 6 (47), 12864-12870.
(22) Lin, J.; Lu, Y.; Li, X.; Huang, F.; Yang, C.; Liu, M.; Jiang, N.; Chen, D. Perovskite Quantum Dots
Glasses Based Backlit Displays. ACS Energy Letters 2021, 6 (2), 519-528.
(23) Su, Y.; Chen, X.; Ji, W.; Zeng, Q.; Ren, Z.; Su, Z.; Liu, L. Highly Controllable and Efficient Synthesis
of Mixed-Halide CsPbX3 (X= Cl, Br, I) Perovskite QDs toward the Tunability of Entire Visible Light. ACS
applied materials & interfaces 2017, 9 (38), 33020-33028.
(24) Wei, Y.; Cheng, Z.; Lin, J. An Overview on Enhancing the Stability of Lead Halide Perovskite
Quantum Dots and Their Applications in Phosphor-Converted LEDs. Chemical Society Reviews 2019, 48
(1), 310-350.
137

(25) Wei, Y.; Cheng, Z.; Lin, J. Correction: An Overview on Enhancing the Stability of Lead Halide
Perovskite Quantum Dots and Their Applications in Phosphor-Converted LEDs. Chemical Society Reviews
2019, 48 (1), 405-405.
(26) Wang, X.; Bao, Z.; Chang, Y.-C.; Liu, R.-S. Perovskite Quantum Dots for Application in High Color
Gamut Backlighting Display of Light-Emitting Diodes. ACS Energy Letters 2020, 5 (11), 3374-3396.
(27) Li, X.; Cao, F.; Yu, D.; Chen, J.; Sun, Z.; Shen, Y.; Zhu, Y.; Wang, L.; Wei, Y.; Wu, Y. All Inorganic
Halide Perovskites Nanosystem: Synthesis, Structural Features, Optical Properties and Optoelectronic
Applications. Small 2017, 13 (9), 1603996.
(28) He, J.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Halide Composition Controls Electron–Hole
Recombination in Cesium–Lead Halide Perovskite Quantum Dots: A Time Domain Ab Initio Study. The
Journal of Physical Chemistry Letters 2018, 9 (8), 1872-1879.
(29) Li, W.; She, Y.; Vasenko, A. S.; Prezhdo, O. V. Ab Initio Nonadiabatic Molecular Dynamics of Charge
Carriers in Metal Halide Perovskites. Nanoscale 2021, 13 (23), 10239-10265.
(30) Shi, R.; Vasenko, A. S.; Long, R.; Prezhdo, O. V. Edge Influence on Charge Carrier Localization and
Lifetime in CH3NH3PbBr3 perovskite: Ab Initio Quantum Dynamics Simulation. The Journal of Physical
Chemistry Letters 2020, 11 (21), 9100-9109.
(31) Gao, G.; Xi, Q.; Zhou, H.; Zhao, Y.; Wu, C.; Wang, L.; Guo, P.; Xu, J. Novel Inorganic Perovskite
Quantum Dots for Photocatalysis. Nanoscale 2017, 9 (33), 12032-12038.
(32) Li, P.; Lu, Y.; Duan, Y.; Xu, S.; Zhang, J. Potential Application of Perovskite Glass Material in
Photocatalysis Field. The Journal of Physical Chemistry C 2021, 125 (4), 2382-2392.
(33) Gao, F.; Yang, W.; Liu, X.; Li, Y.; Liu, W.; Xu, H.; Liu, Y. Highly Stable and Luminescent SilicaCoated Perovskite Quantum Dots at Nanoscale-Particle Level via Nonpolar Solvent Synthesis. Chemical
Engineering Journal 2021, 407, 128001.
(34) Yuan, Y.; Huang, J. Ion Migration in Organometal Trihalide Perovskite and Its Impact on Photovoltaic
Efficiency and Stability. Accounts of Chemical Research 2016, 49 (2), 286-293.
(35) Azpiroz, J. M.; Mosconi, E.; Bisquert, J.; De Angelis, F. Defect Migration in Methylammonium Lead
Iodide and Its Role in Perovskite Solar Cell Operation. Energy & Environmental Science 2015, 8 (7), 2118-
2127.
(36) Eames, C.; Frost, J. M.; Barnes, P. R.; O’regan, B. C.; Walsh, A.; Islam, M. S. Ionic Transport in
Hybrid Lead Iodide Perovskite Solar Cells. Nature Communications 2015, 6 (1), 7497.
(37) Son, D.-Y.; Kim, S.-G.; Seo, J.-Y.; Lee, S.-H.; Shin, H.; Lee, D.; Park, N.-G. Universal Approach
toward Hysteresis-Free Perovskite Solar Cell via Defect Engineering. Journal of the American Chemical
Society 2018, 140 (4), 1358-1364.
(38) Mosconi, E.; De Angelis, F. Mobile Ions in Organohalide Perovskites: Interplay of Electronic Structure
and Dynamics. ACS Energy Letters 2016, 1 (1), 182-188.
138

