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Computational materials design for organic optoelectronics

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COMPUTATIONAL MATERIALS DESIGN FOR ORGANIC OPTOELECTRONICS

by

Daniel Sylvinson Muthiah Ravinson

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)

December 2021

Copyright 2021 Daniel Sylvinson Muthiah Ravinson
ii

Acknowledgements

I would like to start by expressing my heartfelt gratitude to my PhD advisor and mentor,
Prof. Mark Thompson for inviting me into his wonderful research group and giving me the
opportunity to work on a range of interesting projects. I truly appreciate his unwavering support
throughout my PhD journey and for his generous guidance every time I needed it. It has been an
absolute pleasure to work under his advisement.
I would like to express my appreciation to Prof. Sri Narayan, Prof. Andrey Vilesov, Prof.
Ralf Haiges, and Prof. Aiichiro Nakano for serving on my thesis defense and qualifying/screening
exam committees and for their valuable input and feedback.
Special thanks to Prof. Peter Djurovich for his help with various aspects of my research
and for lively discussions and exchange of ideas. I would like to thank my colleagues (current and
former) at the MET group, Dr. Tyler Fleetham, Dr. Rasha Hamze, Dr. Jessica Golden, Dr.
Muazzam Idris, Dr. Shuyang Shi, Abegail Tadle, Savannah Kapper, Jie Ma, Moon Chul Jung, Dr.
Patrick Saris, Lauren Martin, Dr. Narcisse Ukwitegetse, Dr. Thilini Batagoda, Dr. Karim El Roz,
Brenda Ontiveros and Dr. John Facendola for collaboration on several projects and for their
support, guidance, and friendship. I would like to thank all MET group members for creating a fun
work environment and for their friendship and support throughout my time here.
I would like to extend my appreciation to Prof. Stephen R. Forrest, Jongchan Kim, Caleb
Coburn, Chang Ho So and Changyeong Jeong from the University of Michigan for fruitful
collaboration on several projects and helpful discussions. I would also like to thank my
collaborators at the University of Augsburg, Thomas Lampe, Tobias D. Schmidt, and Prof.
Wolfgang Brütting for working closely on OLED outcoupling related projects.
iii

I would also like to thank Judy Fong, Michelle Dea and Magnolia Benitez for
administrative help and support during my time here at USC. Special thanks to the Center for
Advanced Research Computing (CARC) at USC for providing generous access to computational
resources.
I am eternally grateful to my family: my loving parents Ravinson and Sylvia, and my
siblings, Denny and Dolly for their love, encouragement, and sustained support. I would also like
to thank all my friends in Los Angeles (Abegail, Savannah, Caroline, Tyler, Jessica, Brenda,
Cindy, Narcisse, Taylor, Muazzam, Austin, Jie and Konstantin), the Trippers and the LoTs gang
(Ram, Harish, Prasanna, Sumanth, Sivasudhan, Ritwika, Athira, Anu, Yadu, Sisira, and Sreenath)
for their love and support throughout this long journey.

iv

Table of Contents

Acknowledgements ....................................................................................................................... ii
List of Figures ............................................................................................................................. viii
List of Tables .............................................................................................................................. xiii
Abstract ....................................................................................................................................... xiv
Chapter 1. Introduction ............................................................................................................. 1
1.1. OLED device structure .................................................................................................. 1
1.2. Mechanisms of luminescence in molecules................................................................... 4
1.2.1. Fluorescence ................................................................................................................ 4
1.2.2. Phosphorescence ......................................................................................................... 5
1.2.3. TADF (Thermally activated delayed fluorescence) ................................................. 6
1.3. OLED efficiency ............................................................................................................. 6
1.4. Stability: The Blue problem .......................................................................................... 8
1.5. Molecular materials design ......................................................................................... 10
1.6. Density Functional Theory (DFT) .............................................................................. 12
1.6.1. Hohenberg-Kohn theorems ..................................................................................... 13
1.6.2. Kohn Sham Ansatz ................................................................................................... 14
1.6.3. The exchange-correlation functional ...................................................................... 16
1.6.4. Solving the Kohn Sham equations .......................................................................... 18
1.6.5. Time-dependent density functional theory (TDDFT) ........................................... 19
1.7. References ..................................................................................................................... 20
Chapter 2. Virtual screening for stable blue PhOLED host materials ............................... 24
2.1. Introduction .................................................................................................................. 24
2.2. H2P hosts ...................................................................................................................... 27
2.2.1. Computational methods: ........................................................................................... 29
v

2.2.2. Molecular search strategy ........................................................................................ 32
2.2.3. Tier 1 Selection.......................................................................................................... 34
2.2.4. Tier 2 Selection.......................................................................................................... 36
2.2.5. Tier 3 selection ......................................................................................................... 40
2.3. Spiro-linked hosts ......................................................................................................... 48
2.3.1. Library design ........................................................................................................... 48
2.3.2. Tier 1 screening ......................................................................................................... 50
2.3.3. Tier 2 screening ......................................................................................................... 52
2.4. References ..................................................................................................................... 53
Chapter 3. Machine learning to accelerate materials design for organic optoelectronics 59
3.1. Introduction .................................................................................................................. 59
3.2. Library Design .............................................................................................................. 63
3.3. QM methods.................................................................................................................. 65
3.4. ML models and features .............................................................................................. 65
3.5. Benchmarking and validating QM methods .............................................................. 69
3.6. ML workflow ................................................................................................................ 73
3.7. Results and Discussion ................................................................................................. 74
3.8. Fluorescent dopants for hybrid WOLEDs ................................................................. 77
3.9. Singlet fission chromophores....................................................................................... 80
3.10. Conclusion ................................................................................................................. 81
3.11. References .................................................................................................................. 87
Chapter 4. Accurately predicting excited state energies of BODIPY, DIPYR and MR dyes
with low-cost DFT approaches .................................................................................................. 98
4.1. Introduction .................................................................................................................. 98
4.2. Computational Methods ............................................................................................ 100
vi

4.3. Results and Discussion ............................................................................................... 100
4.4. Conclusion ................................................................................................................... 109
4.5. References ................................................................................................................... 112
Chapter 5. Accurately predicting transition dipole vectors of phosphors to understand
outcoupling in thin films ........................................................................................................... 118
5.1. Introduction ................................................................................................................ 118
5.2. SOC-TDDFT calculations ......................................................................................... 120
5.3. Understanding orientation of TDVs in homoleptic Ir complexes .......................... 122
5.4. TDVs of Pt complexes ................................................................................................ 131
5.5. References ................................................................................................................... 133
Chapter 6. Modeling the effects of solvation on the photophysical properties of
chromophores ............................................................................................................................ 138
6.1. Introduction ................................................................................................................ 138
6.2. CAAC-Cu-Cz complex ............................................................................................... 140
6.3. MAC-Cu-Amines and DAC-Cu-Amine complexes ................................................. 143
6.4. Tetradentate Pyridyl-Carbazole Platinum Complexes ........................................... 149
6.5. References ................................................................................................................... 154
Chapter 7. Kinetics of TADF and phosphorescent chromophores.................................... 158
7.1. Simplified kinetic picture of TADF (PL ~100%) .................................................. 158
7.1.1. Case 1: 𝒌𝑺 𝟏 >> kISC ............................................................................................... 160
7.1.2. Case 2: kISC >> 𝒌𝑺𝟏 ................................................................................................ 161
7.1.3. Case 3: kISC ~ 𝒌𝑺𝟏 .................................................................................................. 163
7.2. TADF kinetics of systems with PL < 100% ............................................................ 169
7.3. Emission kinetics of heavy metal based phosphors ................................................. 170
7.4. Kinetics of a general N-state emissive system .......................................................... 172
vii

7.5. Extent of spatial overlap in electronic transitions ................................................... 173
7.6. Blurring the lines between TADF and phosphorescence? ...................................... 178
7.6. References ................................................................................................................... 187

viii

List of Figures

Figure 1.1. Schematic of a typical OLED device structure. ........................................................... 2
Figure 1.2. Different mechanisms of luminescence in molecules. ................................................. 3
Figure 1.3. Bimolecular degradation events in OLEDs. (Taken from Ref.
22
) .............................. 10
Figure 2.1. Commonly used blue PhOLED hosts. ........................................................................ 24
Figure 2.2. High T1 energy bearing fragments. (T1 energies computed at the B3LYP/6-31G*
level) ............................................................................................................................................. 25
Figure 2.3. Core structures of H2P and Spiro-linked hosts. ........................................................ 26
Figure 2.4. Tiered screening of host libraries. ............................................................................. 27
Figure 2.5. Conceptual evolution of H2P design. ......................................................................... 28
Figure 2.6. (left) Elemental enumeration of O, S, NH and CH in the “P-ring” of the H2P
structure. (right) Lowest unoccupied molecular orbital energy vs. triplet energy for iterative
cyclopentaphenanthrene structures. .............................................................................................. 34
Figure 2.8. Aza-substitution patterns in Tier-2 library. ............................................................... 36
Figure 2.9. LUMO vs. triplet energy for second tier iteration of aza-substitution in phenanthrene
section the H-rings of the parent phenantho[4,5-f]imidazole. Compounds 10a-10d are illustrated
by colored circles. ......................................................................................................................... 38
Figure 2.10. Highest occupied molecular orbital and lowest unoccupied molecular orbital
diagrams calculated at the B3LYP/LACV3P** level of theory. The permanent dipole moment
for each molecule is illustrated in the images at the top. .............................................................. 40
Figure 2.11. Center of mass radial distributions [g(r)] from MD simulations of three host
materials, obtained by averaging over 30ns. ................................................................................. 41
Figure 2.12. Histogram plots showing the distribution of hole and electron hopping rates
extracted from the frontier dimer orbital splitting coupling calculations of both the exhaustive
dimer set and the smaller 20 dimer subset for the three host materials (top: 10b, middle: 10c,
bottom: 10d) .................................................................................................................................. 45
Figure 2.13. Eliminating weak exocyclic bonds by spiro linking high T1 components. .............. 48
Figure 2.14. DFT computed energy levels of SF-PCz with different aza-substitution patterns. .. 49
Figure 2.15. Prospective Spiro-linked host design space. ............................................................ 50
Figure 2.16. Tier 1 spiro-linked host library. ................................................................................ 50
ix

Figure 2.17. (top) Scatter plots of T1 against HOMO and LUMO energies for compounds in Tier-
1 sub-library. (bottom) Top 10 candidates ranked according to decreasing order of T1. ............. 51
Figure 2.18. (left to right) Schematic of Tier-2 sub-library and HOMO, LUMO and T1 densities
of XAX.......................................................................................................................................... 53
Figure 2.19. Top 20 candidates from Tier-2 screen ranked according to decreasing order of
LUMO levels. ............................................................................................................................... 53
Figure 3.1. Core structures along with the palette of substitutions for libraries A, B and C. ....... 64
Figure 3.2. GNN architecture employed in this work. .................................................................. 69
Figure 3.3. Benchmarks for DFT predicted HOMO/LUMO energies against UPS/IPES data
86
. 71
Figure 3.4. Schematic of ML workflow used in this work. .......................................................... 74
Figure 3.5. Performance of different ML models with varying training set sizes for the 3
libraries. ........................................................................................................................................ 75
Figure 3.6. (a) Schematic of hybrid WOLED architecture explored here; (b), (c) Scatter plots of
T1 and S1 energies predicted by the GNN(2000) models for libraries A and B respectively with
the region of interest highlighted; (d) Scatter plot of ML and DFT predicted HOMO and LUMO
energies for selected candidates from A and B that satisfy the hybrid WOLED design criteria
(based on ML predictions); (e), (f) Distribution of ML and DFT predicted S1 and T1 energies of
selected candidates from A and B respectively. Hollow circles indicate candidates with T2 < S1
according to DFT calculations. ..................................................................................................... 79
Figure 3.7. (a) Scatter density plots of S1 and T1 energies with the enclosing gray area indicating
the SF parametric space wherein 0 < S1 - 2T1 < 0.2 eV; (b) DFT and ML predicted S1 and T1
energies of selected candidates with gray region as in (a) highlighting the space satisfying the SF
criteria. .......................................................................................................................................... 81
Figure 3.8. Scatter matrix plots of properties predicted by the GNN(2000) model for library A. 82
Figure 3.9. Scatter matrix plots of properties predicted by the GNN(2000) model for library B. 83
Figure 3.10. Scatter matrix plots of properties predicted by the GNN(2000) model for library C.
....................................................................................................................................................... 83
Figure 3.11. Potential fluorescent dopants for WOLEDs obtained by screening library A using
the GNN(2000) model and validated by DFT. ............................................................................. 84
Figure 3.12. Potential fluorescent dopants for WOLEDs obtained by screening library B using
the GNN(2000) model and validated by DFT. ............................................................................. 85
x

Figure 3.13. Potential singlet fission candidates in library C predicted by the GNN(2000) model
and validated by DFT.................................................................................................................... 86
Figure 4.1. Chemical structures of the 35 BODIPY-based dyes (a) and MR dyes (b) considered
in this study. ................................................................................................................................ 101
Figure 4.2. Functional dependence on the accuracy of the ROKS (a,c) and SF-TDDFT (b,d)
methods for the BODIPY (top) and MR (bottom) dyes. The number atop each bar represents the
R
2
values for each corresponding functional. (MAEs are reported in eV) ................................. 103
Figure 4.3. Comparison of the predictions of E(S1) using the TDA (a), TDDFT (b) ROKS (c) and
SF-TDDFT (d) methods using the B3LYP functional against experimental values. (All values in
eV)............................................................................................................................................... 104
Figure 4.4. Comparison of the predictions of E(T1) using TDA (a), TDDFT (b) and SF-TDDFT
(c) methods using the B3LYP functional with experimental values. (All values in eV) ............ 105
Figure 4.5. Dependence of the separation between the transition energy predictions of TDDFT
and those of SF-TDDFT (a) and ADC(3) (b) on corresponding Ω values. ................................ 106
Figure 5.1. Dissipation of radiation via different optical modes in OLEDs for 3 TDV alignment
scenarios: (a) 𝚯 = 0.33 (isotropic) (b) 𝚯 = 0 (horizontal), and (c) 𝚯 = 1 (vertical). (Taken from
Ref.
1
) ........................................................................................................................................... 119
Figure 5.2. The values of δ calculated using SOC-TDDFT for the Ir complexes studied here.
*Experimentally observed δ reported in
30
. ................................................................................ 123
Figure 5.3. Orientation of Ir(ppy)3, Ir(chpy)3, Ir(piq)3 and Ir(phq)3 (clockwise from left) with C3
axis perpendicular to the substrate. (Substrate is assumed to lie perpendicular to the plane of the
paper) .......................................................................................................................................... 124
Figure 5.4. Dependence of 𝚯 on δ for bis-cyclometallated and homoleptic facial tris-
cyclopetallated Ir complexes when their respective C2 and C3 axes are oriented perpendicular to
the substrate based on anisotropy factor simulations. (Taken from Ref.
31
) ................................ 127
Figure 5.5. Structures of newly developed complexes
32
along with calculated δ values. (Ir(ppy)3
and Ir(ppyCF3)3 are shown for reference) ................................................................................... 128
Figure 5.6. Structures of complexes reported by Kim et al.
8
...................................................... 129
Figure 5.7. (a) Observed trend between Θ and aspect ratio for the complexes studied here.
32
(b)
Esp plots of the Ir complexes calculated at the B3LYP/LACVP* level. (c) Computed aspect
ratios. ........................................................................................................................................... 130
xi

Figure 5.8. Computed TDVs and measured Θ of Pt complexes reported in Ref.
33
. ................... 131
Figure 5.9. (a) Chemical structure of PtD. (b) Crystal structure of PtD. (c) Computed TDV of
emission from the 3.35-dimer. (d) Computed energies and oscillator strengths of the triplet
sublevels for both PtD dimers. .................................................................................................... 133
Figure 6.1. Chemical structures of a sampling of complexes studied here. ................................ 138
Figure 6.2. Comparison of vertical excitation energies (in eV) of CAAC-Cu-Cz predicted by
TDDFT using the B3LYP and CAM-B3LYP functionals with experimental data.
1
.................. 140
Figure 6.3. (left) Excitation and emission spectra of CAAC-Cu-Cz in different media. (right)
Emission spectra in 77 K and room temperature (RT). (Adapted from Ref.
1
) ........................... 141
Figure 6.4. Histogram of T1 energies computed for 50 snapshots of the NPT MD run at 300K.
..................................................................................................................................................... 143
Figure 6.5. Structures of MAC/DAC-Cu-Cz complexes (Taken from Ref.
3
). ........................... 143
Figure 6.6. Energy diagram of the
3
Cz states (black),
3
CT states at RT (red) and 77 K (blue) of
complexes 1-4 in 2-MeTHF. ....................................................................................................... 149
Figure 6.7. Emission spectra of PtNON in different media. (Adapted from Ref.
22
) .................. 149
Figure 6.8. Top row: molecular structure of PtNON derivatives. Middle row: LUMO densities
and energies. Bottom row: HOMO densities and energies. DFT calculations were performed at
the B3LYP / LACVP** level. .................................................................................................... 150
Figure 6.9. Natural transition orbitals for the CT (bottom) and LE (top) states in PtNON
derivatives. Blue and red plots refer to hole and electron densities respectively for each
transition. .................................................................................................................................... 153
Figure 7.1. The full kinetic scheme for emission via TADF is shown to the left, where 𝑘 1 , 𝑘 −
1 , 𝑘𝑇 1 and kTnr characterize ISC transitions. The rate constant for TADF (𝑘𝑇𝐴𝐷𝐹 ) is for the
process illustrated by the green arrow. The simplified scheme to the right was generated
assuming PL>0.9 (kr >> knr) and 𝑘𝑇 1<< 𝑘 1 , 𝑘 − 1 , 𝑘𝑆 1. (Taken from Ref.
1
) ...................... 159
Figure 7.3. Kinetic schemes for heavy metal-based phosphors and organic TADF emitters. Note
that the assumption here is that the emission takes place with a luminescence efficiency
approaching 100% in both cases, so nonradiative pathways are not considered. (Taken from
Ref.
1
) ........................................................................................................................................... 170
Figure 7.4. Relationship between experimental kTADF, ΔEST and Λ for the compounds presented
above. .......................................................................................................................................... 176
xii

Table 7.1. Values of kTADF, ΔEST and 𝚲 for the compounds considered above. .......................... 177
Figure 7.5. Dependence of luminescence lifetime on temperature for Ir complexes considered
here. (Data for Ir carbene complexes collected by Dr. Muazzam Idris
65
; Data for fac-Ir(ppy)3
taken from Ref.
66
) ....................................................................................................................... 179
Figure 7.6. Dependence of luminescence lifetime on temperature for Ir complexes considered
here based on the SOC-TDDFT calculations.............................................................................. 183
Figure 7.7. Major contributions of Sn states to triplet sublevels. ............................................... 185

xiii

List of Tables

Table 2.1. Summary of calculated and experimental physical properties for 10b, 10c and 10c. . 39
Table 2.2. Number of - contacts and calculated mobilities for 10b, 10c and 10c. .................. 46
Table 2.3. Efficiency parameters of the OLEDs for 10b, 10c and 10d. (ηr was computed
assuming 𝝌 =1 and 𝜼 𝐞 = 0.2) ........................................................................................................ 47
Table 3.1: Comparison of DFT predicted values with experimentally reported values of relevant
properties for related compounds.................................................................................................. 72
Table 3.2. Error metrics of GNN models trained on 1000, 1500 and 2000 molecules for the 3
libraries on a test set of 450 structures each. The last 3 columns refer to the percentage of
molecules in the test set featuring errors below 0.10, 0.15 and 0.20 eV. ..................................... 76
Table 4.1: MAE (eV) and R2 values associated with the predictions of E(S1) and E(T1) using the
different DFT methods studied in this work at the B3LYP/6-31G(d,p) level ............................ 102
Table 4.2. Summary of ROKS, TDA, TDDFT, SF-TDDFT calculations at the B3LYP/6-
31G(d,p) level. (All energies in eV). .......................................................................................... 109
Table 4.3. Summary of ADC(3)/6-31G(d,p) calculations. (All energies in eV). ....................... 111
Table 6.1. Dipole moment () of complexes 1-6 in ground state (S0), lowest ligand-excited state
(
3
Cz) and excited ICT states. ...................................................................................................... 145
Table 6.2. Natural transition orbitals (NTO) of complex 1-6 in gas phase. ............................... 147
Table 6.3. Excited triplet state energies and dipole moments of the complexes computed using
TDDFT. (T1 and T2 energies were obtained from TD-DFT (CAM-B3LYP/LACVP**) using the
IEFPCM solvation model for THF in the equilibrium and non-equilibrium limit.) ................... 154
Table 7.2. Fit parameters for 3-state triplet model and 4-state TADF model. ............................ 180
Table 7.3. SOC-TDDFT computed energies, f and lifetime for relevant states.......................... 181
Table 7.4. Emission contribution and occupancy of each state based on kinetic models. (Note
that fac-Ir(ppy)
3 is fit to the triplet 3-state model based on data from Ref.
66
).
........................... 186

xiv

Abstract

The field of organic optoelectronics has garnered a lot of interest in recent decades due to
rapid advances in the development of organic light-emitting diodes (OLEDs), organic
photovoltaics (OPVs), optoelectronic sensors, etc. Among them, OLED technologies have
advanced into the realm of commercialization and have been successfully incorporated into a wide
array of color display and lighting products. While OLEDs have several favorable attributes over
traditional display/lighting technologies like amenability to flexible form-factors, high color purity
and contrast, they are plagued by low stability especially for the blue component. Molecular
degradation events during device operation have been identified as the main culprit for the low
stability. Therefore, there is a strong desire to design molecular materials that are robust to such
degradation events but can still be successfully incorporated into efficient OLED device
architectures.
The traditional chemical design process that relies on trial and error, human intuition and
sometimes serendipity is cumbersome and highly resource intensive. Recent advances in
high-performance computing and the development of efficient and accurate molecular modeling
methods and programs have led to increased utilization of computational tools in the chemical
design process in several fields especially drug design, catalysis, semiconductors among others.
Further, the development of data-driven approaches like machine learning has further helped
accelerate the design process. However, the adoption of such approaches in the field of organic
optoelectronics has remained limited and has only recently started to gain traction. Here, we
present the development and application of efficient virtual screening workflows that incorporate
both first principles based multi-scale materials modeling and data-driven machine learning
approaches to aid the design of novel molecular materials particularly for OLEDs. The same
xv

workflows can also be extended to other optoelectronics applications. We also employ
computational approaches to gain deeper insights into the underlying mechanisms of
photo-physical and electronic processes in molecular materials to further inform the design
process.
The basic concepts of electroluminescence and OLEDs are introduced in Chapter 1 along
with a brief description of density functional theory (DFT) which is used extensively throughout
this work to predict key molecular properties. The development of efficient virtual screening
workflows to identify stable host materials for blue phosphorescence-based OLEDs (PhOLEDs)
is presented in Chapter 2. The workflow involves a multi-scale modeling approach incorporating
DFT, molecular dynamics (MD) simulations and charge transport calculations. In Chapter 3, we
introduce new screening workflows for molecular materials that are accelerated by machine
learning methods. We also present a new graph neural network (GNN) model that efficiently
encodes 3D molecular structure and achieves high prediction accuracies comparable with state-of-
the-art deep learning models.
Chapter 4 tackles a long-standing challenge of accurately predicting the excited state
energies of two important classes of chromophores that are crucial for several organic
optoelectronics applications: BODIPYs and MR-TADF dyes. We identified two low-cost DFT
approaches namely, restricted open-shell Kohn Sham (ROKS) and spin-flip time-dependent DFT
(SF-TDDFT) to accurately model the excited states of these compounds through a thorough
benchmarking study across a large collection of compounds.
In Chapter 5, we employ TDDFT calculations that incorporate spin-orbit coupling
(SOC-TDDFT) to compute the transition dipole vectors (TDVs) associated with phosphorescent
emission in Ir and Pt complexes with the goal of understanding their alignment in thin films and
xvi

their consequent impact on light outcoupling efficiency which is a crucial parameter that impacts
OLED performance. The effects of solvation on the photophysical properties of highly
solvatochromic chromophores are explored in Chapter 6 using both implicit and explicit solvation
models. Finally in Chapter 7, we discuss the kinetics of TADF and phosphorescent luminophores
in detail. We use simple kinetic schemes and DFT calculations to understand their luminescence
mechanisms and inform the design of luminophores that feature fast radiative rates.