(39) Yoon, S. J.; Draguta, S.; Manser, J. S.; Sharia, O.; Schneider, W. F.; Kuno, M.; Kamat, P. V. Tracking
Iodide and Bromide Ion Segregation in Mixed Halide Lead Perovskites during Photoirradiation. ACS
Energy Letters 2016, 1 (1), 290-296.
(40) Samu, G. F.; Balog, Á.; De Angelis, F.; Meggiolaro, D.; Kamat, P. V.; Janáky, C. Electrochemical
Hole Injection Selectively Expels Iodide from Mixed Halide Perovskite Films. Journal of the American
Chemical Society 2019, 141 (27), 10812-10820.
(41) Van Reenen, S.; Kemerink, M.; Snaith, H. J. Modeling Anomalous Hysteresis in Perovskite Solar
Cells. The Journal of Physical Chemistry Letters 2015, 6 (19), 3808-3814.
(42) Richardson, G.; O'Kane, S. E.; Niemann, R. G.; Peltola, T. A.; Foster, J. M.; Cameron, P. J.; Walker,
A. B. Can Slow-Moving Ions Explain Hysteresis in the Current–Voltage Curves of Perovskite Solar Cells?
Energy & Environmental Science 2016, 9 (4), 1476-1485.
(43) Chen, R.; Cao, J.; Duan, Y.; Hui, Y.; Chuong, T. T.; Ou, D.; Han, F.; Cheng, F.; Huang, X.; Wu, B.
High-Efficiency, Hysteresis-Less, UV-Stable Perovskite Solar Cells with Cascade ZnO–ZnS Electron
Transport Layer. Journal of the American Chemical Society 2018, 141 (1), 541-547.
(44) Tong, C.-J.; Geng, W.; Prezhdo, O. V.; Liu, L.-M. Role of Methylammonium Orientation in Ion
Diffusion and Current–Voltage Hysteresis in the CH3NH3PbI3 Perovskite. ACS Energy Letters 2017, 2 (9),
1997-2004.
(45) Tong, C.-J.; Li, L.; Liu, L.-M.; Prezhdo, O. V. Synergy Between Ion Migration and Charge Carrier
Recombination in Metal-Halide Perovskites. Journal of the American Chemical Society 2020, 142 (6),
3060-3068.
(46) Li, W.; Long, R.; Tang, J.; Prezhdo, O. V. Influence of Defects on Excited-State Dynamics in Lead
Halide Perovskites: Time-Domain Ab Initio Studies. The Journal of Physical Chemistry Letters 2019, 10
(13), 3788-3804.
(47) Yoon, S. J.; Kuno, M.; Kamat, P. V. Shift happens. How Halide Ion Defects Influence Photoinduced
Segregation in Mixed Halide Perovskites. ACS Energy Letters 2017, 2 (7), 1507-1514.
(48) Landi, G.; Neitzert, H. C.; Barone, C.; Mauro, C.; Lang, F.; Albrecht, S.; Rech, B.; Pagano, S.
Correlation Between Electronic Defect States Distribution and Device Performance of Perovskite Solar
Cells. Advanced Science 2017, 4 (10), 1700183.
(49) Jónsson, H.; Mills, G.; Jacobsen, K. W. Nudged Elastic Band Method for Finding Minimum Energy
Paths of Transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations, World
Scientific, 1998; pp 385-404.
(50) Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.; Prezhdo, O. V. Quantum Zeno Effect
Rationalizes the Phonon Bottleneck in Semiconductor Quantum Dots. Physical Review Letters 2013, 110
(18), 180404.
(51) Kamisaka, H.; Kilina, S. V.; Yamashita, K.; Prezhdo, O. V. Ultrafast Vibrationally-Induced Dephasing
of Electronic Excitations in PbSe Quantum Dots. Nano letters 2006, 6 (10), 2295-2300.
139

(52) Prezhdo, O. V. Photoinduced Dynamics in Semiconductor Quantum Dots: Insights from Time-Domain
Ab Initio Studies. Accounts of Chemical Research 2009, 42 (12), 2005-2016.
(53) Wei, H. H.-Y.; Evans, C. M.; Swartz, B. D.; Neukirch, A. J.; Young, J.; Prezhdo, O. V.; Krauss, T. D.
Colloidal Semiconductor Quantum Dots with Tunable Surface Composition. Nano letters 2012, 12 (9),
4465-4471.
(54) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Physical Review B 1993, 47
(1), 558.
(55) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Physical
Review Letters 1996, 77 (18), 3865.
(56) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.
Physical Review B 1999, 59 (3), 1758.
(57) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and
Morphology Data. Journal of Applied Crystallography 2011, 44 (6), 1272-1276.
(58) Oksenberg, E.; Sanders, E.; Popovitz-Biro, R.; Houben, L.; Joselevich, E. Surface-Guided CsPbBr3
Perovskite Nanowires on Flat and Faceted Sapphire with Size-Dependent Photoluminescence and Fast
Photoconductive Response. Nano Letters 2018, 18 (1), 424-433.
(59) Ma, S.; Kim, S. H.; Jeong, B.; Kwon, H. C.; Yun, S. C.; Jang, G.; Yang, H.; Park, C.; Lee, D.; Moon,
J. Strain‐Mediated Phase Stabilization: A New Strategy for Ultrastable α‐CsPbI3 Perovskite by
Nanoconfined Growth. Small 2019, 15 (21), 1900219.
(60) Ezzeldien, M.; Al-Qaisi, S.; Alrowaili, Z.; Alzaid, M.; Maskar, E.; Es-Smairi, A.; Vu, T. V.; Rai, D.
Electronic and Optical Properties of Bulk and Surface of CsPbBr3 Inorganic Halide Perovskite A First
Principles DFT 1/2 Approach. Scientific Reports 2021, 11 (1), 20622.
(61) Yang, Y.; Hou, C.; Liang, T.-X. Energetic and Electronic Properties of CsPbBr3 Surfaces: A FirstPrinciples Study. Physical Chemistry Chemical Physics 2021, 23 (12), 7145-7152.
(62) Lanigan-Atkins, T.; He, X.; Krogstad, M.; Pajerowski, D.; Abernathy, D.; Xu, G. N.; Xu, Z.; Chung,
D.-Y.; Kanatzidis, M.; Rosenkranz, S. Two-Dimensional Overdamped Fluctuations of the Soft Perovskite
Lattice in CsPbBr3. Nature materials 2021, 20 (7), 977-983.
(63) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for
Finding Saddle Points and Minimum Energy Paths. The Journal of Chemical Physics 2000, 113 (22), 9901-
9904.
(64) Xu, X.; Wu, Z.; Zhao, Z.; Lu, Z.; Gao, Y.; Huang, X.; Huang, J.; Zhang, Z.; Cai, Y.; Qu, Y. FirstPrinciples Study of Detrimental Iodine Vacancy in Lead Halide Perovskite Under Strain and Electron
Injection. Applied Physics Letters 2022, 121 (9).
(65) Shi, Y.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Iodine and Sulfur Vacancy Cooperation Promotes
Ultrafast Charge Extraction at MAPbI3/MoS2 Interface. ACS Energy Letters 2020, 5 (5), 1346-1354.
140