1

Chapter 1. Introduction

The commercial development of organic light-emitting diodes (OLEDs) has transformed
the field of organic optoelectronics from what was initially academic curiosity into the realm of
cutting-edge technology solutions. While OLEDs have garnered most of the attention, other
optoelectronics technologies like organic photovoltaics (OPVs), optoelectronic sensors, etc. have
also seen rapid advancement over time.
The discovery of efficient phosphorescence-based electroluminescence at the turn of the
21
st
century enabled OLEDs to emerge as a commercially viable alternative to inorganic LEDs for
high-performance display (mobile, television etc.) and solid-state lighting applications.
1-4
OLEDs
have several attractive attributes like high efficiency, brightness, contrast, color purity and fast
refresh rates. They can also be designed to be thin, flexible and transparent enabling their adoption
in several niche applications like rollable display panels, smart windows, etc.

1.1. OLED device structure
In its typical configuration, a monochromatic OLED device consists of one or more thin
(10-100 nm) organic layers sandwiched between two electrodes as depicted in Figure 1.1. The
emissive layer typically contains an emissive dye referred to as the “dopant” dispersed in an
amorphous organic matrix referred to as the “host”. The primary reason for such a design is to
prevent aggregation of the dopants which can lead to emission quenching. Although, devices with
neat films used as emissive layers have been reported, they are less common and tend to be less
efficient. The emissive layer is usually surrounded by an electron transport layer (ETL) at the
cathode side and a hole transport layer (HTL) at the anode end that perform their respective
eponymous functions i.e., they facilitate the transport of electrons and holes respectively into the
2

emissive layer. Consequently, the ETL and HTL are composed of electron-rich and
electron-deficient organic materials respectively (See Figure 1.1 for examples). The anode is made
up of a transparent material like ITO (indium tin oxide) while the cathode is often a metal like Ag,
Al, etc. In a typical OLED stack, each of these layers are sequentially deposited either via vacuum
deposition or solution-processing onto a transparent substrate like glass as shown in Figure 1.1.
Most commercial OLED stacks employ much more complicated device architectures featuring
multiple emissive and transport layers, electron/hole/exciton blocking layers, electron/hole
injection layers, charge generation layers etc.

Figure 1.1. Schematic of a typical OLED device structure.

During device operation, electrons and holes are injected into the device from the cathode
3

and anode respectively. The electrons and holes then make their way into the emissive layer
through the transport layers following which they can recombine with each other to form excitons
either on the host or directly on the dopant depending on the alignment of their corresponding
transport levels. The resulting excitons are then transformed into photons at a dopant molecule.
The recombination events at the emissive layer result in a 1:3 mixture of singlet and triplet
excitons by virtue of the fermionic nature of the electrons and holes. The partitioning is a
consequence of the availability of 3 near-degenerate sublevels for the lowest molecular triplet (T1)
state and just one lowest singlet (S1) level in closed-shell molecules (Figure 1.2). The type of
dopant used determines what fraction of the excitons may be harvested into light as discussed
below.

Figure 1.2. Different mechanisms of luminescence in molecules.
4

1.2. Mechanisms of luminescence in molecules
Dopants and luminescent dyes in general can be classified based on the mechanism of
radiative emission into 3 main categories: fluorescence, phosphorescence, TADF (Thermally
activated delayed fluorescence). Other modes of emission like TTA (triplet-triplet annihilation)
up-conversion are less commonly employed in OLEDs and are therefore ignored here. Before
delving into the different modes, it is instructive to discuss the factors that affect the probability of
emission between any two states in a molecule. According to Fermi’s golden rule, the rate of
emission due to transition between two states Ψ
𝑖 and Ψ
𝑓 in a homogenous medium within the
dipole approximation is given by the following expression:
𝑘 𝑒𝑚
( 𝜔 )=
4𝛼 𝜔 3
𝑛 |⟨Ψ
𝑖 |𝐫 |Ψ
𝑓 ⟩|
2
3𝑐 2
( 1.1)

In the above expression, 𝛼 ,𝑐 ,𝜔 and 𝑛 denote the fine-structure constant, speed of light,
emission frequency and refractive index respectively. The integral term, ⟨Ψ
𝑖 |𝐫 |Ψ
𝑓 ⟩ is the transition
dipole moment integral (𝑀 𝑖 𝑓 ) between the 2 states that dictates the probability of emission. Within
the Franck Condon approximation, the vibrational levels can be decoupled from the electronic
state and the transition dipole moment can be written as
𝑀 𝑖 ,𝑣 𝑓 ,𝑣 ′
= ⟨ϕ
𝑖 |𝐫 |ϕ
𝑓 ⟩⟨𝜓 𝑣 𝑖 |𝜓 𝑣 ′
𝑓 ⟩ = 𝜇 𝑖 𝑓 𝑆 𝑣 𝑖 𝑣 ′
𝑓 ( 1.2)
The first term in the expression denotes the electronic transition dipole moment between
the electronic states (𝜇 𝑖 𝑓 ) and 𝑆 𝑣 𝑖 𝑣 ′
𝑓 is the Franck Condon factor for the vibronic levels.

1.2.1. Fluorescence
Fluorescence refers to direct radiative emission exclusively due to deexcitation from the S1
state down to the S0 ground state. This is the mode of emission in most purely organic dyes (Figure
5

1.2). This is a spin-allowed transition as the net change in spin of the system is zero during the
transition (ΔS = 0). The process as a result can typically be very fast and occurs in the nanosecond
(ns) timescale if the transition is also symmetry allowed. Such purely organic systems have
negligible spin-orbit coupling (SOC) due to the absence of heavy atoms. In the absence of SOC,
transitions between states of different spins (ex: S1→T1, T1→S0) are formally forbidden (𝜇 𝑇 1
𝑆 0
= 0)
and therefore the triplet states are dark states in such systems with negligibly small emission rates.
If a fluorescent organic dye is used as the dopant in an OLED, only the electrogenerated
singlet excitons (25%) may be harvested into light as emission from the T 1 state is forbidden in
such systems. The triplet excitons formed are dissipated via non-radiative channels as heat and
consequently the maximum achievable quantum efficiency for such systems, referred to as
fluorescent OLEDs (Fl-OLEDs) is capped at 25%. These were the earliest OLEDs that were
developed.
5

1.2.2. Phosphorescence
This is the mechanism of emission in several heavy metal (Ir, Pt, Ru etc.) complexes. The
presence of the heavy atom/s increases SOC in these systems and as a result the rate of emission
from the T1 state is greatly enhanced (𝜇 𝑇 1
𝑆 0
≠ 0). This also increases the ISC rate from the S1 to the
lower-lying T1 state which often outcompetes the rate of emission from the S1 state. Therefore, the
emission now becomes largely dominated by the T1→S0 transition. Phosphorescence in such heavy
metal complexes occurs in the μs timescale and a few examples of such systems are shown in
Figure 1.2.
OLEDs that employ phosphorescent dopants (henceforth referred to as PhOLEDs) can
reach a theoretical internal quantum efficiency (IQE) of 100% as both singlet and triplet excitons
6

can be harvested into light. The triplet excitons are directly transformed into photons via radiation
from the T1 state while the singlet excitons undergo fast ISC into the triplet state resulting in
emission. The discovery of high efficiency phosphorescence-based electroluminescence was the
key breakthrough that enabled commercialization of OLEDs.
1-4, 6, 7

1.2.3. TADF (Thermally activated delayed fluorescence)
This mode of emission can occur in systems that have very small S1-T1 gaps (<300 meV)
that enable rapid ISC between the S1 and T1 states back and forth at ambient temperature ultimately
resulting in emission from the faster S1 state. The overall process occurs in the μs timescale
comparable with heavy metal phosphorescence. TADF systems can also achieve 100% IQE when
incorporated as dopant in OLEDs as the electrogenerated triplet excitons can thermalize into the
S1 state leading to emission in addition to direct emission from the singlet excitons. Since the
demonstration of this principle by Adachi et al.
8-11
, interest in TADF systems has grown rapidly.
The S1-T1 energy gap in molecular systems can be minimized by reducing the overlap between the
orbitals that contribute to the S1/T1 transitions. However, this can also result in a reduction of the
radiative rate of the S1 state (equation 1.1) and therefore a lot of research in this area has been
aimed at designing systems that optimally balance the two competing parameters to achieve fast
overall emission rates.

1.3. OLED efficiency
A key metric that determines the performance of an OLED device is its external quantum
efficiency (EQE), ηex which is defined as the ratio of the number of photons generated to the
number of electron/hole pairs injected into the device. The ideal OLED would have an EQE of
7

unity where every electron/hole pair is eventually turned into a photon that makes it out of the
device. However, in the real world there are several factors that limit the efficiency to well below
unity. The EQE can be broken down into 4 main factors as shown in the following expression:
𝜂 𝑒𝑥
= 𝜂 𝑟𝑒𝑐
𝜒 Φ
𝑃𝐿
𝜂 𝑜𝑢𝑡 = 𝜂 𝑖𝑛𝑡 𝜂 𝑜𝑢𝑡 ( 1.3)
The first term, 𝜂 𝑟𝑒𝑐
in the above expression is the recombination efficiency that represents
the fraction of recombination events that occur for every electron/hole pair injected. This factor
can be maximized to unity by designing device architectures with low injection barriers and
preventing charge leakage by using blocking layers.
12-16

The second term, 𝜒 accounts for the fraction of usable excitons that are generated in the
device. For a purely fluorescence-based OLED, this factor is capped at 25% since only the singlet
excitons can be utilized. For TADF and Phosphorescence-based OLEDs, this factor is unity
(100%), since both singlet (25%) and triplet (75%) excitons that are electrogenerated can be
effectively converted into radiation as discussed above.
The penultimate term, Φ
𝑃𝐿
is the photoluminescent quantum yield of the emissive layer in
the device i.e., the ratio of photons generated to the number of usable excitons formed in the device.
It can also be defined according to the following expression:
Φ
𝑃𝐿
=
𝑘 𝑟 𝑘 𝑟 + 𝑘 𝑛𝑟
( 1.4)
In the above equation, 𝑘 𝑟 and 𝑘 𝑛𝑟
are the radiative and non-radiative rates of the emitter in
the device. In addition to the intrinsic radiative rate of the emitter, the effective radiative rate, 𝑘 𝑟
is strongly affected by external factors like the Purcell effect that is operational due to the emitter
being enclosed within an optical cavity formed by the partially/completely reflective
electrodes.
17
𝑘 𝑛𝑟
on the other hand is affected by factors like thermal loss to the ground state via
vibronic coupling, quenching due to aggregation/excimers, etc. Several fluorescent,
8

phosphorescent and TADF emitters with photoluminescent quantum yields approaching unity have
been reported. Ir(ppy)3 is an example of a green phosphorescent dopant that can achieve quantum
yield close to unity when doped in an appropriate host like CBP at low concentrations.
6

The three terms described above are often grouped together and referred to as the internal
quantum efficiency (IQE) of the OLED, denoted by 𝜂 𝑖𝑛𝑡 . The final term in equation (1.3), 𝜂 𝑜𝑢𝑡 is
the outcoupling efficiency that represents the fraction of light generated within the device that can
be extracted out to reach the external world. There are several optical modes that prevent light
from leaving the device like substrate modes caused by total internal reflection at the substrate/air
interface, waveguided modes across the high refractive index organic layers and near-field
coupling to surface plasmon polaritons (SPP) at the metallic cathode interface.
18
For a
conventional OLED without any outcoupling enhancement techniques, 𝜂 𝑜𝑢𝑡 ≈ 20% and this is
the major factor that limits the efficiency. Developing techniques to increase 𝜂 𝑜𝑢𝑡 is an active area
of research and to this end several schemes have been developed like attaching macroscopic lens
arrays to the substrate, employing optimally aligned dopants, etc.
19
(This is discussed in more
detail in Chapter 5).

1.4. Stability: The Blue problem
In addition to achieving high efficiency, OLEDs must also maintain high operational
stability to be competitive with other lighting/display technologies. Achieving long operational
lifespan has been a major challenge especially for blue OLEDs. While red and green
phosphorescence-based OLEDs have reached a level of operational stability to be commercially
viable, the same is not true for blue PhOLEDs and TADF-OLEDs. Blue Fl-OLEDs can achieve
longer operational lifetimes but as discussed earlier are limited in efficiency. Therefore, the
9

development of stable blue phosphorescence/TADF-based OLEDs is an active area of research
and development.
There are several factors that can affect stability of a device like non-optimal device
architectures, contamination by impurities/moisture/air, chemical and phase instability of materials
used etc. While several of these factors can be easily mitigated, the main challenge that remains is
the chemical instability of the organic materials especially in the emissive layer during device
operation.
While there are many processes that can lead to chemical degradation during device
operation, the two main processes that are postulated to be the main culprits are triplet-triplet
annihilation (TTA) and triplet-polaron annihilation (TPA).
20, 21
These are bimolecular
recombination events wherein two triplet excitons in the case of the former or a triplet-polaron pair
in the latter case can combine to create a high energy excited state on one of the molecules as
shown in Figure 1.3. This high energy excited state can now lead to molecular degradation via
bond-breakage, rearrangement etc. The reason for the low stability of blue OLEDs relative to the
other colors is now apparent as blue excitons bear significantly higher energies (>2.65 eV) and
therefore the consequent TTA and TPA processes create even higher energy species compared to
red/green excitons. Therefore, the development of robust dopant and host materials devoid of weak
bonds and unstable moieties is an active area of research aimed at solving the “blue problem”. (See
Chapter 2)
Another complimentary approach to limit degradation by TTA/TPA events is to design
TADF/phosphorescent dopants that have very fast radiative rates so that the excitons that are
formed are rapidly transformed into photons reducing their likelihood to engage in these
bimolecular processes. This has been the main motivation to develop phosphorescent/TADF dyes
10

that feature fast radiative rates and correspondingly lifetimes pushing towards the ns regime.

Figure 1.3. Bimolecular degradation events in OLEDs. (Taken from Ref.
22
)

1.5. Molecular materials design
The design of molecular materials for OLEDs and optoelectronics in general involves
optimization of several material properties simultaneously. The key parameters that are crucial for
optoelectronic applications include molecular dipole moment, frontier molecular orbital energies
(HOMO/LUMO), excited state (Sn, Tn) energies and secondary properties like oscillator strengths,
state dipole moment vectors and transition dipole vectors among others. Further, bulk material
properties like electron/hole mobility, molecular aggregation/packing etc. are crucial especially for
hosts and charge transport materials. Other properties like bond dissociation energies of constituent
bonds of the molecules in their ground state, ionic states (i.e., when they are carrying
electrons/holes), excited states may be useful in gauging their chemical stability under device
11

operation. The traditional trial and error approach of synthesizing and characterizing a large
collection of materials either randomly or with some human intuition with the hope of eventually
arriving at a candidate with the optimal set of parameters is highly inefficient and time-consuming
given the almost infinitely large chemical design space that is available. Alternatively, using
computational tools to screen large libraries of materials is a very attractive proposition to
accelerate the materials design process. Such approaches have proven to be very successful in the
design of pharmaceuticals, catalysis etc.
Key molecular properties relevant for optoelectronics applications like HOMO/LUMO
energies, excited state energies, etc. can be computed using quantum mechanics based electronic
structure methods like Hartree-Fock, density functional theory (DFT), Coupled cluster methods
etc. Of the several electronic structure methods that have been developed to date, DFT is by far
the most popular method due to its ability achieve high accuracy at relatively low computational
cost. Bulk material properties like electron/hole mobilities can be computed using hybrid multi-
scale approaches that employ classical Newtonian methods like molecular dynamics (MD)
simulations to model large-scale material morphology while relying on more computationally
intensive quantum mechanics methods like DFT to compute key parameters at the molecular level.
Chapter 2 describes this approach in more detail. The screening workflow can be further
accelerated by using machine learning approaches especially when dealing with large libraries as
discussed in Chapter 3.
Further, electronic structure methods like DFT can also be used to gain detailed insights
into new classes of molecular materials and their optoelectronic properties which can then be used
to deduce molecular design rules to inform the materials design process. Throughout this thesis,
DFT is used extensively both as a computational screening tool as well as to understand the
12

optoelectronic properties of novel materials. Therefore, a brief theoretical description of DFT is
provided below.

1.6. Density Functional Theory (DFT)
Density functional theory (DFT) has emerged as the most popular electronic structure
method due to its ability to achieve high predictive accuracy for most chemical systems at low
computational cost. The favorable ~N
3
scaling of DFT makes it very attractive in modeling
moderately sized systems (<500 atoms) and as a result has become the workhorse of the
computational tool kit. The fundamental principle behind DFT is that the energy and all other
properties of an electronic system can be expressed in terms of its electron probability density (𝜌 ).
The main advantage of this approach over wavefunction-based approaches is that the electron
density is just a three-dimensional function whereas in the latter case, all electronic properties need
to be expressed in terms of a 3N dimensional function with further imposition of constraints to
ensure they are anti-symmetric.
DFT like most electronic structure methods is a general formalism that deals with
electronic systems that are described by the non-relativistic electronic Schrödinger equation in the
Born-Oppenheimer approximation:
𝑯 ̂
𝜳 ( 𝐫 )= 𝑬𝜳 ( 𝐫 ) ( 1.5)
The Hamiltonian (𝑯 ̂
) in the above equation is given by
𝑯 ̂
= −∑
𝟏 𝟐 𝑵 𝒊 𝛁 𝒊 𝟐 − ∑∑
𝒁 𝒎 |𝒓 𝒊 − 𝒓 𝑰 |
+
𝟏 𝟐 ∑
𝟏 |𝒓 𝒊 − 𝒓 𝒋 |
𝑵 𝒊 ≠𝒋 𝑴 𝑰 𝑵 𝒊 ( 1.6)
The first term in the Hamiltonian describes the electronic kinetic energy while the last term
denotes the electronic repulsion interactions and the term in the middle represents the coulombic
13

interactions between the electrons and the nuclei in a general N-electrons, M-nuclei chemical
system. Note that the Hamiltonian is written in atomic units for the sake of simplicity. The
electronic wavefunction of the system, 𝚿 ( 𝐫 ) depends on the spatial coordinates of every electron
in the system (𝐫 = 𝒓 𝟏 ,𝒓 𝟐 ,…𝒓 𝑵 ) and is therefore a 3N-dimensional function (excluding spin
components). Therefore, while equation (1.5) can be numerically solved for small systems like H2,
He, etc., it becomes prohibitively expensive for larger systems. The DFT formalism provides a
workable solution to this problem as described below.