(66) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
(67) Ran, J.; Wang, B.; Wu, Y.; Liu, D.; Mora Perez, C.; Vasenko, A. S.; Prezhdo, O. V. Halide Vacancies
Create No Charge Traps on Lead Halide Perovskite Surfaces but Can Generate Deep Traps in the Bulk. The
Journal of Physical Chemistry Letters 2023, 14, 6028-6036.
(68) Li, W.; Vasenko, A. S.; Tang, J.; Prezhdo, O. V. Anharmonicity Extends Carrier Lifetimes in Lead
Halide Perovskites at Elevated Temperatures. The Journal of Physical Chemistry Letters 2019, 10 (20),
6219-6226.
(69) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on A
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(70) Strandell, D.; Mora Perez, C.; Wu, Y.; Prezhdo, O. V.; Kambhampati, P. Excitonic Quantum
Coherence in Light Emission from CsPbBr3 Metal-Halide Perovskite Nanocrystals. Nano Letters 2023.
(71) Chu, W.; Saidi, W. A.; Zhao, J.; Prezhdo, O. V. Soft Lattice and Defect Covalency Rationalize
Tolerance of β‐CsPbI3 Perovskite Solar Cells to Native Defects. Angewandte Chemie International Edition
2020, 59 (16), 6435-6441.
(72) Chu, W.; Zheng, Q.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Low-Frequency Lattice Phonons in Halide
Perovskites Explain High Defect Tolerance toward Electron-Hole Recombination. Science advances 2020,
6 (7), eaaw7453.
(73) Li, W.; Sun, Y.-Y.; Li, L.; Zhou, Z.; Tang, J.; Prezhdo, O. V. Control of Charge Recombination in
Perovskites by Oxidation State of Halide Vacancy. Journal of the American Chemical Society 2018, 140
(46), 15753-15763.
(74) Qiao, L.; Fang, W.-H.; Long, R.; Prezhdo, O. V. Elimination of Charge Recombination Centers in
Metal Halide Perovskites by Strain. Journal of the American Chemical Society 2021, 143 (26), 9982-9990.
(75) Zhang, Z.; Long, R.; Tokina, M. V.; Prezhdo, O. V. Interplay Between Localized and Free Charge
Carriers Can Explain Hot Fluorescence in the CH3NH3PbBr3 Perovskite: Time-Domain Ab Initio Analysis.
Journal of the American Chemical Society 2017, 139 (48), 17327-17333.
(76) Zhang, Z.-Y.; Wang, H.-Y.; Zhang, Y.-X.; Hao, Y.-W.; Sun, C.; Zhang, Y.; Gao, B.-R.; Chen, Q.-D.;
Sun, H.-B. The Role of Trap-Assisted Recombination in Luminescent Properties of Organometal Halide
CH3NH3PbBr3 Perovskite Films and Quantum Dots. Scientific Reports 2016, 6 (1), 27286.
(77) Wetzelaer, G. J. A.; Scheepers, M.; Sempere, A. M.; Momblona, C.; Ávila, J.; Bolink, H. J. Trap‐
Assisted Non‐Radiative Recombination in Organic–Inorganic Perovskite Solar Cells. Advanced Materials
2015, 27 (11), 1837-1841.
(78) Glazer, A. M. The Classification of Tilted Octahedra in Perovskites. Acta Crystallographica Section
B: Structural Crystallography and Crystal Chemistry 1972, 28 (11), 3384-3392.
141

(79) Woodward, P. M. Octahedral Tilting in Perovskites. I. Geometrical Considerations. Acta
Crystallographica Section B: Structural Science 1997, 53 (1), 32-43.
(80) Prezhdo, O. V. Multiple Excitons and the Electron–Phonon Bottleneck in Semiconductor Quantum
Dots: An Ab Initio Perspective. Chemical Physics Letters 2008, 460 (1-3), 1-9.
(81) Jankowska, J.; Long, R.; Prezhdo, O. V. Quantum Dynamics of Photogenerated Charge Carriers in
Hybrid Perovskites: Dopants, Grain Boundaries, Electric Order, and Other Realistic Aspects. ACS Energy
Letters 2017, 2 (7), 1588-1597.
(82) Chistyakov, A.; Zvaigzne, M.; Nikitenko, V.; Tameev, A.; Martynov, I.; Prezhdo, O. Optoelectronic
Properties of Semiconductor Quantum Dot Solids for Photovoltaic Applications. The Journal of Physical
Chemistry Letters 2017, 8 (17), 4129-4139.
(83) Wang, B.; Wu, Y.; Liu, D.; Vasenko, A. S.; Casanova, D.; Prezhdo, O. V. Efficient Modeling of
Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics. The
Journal of Physical Chemistry Letters 2023, 14 (37), 8289-8295.
(1) Ezzeldien, M.; Al-Qaisi, S.; Alrowaili, Z.; Alzaid, M.; Maskar, E.; Es-Smairi, A.; Vu, T. V.; Rai, D.
Electronic and Optical Properties of Bulk and Surface of CsPbBr3 Inorganic Halide Perovskite A First
Principles DFT 1/2 Approach. Scientific Reports 2021, 11 (1), 20622.
(2) Yi, Z.; Ladi, N. H.; Shai, X.; Li, H.; Shen, Y.; Wang, M. Will Organic–Inorganic Hybrid Halide Lead
Perovskites Be Eliminated from Optoelectronic Applications? Nanoscale Advances 2019, 1 (4), 1276-1289.
(3) Maafa, I. M. All-Inorganic Perovskite Solar Cells: Recent Advancements and Challenges.
Nanomaterials 2022, 12 (10), 1651.
(4) Jiao, Y.; Qin, S.; Li, B.; Hao, W.; Wang, Y.; Li, H.; Yang, Z.; Dong, D.; Li, X.; Zhao, J. Ferroelasticity
Mediated Energy Conversion in Strained Perovskite Films. Advanced Electronic Materials 2022, 8 (11),
2200415.
(5) He, Y.; Hadar, I.; Kanatzidis, M. G. Detecting Ionizing Radiation Using Halide Perovskite
Semiconductors Processed Through Solution and Alternative Methods. Nature Photonics 2022, 16 (1), 14-
26.
(6) Vescio, G.; Frieiro, J. L.; Gualdrón‐Reyes, A. F.; Hernández, S.; Mora‐Seró, I.; Garrido, B.; Cirera, A.
High Quality Inkjet Printed‐Emissive Nanocrystalline Perovskite CsPbBr3 Layers for Color Conversion
Layer and LEDs Applications. Advanced Materials Technologies 2022, 7 (7), 2101525.
(7) Kang, J.; Wang, L.-W. High Defect Tolerance in Lead Halide Perovskite CsPbBr3. The Journal of
Physical Chemistry Letters 2017, 8 (2), 489-493.
(8) Nguyen, X. T.; Winte, K.; Timmer, D.; Rakita, Y.; Ceratti, D. R.; Aharon, S.; Ramzan, M. S.; Cocchi,
C.; Lorke, M.; Jahnke, F. Phonon-Driven Intra-Exciton Rabi Oscillations in CsPbBr3 Halide Perovskites.
Nature Communications 2023, 14 (1), 1047.
142