1.6.1. Hohenberg-Kohn theorems
The DFT formalism depends on the validity of two fundamental theorems referred to as
the Hohenberg-Kohn theorems.
23
The first theorem states that the ground-state energy of a system
of interacting electrons in an external potential is uniquely determined by the ground state electron
density. Consequently, for a system of electrons in a potential due to the stationary nuclei 𝒗 ( 𝒓 )=
∑
𝒁 𝒎 |𝒓 − 𝒓 𝑰 |
𝑴 𝑰 , we can define the electronic energy functional as:
𝑬 [𝝆 ] = 𝑻 [𝝆 ] + 𝑽 𝒆𝒆
[𝝆 ] + ∫𝝆 ( 𝐫 ) 𝒗 ( 𝐫 ) 𝒅 𝐫 ( 1.7)
In the above expression, 𝑻 [𝝆 ] and 𝑽 𝒆𝒆
[𝝆 ] represent the kinetic energy and
electron-electron coulombic repulsion energy functionals of the system.
The second theorem states that for a trial density 𝝆 ′ , the corresponding energy functional
𝑬 [𝝆 ′] cannot be lower than the ground state energy of the system. i.e.
𝑬 [𝝆 ′
] ≥ 𝑬 𝟎 ( 1.8)
Therefore, the theorems suggest that the ground state energy of the system can be obtained
by minimizing the energy functional (𝑬 [𝝆 ]) using a variational procedure. Further, we know that
14

the electron density 𝝆 ( 𝐫 ) must integrate to the total number of electrons in the system (N):
∫𝝆 ( 𝐫 ) 𝒅 𝐫 = 𝑁 ( 1.9)
Therefore, the minimization condition for the energy functional subject to the above
constraint can be given by
𝜹 ( 𝑬 [𝝆 ] − 𝝀 ∫𝝆 ( 𝐫 ) 𝒅 𝐫 )= 𝟎 ( 1.10)
where the Lagrange multiplier 𝝀 can be written as
𝝀 =
𝜹𝑬 [𝝆 ]
𝜹𝝆 ( 𝐫 )
= 𝒗 ( 𝐫 )+
𝜹𝑻 [𝝆 ]
𝜹𝝆 ( 𝐫 )
+
𝜹 𝑽 𝒆𝒆
[𝝆 ]
𝜹𝝆 ( 𝐫 )
( 1.11)
The formal proofs for the theorems were provided by P. Hohenberg and W. Kohn in 1964.
23

1.6.2. Kohn Sham Ansatz
In 1965, Walter Kohn and Lu Jeu Sham posited that if one were to devise a system of N
non-interacting electrons in an external fictitious potential 𝒗 ′( 𝐫 ) but has the same electron density
𝝆 ( 𝐫 ) as a real system of N interacting electrons then in accordance with the Hohenberg Kohn
theorems, the ground state energy and corresponding properties would be identical.
The Hamiltonian for the fictitious system can be written as just the sum of the Hamiltonians
of the individual electrons:
𝑯 ̂
𝒇𝒊𝒄𝒕 = ∑𝑯 ̂
𝒊 𝑲𝑺
𝑵 𝒊 = ∑−
𝑵 𝒊 𝟏 𝟐 𝛁 𝒊 𝟐 + 𝒗 ′
( 𝒓 𝒊 ) ( 1.12)
The corresponding eigenfunctions of the one-electron Hamiltonians 𝑯 ̂
𝒊 𝑲𝑺
referred to as the
Kohn-Sham wavefunctions 𝚿 𝒊 𝑲𝑺
can be obtained by solving each of the N one-electron
Schrödinger equations separately:
𝑯 ̂
𝒊 𝑲𝑺
𝚿 𝒊 𝑲𝑺
= 𝜺 𝒊 𝑲𝑺
𝚿 𝒊 𝑲𝑺
( 1.13)
15

The total electron density of the entire fictitious system 𝝆 ( 𝐫 ) can then be given by
𝝆 ( 𝐫 )= ∑|𝚿 𝒊 𝑲𝑺
( 𝐫 ) |
2
𝑁 𝑖 ( 1.14)
Adding the kinetic and coulombic interaction terms of the fictitious system on both sides
of equation (1.7) gives
𝑬 [𝝆 ] + 𝑻 𝒇𝒊𝒄𝒕 [𝝆 ] + 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ] = 𝑻 [𝝆 ] + 𝑽 𝒆𝒆
[𝝆 ] + ∫𝝆 ( 𝐫 ) 𝒗 ( 𝐫 ) 𝒅 𝐫 + 𝑻 𝒇𝒊𝒄𝒕 [𝝆 ] + 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ]
As noted earlier, the electron density 𝝆 is taken to be identical for both the real interacting
system and fictitious non-interacting system. Rearranging the terms in the above equation leads
to the following
𝑬 [𝝆 ] = 𝑻 𝒇𝒊𝒄𝒕 [𝝆 ] + 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ] + ∫𝝆 ( 𝐫 ) 𝒗 ( 𝐫 ) 𝒅 𝐫 + 𝑬 𝑿𝑪
[𝝆 ] ( 1.15)
where 𝑬 𝑿𝑪
[𝝆 ] = 𝑻 [𝝆 ] + 𝑽 𝒆𝒆
[𝝆 ] − 𝑻 𝒇𝒊𝒄𝒕 [𝝆 ] − 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ]
Applying the minimization condition to the above energy functional with the constraint on
the electron density (equation 1.9) as done earlier gives
𝝀 =
𝜹𝑬 [𝝆 ]
𝜹𝝆 ( 𝐫 )
= 𝒗 ( 𝐫 )+
𝜹 𝑻 𝒇𝒊𝒄𝒕 [𝝆 ]
𝜹𝝆 ( 𝐫 )
+
𝜹 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ]
𝜹𝝆 ( 𝐫 )
+
𝜹 𝑬 𝑿𝑪
[𝝆 ]
𝜹𝝆 ( 𝐫 )
= 𝒗 𝒆𝒇𝒇
( 𝐫 )+
𝜹 𝑻 𝒇𝒊𝒄𝒕 [𝝆 ]
𝜹𝝆 ( 𝐫 )
( 1.16)
where 𝒗 𝒆𝒇𝒇
( 𝐫 )= 𝒗 ( 𝐫 )+
𝜹 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ]
𝜹𝝆 ( 𝐫 )
+
𝜹 𝑬 𝑿𝑪
[𝝆 ]
𝜹𝝆 ( 𝐫 )

In the equations above, the classical coulombic interaction term is the same for both the
real and fictitious system i.e., 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ] = 𝑱 [𝝆 ] =
1
2
∫
𝝆 ( 𝒓 ) 𝝆 ( 𝒓 ′
)
|𝒓 −𝒓 ′
|
𝒅𝒓 𝒅 𝒓 ′
and its derivative is given by
𝜹 𝑱 𝒇𝒊𝒄𝒕 [𝝆 ]
𝜹𝝆 ( 𝐫 )
=
𝜹𝑱 [𝝆 ]
𝜹𝝆 ( 𝐫 )
=
1
2
∫
𝝆 ( 𝐫 ′
)
|𝐫 − 𝒓 ′
|
𝒅 𝐫 ′
( 1.17)
The effective potential in equation (1.16) can now be written as
𝒗 𝒆𝒇𝒇
( 𝐫 )= 𝒗 ( 𝐫 )+
1
2
∫
𝝆 ( 𝐫 ′
)
|𝐫 − 𝒓 ′
|
𝒅 𝐫 ′
+ 𝒗 𝑿𝑪
( 𝐫 ) ( 1.18)
16

where the exchange-correlation potential 𝒗 𝑿𝑪
( 𝐫 )=
𝜹 𝑬 𝑿𝑪
[𝝆 ]
𝜹𝝆 ( 𝐫 )

Note that equation (1.16) is analogous to the minimization condition that would be derived
for the fictitious non-interacting system with the fictitious potential 𝒗 ′( 𝐫 ) which is given as
𝝀 =
𝜹𝑬 [𝝆 ]
𝜹𝝆 ( 𝐫 )
= 𝒗 ′
( 𝐫 )+
𝜹 𝑻 𝒇𝒊𝒄𝒕 [𝝆 ]
𝜹𝝆 ( 𝐫 )
( 1.19)
Consequently, one can arrive at the electron density, energy, and all other ground state
properties of the real interacting N electron system by simply solving the set of N independent one-
electron Schrodinger equations henceforth referred to as the Kohn-Sham equations (equation 1.13)
for a fictitious external potential 𝒗 ′
( 𝐫 ) given by
𝒗 ′
( 𝐫 )= 𝒗 𝒆𝒇𝒇
( 𝐫 )= 𝒗 ( 𝐫 )+
𝟏 𝟐 ∫
𝝆 ( 𝐫 ′
)
|𝐫 − 𝒓 ′
|
𝒅 𝐫 ′
+ 𝒗 𝑿𝑪
( 𝐫 ) ( 1.20)
In summary, the Kohn Sham approach reduces the complexity of solving equation (1.6) for
an N-electron system with 3N spatial variables to simply solving a set of N one-electron Kohn-
Sham equations independently each with only 3 spatial variables.

1.6.3. The exchange-correlation functional
In order to solve the Kohn Sham equations, one must know the functional form of 𝑬 𝑿𝑪
[𝝆 ]
but unfortunately its exact form for a generalized system is as-yet unknown and herein lies the
major challenge for DFT. Several approximate forms of 𝑬 𝑿𝑪
[𝝆 ] and its corresponding potential
𝒗 𝑿𝑪
have been developed over time. The simplest class of exchange-correlation functionals is the
local density approximation (LDA) class of functionals. These functionals take the general form:
𝑬 𝑿𝑪
𝑳𝑫𝑨
[𝝆 ] = ∫𝒇 ( 𝝆 ( 𝐫 ) ) 𝒅 𝐫 ( 1.21)
In the above expression, 𝒇 is an appropriate function of 𝝆 ( 𝐫 ) and in its simplest form can
17

be given by the Slater-Dirac expression that is derived for an infinite homogenous electron gas,
𝒇 ( 𝝆 ( 𝐫 ) )= 𝑨 𝝆 ( 𝐫 )
𝟒 /𝟑 where 𝑨 is a constant. These functionals are inadequate for molecular
systems which feature significant inhomogeneities in their electron density. This is improved by
the generalized-gradient approximation (GGA) functionals which incorporates the gradient of the
density (𝛁 𝝆 ( 𝐫 ) ) in addition to the electron density 𝝆 ( 𝐫 ) and their general form can be expressed
as:
𝑬 𝑿𝑪
𝑮𝑮𝑨 [𝝆 ] = ∫𝒇 ( 𝝆 ( 𝐫 ) ,𝛁 𝝆 ( 𝐫 ) ) 𝒅 𝐫 ( 1.22)
An extension of the GGA approach is the meta-GGA (mGGA) approximation which
additionally includes the Laplacian of the density 𝛁 𝟐 𝝆 ( 𝐫 ) and optionally the kinetic energy density,
𝛕 ( 𝐫 )= ∑|𝛁 𝚿 𝒊 𝑲𝑺
( 𝐫 ) |
𝟐 𝑵 𝒊 . The general form of an mGGA functional can be written as:
𝑬 𝑿𝑪
𝒎𝑮𝑮𝑨 [𝝆 ] = ∫𝒇 ( 𝝆 ( 𝐫 ) ,𝛁 𝝆 ( 𝐫 ) ,𝛁 𝟐 𝝆 ( 𝐫 ) ,𝛕 ( 𝐫 ) )𝒅 𝐫 ( 1.23)
The functions 𝒇 in most exchange-correlation functionals contain several adjustable
parameters that are often fit to experimental data. The most commonly used class of functionals
are global hybrid (GH) functionals like B3LYP, PBE0 etc. which include a fraction of exact
Hartree-Fock exchange (𝑬 𝑿 𝑯𝑭
) to any of the functionals described above. These functionals offer
an optimal balance between computational cost and accuracy for most systems. The general form
of this class of functionals can be given as
𝑬 𝑿𝑪
𝑮𝑯
[𝝆 ] = 𝒄 𝑬 𝑿 𝑯𝑭
+ ( 𝟏 − 𝒄 ) 𝑬 𝑿𝑪
𝑫𝑭𝑻 ( 1.24)
Other classes of functionals like range-separated hybrid (RSH) functionals
24-26
that are
described in Chapter 6, double hybrid (DH) functionals
27-29
among others have been developed to
accurately describe more complex systems.

18

1.6.4. Solving the Kohn Sham equations
As noted earlier, the Kohn Sham ansatz allows us to express the total ground state energy
of a general molecular system as
𝑬 [𝝆 ] = 𝑻 [𝝆 ] + ∫𝝆 ( 𝐫 ) 𝒗 ( 𝐫 ) 𝒅 𝐫 + 𝑱 [𝝆 ] + 𝑬 𝑿𝑪
[𝝆 ] ( 1.25)
The total electron density of the system 𝝆 can be expressed in terms of the Kohn Sham
orbitals 𝚿 𝒊 𝑲𝑺
as shown in equation (1.14) which in turn can be expanded as a linear combination
of a finite set of atom-centered basis functions {𝝓 𝒂 }:
𝚿 𝒊 𝑲𝑺
= ∑𝒄 𝒂𝒊
𝝓 𝒂 𝒂 ( 1.26)

The electron density can therefore be expressed in terms of the basis functions as
𝝆 ( 𝐫 )= ∑|𝚿 𝒊 𝑲𝑺
( 𝐫 ) |
2
𝑁 𝑖 = ∑𝑷 𝒂𝒃
𝝓 𝒂 ( 𝐫 )
𝑎𝑏
𝝓 𝒃 ( 𝐫 ) ( 1.27)
where 𝑷 𝒂𝒃
= ∑𝒄 𝒂𝒊
𝒄 𝒃𝒊
𝑵 𝒊 are elements of the one-electron density matrix P. Several
standardized atom-centered basis sets of varying sizes have been developed for all atoms in the
periodic table and are available readily in most quantum chemistry software packages. The terms
in equation (1.25) can now therefore also be expanded in terms of the basis functions:
𝐄 𝑻 = 𝑻 [𝝆 ] = ∑ ⟨𝚿 𝒊 𝑲𝑺
|−
𝟏 𝟐 𝛁 𝟐 |𝚿 𝒊 𝑲𝑺
⟩ =
𝑵 𝒊 ∑𝑷 𝒂𝒃
⟨𝝓 𝒂 ( 𝐫 ) |−
𝟏 𝟐 𝛁 𝟐 |𝝓 𝒃 ( 𝐫 ) ⟩
𝒂𝒃

𝐄 𝑽 = ∫ 𝝆 ( 𝐫 ) 𝒗 ( 𝐫 ) 𝒅 𝐫 = ∑𝑷 𝒂𝒃
⟨𝝓 𝒂 ( 𝐫 ) |𝒗 ( 𝐫 ) |𝝓 𝒃 ( 𝐫 ) ⟩
𝒂𝒃

𝐄 𝑱 = 𝑱 [𝝆 ] =
𝟏 𝟐 ∫
𝝆 ( 𝒓 ) 𝝆 ( 𝒓 ′
)
|𝒓 − 𝒓 ′
|
𝒅𝒓 𝒅 𝒓 ′
=
𝟏 𝟐 ∑ ∑𝑷 𝒂𝒃
𝒄𝒅
𝑷 𝒄𝒅
∬𝝓 𝒂 ( 𝒓 ) 𝝓 𝒃 ( 𝒓 )
𝟏 |𝐫 − 𝒓 ′
|
𝝓 𝒄 ( 𝒓 ′) 𝝓 𝒅 ( 𝒓 ′)𝒅𝒓 𝒅 𝒓 ′
𝒂𝒃

19

𝐄 𝑿𝑪
= 𝑬 𝑿𝑪
[𝝆 ] = ∫𝒇 ( 𝝆 ( 𝐫 ) ,𝛁 𝝆 ( 𝐫 ) ,…) 𝒅 𝐫
∴ 𝐄 = 𝐄 𝑻 + 𝐄 𝑽 + 𝐄 𝑱 + 𝐄 𝑿𝑪
( 1.28)

The Kohn Sham equations can therefore be solved by minimizing equation (1.28) with
respect to the unknown Kohn Sham orbital coefficients {𝒄 𝒂𝒊
} using a self-consistent field (SCF)
optimization procedure like the one used in the Hartree-Fock method. The procedure involves
starting with an initial guess of the MO coefficients to compute the density 𝝆 and the energy E
(1.27 and 1.28) and repeating the process iteratively each time with a new set of coefficients until
convergence is reached (i.e., the change in E falls below a certain threshold). This can be
accomplished using an efficient SCF optimization algorithm like DIIS (Direct inversion in the
iterative subspace), GDM (Geometric direct minimization) etc. The KS orbitals obtained from the
optimized set of coefficients can then be used to compute all other ground state molecular
properties including energy derivatives with respect to nuclear coordinates which can in turn be
used to find stationary points along the molecular potential energy surface like the lowest energy
geometry of the molecule through a minimization procedure like steepest decent, conjugate
gradient methods etc.

1.6.5. Time-dependent density functional theory (TDDFT)
Time-dependent DFT (TDDFT) is an extension of DFT that can be used to compute
energies and properties of excited states. Within the Kohn Sham formalism, TDDFT in the linear
response approximation involves solving the following non-Hermitian eigenvalue equation
30
:
(
𝐀 𝐁 𝐁 𝐀 )(
𝐗 𝐘 )= 𝝎 (
𝟏 𝟎 𝟎 −𝟏 )(
𝐗 𝐘 ) ( 1.29)
The matrix elements of the A and B matrices in the above equation take the following form
20

𝑨 𝒊𝒂𝒋𝒃 = 𝜹 𝒊𝒋
𝜹 𝒂𝒃
( 𝜺 𝒂 𝑲𝑺
− 𝜺 𝒊 𝑲𝑺
)+ ⟨𝚿 𝒊 ( 𝒓 ) 𝚿 𝒋 ( 𝒓 ′) |
𝟏 |𝒓 − 𝒓 ′
|
|𝚿 𝒂 ( 𝒓 ) 𝚿 𝒃 ( 𝒓 ′) ⟩
+ ⟨𝚿 𝒊 ( 𝒓 ) 𝚿 𝒋 ( 𝒓 ′) |𝒗 𝑿𝑪
|𝚿 𝒂 ( 𝒓 ) 𝚿 𝒃 ( 𝒓 ′) ⟩
𝑩 𝒊𝒂𝒋𝒃 = ⟨𝚿 𝒊 ( 𝒓 ) 𝚿 𝒃 ( 𝒓 ′
) |
𝟏 |𝒓 − 𝒓 ′
|
|𝚿 𝒂 ( 𝒓 ) 𝚿 𝒋 ( 𝒓 ′
) ⟩ + ⟨𝚿 𝒊 ( 𝒓 ) 𝚿 𝒃 ( 𝒓 ′
) |𝒗 𝑿𝑪
|𝚿 𝒂 ( 𝒓 ) 𝚿 𝒋 ( 𝒓 ′
) ⟩ ( 1.30)
where, the indices i,j represent occupied ground state Kohn Sham orbitals while a,b
represent virtual/unoccupied ground state Kohn Sham orbitals. Equation (1.29) can be solved to
obtain the excitation energies, 𝝎 for the lowest set of excited states. It can be seen that the A
matrix represents excitations from the occupied to the virtual orbitals of the ground state reference
wavefunction while the B matrix represent deexcitations from virtual to occupied orbitals. Ignoring
the B matrix results in the commonly used Tamm-Dancoff approximation (TDA)
31
which reduces
equation (1.29) to 𝐀𝐗 = 𝝎 𝐗 which is analogous to the single excitation configuration interaction
(CIS) approach derived from HF wavefunctions. The computational cost of the TDA/TDDFT
approaches is similar to the CIS approach. However, unlike the CIS approach which does not
account for electron correlation effects, the TDA/TDDFT approaches account for these effects
implicitly via the exchange correlation functional term and have therefore become the method of
choice to accurately compute excited state energies and properties.