(9) Cohen, A. V.; Egger, D. A.; Rappe, A. M.; Kronik, L. Breakdown of the Static Picture of Defect
Energetics in Halide Perovskites: the Case of the Br Vacancy in CsPbBr3. The Journal of Physical
Chemistry Letters 2019, 10 (16), 4490-4498.
(10) Chu, W.; Saidi, W. A.; Zhao, J.; Prezhdo, O. V. Soft Lattice and Defect Covalency Rationalize
Tolerance of β‐CsPbI3 Perovskite Solar Cells to Native Defects. Angewandte Chemie International Edition
2020, 59 (16), 6435-6441.
(11) Liu, D.; Wu, Y.; Vasenko, A. S.; Prezhdo, O. V. Grain Boundary Sliding and Distortion on a
Nanosecond Timescale Induce Trap States in CsPbBr3: Ab Initio Investigation with Machine Learning
Force Field. Nanoscale 2023, 15 (1), 285-293.
(12) Walsh, A. Principles of Chemical Bonding and Band Gap Engineering in Hybrid Organic–Inorganic
Halide Perovskites. The Journal of Physical Chemistry C 2015, 119 (11), 5755-5760.
(13) Liu, Y.; Long, R.; Fang, W.-H.; Prezhdo, O. V. Nuclear Quantum Effects Prolong Charge Carrier
Lifetimes in Hybrid Organic–Inorganic Perovskites. Journal of the American Chemical Society 2023, 145
(25), 14112-14123.
(14) Pandech, N.; Kongnok, T.; Palakawong, N.; Limpijumnong, S.; Lambrecht, W. R.; Jungthawan, S.
Effects of the van der Waals Interactions on Structural and Electronic Properties of CH3NH (Pb, Sn)(I, Br,
Cl)3 Halide Perovskites. ACS Omega 2020, 5 (40), 25723-25732.
(15) Huang, B.; von Rudorff, G. F.; von Lilienfeld, O. A. The Central role of density functional theory in
the AI age. Science 2023, 381 (6654), 170-175.
(16) Song, S.; Vuckovic, S.; Kim, Y.; Yu, H.; Sim, E.; Burke, K. Extending Density Functional Theory
with Near Chemical Accuracy beyond Pure Water. Nature Communications 2023, 14 (1), 799.
(17) Liu, X.; Jiao, Y.; Zheng, Y.; Jaroniec, M.; Qiao, S.-Z. Mechanism of CN Bonds Formation in
Electrocatalytic Urea Production Revealed by Ab Initio Molecular Dynamics Simulation. Nature
Communications 2022, 13 (1), 5471.
(18) Araujo, R. B.; Rodrigues, G. L.; Dos Santos, E. C.; Pettersson, L. G. Adsorption Energies on Transition
Metal Surfaces: towards An Accurate and Balanced Description. Nature Communications 2022, 13 (1),
6853.
(19) Rabiee, N.; Ahmadi, S.; Rabiee, M.; Bagherzadeh, M.; Vahabi, H.; Jouyandeh, M.; Saeb, M. R. Green
Carbon-Based Nanocomposite Biomaterials through the Lens of Microscopes. Emergent Materials 2022,
5 (3), 665-671.
(20) Chen, B. W.; Xu, L.; Mavrikakis, M. Computational Methods in Heterogeneous Catalysis. Chemical
Reviews 2020, 121 (2), 1007-1048.
(21) Yuan, D.; Zhang, Y.; Ho, W.; Wu, R. Effects of van der Waals Dispersion Interactions in Density
Functional Studies of Adsorption, Catalysis, and Tribology on Metals. The Journal of Physical Chemistry
C 2020, 124 (31), 16926-16942.
143

(22) Stöhr, M.; Tkatchenko, A. Quantum Mechanics of Proteins in Explicit Water: The Role of PlasmonLike Solute-Solvent Interactions. Science Advances 2019, 5 (12), eaax0024.
(23) Freire, R. L.; Guedes-Sobrinho, D.; Kiejna, A.; Da Silva, J. L. Comparison of the Performance of van
der Waals Dispersion Functionals in the Description of Water and Ethanol on Transition Metal Surfaces.
The Journal of Physical Chemistry C 2018, 122 (3), 1577-1588.
(24) Shirali, K.; Shelton, W. A.; Vekhter, I. Importance of van der Waals Interactions for Ab Initio Studies
of Topological Insulators. Journal of Physics: Condensed Matter 2020, 33 (3), 035702.
(25) Grimme, S. Semiempirical GGA‐Type Density Functional Constructed with a Long‐Range Dispersion
Correction. Journal of Computational Chemistry 2006, 27 (15), 1787-1799.
(26) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of
Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. The Journal of Chemical
Physics 2010, 132 (15).
(27) Tkatchenko, A.; Scheffler, M. Accurate Molecular van der Waals Interactions from Ground-State
Electron Density and Free-Atom Reference Data. Physical Review Letters 2009, 102 (7), 073005.
(28) Tkatchenko, A.; DiStasio Jr, R. A.; Car, R.; Scheffler, M. Accurate and Efficient Method for ManyBody van der Waals Interactions. Physical Review Letters 2012, 108 (23), 236402.
(29) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density
Functional Theory. Journal of Computational Chemistry 2011, 32 (7), 1456-1465.
(30) Reckien, W.; Janetzko, F.; Peintinger, M. F.; Bredow, T. Implementation of Empirical Dispersion
Corrections to Density Functional Theory for Periodic Systems. Journal of Computational Chemistry 2012,
33 (25), 2023-2031.
(31) Hirshfeld, F. L. Bonded-Atom Fragments for Describing Molecular Charge Densities. Theoretica
Chimica Acta 1977, 44, 129-138.
(32) Becker, M. A.; Vaxenburg, R.; Nedelcu, G.; Sercel, P. C.; Shabaev, A.; Mehl, M. J.; Michopoulos, J.
G.; Lambrakos, S. G.; Bernstein, N.; Lyons, J. L. Bright Triplet Excitons in Caesium Lead Halide
Perovskites. Nature 2018, 553 (7687), 189-193.
(33) Beck, H.; Gehrmann, C.; Egger, D. A. Structure and Binding in Halide Perovskites: Analysis of Static
and Dynamic Effects from Dispersion-Corrected Density Functional Theory. APL Materials 2019, 7 (2).
(34) Latimer, K.; Dwaraknath, S.; Mathew, K.; Winston, D.; Persson, K. A. Evaluation of Thermodynamic
Equations of State across Chemistry and Structure in the Materials Project. NPJ Computational Materials
2018, 4 (1), 40.
(35) Ghaithan, H. M.; Alahmed, Z. A.; Qaid, S. M.; Hezam, M.; Aldwayyan, A. S. Density functional Study
of Cubic, Tetragonal, and Orthorhombic CsPbBr3 Perovskite. ACS Omega 2020, 5 (13), 7468-7480.
144