1.7. References

1. Adachi, C.; Baldo, M. A.; Forrest, S. R.; Lamansky, S.; Thompson, M. E.; Kwong, R.
C., High-efficiency red electrophosphorescence devices. Applied Physics Letters 2001, 78 (11),
1622-1624.
2. Adachi, C.; Baldo, M. A.; Thompson, M. E.; Forrest, S. R., Nearly 100% internal
phosphorescence efficiency in an organic light-emitting device. Journal of Applied Physics 2001,
90, 5048-5051.
21

3. Baldo, M.; Lamansky, S.; Burrows, P.; Thompson, M.; Forrest, S., Very high-efficiency
green organic light-emitting devices based on electrophosphorescence. Applied Physics Letters
1999, 75, 4.
4. Baldo, M. A.; O'brien, D.; You, Y .; Shoustikov, A.; Sibley, S.; Thompson, M.; Forrest,
S., Highly efficient phosphorescent emission from organic electroluminescent devices. Nature
1998, 395 (6698), 151-154.
5. Tang, C. W.; VanSlyke, S. A., Organic electroluminescent diodes. Applied physics letters
1987, 51 (12), 913-915.
6. Adachi, C.; Baldo, M. A.; Forrest, S. R.; Thompson, M. E., High-efficiency organic
electrophosphorescent devices with tris (2-phenylpyridine) iridium doped into electron-
transporting materials. Applied Physics Letters 2000, 77 (6), 904.
7. O’brien, D.; Baldo, M.; Thompson, M.; Forrest, S., Improved energy transfer in
electrophosphorescent devices. Applied Physics Letters 1999, 74 (3), 442-444.
8. Zhang, Q. S.; Li, J.; Shizu, K.; Huang, S. P.; Hirata, S.; Miyazaki, H.; Adachi, C.,
Design of Efficient Thermally Activated Delayed Fluorescence Materials for Pure Blue Organic
Light Emitting Diodes. Journal of the American Chemical Society 2012, 134 (36), 14706-14709.
9. Uoyama, H.; Goushi, K.; Shizu, K.; Nomura, H.; Adachi, C., Highly efficient organic
light-emitting diodes from delayed fluorescence. Nature 2012, 492 (7428), 234-+.
10. Goushi, K.; Yoshida, K.; Sato, K.; Adachi, C., Organic light-emitting diodes employing
efficient reverse intersystem crossing for triplet-to-singlet state conversion. Nature Photonics
2012, 6 (4), 253-258.
11. Endo, A.; Sato, K.; Yoshimura, K.; Kai, T.; Kawada, A.; Miyazaki, H.; Adachi, C.,
Efficient up-conversion of triplet excitons into a singlet state and its application for organic light
emitting diodes. Applied Physics Letters 2011, 98 (8), 3.
12. He, G. F.; Pfeiffer, M.; Leo, K.; Hofmann, M.; Birnstock, J.; Pudzich, R.; Salbeck, J.,
High-efficiency and low-voltage p-i-n electrophosphorescent organic light-emitting diodes with
double-emission layers. Applied Physics Letters 2004, 85 (17), 3911-3913.
13. He, G. F.; Schneider, O.; Qin, D. S.; Zhou, X.; Pfeiffer, M.; Leo, K., Very high-
efficiency and low voltage phosphorescent organic light-emitting diodes based on a p-i-n
22

junction. Journal of Applied Physics 2004, 95 (10), 5773-5777.
14. Pfeiffer, M.; Leo, K.; Zhou, X.; Huang, J. S.; Hofmann, M.; Werner, A.; Blochwitz-
Nimoth, J., Doped organic semiconductors: Physics and application in light emitting diodes.
Organic Electronics 2003, 4 (2-3), 89-103.
15. Pfeiffer, M.; Forrest, S. R.; Leo, K.; Thompson, M. E., Electrophosphorescent p-i-n
organic light-emitting devices for very-high-efficiency flat-panel displays. Advanced Materials
2002, 14 (22), 1633-1636.
16. Adamovich, V . I.; Cordero, S. R.; Djurovich, P. I.; Tamayo, A.; Thompson, M. E.;
D'Andrade, B. W.; Forrest, S. R., New charge-carrier blocking materials for high efficiency
OLEDs. Organic Electronics 2003, 4 (2-3), 77-87.
17. Purcell, E. M., SPONTANEOUS EMISSION PROBABILITIES AT RADIO
FREQUENCIES. Physical Review 1946, 69 (11-1), 681-681.
18. Smith, L. H.; Wasey, J. A. E.; Samuel, I. D. W.; Barnes, W. L., Light out-coupling
efficiencies of organic light-emitting diode structures and the effect of photoluminescence
quantum yield. Advanced Functional Materials 2005, 15 (11), 1839-1844.
19. Schmidt, T. D.; Lampe, T.; Sylvinson, D. M. R.; Djurovich, P. I.; Thompson, M. E.;
Brutting, W., Emitter Orientation as a Key Parameter in Organic Light-Emitting Diodes. Physical
Review Applied 2017, 8 (3), 28.
20. Scholz, S.; Kondakov, D.; Lussem, B.; Leo, K., Degradation Mechanisms and Reactions
in Organic Light-Emitting Devices. Chemical Reviews 2015, 115 (16), 8449-8503.
21. Giebink, N. C.; D'Andrade, B. W.; Weaver, M. S.; Mackenzie, P. B.; Brown, J. J.;
Thompson, M. E.; Forrest, S. R., Intrinsic luminance loss in phosphorescent small-molecule
organic light emitting devices due to bimolecular annihilation reactions. Journal of Applied
Physics 2008, 103 (4), 9.
22. Giebink, N.; D’Andrade, B.; Weaver, M.; Mackenzie, P.; Brown, J.; Thompson, M.;
Forrest, S., Intrinsic luminance loss in phosphorescent small-molecule organic light emitting
devices due to bimolecular annihilation reactions. Journal of Applied Physics 2008, 103 (4),
044509.
23. Hohenberg, P.; Kohn, W., INHOMOGENEOUS ELECTRON GAS. Physical Review B
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1964, 136 (3B), B864-+.
24. Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K., A long-range correction scheme for
generalized-gradient-approximation exchange functionals. Journal of Chemical Physics 2001,
115 (8), 3540-3544.
25. Chai, J. D.; Head-Gordon, M., Long-range corrected double-hybrid density functionals.
Journal of Chemical Physics 2009, 131 (17).
26. Chai, J. D.; Head-Gordon, M., Systematic optimization of long-range corrected hybrid
density functionals. Journal of Chemical Physics 2008, 128 (8), 15.
27. Grimme, S.; Neese, F., Double-hybrid density functional theory for excited electronic
states of molecules. Journal of Chemical Physics 2007, 127 (15).
28. Schwabe, T.; Grimme, S., Double-hybrid density functionals with long-range dispersion
corrections: higher accuracy and extended applicability. Physical Chemistry Chemical Physics
2007, 9 (26), 3397-3406.
29. Grimme, S., Semiempirical hybrid density functional with perturbative second-order
correlation. Journal of Chemical Physics 2006, 124 (3), 16.
30. Hirata, S.; Head-Gordon, M., Time-dependent density functional theory for radicals - An
improved description of excited states with substantial double excitation character. Chemical
Physics Letters 1999, 302 (5-6), 375-382.
31. Hirata, S.; Head-Gordon, M., Time-dependent density functional theory within the
Tamm-Dancoff approximation. Chemical Physics Letters 1999, 314 (3-4), 291-299.
24

Chapter 2. Virtual screening for stable blue PhOLED host materials

2.1. Introduction
As mentioned in Chapter 1, the host matrix is a critical component of the emissive layer
in an OLED device. Several stable and effective host materials have been discovered for red and
green phosphorescent dopants which enabled the development and commercialization of stable
red and green PhOLEDs. However, blue PhOLEDs suffer from low stability and short operational
lifespan which have impeded their commercialization. This can be mainly attributed to the lack of
stable host and dopant materials that can tolerate or mitigate TTA and TPA events that occur during
device operation.
1, 2
The resultant species generated by TTA/TPA events that involve triplet
excitons in the blue energy regime (>2.65 eV) are more energetic and unstable relative to those
formed by triplet excitons in the red/green regime. For instance, the combination of two blue triplet
excitons of 2.65 eV each can result in a highly energetic species with an energy as high as 5.30 eV
(2 x 2.65) which is higher than the bond dissociation energies of most Aryl-N/O/S/P single bonds
(that are present most host materials) and can therefore result in irreversible molecular
decomposition. This has been a major challenge in the commercial development of stable blue
PhOLEDs. The development of stable blue PhOLED hosts that can tolerate such TTA/TPA events
has therefore remained an active area of research.

Figure 2.1. Commonly used blue PhOLED hosts.

25

In addition to having a robust and stable chemical structure, successful blue PhOLED hosts
must satisfy several other design criteria simultaneously. Critically, the lowest molecular triplet
(T1) energy of the hosts must be higher than that of the dopant to avoid triplet exciton trapping on
the host (i.e., T1 >> 2.65 eV). The hosts must also exhibit morphological stability (resistant to
phase transitions/high glass transition temperature, etc.) and high hole and electron mobility.
Finally, they must have appropriate HOMO/LUMO energy levels to enable their incorporation into
an efficient device architecture. Designing hosts that possess all the above-mentioned attributes is
unsurprisingly a challenging task.

Figure 2.2. High T1 energy bearing fragments. (T1 energies computed at the B3LYP/6-31G*
level)

A sampling of commonly used blue PhOLED hosts is shown in Figure 2.1. The prevalence
of weak Aryl-N/O/Si/P bonds (for example, bond dissociation energy of Aryl-N bond in CBP =
3.9 eV/ 90 kcal/mol) in these hosts has been suspected to be the reason for the low stability of such
materials under device operation.
3, 4
Therefore, designing hosts without such weak linkages could
potentially lead to better resilience to TTA/TPA events and ultimately improved stability. Another
26

challenge in designing blue PhOLED hosts is the rather modest chemical design space available
stemming from the constraint that T1 be >> 2.65 eV . This limits the design space to only those
structures that may be constructed from the handful of known molecular fragments whose T 1
energies are above the threshold (Figure 2.2). Accordingly, we focused on two new molecular
frameworks constructed from high T1 fragments and devoid of the aforementioned weak exocyclic
linkages which we refer to as H2P and Spiro-linked hosts and their structures are depicted in
Figure 2.3.

Figure 2.3. Core structures of H2P and Spiro-linked hosts.

It can be seen that a combinatorial enumeration across just a few types of chemical
substitutions can generate a large unwieldy library that scales as q
p
where p is the number of sites
within the structure where chemical modifications may be made, and q is the number of types of
chemical substitutions that are being explored. To keep the size of the library manageable, we
restrict the sites of chemical modification and the types of modification to those that are
synthetically feasible. Further, we use a tiered approach to screen each library (depicted in Figure
2.4), wherein a sub-library is generated by performing a combinatorial enumeration of the defined
chemical modifications within one fragment of the parent structure. Computational tools like
Density Functional Theory (DFT) are then used to predict key parameters like T 1/S1,
27

HOMO/LUMO energies etc. for each candidate within the sub-library. Candidates that best satisfy
the design criteria are selected and moved into the next tier where another sub-library is built by
performing combinatorial enumeration on each of the selected candidates across a different
fragment and is then screened again using computational tools. Depending on the complexity of
the starting molecular parent framework, the same process can be repeated through more tiers
ultimately resulting in a manageable number of candidates that best satisfy the design criteria.
These candidates may then be carried forward into the experimental verification stage. Using such
a tiered approach can reduce the q
p
scaling problem to ∑𝑞 𝑛 𝑝 𝑛 𝑛 where 𝑝 𝑛 and 𝑞 𝑛 are now the
number of sites and types of modifications explored in the 𝑛 𝑡 ℎ
tier respectively. This leads to a
drastic acceleration of the screening process and reduction in computational cost as will be evident
in the following sections.

Figure 2.4. Tiered screening of host libraries.

2.2. H2P hosts
(Note: This work was done in collaboration with co-workers Lauren H. Martin, Patrick J.
G. Saris, Hsiao-Fan Chen and Mark E. Thompson.
5
)
The conceptual starting point of our search for high triplet energy blue host materials that
ultimately lead to H2P host framework is triphenylene, which has a triplet energy in the deep-blue
range (ET = 425nm, 2.9 eV) as well as a large aromatic system, leading to efficient charge
transport.
6, 7
Additionally, the rigid tetracyclic structure inhibits one potential OLED degradation
28

pathway involving exocyclic bond cleavage of the host material, as is widely suspected for the
standard phenylcarbazole derivatives.
3, 4
Due to the synthetic challenges and structural limitations
inherent to the synthesis of regiospecifically substituted heterotriphenylenes,
8
this work explores
a related but more synthetically accessible class of molecular structures in which one of the 6
membered rings of triphenylene is replaced with a 5 membered heterocyclic ring, which can
readily be formed from orthoquinone precursors (Figure 2.5). This phenanthroheterole based
structure is referred to as H2P, due to its two peripheral hexagonal “H-rings” and one pentagonal
“P-ring”.

Figure 2.5. Conceptual evolution of H2P design.

The initial screening of candidate materials was carried out with Density Functional Theory
(DFT) modeling of the electronic properties of a number of structures with different heterocyclic
P-rings (Figure 2.5) to identify those with high triplet energies and frontier orbital energies
suitable for hosting our desired sky blue dopant phosphor, i.e. iridium(III)bis((4,6-di-
fluorophenyl)-pyridinato-N,C2’)picolinate (FIrpic). The primary requirement for hosting FIrpic
is a triplet energy greater than 2.7 eV
9
in order to prevent luminescence quenching by triplet energy
transfer. The first Tier of our screening process examined a range of P-ring substitutions to find
the heteroatom substitutions that gave the highest triplet energy. A second Tier of screening started
with imidazole for the P-ring and involved nitrogen incorporation into the H-rings, leading to the
choice of three promising organic host materials to be prepared and tested in FIrpic based
29

phosphorescent OLEDs. A third Tier of screening searched for high charge carrier mobilities by
modeling the solid-state properties of the three materials through molecular dynamics (MD)
simulations. Computationally inexpensive electron coupling dimer splitting calculations were used
to predict charge transport properties from MD simulations, revealing poor electron mobility
predicted for one of the three materials. Although our gas phase DFT predictions (Tiers 1 and 2)
and experimental measurements of the physical properties of the three materials showed them to
be very similar, OLEDs prepared with each as a host for a blue phosphorescent dopant gave
different performances, as predicted by Tier 3, with external efficiencies ranging from 0.6 % to
9 %.

2.2.1. Computational methods:
DFT calculations
All QM calculations reported in this work were performed using the Materials Science
Suite
10
of programs developed by Schrödinger LLC. on a 64-core workstation. Density functional
theory was used for ground state optimization and estimation of HOMO/LUMO energies, T1
(triplet) state energy and hole/electron reorganization energies (
+
, 
-
) for the molecules.
Hole/electron reorganization energies were calculated per equations (2.1) and (2.2).
𝜆 +
= ( 𝐸 +
0
− 𝐸 0
0
)+ ( 𝐸 0
+
− 𝐸 +
+
) ( 2.1)
𝜆 −
= ( 𝐸 −
0
− 𝐸 0
0
)+ ( 𝐸 0
−
− 𝐸 −
−
) ( 2.2)
In the above expressions, the superscripts represent the state of the molecule (0, +, and – for
neutral, anionic and cationic states respectively) while subscripts indicate the state at which the
structure is optimized. For instance, according to this terminology 𝐸 +
0
represents the energy of the
neutral ground state at the cation-optimized geometry.
30

Calculations involving cationic, anionic and the triplet state were performed using the
unrestricted Kohn-Sham DFT scheme. Excited singlet state calculations were performed using
Time-dependent DFT (TD-DFT).
DFT calculations in Tier 1 and Tier 2 were performed using B3LYP/MIDIX and
B3LYP/LACV3P** levels for screening, respectively. All DFT calculations were implemented
using Schrödinger’ s Jaguar
11, 12
program. Canvas
13
was used to visualize and sort results between
Tiers.
Molecular Dynamics/Electron coupling calculations
All MD simulations reported in this work were carried out using the Desmond
14
module in
the Materials Science Suite on a GPU workstation. The following multi-stage MD simulation
protocol was implemented for each of the molecular systems reported in this work: A disordered
system of 125 molecules in the simulation box (with periodic boundary conditions) was prepared
using the disordered system builder facility available within Schrodinger’s Materials Science
Suite
10
following which a series of six short MD simulations of 1.2 ns each were performed in the
canonical (NVT) ensemble with the temperature between two consecutive stages stepped up by
100 K increments starting from 300 K to 800 K for the final stage. Following the NVT stages, a
30 ns long MD simulation was carried out in the isothermal-isobaric (NPT) ensemble at a fixed
temperature and pressure of 300 K and 1.01 atm. In order to expedite the simulation process. Post
simulation trajectory analysis on the last 6 ns of the NPT stimulation was performed to log density.
The standard deviation of the calculated density was found to be less than 0.5 % of the averaged
densities calculated for all the systems ensuring convergence. The OPLS-2005 force-field
15

available in the Materials Science Suite was used for all the simulations.
In order to calculate the hole/electron hopping rates, charge coupling calculations were
31

performed on the MD equilibrated structures. The hopping rates (𝜅 ) for charge transfer between
two molecules can be calculated using Marcus theory, equation (2.3).
𝜅 =
4𝜋 2

ℎ

𝐻 𝑎𝑏
2
√4𝜋𝜆 𝑘 𝐵 𝑇 exp(−
( 𝜆 + 𝛥𝐺 )
2
4𝜆 𝑘 𝐵 𝑇 ) ( 2.3)

Here, λ, Hab, 𝑘 𝐵 and T denote the hole/electron reorganization energy, intermolecular
coupling parameter, Boltzmann constant and temperature respectively. 𝛥𝐺 is the free energy
difference for the charge transfer process which is equal to the enthalpy difference for the process
in this case. It should be noted that the reorganization energy, λ is made up of two terms: inner-
sphere reorganization energy (λin) accounting for the change in energy caused by geometric
relaxation of a molecule upon addition/removal of an electron and outer-sphere reorganization
energy (λout) accounting for relaxation/polarization of the surrounding medium which is expected
to be much smaller in rigid solids and is hence neglected in the computation of mobility in most
cases. Additionally, λout is more tedious to compute than λin which can be easily derived from gas
phase DFT calculations (as described in the methods section). Therefore, in this work λout is
neglected and λ in equation (2.3) becomes λin. The hopping rates are computed by two different
approaches in this study. In the first approach, Hab is approximated as half the difference between
the LUMO and LUMO+1 energies of the neutral dimer for electron transfer, 𝐻 𝑎𝑏
−
≈
1
2
( 𝐸 𝐿𝑈𝑀𝑂 +1
−
𝐸 𝐿𝑈𝑀𝑂 ) and similarly half the difference between HOMO and HOMO-1 energies of the dimer for
hole transfer,𝐻 𝑎𝑏
+
≈
1
2
( 𝐸 𝐻𝑂𝑀𝑂 − 𝐸 𝐻𝑂𝑀𝑂 −1
). These dimer frontier orbital splittings are a measure
of the intermolecular coupling for the electron and hole transfer processes and are obtained from
single point DFT calculations on all dimer pairs in the MD equilibrated structure within a closest
approach distance of 4Å between them. This approach is commonly referred to as the Energy-
32

Splitting-in-Dimer method in literature
16-27
. Using the dimer frontier orbital splitting as a surrogate
for the coupling parameter vastly reduces computational cost compared to more rigorous
treatments, such as Constrained-DFT (CDFT) based approaches. It should be noted that in this
approach, the free energy change for the process is not computed and set to zero for all the dimer
pairs. It has been shown that this approach can lead to an overestimation of the coupling parameter
for non-symmetrical cases and does not account for variation in on-site energies, so while being
computationally very inexpensive, it is clearly not the best method to estimate coupling
28
. To
confirm the validity of this rather crude approach in describing the charge transport properties of
the systems under study, a more sophisticated treatment based on CDFT was implemented
29-31
. In
this approach, Hab is taken as the coupling matrix element between the wavefunction of the initial
state where the electron/hole is localized on one of the monomers and the final state where the
electron/hole is localized on the other monomer. 𝛥𝐺 is approximated as just the computed energy
difference between the two states. CDFT is used to localize the electron/hole onto just one
monomeric unit. To include electrostatic effects on the charge transfer process from the
neighboring molecules, the CDFT calculations were performed with each dimer embedded in a
field of atomic point charges obtained from the partial charges (charges from the OPLS2005 Force
Field) of the atoms in the neighboring molecules within 4Å from the dimer. The CDFT coupling
calculations were performed on 80 randomly selected dimer pairs that are within a distance of 4Å
apart. Both the CDFT and dimer frontier orbital splitting coupling calculations were carried out at
the B3LYP/LACV3P** level.

2.2.2. Molecular search strategy
For our study, we chose to search for host materials for the well-studied sky-blue dopant
33

FIrpic. The choice of this phosphorescent dopant sets limits on the electronic properties for the
host material. To achieve a high luminance efficiency for a FIrpic dopant, the triplet energy of the
host must be > 2.65 eV . In order to use the FIrpic doped host material in an efficient OLED stack
the LUMO of the host needs to be near or above that of FIrpic, so the desired LUMO energies of
the host are > -2.1 eV . Thus, we will use these two criteria to identify the most promising
compounds in our computational searching of the H2P structure space to carry into experimental
study. Isoelectronic, heteroatomic transmutations of CH fragments of the parent
cyclopentaphenanthrene structure (Figure 2.5) have qualitatively different effects whether they be
in the P- or H- rings. For neutral aromatic structures, the H-rings may include pnictogens (only N
was considered), while the P-ring may also include chalcogens (O and S were considered).
Because the chalcogens, which provide a large chemical space with potentially desirable
properties, are only available to the P- ring, our structure search was broken into two Tiers: Tier
1 selection (Figure 2.6) focused on the heteroatoms of the P-ring heterocycle, while Tier 2 focused
on aza substitution in the H-ring, using the best candidates identified in Tier 1.
Tier 1 identified the candidates with triplet energies over 2.7 eV , based on a FIrpic dopant.
Furthermore, the selection strategy in Tier 1 involved maximizing the LUMO energy, rather than
optimizing it based on the LUMO of FIrpic. This strategy anticipates the aza substitution in Tier
2 which will categorically stabilize LUMO energies, so a destabilized LUMO energy from Tier 1
allows room for tunability through the desired range of LUMO energies in Tier 2
32
.
The Tier 1 selection involved a survey of 15 P-ring heterocycles and the Tier 2 selection
involved 37 unique H-ring aza substitution patterns. By carrying out the selection processes
serially, choosing the best candidate in Tier 1 to carry into Tier 2, the number of structures that
needed to be modeled dropped from 555 (15 * 37), corresponding to all H-ring substitutions for
34

each P-ring structure, to 52 (15 + 37) calculations necessary to survey the optimal chemical space
of H2P structures.
2.2.3. Tier 1 Selection
The first tier selection involved incorporation of oxygen, sulfur and nitrogen for X into the
P-ring of the H2P framework to produce the library of chemically relevant structures shown in
Figure 2.6.

Figure 2.6. (left) Elemental enumeration of O, S, NH and CH in the “P-ring” of the H2P
structure. (right) Lowest unoccupied molecular orbital energy vs. triplet energy for iterative
cyclopentaphenanthrene structures.

DFT calculations were performed at the B3LYP/MIDIX level for screening, which is a low
level of theory suited for rapid screening. The triplet energies of S and O substituted P-rings were
lower than that of N-substituted compounds, with non-chalcogen containing compounds 10-15
having the highest triplet energies. The highest triplet energies were predicted for triazoles 12 and
13, which, while are promising candidates, fail to meet the Tier 1 requirement of maximized
LUMO energy. Tier 2 N-substitutions of 12 and 13 would likely result in LUMO energies below
the desired range. The target structures were therefore 5, 6, and 10, since they present both high
triplet and less negative LUMO energies. Compound 10 was selected because it and substituted
2.4 2.6 2.8 3.0
-1.4
-1.2
-1.0
-0.8
-0.6 P-ring substitution
O and N,O
S and N,S
N only

LUMO (eV)
Triplet Energy (eV)
4
8
3
2
9
1
7
11
15
14
12
13
10
5
6
35

versions of it can be readily prepared from phenanthrene-9,10-dione or its aza-substituted analogs,
as illustrated in Figure 2.7. It is noteworthy that while 6,6,6,5-membered tetracyclic
imidazo[4,5-f]-1,10-phenanthroline derivatives have been investigated as ligands in
phosphorescent emitters for OLEDs,
33-35
they have never been used as host materials for either
fluorescent or phosphorescent OLEDs. Anticipating a crystalline rather than glassy morphology
of vapor deposited films of planar 10, as well as potentially recalcitrant synthetic preparations,
substituent functional groups were chosen for the imidazole before Tier 2 selection. When R1 =
phenyl, the singlet and triplet energies are markedly red shifted, due to conjugation of the phenyl
group with the imidazole ring. For example, when R1 = R2 = H, the S1/T1 energies are predicted
by DFT to be 3.54/2.96 eV , while when R1 = Ph, R2 = H the S1/T1 energies are predicted to be
3.33/2.56 eV . Thus, R1 = H or alkyl is preferred for high triplet energy, however, in synthetic trials
we found that when R1 is methyl, ethyl, or isopropyl, the reaction does not give 10, but the
corresponding alkylidine 2H-imidazole compound instead (Figure 2.7 far right). The derivative
with R2 = tert-butyl derivative is well behaved due to the lack of α-protons, giving exclusively the
desired imidazo-phenanthrene and is therefore the best choice in terms of S 1/T1 energies as well
as stability and solubility of the compound. In contrast to R1 = phenyl, when R2 is phenyl steric
interactions force the aromatic ring out of conjugation, so the orbital and excited state energies are
largely unaffected, e.g. R1 = H, R2 = Ph give S1/T1 energies of 3.30/2.89 eV (based on DFT
calculations).

Figure 2.7. Scheme depicting possible side products.
36

2.2.4. Tier 2 Selection
The second tier selection explored nitrogen substitution in the H-rings of 10. Incorporating
0, 1 or 2 nitrogens into the H-rings of the parent phenanthro[4,5-f]imidazole gives a total of 37
unique aza-substituted compounds (Figure 2.8). For the Tier 2 screening, we chose to carryout
DFT calculations on the 37 aza-substitutions of 10 with R1 = tert-butyl and R2 = phenyl using the
B3LYP hybrid functional and LACV3P** basis set.

Figure 2.8. Aza-substitution patterns in Tier-2 library.

In Tier 2 we chose a markedly larger basis set than was used in Tier 1, so direct comparisons
of theoretically predicted properties to experimentally determined values will be meaningful. In
37

these calculations, we predicted a number of parameters, including singlet and triplet energies, as
well as molecular orbital energies and surfaces for each of the 37 molecules. The number of
nitrogens and the site of nitrogen substitution in the H-rings markedly affects the electronic
properties of the H2P molecules. Figure 2.9 plots two of the calculated Tier 2 properties: LUMO
energy vs. triplet energy. As expected,
32, 36
the LUMO is stabilized with nitrogen substitution in
the H-ring, shifting from -1.0 eV for 10a to a range of -1.2 to -1.4 for a single nitrogen to -1.4
to -1.9 for two nitrogens, with the site of nitrogen substitution markedly affecting the degree of
stabilization of the LUMO. The greatest stabilization is seen for substitution in the 3- and
8-postions and the least for substitution at the 2- and 9-positions. The larger range of LUMO
energies seen for the molecules with two nitrogens is due to an additive effect when both nitrogens
are in a single H-ring. The ortho, meta, and para derivatives together give LUMO energies within
a range of roughly 0.2 eV and an average of -1.7 eV , while the materials with a single nitrogen in
each H-ring give the same range of LUMO energies, but with an average LUMO energy of -1.55
eV . The site of nitrogen substitution also effects the triplet energy, but not in the same manner as
it does the LUMO energies. Substitution of a single nitrogen into the two H-rings, two nitrogens
meta in a single H-ring or a single nitrogen in both H-rings gives a minimal change in the triplet
energy of the molecule, relative to the unsubstituted compound 10a. In contrast, substitution of
two nitrogens into a single H-ring in either an ortho or para disposition lowers the triplet energy
substantially below 2.8 eV in nearly every case (the exception has N in the 2,3-positions). The
reason for the marked red shift in the ortho- and para-substituted derivatives is a filled-filled
interaction
37
of the two nitrogen lone pairs in these compounds, leading to a marked destabilization
of the out of phase combination of the lone pair orbitals and a resultant narrowing of the HOMO-
LUMO gap. This interaction of filled non-bonding orbitals is not seen for the meta-substituted
38

derivative or those with a single nitrogen in each H-ring.

Figure 2.9. LUMO vs. triplet energy for second tier iteration of aza-substitution in phenanthrene
section the H-rings of the parent phenantho[4,5-f]imidazole. Compounds 10a-10d are illustrated
by colored circles.

The Tier 2 screen also included estimation of the electron and hole reorganization energies
for each of the H2P molecules. Reorganization energies are useful parameters to evaluate the
kinetics of intermolecular hole and electron hopping and assess charge carrier conduction. A lower
reorganization energy reduces the barrier to carrier hopping between molecules in the thin film
and efficient carrier conduction is more favorable for a given material. The compounds in the Tier
2 screen ranged from low to moderate reorganization energies for holes (0.24-0.30 eV) and
electrons (0.18-0.40 eV), suggestive of efficient carrier transport in the H2P family.
We chose to focus on three imidazo[4,5-f]phenanthroline derivatives 10b, 10c and 10d for
characterization and study in blue OLEDs due to their high triplet energies and favorable reduction
2.0 2.2 2.4 2.6 2.8 3.0
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
10c
10b
10d

parent 10a
one N
Two N:
One N in each ring
ortho
meta
para
LUMO (eV)
Triplet Energy (eV)
10a
39

potentials. Additionally, these three materials have symmetric nitrogen substitution patterns in the
H-rings, so only a single regioisomer will be formed for each derivative by our synthetic approach.
Figure 2.10 shows the DFT optimized ground state geometries along with the HOMO and
LUMO orbitals for 10a-10d. The orbital density distribution of the HOMOs and LUMOs for
10b-10d are very similar. The LUMOs are localized on the phenanthroline while the HOMOs
involve both the phenanthroline and imidazole fragments. The addition of tert-butyl and phenyl
groups have a negligible effect on the composition of the HOMO or LUMO of these compounds.
For comparison, the HOMO and LUMO are shown for 10a as well. The HOMO matches that seen
for 10b-10d, but the LUMO of 10a is localized on the phenyl group, rather than the phenanthroline,
due to the relative difficulty of reducing phenanthrene compared to phenanthroline. The LUMO+1
orbital of 10a is a good match to the LUMO orbital of 10b-10d. Nitrogen substitution in the
H-rings stabilizes the phenanthrene system, such that the phenanthroline orbitals fall below the
phenyl based -orbitals for 10b-10d.
Table 2.1. Summary of calculated and experimental physical properties for 10b, 10c and 10c.

E
ox
/E
red

HOMO (eV)

LUMO (eV) (+)
e

(eV)
(-)
f
(eV)

E T (eV)
 PL
g

(V/V)
a
Calc. Exp.
d
Calc. Exp.
d
Calc. Solution Solid

(sol-sol)
10a 0.89
b
/-2.97
b
-5.47 -5.85 -1.04 -1.27 0.24 0.21 2.90 2.86 2.70 0.16 --
10b 1.15
c
/-2.54
b
-5.91 -6.21 -1.54 -1.76 0.27 0.40 2.91 2.92 2.65 0.27 0.40
10c 1.11
c
/-2.25
b
-5.88 -6.15 -1.77 -2.10 0.25 0.30 2.84 2.71 2.47 0.24 0.20
10d 1.17
b
/-2.51
b
-5.82 -6.24 -1.41 -1.79 0.28 0.22 2.90 2.85 2.62 0.23 0.61
a
Oxidation and reduction potentials vs. ferrocene/ferrocenium redox couple.
b
Quasi-reversible.
c
irreversible.
d
HOMO and
LUMO energy levels were calculated from the redox potential with published correlation.
51, 52

e
Calculated hole reorganization
energy.
f
Calculated electron reorganization energy.
g
Photoluminescent quantum yield of vacuum deposited films containing
10% FIrpic-doped H2P .

The HOMO and LUMO values for 10a-10d were computed using the adiabatic scheme
(implemented in the Materials Science Suite) at the B3LYP/LACV3P** level where single-point
40

energies were computed for the cation, anion and neutral species using the finite-element Poisson-
Boltzmann solver (PBF) continuum solvent model
38, 39
with DMF as the solvent on the
corresponding gas-phase optimized structures. The HOMO/LUMO energies calculated using this
procedure are in reasonable agreement with experimental values as seen in Table 2.1, differing by
0.2-0.3 eV , however, the trends in the values between the four compounds experimentally were
reproduced in the theoretical values.

Figure 2.10. Highest occupied molecular orbital and lowest unoccupied molecular orbital
diagrams calculated at the B3LYP/LACV3P** level of theory. The permanent dipole moment
for each molecule is illustrated in the images at the top.

2.2.5. Tier 3 selection
The gas phase calculations in Tiers 1 and 2 agree well with the properties of the three host
41

compounds in fluid solution. However, these single-molecule calculations cannot predict the
solid-state properties of the bulk materials. The decrease in triplet energy from solution to neat
solid prompted us to include a third Tier of modeling to address solid–state properties. Because
modeling excited state energies in amorphous solids is challenging, and because triplet energy
depression were similar for the three materials, attention was turned to charge transport, the critical
role of a host material. In order to screen for the performance of 10b-10d as host materials, we
carried out theoretical studies of the three materials as amorphous solids using MD and electron
coupling DFT calculations. The search criterion for this Tier 3 screen is a maximization of charge
mobility. MD simulations were performed on a cell of 125 molecules of each host material with
periodic boundary conditions in order to model solid state morphologies. The final density for each
simulation was between 1.11-1.14 g/cm
3
.
3 4 5 6 7 8
0.0
0.5
1.0
1.5

g(r)
r (Å)
10b
10c
10d

Figure 2.11. Center of mass radial distributions [g(r)] from MD simulations of three host
materials, obtained by averaging over 30ns.

As a first approximation of charge mobility, the number of π-π interactions for 10b, 10c
and 10d were counted, with more interactions presumably being favorable for charge transport.
Here, the - interactions are classified into two types: 1) face-face interactions where two
42

aromatic rings are within a distance of 4.4 Å and a maximum angle of 30

with respect to each
other, and 2) edge-face interactions where two aromatic rings are within a distance of 5.5 Å with
a minimum subtended angle of 60

between them. The number of - contacts includes the total
number of face-face and edge-face interactions, giving a total of 324, 409, and 364 for 10b, 10c,
and 10d, respectively. Compound 10c has substantially more face-to-face -contacts than either
10b or 10d, while 10d has more face-to-edge -contacts than the other two compounds. This
preliminary analysis suggests a trend in charge transport as: 10c > 10d > 10b. A similar trend is
seen for the center of mass (COM) radial distribution functions (RDF), as shown in Figure 2.11.
The COM RDFs reflect differences in solid state center-to-center distances, which could have an
effect on charge transport in the host material. The 10b RDF clearly shows differences in distances
in the range of 4-6 Ǻ. There is approximately a 35% and 50% difference in height between the
nearest-neighbor peak maximum of the 10b RDF and the nearest-neighbor peak maximum of 10d
and 10c RDFs, respectively. This indicates a lower proportion of short center-to-center distances
in bulk 10b with respect to the other H2Ps.
A plausible explanation for the dissimilar morphologies of 10b from 10c and 10d involves
the dipole moments of each molecule. In all three cases the permanent dipole moment for each
molecule lies in the H2P plane, however, in 10c and 10d the dipole extends from the imidazole
ring into the phenanthroline, while in 10b the dipole is largely within the imidazole ring (Figure
2.10). In the amorphous solid, the molecules tend to form dimer pairs with adjacent dipoles in a
roughly antiparallel orientation. For 10c and 10d, closely spaced dimers can be formed with
antiparallel dipoles, however, for 10b overlapping the dipoles of adjacent molecules are sterically
hindered by the tert-butyl and phenyl groups on the imidazoles.
Complimentary to structural analysis of MD simulations, a quantum mechanical analysis
43

was performed. Dimer frontier orbital splitting electron coupling calculations (see methods
section) were performed on the MD equilibrated structure for all dimer pairs within a contact
distance of 4Å from each other (note that this is the closest atom-atom distance for any pair, not
the center-to-center distance or radius) amounting to a total of 838, 857, and 880 dimer pairs for
10b, 10c, and 10d respectively). These calculations were used to estimate the charge carrier
hopping rates according to equation (2.3) to assess variations in charge transport between neat host
materials. Figure 2.12 shows histograms of the calculated hole and electron hopping rates.
Notably, the distribution of electron hopping rates for 10b is significantly narrower and the rates
are slower than those of 10c and 10d. There were no significant differences in hole hopping rates
between the three host materials. This suggests that on average the dimer pairs formed for 10b
give comparable HOMO-HOMO overlap to those of 10c and 10d, but poorer LUMO-LUMO
overlap compared to 10c and 10d.
While feasible for this study, transport calculations carried out for a large number of dimer
pairs of molecules is too time consuming and impractical to be repeated for a large number of
different materials. In order to develop a more rapid, high-throughput Tier 3 materials screen, we
sought to test the validity of a smaller scale estimate of the hopping rates for each of the materials
using a truncated random subset of dimer pairs. Calculations were repeated for twenty random
dimers from the exhaustive set of dimer pairs with a spacing of 4 Ǻ or less. The distribution of
hopping rates for the smaller sets mirrors what we observed for the exhaustive calculations (Figure
2.12), suggesting that a less rigorous calculation could be used in the future to compare the range
of hoping rates expected for different materials.
The calculated hopping rates of 500 randomly selected dimer pairs from the exhaustive
dimer splitting coupling calculations of each system were then used to compute charge carrier
44

mobilities (Table 2.2). The mobilities were also computed for the hopping rates (80 dimers)
calculated from the CDFT approach in order to validate the simple dimer-splitting method. A
simple transport model proposed by Goddard, et. al
40
was used to compute the mobilities. In this
model, the carrier mobility is described by the Einstein relation:
𝜇 ℎ/𝑒 =
𝑒𝐷
𝑘 𝐵 𝑇 ( 2.4)
where D, the charge diffusivity is calculated from the hopping rates (𝜅 𝑖 ) obtained from the coupling
calculations, equations (2.5) and (2.6).

𝐷 =
1
6
∑ 𝑟 𝑖 2
𝜅 𝑖 𝑖 𝑃 𝑖 ( 2.5)
𝑃 𝑖 =
𝜅 𝑖 ∑ 𝜅 𝑖 𝑖 ( 2.6)

The index i runs over all dimer pairs for which coupling calculations were done.
Both coupling methods predict that the electron mobility of 10b would be significantly lower
than that of 10c and 10d. The dimer-splitting method was found to predict a greater disparity in
the electron mobility of 10c/10d versus 10b. Also, the hole mobility of 10c is predicted by the
CDFT approach is much larger than that of 10b and 10d compared to the dimer-splitting method.
The reason for this disparity between the two methods may be attributed to the fact that the dimer-
splitting approach does not account for the Gibbs free energy change (𝛥𝐺 in eqn. 2.3) associated
with the charge-transfer process in different dimer pairs which can be substantial in disordered
systems.
41, 42
It is important to stress that the dimer-splitting method is only useful in qualitative
estimates of the coupling, used for rank-ordering carrier mobility properties in the structurally
similar molecules of a Tier 3 set. The average coupling parameters computed using the two
methods are in good agreement with each other. The low electron mobility for 10b is consistent
45

with its greater center-of-mass intermolecular spacing leading to a lower average hoping rate for
the 500 dimer pairs examined. Tier 3, performed at various levels of theory, predicts that 10b may
display poor electron mobility in the solid state and therefore fails to meet the selection criterion.
It should be noted that the crude mobility calculations presented above are used here to
qualitatively gauge the trends in the transport properties of the candidates and are not expected to
be quantitatively accurate. More sophisticated multi-scale methods like Kinetic Monte Carlo
(KMC) based approaches among others have been developed to adequately compute mobilities of
amorphous organic materials but tend to be more computationally expensive.
41-47
After 3 Tiers of
screening on a 555 membered structure space, 2 materials were selected: 10c and 10d. For the
benefit of validating the above theoretical methods, 10b was also investigated experimentally as
an example of a poorly performing material.

Figure 2.12. Histogram plots showing the distribution of hole and electron hopping rates
extracted from the frontier dimer orbital splitting coupling calculations of both the exhaustive
dimer set and the smaller 20 dimer subset for the three host materials (top: 10b, middle: 10c,
bottom: 10d)
46

Blue PhOLEDs fabricated using 10b, 10c and 10d as hosts as reported in Sylvinson et al.
5

achieved maximum EQE values of 0.7 %, 5.0 % and 9.0 %, respectively. It is useful to compare
these OLEDs to FIrpic based OLEDs with a similar architecture, but a conventional host material.
N,N’-dicarbazolyl-4,4’-biphenyl (CBP) is a common OLED host with a triplet energy comparable
to 10c (2.6 eV) is used as the host in a device architecture very similar to the one used here the
peak EQE was reported as 6.1%.
48
Shifting to a host material with a triplet energy of 2.9 eV , i.e.
mCP, puts the host triplet close to those of 10b and 10d. The FIrpic doped mCP OLED gave a
peak efficiency of 7.5%.
48
The efficiencies of OLEDs based on 10c and 10d are comparable to
those made with similar triplet energy carbazole-based hosts, while the efficiency of 10b based
devices fall well short of comparable carbazole-based OLED.
Table 2.2. Number of - contacts and calculated mobilities for 10b, 10c and 10c.

-contacts
Isotropic mobility (x10
-4
m
2
/Vs)
Dimer-splitting CDFT
Total
-ff
(face-
face)
-ef
(edge-
face)
-ff/-ef

µ h µ e µ h
µ e

10b 324 77 247 0.31 4.45 0.67 20.3 23.4
10c 409 142 267 0.53 6.47 3.46 27.5 53.8
10d 364 72 292 0.25 6.16 5.34 14.9 41.7

In order to understand the source of the differences in device efficiencies, we roughly
deconvoluted the EQE into four limiting factors as shown in equation (2.7). The photoluminescent
quantum yield (ΦPL) was measured for phosphor doped host films and is assumed to be unchanged
in the device. The usable exciton fraction (χ) takes into account the statistical branching ratio of
electro-generated singlets to triplets with respect to the emissive species, which is unity for a
phosphorescent dopant such as Firpic. The outcoupling factor (ηe) accounts for losses due to
47

wave-guiding and plasmon absorption, and is usually 0.2-0.3.
49
Lastly, the charge recombination
factor (ηr) is the ratio of excitons formed to injected charge carrier pairs, sometimes referred to as
charge balance. Charge recombination factors that are less than unity are due to differential charge
injection or transport between electrons and holes.
Table 2.3 lists the parameters from equation (2.7) for each host. The EQE and ΦPL were
measured from devices and thin films, respectively. The χ and ηe are assumed to be 1 and 0.2,
respectively. The ηr is calculated from the other four parameters.
Φ
EL
= Φ
PL
𝜒 𝜂 r
𝜂 e
( 2.7)
Table 2.3. Efficiency parameters of the OLEDs for 10b, 10c and 10d. (ηr was computed
assuming 𝝌 =1 and 𝜼 𝐞 = 0.2)
Host
EQE
(%)
 PL
Charge
recombination
factor ( r)
10b 0.7 0.4 0.09
10c 4 0.2 1
10d 9 0.6 0.75

The highest efficiency is seen for the device with a 10d based emissive layer. The device
performance with 10c is noteworthy since the device exhibited an EQE at its theoretical limit.
Considering a 20 % PL and out-coupling of 0.2, the maximum achievable efficiency for the
OLEDs is no greater than 4%, assuming that the dopant is isotropically dispersed in the 10c host.
50

This suggests near unit efficiency for carrier recombination in these devices. The 10b-based device
exhibited the lowest device efficiency among the three hosts despite a 40% QY in a 10%
FIrpic-doped film, due to a very low charge recombination factor. The trend in J-V characteristics
shows current densities of 10c > 10d > 10b at a given voltage, agreeing well with the Tier 3
screening. Furthermore, the turn-on voltage (voltage at a brightness of 0.1 cd/m
2
) for devices
48

utilizing 10b is ca. 2 V higher than those for devices with 10c and 10d. The turn-on voltage is tied
to both injection barriers and the carrier mobilities. The dependence on carrier mobility is due to
the need for both carriers to diffuse into the EML prior to recombination to avoid exciplex
formation at the interfaces between the EML and the transport layers. We expect the barriers to
charge injection of the three host materials to be the same, so the principal factor controlling the
turn-on voltage is likely the carrier mobilities of the devices. The trend in turn-on voltages is
consistent with charge carrier mobilities within the devices of 10c, 10d > 10b.