(36) Jiang, N.; Ma, G.; Song, D.; Qiao, B.; Liang, Z.; Xu, Z.; Wageh, S.; Al Ghamdi, A. A.; Zhao, S. Defects
in Lead Halide Perovskite Light-Emitting Diodes under Electric Field: from Behavior to Passivation
Strategies. Nanoscale 2024.
(37) Li, W.; She, Y.; Vasenko, A. S.; Prezhdo, O. V. Ab Initio Nonadiabatic Molecular Dynamics of Charge
Carriers in Metal Halide Perovskites. Nanoscale 2021, 13 (23), 10239-10265.
(38) Li, W.; Sun, Y.-Y.; Li, L.; Zhou, Z.; Tang, J.; Prezhdo, O. V. Control of Charge Recombination in
Perovskites by Oxidation State of Halide Vacancy. Journal of the American Chemical Society 2018, 140
(46), 15753-15763.
(39) Agiorgousis, M. L.; Sun, Y.-Y.; Zeng, H.; Zhang, S. Strong Covalency-Induced Recombination
Centers in Perovskite Solar Cell Material CH3NH3PbI3. Journal of the American Chemical Society 2014,
136 (41), 14570-14575.
(40) Ran, J.; Wang, B.; Wu, Y.; Liu, D.; Mora Perez, C.; Vasenko, A. S.; Prezhdo, O. V. Halide Vacancies
Create No Charge Traps on Lead Halide Perovskite Surfaces but Can Generate Deep Traps in the Bulk. The
Journal of Physical Chemistry Letters 2023, 14 (26), 6028-6036.
(41) Wu, Y.; Liu, D.; Chu, W.; Wang, B.; Vasenko, A. S.; Prezhdo, O. V. Fluctuations at Metal Halide
Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis.
ACS Applied Materials & Interfaces 2022, 14 (50), 55753-55761.
(42) Brenes, R.; Eames, C.; Bulović, V.; Islam, M. S.; Stranks, S. D. The Impact of Atmosphere on the
Local Luminescence Properties of Metal Halide Perovskite Grains. Advanced Materials 2018, 30 (15),
1706208.
(43) Shi, H.; Du, M.-H. Shallow Halogen Vacancies in Halide Optoelectronic Materials. Physical Review
B 2014, 90 (17), 174103.
(44) Chu, W.; Zheng, Q.; Prezhdo, O. V.; Zhao, J.; Saidi, W. A. Low-Frequency Lattice Phonons in Halide
Perovskites Explain High Defect Tolerance toward Electron-Hole Recombination. Science Advances 2020,
6 (7), eaaw7453.
(45) Wang, B.; Chu, W.; Wu, Y.; Casanova, D.; Saidi, W. A.; Prezhdo, O. V. Electron-Volt Fluctuation of
Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale. The Journal of Physical Chemistry
Letters 2022, 13 (25), 5946-5952.
(46) Zheng, Q.; Chu, W.; Zhao, C.; Zhang, L.; Guo, H.; Wang, Y.; Jiang, X.; Zhao, J. Ab Initio Nonadiabatic
Molecular Dynamics Investigations on the Excited Carriers in Condensed Matter Systems. Wiley
Interdisciplinary Reviews: Computational Molecular Science 2019, 9 (6), e1411.
145

Abstract (if available)

Abstract This thesis explores the applications of computational chemistry and machine learning to study the behaviors and properties of inorganic materials, with a focus on metal halide perovskites and 2D materials. It centers the impact of defects in these materials on their performance, including vacancies, interstitials, and grain boundaries, and their effects on ionic conductivity and charge carrier mobility. The work also includes the examinations of the midgap trap states and ion migration in perovskites, highlighting the critical influence of van der Waals interactions. Through the application of machine learning techniques, this thesis develops predictive models for material properties, aiming to advance the understanding of metal halide perovskites for photovoltaic applications and improve the efficiency and stability of devices. This research not only leads the frontier of knowledge in computational chemistry and materials science but also sets the groundwork for significant technological advancements in renewable energy and electronics. By providing deeper insights into the atomic-level interactions within metal halide perovskites and 2D materials, this work paves the way for the development of more efficient, stable, and cost- effective photovoltaic devices and electronic applications. Ultimately, the predictive models and fundamental understanding gained through this thesis have the potential to revolutionize the design and optimization of materials for a wide range of critical applications, contributing to the global efforts in sustainable energy and environmental preservation.

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Creator Ran, Jingyi (author)

Core Title From first principles to machine intelligence: explaining charge carrier behavior in inorganic materials

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Degree Conferral Date 2024-05

Publication Date 04/17/2024

Defense Date 03/29/2024

Publisher Los Angeles, California (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag charge carrier behavior,energy solutions,inorganic materials,machine learning applications,non-adiabatic molecular dynamics,OAI-PMH Harvest

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nakano, Aiichiro (committee member), Prezhdo, Oleg (committee member), Wittig, Curt (committee member)

Creator Email jingyi.ran81@gmail.com,jran@usc.edu

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