2.3. Spiro-linked hosts
2.3.1. Library design

Figure 2.13. Eliminating weak exocyclic bonds by spiro linking high T1 components.

As noted earlier, commonly used host materials bear weak exocyclic Aryl-N/O/P/S linkages
that are suspected to be the reason for their low stability. The spiro-linked family hosts were
designed to solve this issue by converting the weak exocyclic bonds of commonly used hosts or
their components like PCz into endocyclic bonds by attaching high T1 spiro-linked units (spiro-
fluorenes etc.) as shown in Figure 2.13. Such a design is expected to be more robust against
TTA/TPA events since molecular degradation would now require the breakage of two endocyclic
bonds compared to just a single weak Aryl-heteroatom linkage that would lead to dissociation in
traditional hosts. Furthermore, the spiro-linked unit is by virtue of the tetrahedral linkage, nearly
49

orthogonal to the aromatic system that it is attached to, thereby eliminating the possibility of
extended conjugation between the units which would otherwise lead to lowering of the T1 energy
of the composite system.

Figure 2.14. DFT computed energy levels of SF-PCz with different aza-substitution patterns.

Another advantage of the orthogonal linkage is that it opens the possibility of independently
tuning individual properties like HOMO/LUMO/T1 etc. by simple strategic chemical modification
on one of the units. This is demonstrated in Figure 2.14 for SF-PCz which is an example of a
spiro-linked host which is built by spiro-linking a fluorene unit to Phenyl Carbazole (PCz). Per
DFT calculations at the B3LYP/6-311G** level, the LUMO is localized on the fluorene unit while
the HOMO densities and T1 spin densities are localized mainly on the PCz unit. Therefore,
different aza substitution patterns in the fluorene unit can modulate the LUMO levels over a large
range without affecting the HOMO and T1 levels.

Based on the aforementioned design philosophy, a large library of prospective host materials
may be conceived as depicted in Figure 2.15. Owing to the large size of the library, we again
50

implement a tier-based screening approach similar to the one used for the H2P hosts.

Figure 2.15. Prospective Spiro-linked host design space.

2.3.2. Tier 1 screening

Figure 2.16. Tier 1 spiro-linked host library.
Y =
51

A subset of all the core structures presented in Figure 2.15 were selected based on practical
considerations like ease of synthetic accessibility and are shown in Figure 2.16. As in the case of
the H2P hosts, DFT/TDDFT calculations at the B3LYP/6-311G** level (ground state optimization
performed at the B3LYP/MIDIX level) were used to compute critical parameters including T1/S1,
HOMO/LUMO energy levels for the compounds. Scatter plots of the computed T1 energies against
HOMO and LUMO levels are shown in Figure 2.17.

Figure 2.17. (top) Scatter plots of T1 against HOMO and LUMO energies for compounds in
Tier-1 sub-library. (bottom) Top 10 candidates ranked according to decreasing order of T1.

Most compounds shown above exhibit T1 energies in excess of 2.8 eV and therefore are
very attractive blue PhOLED host candidates. However, as seen for the H2P hosts, a significant
T
1
HOMO LUMO
1
3.58 -6.09 -0.95
2
3.57 -5.29 -1.07
3
3.53 -6.23 -0.90
4
3.47 -6.06 -1.06
5
3.44 -5.24 -0.90
6
3.25 -5.10 -0.75
7
3.22 -5.21 -0.60
8
3.20 -5.05 -0.86
9
3.20 -5.23 -0.76
10
3.19 -5.32 -0.88
-1.6 -1.2 -0.8 -0.4
2.8
3.0
3.2
3.4
3.6
T1
LUMO
-6.4 -6.0 -5.6 -5.2 -4.8
2.8
3.0
3.2
3.4
3.6
T1
HOMO
52

red shifting of T1 in the solid-state due to packing effects is expected for these materials as well
due to the availability of large π faces. Therefore, it is beneficial to choose structures with the
highest T1 energies for further exploration in the next tier. Accordingly, the structures were ranked
in decreasing order of their T1 energies, and the top 10 candidates are shown in Figure 2.17.
Among them, the structure bearing two Xanthene units spiro-linked to a dihydroanthracene core
(XAX, shown in blue in Figure 2.17) was selected for further exploration in the next tier due to
its symmetric structure and synthetic feasibility.

2.3.3. Tier 2 screening
While the XAX structure has a very favorable T1 energy, its very shallow LUMO makes it
a challenge to incorporate into an efficient device architecture. Therefore, in this tier, we explore
chemical modifications to lower the LUMO level to an acceptable range (-1.5 to -3 eV). Inspection
of the HOMO/LUMO densities and T1 spin density of the XAX parent structure indicates that the
LUMO is largely delocalized across the structure with a slightly higher localization on the central
unit while both HOMO and T1 densities are localized mainly on the Xanthene units. Therefore,
chemical modifications on the central unit are likely to modulate the LUMO levels without
affecting the HOMO and T1 levels. Since, the goal is to find candidates with deeper LUMO levels
relative to the parent structure, electron-withdrawing substitutions like aza-transmutations on the
central unit were explored. Accordingly, a library of all possible aza substitution patterns was
developed and DFT/TDDFT calculations at the B3LYP/6-31G* level were used to compute the
critical parameters. Figure 2.19 shows the top 20 structures in the library ranked according to the
depth of their computed LUMO levels. It may be seen that the structures still maintain high T 1
energies with many now bearing LUMO levels that are appropriate for effective integration into a
53

typical OLED device architecture.

Figure 2.18. (left to right) Schematic of Tier-2 sub-library and HOMO, LUMO and T1 densities
of XAX.

Figure 2.19. Top 20 candidates from Tier-2 screen ranked according to decreasing order of
LUMO levels.

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59

Chapter 3. Machine learning to accelerate materials design for organic
optoelectronics

3.1. Introduction
Machine learning (ML) has emerged as a useful tool aiding the advancement of virtually
every field of science and technology. The current decade has seen an explosion of reports on the
application of ML-based approaches in various aspects of materials design ranging from synthetic
design to physical property prediction.
1-25
The availability of large, structured databases and
repositories that have consistently logged inorganic material properties and structures over several
years have led to numerous studies employing ML approaches for inorganic solid-state materials
design.
26-31
Studies exploring the application of ML methods in organic molecular materials design
on the other hand have remained comparatively scarce but are growing rapidly.
17, 18, 21, 32-38
A key
aspect of developing data-driven ML solutions to the design process involves the utilization of ML
algorithms to learn structure-property relationships from available data. Several challenges plague
the development of a successful property-prediction ML workflow for organic materials like the
lack of large, structured databases consistently cataloging structure-property relationships,
morphological flexibility ranging amorphous/disordered to crystalline, inconsistency of electronic
structure methods to name a few. These challenges are exacerbated for organic optoelectronic
applications wherein viability of candidates is dependent on satisfying multiple narrowly defined
criteria, therefore requiring extremely accurate property predictions. The parameters that are most
critical for optoelectronic applications like OPVs, OLEDs etc. are energetic molecular properties
like HOMO, LUMO and excited state (Sn, Tn) energies. Developing accurate ML models to predict
these properties across large chemical libraries would significantly accelerate the discovery of
promising candidates. In lieu of a widely accessible large-scale database listing experimentally
60

derived optoelectronic properties of molecular materials, the alternative is to rely on electronic
structure methods. Recently, databases containing DFT-predicted properties of compounds
relevant for optoelectronics applications through projects like the Harvard Clean Energy Project
39

and the PubChemQC project
40
have been developed. The development of the QM7, QM8 and
QM9 libraries containing a chemical universe of molecules with up to 7, 8 and 9 non-H atoms (C,
O, N, F) respectively albeit less relevant for optoelectronic applications have served as a test bed
for benchmarking various ML strategies.
41-45
A recent report demonstrated that chemical accuracy
(~0.04 eV) could be reached for atomization energy predictions on the QM9 database using 0.7%
of the database for training indicating that highly data-efficient models can indeed be developed
for well-defined chemical subspaces.
46
Montavon et al. trained deep neural networks using
coulomb matrices as descriptors to directly predict molecular properties based on QM data albeit
on a small scale (7211 small molecules) and reported out of sample root mean square errors
(RMSE) greater than 0.2 eV and 1.7 eV for MO energies and excitation energies respectively
while using a training set that contained 70% of the database.
47
Ghosh et al. explored several deep
neural net architectures including multilayer perceptron (MLP), convolutional neural network
(CNN), and deep tensor neural network (DTNN) on a dataset of 132,000 molecules and noted that
the prediction errors were still ~0.2 eV for MO energies despite using a training set that contains
90% of the dataset.
48
The SchNet deep learning architecture was able to achieve chemical accuracy
for HOMO/LUMO energies using 84% of the QM9 database for training.
14
Recently, Kang et al.
reported random forest models using a combination of descriptors like extended connectivity
fingerprints (ECFP), molecular access system (MACCS) keys, etc. to predict excitation energies
of a subset of molecules in the PubChemQC database and the reported RMSE was still >0.4 eV,
inadequate for any virtual screening strategy.
49
Alternatively, Ramakrishnan et al. proposed a
61

hybrid approach referred to as the Δ-ML approach, wherein instead of directly predicting the
absolute values of the molecular properties from the chemical descriptors, ML models are trained
to recover the error differential between a low-level QM method like DFT and a more sophisticated
method like CC2. Using this approach, the authors reported that excitation energies can be
predicted at the level of accuracy of the CC2 method using TDDFT and the ML model trained on
CC2 data from a fraction of the database.
50
The obvious downside of this approach is that these
low-level calculations would still need to be performed on the whole database which becomes
untenable for large-scale databases.
Given the apparent infinite size of the chemical universe, an exhaustive search of this space
to identify compounds for one or more target applications appears seemingly impossible.
Furthermore, the studies mentioned above demonstrate the challenge in developing a generalized
ML model capable of predicting properties of entities in the entire chemical universe with
sufficient accuracy due to the relative sparsity and/or lack of sufficient chemical diversity of any
finite sub-library that may be developed to train such models. A further complication is that while
ab initio methods like coupled-cluster, quantum monte carlo methods etc. can achieve predictive
chemical accuracy (< 0.04 eV), they become prohibitively expensive for medium-large systems
relevant for most optoelectronic applications. Density functional theory (DFT) based methods can
often serve as a compromise between accuracy and cost. Unfortunately, a fundamental problem
with using DFT based methods to predict properties of diverse chemical spaces is the inexistence
of a single universal DFT functional that can accurately predict molecular properties of all
compounds in the chemical universe. This is even more of an issue for excited state properties, for
example, TDDFT using a common hybrid functional like B3LYP can reliably predict excited state
energies for most organic chromophores featuring simple localized transitions (π→π*, n→π*) but
62

fails in systems featuring strong charge transfer (CT) transitions which require the use of
range-separated hybrid (RSH) functionals with range separation (ω) parameters that may have to
be tuned for each system based on the extent of CT.
51-56
Furthermore, there are certain classes of
compounds like cyanine based chromophores which are of great import for optoelectronic
applications, but whose excited state properties cannot be accurately captured by traditional
TDDFT methods irrespective of the choice of functionals (errors > 0.4 eV) on account of strong
correlation effects and require more sophisticated treatments.
57
In recognition of these challenges,
here, we adopt a more conservative yet practical approach wherein localized chemical subspaces
combinatorially built by well-defined chemical modifications on one or few core chemical
structures are explored. ML models are trained on a small yet sufficiently representative subset of
this pre-defined subspace based on DFT/other QM methods that are known to predict relevant
properties accurately for the class of molecules in this space. The core structures chosen to be
explored would be ones that are, from a synthetic standpoint, amenable to a wide variety of
chemical functionalization patterns across a large number of sites/positions to increase the
likelihood of discovering candidates that satisfy design criteria for target applications. Analysis of
pertinent literature reports and chemical intuition may also help guide the process of choosing core
structures and the palette of chemical functionalities that define the exploration space. The
practicality of this approach is augmented by the fact that the entire library maybe accessible
through one or few generalizable synthetic strategies. In this work, we demonstrate that libraries
spanning millions of structures and a wide-spanning parametric design space can be generated
using this approach. We further illustrate that predictive and actionable ML models can be
developed for the generated libraries with minimal computational overhead at the accuracy
requisite for practical screening strategies vis-à-vis optoelectronic applications.
63

3.2. Library Design
The libraries used in this study were derived from 3 core structures: boron difluoride aza
dipyridylmethene (DIPYR), boron difluoride aza diquinolylmethene (α-azaDIPYR) and Pentacene
as depicted in Figure 3.1 and the corresponding libraries generated thereof will henceforth be
referred to as A, B and C respectively. The azaDIPYR and α-azaDIPYR cores represent a
relatively underexplored class of dyes that are pyridine and quinoline based analogues of the more
popular boron dipyrromethene (BODIPY) based dyes that are widely used in numerous
applications ranging photovoltaics
58-60
, lasers
61
, bio-imaging
62-65
, etc. Reported dyes based on this
core structure generally feature high extinction coefficients, high PLQY, sharp absorption and
emission profiles like several of the BODIPY dyes lending themselves to optoelectronic
applications like OPVs, OLEDs, etc.
66
However, despite their favorable properties, there have been
very few reports of their employment in optoelectronics applications. The molecular properties of
dyes based on these cores have been shown to be easily tunable by simple chemical modifications.
For instance, the unsubstituted DIPYR compound exhibits green emission while substitution of a
N atom or a CN functionality at the meso position shifts the emission to the blue region.
67, 68

Furthermore, it is possible to envision feasible synthetic routes (like Buchwald Hartwig couplings)
to a large library of compounds built from a wide array of substitution patterns on the cores from
readily available precursors. The palette of functionalities used to build combinatorial libraries
were chosen based on 2 main considerations, the first being, synthetic ease of access to all/most
compounds in the resulting library. This includes availability/synthesizability of precursors
bearing most possible combinations of the functionalities. The second consideration is chemical
disparity/diversity of functionalities within the palette. A more diverse palette would yield a more
diverse chemical space, consequently widening the ambit of property space (HOMO, LUMO, S 1,
64

T1, etc..) that may be accessed. Library A was built per the definition in Figure 3.1 with 9 different
substituents covering a wide range of electro/nucleophilicity. The positions marked Y were
restricted to only CH, aza- and fluoro-substitutions to avoid steric clashes with the BF2 group of
the core structure. The substituents on each pyridine ring are restricted to a maximum of 3 types
to maintain synthetic feasibility. This yields a total of 695,610 unique structures. Library B based
off the α-azaDIPYR core was built using a smaller palette of substituents: aza, methoxy, fluoro
and cyano groups but across a higher number of sites. The Y sites were restricted to
aza-substitutions to avoid steric clashes with the BF2 group. A maximum of 2 different types of
non-aza-substitutions and no more than 3 types including aza-substitutions are allowed for each
quinoline ring. Further, the number of aza-substitutions on each of the α-rings is restricted to 2.
These filters eliminate synthetically infeasible compounds. Upon application of these filters, a
library containing 2,286,591 unique compounds is obtained.

Figure 3.1. Core structures along with the palette of substitutions for libraries A, B and C.
65

Library C based on the pentacene core structure was built primarily with OPV applications
in mind. Pentacene based structures are attractive due to their ability to undergo singlet fission and
also the presence of a large π cloud make them potential non-fullerene acceptor candidates.
69, 70

The library was built using a palette of aza and fluoro-substitutions across 14 sites as depicted in
Figure 3.1. These substitutions are known to stabilize the LUMO, making them more likely to
serve as acceptor candidates for OPVs.
71
The number of aza and fluoro substitutions are restricted
to under 5 each, resulting in a total of 978,888 compounds. The level of chemical diversity follows
the order: A > B > C and library size follows the order B > C > A.
3.3. QM methods
The structures in the training and test sets of all 3 libraries were initially optimized using
the PM7 semi-empirical as implemented in the MOPAC2016 package.
72
The PM7 optimized
geometries were then optimized using Density Functional Theory (DFT) using the B3LYP
functional and 6-31G(d,p) basis set. All DFT calculations reported in this work were performed
using the Q-Chem 5.1 package.
73
Excited state energies were computed on the ground state
optimized structures using Time-dependent DFT (TDDFT). The triplet excited states of the
pentacene based structures were computed using the Tamm-Dancoff approximation (TDA)
74
while
in all other cases full linear response TDDFT was used. Additionally, the S1 energies of the
cyanine-based structures (A and B libraries) were computed using the restricted open-shell Kohn
Sham (ROKS) ΔSCF approach
75, 76
as implemented in Q-Chem.

3.4. ML models and features
To develop ML models, the structural information associated with each molecule in the
library like atom connectivity, bonding patterns, 3D geometry, etc. would need to be uniquely
66

encoded into a feature vector to serve as inputs to an ML model. The ML task boils down to
learning an accurate functional mapping from the feature vectors that encode chemical structure
to the associated molecular properties. Several different types of molecular feature representations
like extended connectivity fingerprints (ECFPs)
77
, Coulomb matrices
44
, bag of bonds
78
and
connectivity counts
79
have been developed to train ML models for molecular property predictions.
In this work, we use the 12
NP
3
B
featurization that was recently reported by Collins et al. and was
found to perform well for several molecular property prediction tasks especially for energetic
parameters.
79
The features were generated for the molecules in the library using the molml 0.9.0
python library that was developed by the authors who proposed this approach. The features encode
the 3D geometrical information as well as the bonding (single, double, etc.) and connectivity
information of the molecules. More details regarding the approach and its implementation can be
found in the paper published by Collins et al.
79

Two types of commonly used supervised ML methods mated with the 12
NP
3
B
featurization
have been explored in this work: Kernel ridge regression (KRR) and Gaussian processes (GP).
KRR models based on Gaussian and Laplacian kernels were explored while GP models using the
rational quadratic (RQ) and Matern kernels were developed for each library. These models were
chosen in this study on account of their ease of implementation and prior literature reporting their
efficacy for similar molecular property prediction tasks.
46, 50, 79
The mathematical forms of all 4
kernels are given below:
𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛 𝑘𝑒𝑟𝑛𝑒𝑙 : 𝑘 ( 𝑥 𝑖 ,𝑥 𝑗 )= exp ( −𝛾 𝑑 ( 𝑥 𝑖 ,𝑥 𝑗 )
2
)
𝐿𝑎𝑝𝑙𝑎𝑐𝑖𝑎𝑛 𝑘𝑒𝑟𝑛𝑒𝑙 : 𝑘 ( 𝑥 𝑖 ,𝑥 𝑗 )= exp ( −𝛾 ∥ 𝑥 𝑖 − 𝑥 𝑗 ∥
1
)
𝑅𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑄𝑢𝑎𝑑𝑟𝑎𝑡𝑖𝑐 𝑘𝑒𝑟𝑛𝑒𝑙 ( 𝑅𝑄 ) : 𝑘 ( 𝑥 𝑖 ,𝑥 𝑗 )= ( 1+
𝑑 ( 𝑥 𝑖 ,𝑥 𝑗 )
2
2𝛽 𝑙 2
)
−𝛽
67

𝑀𝑎𝑡𝑒𝑟𝑛 𝑘𝑒𝑟𝑛𝑒𝑙 : 𝑘 ( 𝑥 𝑖 , 𝑥 𝑗 )=
1
Γ( 𝜈 ) 2
𝜈 −1
(
√2𝜈 𝑙 𝑑 ( 𝑥 𝑖 ,𝑥 𝑗 ) )
𝜈 𝐾 𝜈 (
√2𝜈 𝑙 𝑑 ( 𝑥 𝑖 ,𝑥 𝑗 ) )
where 𝛽 , α, γ, l and ν are hyperparameters that will be tuned during training to find the
optimal model in each case as described below. 𝐾 𝜈 and Γ( 𝜈 ) are the modified Bessel function and
gamma function, respectively. 𝑑 ( 𝑥 𝑖 ,𝑥 𝑗 ) and ∥ 𝑥 𝑖 − 𝑥 𝑗 ∥
1
are the Euclidean and Manhattan
distances.
The hyperparameters of the KRR models (γ and the regularization parameter, α) were tuned
using a 5-fold cross-validation scheme using the training set across a 2D grid of values [10
-15
,
10
-14
,...,10
2
, 10
3
] for α and γ. The 𝛽 and l hyperparameters for the RQ models were tuned across
the range of values between 10
-12
and 10
12
. Similarly, for the Matern models, the length scale
hyperparameter (l) was tuned across a range between 10
-12
and 10
12
while two discrete values for
ν (0.5 and 1.5) were explored. All ML models reported here were implemented using the
scikit-learn python library.
80

Graph neural networks (GNN) like the ones used in PhysNet
13
, SchNet
14, 81
etc. is another
approach wherein an effective featurization is learnt on the fly during training and can therefore
offer better performance. Most GNNs that encode 3D structural information use distance matrices
or other approaches that scale exponentially with system size.
82
Here, we implement a simple
linear scaling approach to encode 3D molecular structure uniquely and efficiently within a GNN
framework. In order to uniquely represent the 3D structure of a molecule, we first build a matrix
M that represents the chemical structure in some arbitrary cartesian coordinate system:
𝑀 = [
𝑍 1
𝑥 1
𝑍 1
𝑦 1
𝑍 1
𝑧 1

⋮ ⋮ ⋮
𝑍 𝑛 𝑥 𝑛 𝑍 𝑛 𝑦 𝑛 𝑍 𝑛 𝑧 𝑛 ]
68

where, 𝑍 𝑖 , 𝑥 𝑖 , 𝑦 𝑖 , 𝑧 𝑖 represent the atomic number, x, y and z atomic coordinates respectively. Next,
3 mutually orthogonal principal axes of the molecule are determined by performing principal
component analysis (PCA) on M without dimensionality reduction. This yields 3 principal
components (𝑢 ,𝑣 ,𝑤 ) that represent 3 mutually perpendicular molecular axes in the order of
decreasing chemical variance from u through w. The original molecular coordinates can now be
transformed into the new (𝑢 ,𝑣 ,𝑤 ) coordinate system:
𝑅 = [
𝑥 ′
1
𝑦 ′
1
𝑧 ′
1

⋮ ⋮ ⋮
𝑥 ′
𝑛 𝑦 ′
𝑛 𝑧 ′
𝑛 ] = [
𝑥 1
𝑦 1
𝑧 1

⋮ ⋮ ⋮
𝑥 𝑛 𝑦 𝑛 𝑧 𝑛 ] [
𝑢 1
𝑣 1
𝑤 1

𝑢 2
𝑣 2
𝑤 2
𝑢 3
𝑣 3
𝑤 3
]
A molecular graph with 𝑛 nodes, each representing a constituent atom can now be
constructed by encoding the new transformed atomic coordinates (𝑥 ′
𝑖 , 𝑦 ′
𝑖 , 𝑧 ′
𝑖 ) as node features of
the graph. The node features are also appended/prepended by an atomic identifier that encodes the
kind of atom that the node represents. This can be either just the atomic number or a one-hot
encoding vector of atom type. The molecular graphs so constructed can now be fed as inputs into
a GNN. Like the distance matrix approaches, this approach retains rotational, translational and
permutational invariance yet its node features scales linearly with system size. Further, the distance
matrix does not fully encode 3D molecular shape information while the current approach offers a
complete representation of the molecular structure and is therefore expected to be more powerful
especially for prediction of intensive molecular properties that tend to require more global
descriptors.
The GNN architecture used in this work is shown in Figure 3.2. The model consists of a
series of GNN layers followed by a pooling layer and a series of classical MLP (Multi-layer
Perceptron) layers. The number of GNN (m = 6, 8, 10, 12) and MLP layers (n = 6, 8, 10, 12) is a
69

hyperparameter in the model, as are the number of nodes (N = 512, 1024) in each layer, aggregation
functions (sum, average), batch size (16, 32, 64) and learning rate (10
-1
-10
-3
). A grid search across
hyperparameter size was performed to find the optimal model. The ReLU activation function was
used for all neurons in the model. The hyperparameter that yielded the best model for the dataset
are as follows: m = 12; n = 6; N = 1024; Batch size = 16; Aggregation = Sum; Learning rate = 10
-
2
. The GNN models were built using the Spektral 1.0 library.
83

Figure 3.2. GNN architecture employed in this work.

3.5. Benchmarking and validating QM methods
The success of any computational screening/exploration method hinges on how reliably
and accurately relevant properties can be computed. With respect to optoelectronic applications,
excited state energies (Sn,Tn) are the most crucial parameters and predicting them with a high level
of accuracy is vital. As noted earlier, TDDFT is often the method of choice for computing excited
state energies due to its ease of implementation, a balance of low computational cost and high
PCA transformed graph
GNN-1
MLP-n
GNN-m
MLP-1
Output
Pooling layer
Batch Normalization
Aggregation
Activation
70

accuracy in most cases. Unfortunately, TDDFT based methods fail to accurately predicted S 1
energies of the cyanine family of dyes to which both the DIPYR and α-DIPYR based compounds
belong, with errors in excess of 0.4 eV irrespective of the choice of the functional.
57, 66
For instance,
the S1 energy of BODIPY, a green luminescent dye predicted by TDDFT at the B3LYP/6-31G(d,p)
level is 3.1 eV (violet). The errors likely stem from the breakdown of the adiabatic approximation
used in traditional TDDFT methods and warrants the need for more sophisticated treatments (See
Chapter 4 for more details). ΔSCF methods like MOM (Maximum overlap method) and Restricted
Open-shell Kohn Sham method (ROKS) have recently been shown to accurately predict excitation
energies in such cases.
84
Such methods are very attractive since their costs are on par with TDDFT.
In this work, we employ the Restricted Open-shell Kohn Sham method (ROKS) which is a ΔSCF
method like MOM but is expected to be more reliable in converging to the lowest excited singlet
state (S1).
76
We have performed ROKS calculations at the B3LYP/6-31G(d,p) level for a series of
DIPYR and α-DIPYR based dyes for which experimental data is available and are compared in
Table 3.1. The S1 energies predicted by ROKS are found to be in excellent agreement with the
experimental values while TDDFT based methods grossly overestimate the energies. The T1
energy is another key parameter that should be considered while designing materials for
optoelectronic application especially ones like OPVs and OLEDs due to the relevance of
triplet-based processes like TTA, TPA, Voc losses in OPVs via triplet channels, luminescence
losses in OLEDs through ISC, etc. Additionally, recent reports have indicated that the T 2 state in
the DIPYR parent structure is slightly lower in energy than the S1 state and has been blamed for
PLQY losses via ISC into the T2 state which is further enhanced since the T2 state bears a different
symmetry (El Sayed’s rule) relative to the S1 state.
66
Therefore, the T2 state is another parameter
that needs to be considered while exploring these compounds for optoelectronic applications. The
71

TDDFT predicted T1 energies, unlike the S1 energies are in good agreement with experimental
values. Unfortunately, there are no reports that have reported the experimentally measured T2
energies for any of these systems and hence we are forced to rely on the TDDFT computed values.
With respect to the pentacene based structures for which experimental data is available, the S 1
energies calculated by TDDFT are found to be in good agreement with experimental values (Table
3.1). However, TDDFT without the Tamm Dancoff approximation (TDA)
74
is known to
underestimate the triplet state energies of pentacene.
85
Therefore, TDA was used to predict triplet
energies for all pentacene-based structures reported here and it can be seen from Table 3.1 that the
TDA values are in good agreement with experimental values.

Figure 3.3. Benchmarks for DFT predicted HOMO/LUMO energies against UPS/IPES data
86
.
72

Table 3.1: Comparison of DFT predicted values with experimentally reported values of relevant
properties for related compounds.

HOMO LUMO S 1 T 1
Reference
Exp. Calc. Exp. Calc. Exp. Calc. Exp. Calc.
1 -4.95 -5.27 -2.09 -1.89 2.57 2.54*

2.15 2.11 Ref.
87

2 -5.25 -5.41 -2.53 -2.33 2.37 2.22* 1.94 1.86 Ref.
87

3 -5.88 -5.95 -2.06 -2.00 3.11 3.04* 2.64 2.65 Ref.
68

4 -6.21 -6.02 -2.52 -2.42 2.86 2.73* 2.56 2.40 Ref.
68

5 -4.85 -5.02 -2.70 -2.68 1.86 1.94 0.86
0.58,
0.98
Ref.
69, 85, 86

6 - -5.93 - -3.26 2.14 2.13 -
0.82,
1.16
Ref.
71

*ROKS(B3LYP/6-31G(d,p))

In addition, frontier molecular orbital (HOMO/LUMO) energies are another set of
parameters that need to be considered while designing optoelectronics materials. Several studies
have benchmarked HOMO/LUMO energies calculated by DFT methods in vacuo against UPS and
IPES measurements for a range of organic semiconductor materials and have arrived at linear
correlations.
86, 88
For consistency, we have also derived linear correlations between the reported
UPS/IPES derived HOMO/LUMO values with the DFT computed values at the
B3LYP/6-31G(d,p) level, the methodology used in this study and obtain good R
2
values (see
Figure 3.3). While UPS/IPES data is unavailable for DIPYR, α-DIPYR and pentacene-based
73

compounds, electrochemical oxidation and reduction potentials have been reported for a few of
these and related compounds and may be used as surrogates. Linear correlations between
oxidation/reduction potentials and UPS/IPES derived HOMO/LUMO values have been reported
for common organic semiconductors.
86, 88, 89
The correlation factors reported in Janus et al.
86
were
used for the current study. The DFT computed HOMO/LUMO values with the correlation factors
(UPS/IPES→DFT) applied are compared with the values derived from electrochemical
measurements with the corresponding correlation factors (UPS/IPES→Ox./Red. Potentials) and
are found to be in good agreement with each other (Table 3.2). Higher excited states (S2-S5 and
T3-T5) though less critical for most optoelectronics applications have also been computed and
correspondingly ML models may be similarly developed.

3.6. ML workflow
A schematic of the workflow used in this work is shown in Figure 3.4. Once the libraries
are generated, the 3D geometry of each molecule is converted to its 12
NP
3
B
encoding for the
classical KRR and GPR ML models while the GNN models accept 3D cartesian coordinate
information as their input (described in the methods section). Each library is split into three sets: a
training set which will be used to train the ML models, a test set that will be used to test the validity
of the ML models and assess their accuracy and finally, the prediction set is the rest of the library
for which predictions are made using the ML models. DFT calculations parametrized by the
aforementioned benchmarks would need to be performed for the molecules in the training and test
sets in order to develop the ML models. During training, the ML model takes the geometric
encodings and the DFT computed properties of the molecules in the training set as inputs and
attempts to learn the relationship between them. The size of the training set was initially set to 100
74

and was gradually increased stepwise in increments of 250 molecules by borrowing molecules
from the prediction set. At each step, the error metrics (MAE, R
2
) of the trained ML model is
computed for predictions on the test set. The training set size may be increased until the desired
accuracy is reached or until the error metrics cease to improve appreciably. The size of the test set
was set at 450 molecules for all 3 libraries as further increases in size did not lead to significant
differences in the error metrics indicating that a sufficiently representative sampling of the whole
library was reached. Finally, the optimized ML model may then be used to make predictions on
the rest of the library (prediction set).

Figure 3.4. Schematic of ML workflow used in this work.

3.7. Results and Discussion
The performance of 2 kernel ridge regression (KRR:Gaussian and KRR:Laplacian) models
and 3 gaussian process regression (Rational quadratic and 2 variants of Matern) ML methodologies
Library Generation
Test Set Training Set Prediction Set
Geometrical
Descriptors
DFT
Geometrical
Descriptors
ML Model
Optimized ML
Model
ML errors
<<
threshold
?
True
False
Increase Training : Prediction
set ratio
Prediction
75

was compared with the GNN models developed in this work for each of the 3 libraries (see methods
section for details). Matern (ν = 1.5) models for libraries A and B failed to converge for training
set sizes below 750 and 500 respectively while GNN models were only trained for 1000, 1500 and
2000 training set sizes. The GNN models outperformed the classical ML models and featured the
best prediction metrics (MAE and R
2
) while the Matern (ν= 0.5) model exhibits the worst metrics
among all the models as seen in Figure 3.5. It should be noted that the metrics reported are
averaged across the 5 most pertinent energetic parameters (HOMO, LUMO, S1, T1 and T2).
0 500 1000 1500 2000
0.05
0.1
0.15
0.2
KRR (Gaussian) KRR (Laplacian) RQ Matern (0.5) Matern (1.5) GNN
MAE (eV)
Training set size
A B C
0.4
0.6
0.8
1
0 500 1000 1500 2000
0
0.05
0.1
0.15
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000
0
0.05
0.1
0.15
0.2
0.4
0.6
0.8
1
R
2

Figure 3.5. Performance of different ML models with varying training set sizes for the 3
libraries.

The GNN models were used for all further analyses as they were the best performing
models across the board. The errors follow a normal distribution and expectedly becomes narrower
with increasing training set size. In all cases, the error distribution is broadest for the energy of the
T2 state. Library A shows the broadest distribution with about 89.2% and 98.9% of the errors
within the 0.1 eV and 0.2 eV bins respectively for the model trained on 2000 samples. This can be
attributed the fact that this is the most chemically diverse of all 3 libraries considered. For library
B, the model trained on 2000 molecules was able to restrict 92.5% and 99.5% of errors within the
0.1 and 0.2 eV bins respectively on average. For library C on the other hand, the model trained on
just 1000 samples was able to confine about 97% of the errors within 0.1 eV. A detailed list of the
76

metrics for individual properties obtained from the models are tabulated in Table 3.2 for the 3
libraries.
Table 3.2. Error metrics of GNN models trained on 1000, 1500 and 2000 molecules for the 3
libraries on a test set of 450 structures each. The last 3 columns refer to the percentage of
molecules in the test set featuring errors below 0.10, 0.15 and 0.20 eV.

MAE RMSE
R
2

%(<0.10) %(<0.20)

1000 1500 2000 1000 1500 2000 1000 1500 2000 1000 1500 2000 1000 1500 2000
A
HOMO 0.085 0.059 0.052 0.110 0.080 0.067 0.971 0.984 0.991 66.3 83.1 86.6 93.1 98.2 99.2
LUMO 0.074 0.045 0.044 0.097 0.057 0.055 0.975 0.990 0.993 73.8 91.1 92.9 95.7 100.0 100.0
S
1
0.062 0.050 0.040 0.080 0.065 0.052 0.915 0.944 0.968 82.1 90.4 95.3 98.4 99.4 99.6
T
1

0.076 0.061 0.046 0.103 0.077 0.059 0.894 0.940 0.964 72.8 84.1 92.1 92.9 98.6 99.2
T
2

0.084 0.071 0.067 0.110 0.094 0.090 0.863 0.897 0.920 66.7 76.8 79.1 93.1 95.9 96.7
Avg. 0.076 0.057 0.050 0.100 0.075 0.065 0.924 0.951 0.967 72.3 85.1 89.2 94.6 98.4 98.9
B
HOMO 0.066 0.040 0.039 0.088 0.053 0.051 0.984 0.992 0.993 80.1 93.3 95.1 96.5 99.8 99.8
LUMO 0.064 0.037 0.040 0.084 0.048 0.050 0.987 0.995 0.997 79.7 94.1 95.5 97.0 99.8 100.0
S
1
0.049 0.040 0.031 0.064 0.052 0.039 0.908 0.958 0.969 88.6 94.7 98.6 99.6 100.0 100.0
T
1

0.059 0.037 0.034 0.077 0.050 0.043 0.917 0.963 0.973 81.9 93.9 97.2 98.8 99.6 100.0
T
2

0.098 0.065 0.068 0.122 0.084 0.086 0.898 0.941 0.955 58.5 77.0 76.2 89.2 97.8 97.6
Avg. 0.067 0.044 0.042 0.087 0.058 0.054 0.939 0.970 0.977 77.8 90.6 92.5 96.2 99.4 99.5
C
HOMO 0.031 0.020 0.011 0.036 0.025 0.014 0.994 0.994 0.999 100.0 100.0 100.0 100.0 100.0 100.0
LUMO 0.042 0.015 0.013 0.049 0.020 0.015 0.993 0.995 0.999 99.0 99.8 100.0 100.0 100.0 100.0
S
1
0.035 0.032 0.024 0.043 0.041 0.029 0.959 0.939 0.988 99.2 97.8 99.4 100.0 100.0 100.0
T
1

0.023 0.026 0.025 0.028 0.032 0.028 0.956 0.948 0.991 100.0 99.8 100.0 100.0 100.0 100.0
T
2

0.049 0.057 0.025 0.067 0.080 0.035 0.935 0.947 0.981 86.8 84.3 98.4 98.6 96.1 100.0
Avg. 0.036 0.030 0.020 0.044 0.040 0.024 0.967 0.965 0.991 97.0 96.3 99.6 99.7 99.2 100.0

77

For each library, the GNN models trained on 2000 samples were used to make predictions
on the rest of the library (prediction set). The predictions on A and B indicate that luminophores
across the entire visible spectrum may be accessible with S1 energies spanning 1.3 – 3.5 eV.
Predictions on library C also span a wide parametric design space vis-à-vis OPV applications. The
scatter plots for the properties are given in Figure 3.8-3.10. The validity of these predictions is
demonstrated for two niche applications that our research group has been interested in and is
actively pursuing.

3.8. Fluorescent dopants for hybrid WOLEDs
The first involves developing an efficient blue fluorophore that has the optimal energetic
alignment of energy levels to be viable in a hybrid white-OLED (WOLED) architecture like the
one proposed by Sun et al.
90
The generation of white light for solid-state lighting applications
requires red, green and blue-emitting components (or alternatively blue and yellow). The ideal
luminophore for these components would be phosphors as they are capable of harvesting both
singlet and triplet excitons that are electrogenerated in a 1:3 ratio within the OLED and can
therefore reach internal quantum efficiencies as high as 100%.
91-94
Fluorophores on the other hand
can only harvest singlet excitons which caps the maximum IQE achievable at 25%. While several
efficient red, green and yellow phosphors have been developed that are stable and have operational
lifetimes >10,000 hours, a stable and efficient blue phosphor with a long operational lifetime viable
for commercial applications is still elusive. Blue fluorophores can reach longer operational
lifetimes necessary for commercial viability but as mentioned earlier are capped at 25% IQE. A
hybrid architecture like the one depicted in Figure 3.6(a) which uses a blue fluorophore doped
near the exciton formation zone along with red and green (or yellow) phosphors doped a certain
78

distance (greater than the singlet exciton diffusion distance but within that of the triplet excitons)
away from the zone within a single stack would in principle be able to achieve white light emission
with 100% IQE while eliminating the need for a stable blue phosphor.
90, 95
This is possible because
within such an architecture, provided the energy levels of the components are aligned as depicted,
all singlet excitons (25%) formed within the device would be harvested by the blue fluorophore
while all the triple excitons (75%) formed would diffuse to the red and green (or yellow) phosphors
resulting in emission. The energy level requirements are as follows: The fluorophore should be
blue emissive, therefore its S1 state would preferably be in the 2.64 - 3.1 eV range while its T1 state
would need to be higher in energy than that of the host which would in turn be higher than that of
the green/yellow phosphors used in the device. This translates to the constraint that ideally the T1
state of the fluorophore be > 2.3 eV to ensure that the triplet excitons can diffuse to the phosphors
and are not trapped on the fluorophore. Libraries A and B were built with this application in mind
as these classes of molecules are known to exhibit very high fluorescence quantum yields with
sharp emission lines making them very attractive as dopants. There has been some suggestion from
previous reports that the quantum yield can be diminished if the T2 state lies below the S1 state in
these classes of compounds.
66
Therefore, the condition that T2 >> S1 would be an additional
criterion that would need to be satisfied by a viable candidate from these libraries. The predictions
from the GNN(2000) models for libraries A and B were used to screen for blue fluorophores viable
for the current application based on the 3 conditions mentioned above, namely, 2.64 < S1 < 3.1 eV
, T1 > 2.3 eV and T2 > S1. This yields a total of 62,359 and 218,384 candidates from A and B
respectively that satisfy these criteria. These were further filtered to include only compounds with
3 or fewer substitutions as these are more attractive from a synthetic standpoint, yielding 751 and
220 candidates, respectively. Of the 751 compounds selected from library A, the top 100
79

candidates ranked according to their T2-S1 gap were chosen for further analysis (i.e. validation by
DFT) to keep size of the library manageable while all 220 compounds from B were carried forward
to the next step.
a b c

d e f
-7 -6.5 -6 -5.5
-3
-2.5
-2
-1.5
2.6 2.8 3 3.2
2.2
2.4
2.6
2.8
3
2.6 2.7 2.8 2.9 3
2.2
2.3
2.4
2.5
2.6
2.7
A (DFT)
A (ML)
B (DFT)
B (ML)
LUMO
HOMO
DFT (T
2
> S
1
)
DFT (T
2
< S
1
)
ML
T
1
S
1
DFT (T
2
> S
1
)
DFT (T
2
< S
1
)
ML
T
1
S
1

Figure 3.6. (a) Schematic of hybrid WOLED architecture explored here; (b), (c) Scatter plots of
T1 and S1 energies predicted by the GNN(2000) models for libraries A and B respectively with
the region of interest highlighted; (d) Scatter plot of ML and DFT predicted HOMO and LUMO
energies for selected candidates from A and B that satisfy the hybrid WOLED design criteria
(based on ML predictions); (e), (f) Distribution of ML and DFT predicted S1 and T1 energies of
selected candidates from A and B respectively. Hollow circles indicate candidates with T2 < S1
according to DFT calculations.

DFT calculations (as detailed in the methods section) were then performed on the selected
candidates from the previous step to confirm the validity of the ML models and the results are
80

shown in Figure 3.6 (d, e, f). Based on the DFT calculations, 71.0% and 87.7% of the compounds
from A and B respectively, predicted by the GNN(2000) ML models were confirmed to satisfy the
aforementioned design criteria. The chemical structures of the compounds that satisfy the criteria
are shown in Figure 3.11 and Figure 3.12. It should be noted that analysis of false negatives within
the margins were ignored to limit computational overhead and are expected to mirror the false
positivity rate due to the symmetric nature of the normal error distribution.
3.9. Singlet fission chromophores
The second application explored here is associated with singlet fission (SF), a phenomenon
where upon absorption of a photon, the resulting singlet exciton splits into two triplet excitons.
69

This usually occurs in molecules whose T1 state energy is roughly half that of the S1 state. Singlet
fission is very attractive for photovoltaic applications as this enables the utilization of some of the
excess energy of high energy excitons (above the junction gap) which would otherwise be lost as
heat in a traditional single-junction cell.
96
SF materials may be used as sensitizers in OPVs or
inorganic solar cells to boost efficiency potentially beyond the Shockley-Queisser limit.
69, 96, 97

Pentacene-based structures are among the few classes of molecules that have been shown to exhibit
singlet fission.
69
From a design standpoint, having a slate of SF materials with a wide range of
S1/T1 and HOMO/LUMO parameters would enable their incorporation in a range of device
configurations and allow for greater flexibility in optimizing for maximal performance. Given the
limited number of SF materials that have been identified so far and the desire for a wide gamut of
parametric space, Library C, based off the pentacene core was developed.
A viable SF candidate would satisfy the condition that S1 ≈ 2T1 and more preferably 0 <
S1 - 2T1 < 0.2 eV to minimize energy losses. An additional condition: T2 > 2T1 may be imposed to
ensure that bimolecular T1-T1 annihilation events leading to T2 excitons are disfavored.
69, 96

81

Application of the above constraints to predictions of the GNN(2000) model on library C yields
11,691 SF-likely structures occupying a wide parametric space with HOMO/LUMO energies
spanning across a ~2 eV range with S1 energies ranging 1.2-2 eV (Figure 3.7(a)). The scope was
further narrowed to include only structures with 6 or fewer substitutions yielding a set of 1,935
structures. DFT calculations were performed on a random collection of 150 structures from this
set to confirm the validity of the model and the results are depicted in Figure 3.7(c). Of the 150
structures, 112 (75%) were confirmed by the DFT calculations to satisfy the SF criteria as defined
strictly while the rest remain close to the margins as shown in Figure 3.7(b), demonstrating the
efficacy of the model in identifying viable SF candidates.
a b

1.6 1.7 1.8 1.9
0.8
0.9
1
T
1
S
1
DFT
ML

Figure 3.7. (a) Scatter density plots of S1 and T1 energies with the enclosing gray area indicating
the SF parametric space wherein 0 < S1 - 2T1 < 0.2 eV; (b) DFT and ML predicted S1 and T1
energies of selected candidates with gray region as in (a) highlighting the space satisfying the SF
criteria.

3.10. Conclusion
In this study, large chemical libraries were combinatorially built based on 3 core structures
with the goal of identifying suitable candidates for target optoelectronic applications. QM methods
82

that accurately and cost-effectively predict crucial optoelectronic parameters for the classes of
molecules contained in the libraries were identified and benchmarked. Accurate ML models for
predicting these optoelectronic parameters were trained based on the benchmarked QM
calculations on a fraction (<0.3%) of the library. The predictions from the models were then used
to screen the libraries and identify suitable candidates for 2 target applications which were again
verified by DFT. We have therefore demonstrated that using the prescriptions presented here,
predictive ML models can be obtained for local chemical spaces at the level of accuracy needed
to screen and identify suitable candidates for target optoelectronic applications with limited
computational resources. While the models presented here already achieve high accuracies using
small training sets, future work will be aimed at exploring other types of featurization and ML
algorithms that will hopefully achieve even higher data-efficiency and accuracy across more
diverse chemical spaces. We also hope that this work motivates the employment of more data-
driven solutions in the design of materials for optoelectronic applications at large.

Figure 3.8. Scatter matrix plots of properties predicted by the GNN(2000) model for library A.
83

Figure 3.9. Scatter matrix plots of properties predicted by the GNN(2000) model for library B.

Figure 3.10. Scatter matrix plots of properties predicted by the GNN(2000) model for library C.

84

Figure 3.11. Potential fluorescent dopants for WOLEDs obtained by screening library A using
the GNN(2000) model and validated by DFT.
85

Figure 3.12. Potential fluorescent dopants for WOLEDs obtained by screening library B using
the GNN(2000) model and validated by DFT.

86

Figure 3.13. Potential singlet fission candidates in library C predicted by the GNN(2000) model
and validated by DFT.
87

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98

Chapter 4. Accurately predicting excited state energies of BODIPY, DIPYR
and MR dyes with low-cost DFT approaches

4.1. Introduction
BODIPYs (Boron–dipyrromethenes) represent a very important class of organic dyes that
generally feature sharp absorption and emission profiles, small Stokes shift, high PLQY and
extinction coefficients making them very attractive for a wide-range of applications.
1-3
Some of
these applications include solar cells
4-6
, lasers
7
, photodynamic therapy
8-11
, bio-labeling
8, 12-15
etc.
Over time, a large collection of dyes based on this platform have been developed and
characterized.
1, 2, 16-18
Our lab has been interested in this class of dyes for both OLED (as
fluorescent dopants, see Chapter 3.8) and OPV applications. However, accurately predicting the
excited state properties of this class of dyes using quantum chemistry methods has posed a
significant challenge.
9, 19-22
Time-dependent Density functional Theory (TDDFT), the method of
choice to predict excited state energies due to its cost-effectiveness has been found to drastically
over-estimate S0-S1 vertical excitation energies (often >0.4 eV) across a range of functionals.
19

Previous reports have indicated that the errors may be a result of significant double excitation
character of the S1 state which cannot be captured by TDDFT which is a single excitation method
in its traditional implementation.
9, 19
Such states can be accurately described by expensive
correlated wavefunction approaches like CASPT2, XMCQDPT2, ADC(3) etc. but become
unviable even for moderately sized systems that may be considered for practical applications.
19, 23

Empirically derived linear correction factors to offset TDDFT errors have been estimated for
several functionals
19, 24
based on experimental data but this presents a less than ideal solution as
their extent of generalizability is unclear. Momeni et al. noted that moderately expensive correlated
ab initio approaches like LCC2* (local coupled cluster second order) and SAC-CI methods reduce
99

prediction errors relative TDDFT and surprisingly to more expensive and rigorous correlated
excited state approaches like EOM-CCSD and attributed the anomaly to cancellation of errors.
19

Recently, a new version of the EOM-CCSD approach, DLPNO-STEOM-CCSD was shown to
achieve a very high level of accuracy with errors as low as 0.07 eV on average for a collection of
51 BODIPY dyes.
22
Jacquemin et al. reported that SOS-CIS(D), the semi empirically scaled
opposite spin variant of CIS(D) was able to offer improved accuracy (~0.1 eV for a collection of
47 BODIPY dyes) but this approach still scales roughly as the 4
th
power of system size compared
to the ~2
nd
order scaling of TDDFT.
21
More recently, the Spin-flip TDDFT (SF-TDDFT) approach
which accounts for certain double excitation configurations at the same cost as traditional TDDFT
was shown to offer accurate predictions.
25

Recently, another similar class of aza-boron-based polycyclic dyes sometimes referred to
as MR (Multi-resonance) dyes have garnered a lot of attention due to their application in OLEDs
as efficient TADF dopants.
26-30
Like BODIPY dyes, they feature sharp absorption/emission
profiles, high extinction coefficients, PLQY and additionally most of these dyes have small S1-T1
gaps which enables efficient TADF.
26, 29
A representative collection of this class of dyes is shown
in Figure 4.1. It has been reported that these dyes present the same challenge as BODIPYs wherein
the TDDFT-computed S0-S1 vertical excitation energies are overestimated irrespective of the
choice of functional used and since these dyes have only recently gained prominence, there have
been very few computational studies on these dyes and the source of the errors remains unclear.
28

In this work, we explore the applicability of two low-cost DFT-based approaches namely,
Restricted Open-shell Kohn Sham (ROKS)
31, 32
and the aforementioned Spin-flip TDDFT (SF-
TDDFT) approach
33
in predicting vertical excitation energies of these two important classes of
dyes. A key motivation for exploring these methods is the fact that both methods are well-suited
100

to handle states with double excitation character at a cost comparable with traditional TDDFT.
34,
35

4.2. Computational Methods
All calculations reported in this work were performed using the Q-Chem 5.3 software
package.
36
Ground state optimization was performed for all structures at the B3LYP/6-31G(d,p)
level in vacuum. All subsequent excited state calculations were performed on these optimized
structures. The long alkyl chains in M13, M14 and M15 were replaced by methyl groups to reduce
computational effort. For the ROKS calculations, the DIIS algorithm was used in most instances
but in cases where DIIS failed, the GDM algorithm was used instead. The SCF convergence
criteria in all cases were set to 10
-8
Hartree. SF-TDDFT calculations were performed using both
the collinear approach
33
and Ziegler’s non-collinear kernel
37
as implemented in Q-Chem. TDDFT
calculations were performed both with and without the Tamm Dancoff approximation (TDA) for
all the functionals surveyed in this work. All functionals were used in their standard forms as
implemented in Q-Chem. The 6-31G(d,p) basis set was used for all ROKS,TDA/TDDFT and SF-
TDDFT calculations. Excited states were also computed using ADC(3) (third order Algebraic
Diagrammatic Construction scheme) with the VDZ basis set for a subset of 22 compounds that
were small enough for the calculations to be feasible.
4.3. Results and Discussion
The structures of all 35 BODIPY and 20 MR dyes considered in this work are shown in
Figure 4.1 (a) and (b) respectively. Compounds B1-B23 are the collection of dyes that were
considered in the exhaustive benchmarking study done by Momeni et al. and the experimental
S0→S1 excitation energies reported therein are used in the current work as well.
19
In that study, for
cases where experimental data was unavailable (B2, B3 and B8) CASPT2 results were used
101

instead. Additionally, B4 was found to be rather anomalous with all methods considered in the
study including CASPT2 seemingly underestimating the S0→S1 excitation energy relative to the
reported experimental value (4.175 eV) by large margins.
19, 38
The compound was also reported to
exhibit a large stokes shift of ~0.5 eV which is quite uncommon for this class of dyes.
38

Figure 4.1. Chemical structures of the 35 BODIPY-based dyes (a) and MR dyes (b) considered
in this study.

102

It was also reported that the fluorescent emission was highly solvatochromic while the
absorption spectrum was largely unaffected by different solvents. This seems to suggest that the
S1 state is likely a charge-transfer (CT) state with low oscillator strength (f) and that a higher bright
state may have been misidentified as the S1 state based on the absorption spectra. Based on the
natural transition orbitals (NTOs) computed at the B3LYP/6-31G(d,p) level, the S1 state was found
to largely be a CT transition from the 5-membered ring to the 6-membered ring. The computed f
for the transition was 0.1, much lower than the oscillator strengths of most other BODIPY dyes.
On the other hand, the transition to the S2 state had a computed f of 0.3 suggesting that this higher
transition may have been perhaps incorrectly assigned as the S0→S1 transition. Therefore, to avoid
these ambiguities, the CASPT2 excitation energy (3.278 eV) reported by Momeni et al. was used
as the ground truth instead of the experimental value for B4.

Table 4.1: MAE (eV) and R2 values associated with the predictions of E(S1) and E(T1)
using the different DFT methods studied in this work at the B3LYP/6-31G(d,p) level.

Method
E(S
1
) E(T
1
)
MAE
R
2

MAE
R
2

BPY MR All BPY MR All BPY MR All BPY MR All
TDA 0.600 0.279 0.484 0.800 0.895 0.700 0.060 0.083 0.073 0.936 0.901 0.878
TDDFT 0.387 0.210 0.323 0.875 0.937 0.853 0.097 0.056 0.074 0.941 0.919 0.875
ROKS 0.088 0.080 0.085 0.977 0.943 0.963 - - - - - -
SF-TDDFT
(col.)
0.155 0.268 0.196 0.949 0.973 0.949 0.119 0.091 0.103 0.931 0.910 0.820
SF-TDDFT
(non-col.)
0.090 0.189 0.126 0.968 0.972 0.960 0.061 0.132 0.102 0.930 0.900 0.842

103

The experimental data for compounds B24-B35 is based on our previous works
23, 39
while
the data for the MR dyes, M1-M20 are based on recent literature reports.
26, 27, 29, 40-47
In all cases,
the vertical S0→S1 transition energy is based on the λmax of the absorption spectra. Wherever,
absorption spectra in multiple solvents/media are available, the spectrum measured in the least
polar medium is used in order to minimize solvation effects. Fortunately, most of these dyes exhibit
minimal solvatochromism greatly simplifying the task of benchmarking calculations performed
in-vacuo.
0.98 0.87
0.92
0.91
0.59
0.82
0.64 0.53
0.42
0.47
0.95
0.96
0.93
0.94
0.92
0.97
0.98
0.92 0.93
0.94
0.95
0.92 0.92
0.95
0.89
0.85
0.90 0.83
0.80
0.86
0.97
0.97
0.96 0.95
0.95
0.97
0.97
0.94
0.94
0.94
B3LYP
PBE0
B97M-V
BLYP
M06-2X
M06-HF
M08-HX
CAM-B3LYP
ωB97M-V
ωB97X-D
0
0.2
0.4
0.6
0.8
MAE
ROKS
B3LYP
PBE0
PBE50
B5050LYP
CAM-B3LYP
0
0.2
0.4
0.6
0.8
MAE
Collinear SF-TDDFT
Non-collinear SF-TDDFT
BODIPY MR
B3LYP
PBE0
B97M-V
BLYP
M06-2X
M06-HF
M08-HX
CAM-B3LYP
ωB97M-V
ωB97X-D
0
0.2
0.4
0.6
0.8
MAE
B3LYP
PBE0
PBE50
B5050LYP
CAM-B3LYP
0
0.2
0.4
0.6
0.8
MAE
a b
c
d

Figure 4.2. Functional dependence on the accuracy of the ROKS (a,c) and SF-TDDFT (b,d)
methods for the BODIPY (top) and MR (bottom) dyes. The number atop each bar represents the
R
2
values for each corresponding functional. (MAEs are reported in eV)

Several popular DFT functionals across different rungs were surveyed for both the ROKS
and SF-TDDFT methods and their performance in predicting the S0→S1 transition energies of both
104

classes of dyes is summarized in Figure 4.2. For simplicity, the vertical transition energies to the
excited states will henceforth be referred to simply as E(S1), E(T1) etc. Several other works have
surveyed functional dependence on the accuracy of traditional TDDFT for these classes of dyes
and have found that none of the functionals provide satisfactory accuracy.
19, 28
In this work, we
therefore do not attempt another functional survey for TDDFT but instead use TDDFT with the
popular B3LYP functional as the point of reference against which the performance of the ROKS
and SF-TDDFT methods is assessed. It should be noted that as has been reported,
20
the predictions
of E(S1) for these dyes are drastically different depending on whether TDDFT is performed with
or without the Tamm Dancoff approximation (TDA) and henceforth will be referred to as TDA
and TDDFT respectively. TDA tends to overestimate the E(S1) to a greater extent and hence
exhibits larger errors as shown in Table 4.1 and Figure 4.3. The gulf between the accuracy of the
two methods is greater for the BODIPY dyes (ΔMAE
(TDDFT-TDA)
= 0.213 eV) relative to the MR
dyes (ΔMAE
(TDDFT-TDA)
= 0.069 eV).
1.5 2 2.5 3 3.5 4
1.5
2
2.5
3
3.5
4
1.5 2 2.5 3 3.5 4
1.5
2
2.5
3
3.5
4
1.5 2 2.5 3 3.5 4
1.5
2
2.5
3
3.5
4
1.5 2 2.5 3 3.5 4
1.5
2
2.5
3
3.5
4
TDA (S
1
)
*Exptl. (S
1
)
BODIPY
MR
MAE = 0.484 eV
R
2
= 0.700
MAE = 0.085 eV
R
2
= 0.963
MAE = 0.323 eV
R
2
= 0.853
MAE = 0.126 eV
R
2
= 0.960
TDDFT(S
1
)
*Exptl. (S
1
)
BODIPY
MR
a
c
b
d
ROKS (S
1
)
*Exptl. (S
1
)
BODIPY
MR
SF-TDDFT(S
1
)
*Exptl. (S
1
)
BODIPY
MR

Figure 4.3. Comparison of the predictions of E(S1) using the TDA (a), TDDFT (b) ROKS (c)
and SF-TDDFT (d) methods using the B3LYP functional against experimental values. (All
values in eV)
105

For the ROKS method, 10 DFT functionals were explored including 1 GGA functional
(BLYP), 1 meta-GGA functional (B97M-V), 2 global hybrid (GH) GGA functionals (B3LYP,
PBE0), 3 GH meta-GGA functionals (M06-2X, M06-HF, M08-HX), 2 range-separated hybrid
(RSH) GGA functionals (CAM-B3LYP, ωB97X-D) and 1 RSH meta-GGA (ωB97M-V)
functional. The global hybrid GGA (B3LYP, PBE0) and meta-GGA (B97M-V) functionals
outperform all other functionals with B3LYP offering the best accuracy in predicting E(S1) across
both classes of dyes. The B3LYP functional in the ROKS scheme achieved excellent MAE and R
2

values of 0.088 eV and 0.977 respectively for the BODIPY class while the corresponding values
for the MR dyes were 0.080 eV and 0.943. In comparison, the same metrics for TDDFT with the
same functional was 0.387 eV and 0.875 for the BODIPYs and correspondingly for the MR dyes
they were 0.210 and 0.937, respectively. It is worth remarking that all GH meta-GGA and RSH
functionals show less systematic errors as indicated by the low R
2
values and hence are not
recommended.
2 2.5 3
2
2.5
3
2 2.5 3
2
2.5
3
2 2.5 3
2
2.5
3
BODIPY
MR
TDA (T
1
)
Exptl. (T
1
)
MAE = 0.073 eV
R
2
= 0.878
MAE = 0.074 eV
R
2
= 0.875
MAE = 0.102 eV
R
2
= 0.842
a b c
BODIPY
MR
TDDFT (T
1
)
Exptl. (T
1
)
BODIPY
MR
SF-TDDFT (T
1
)
Exptl. (T
1
)

Figure 4.4. Comparison of the predictions of E(T1) using TDA (a), TDDFT (b) and SF-TDDFT
(c) methods using the B3LYP functional with experimental values. (All values in eV)

5 DFT functionals were tested for the SF-TDDFT method: B3LYP, PBE0, B5050LYP,
PBE50 and CAM-B3LYP. The B5050LYP and PBE50 are reparametrized versions of B3LYP and
106

PBE0 respectively that include 50% HF exchange and have been shown to offer accurate
predictions of excitation energies within the SF-TDDFT framework.
48
For all functionals, SF-
TDDFT calculations were preformed using the original formulation using a collinear exchange-
correlation potential and using the non-collinear variant developed by Ziegler et al.
37
In all cases
the non-collinear variant performed significantly better that their collinear counterparts as shown
in Figure 4.2. Like with the ROKS approach, the B3LYP and PBE0 functionals showed the best
accuracies for the S1 energies across both classes of dyes with B3LYP being the best. Non-collinear
SF-TDDFT with the B3LYP functional offers huge improvements over traditional TDDFT using
the same functional for the BODIPY class with MAE and R
2
values of 0.090 eV and 0.968
respectively that are comparable with the ROKS approach. However, for the MR class of dyes, the
improvement over TDDFT is only marginal with MAE and R
2
values of 0.189 eV and 0.972
respectively.
0.92 0.97 0.98 0.99 1
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0.75 0.8 0.85
-0.5
-0.25
0
0.25
0.5
0.75
BODIPY (S
1
)
MR (S
1
)

TDDFT
SF-TDDFT
W
SF-TDDFT
a b
BODIPY (S
1
)
BODIPY (T
1
)
MR (S
1
)
MR (T
1
)

TDDFT
ADC(3)
W
ADC(3)

Figure 4.5. Dependence of the separation between the transition energy predictions of TDDFT
and those of SF-TDDFT (a) and ADC(3) (b) on corresponding Ω values.

In several applications like TADF, PDT, etc., the T1 state plays a key role and hence
accurate predictions of the T1 energies are crucial. Therefore, predictions of E(T1) obtained from
107

the TDA/TDDFT and SF-TDDFT methods were compared against experimental values based on
the phosphorescence spectra (λmax) of the dyes where available. Fortunately, since most of these
dyes feature small Stokes shifts (<0.1 eV) and narrow absorption/emission line shapes, comparing
the vertical (S0→T1) transition energies computed at ground state geometry with the
phosphorescence spectra may be justified. Unlike E(S1), predictions of E(T1) using TDA and
TDDFT with the B3LYP functional are congruent with each other as seen in Figure 4.4. They are
also found to be in excellent agreement with the experimental values and do not exhibit the gross
overestimation of the transition energies observed for the S1 state (Table 4.1 and Figure 4.3). The
overall MAE across both classes of dyes for TDA and TDDFT are nearly identical at 0.073 and
0.074 eV while the R
2
values are 0.878 and 0.875, respectively. The SF-TDDFT methods were
found to be slightly less accurate in predicting E(T1) compared to traditional TDA/TDDFT (Table
4.1 and Figure 4.4).
Momeni et al. attributed the drastic errors of TDA/TDDFT in predicting E(S 1) to significant
double-excitation character of the S1 state for the BODIPY class of dyes.
19
TDA/TDDFT formally
being a single excitation method would therefore be inadequate in accurately describing such
states. SF-TDDFT on the other hand can access a subset of double-excitation configurations that
include at least a single electron occupancy on the LUMO. This is possible since SF-TDDFT
describes excitations via spin-flip operations from a high spin triplet reference state. Therefore
double excitations (involving the LUMO) relative to the ground state can be achieved via a single
spin-flip.
35
To gauge the extent of double excitation character in the SF-TDDFT S1 state for each
dye, we computed the squared norm of the 1-electron transition density matrix with the ground
state reference, Ω which estimates the extent of single-excitation character.
49-51
Therefore, an Ω
value of 1 would indicate a purely single excitation transition while lower values would indicate
108

the presence of double excitations. It can be seen in Figure 4.5 (a) that the energy separation
between E(S1) values computed with TDDFT and SF-TDDFT (∆
𝑆𝐹 −𝑇𝐷𝐷𝐹𝑇 𝑇𝐷𝐷𝐹𝑇 ) using the B3LYP
functional inversely trends with ΩSF-TDDFT indicating the role of double-excitations in the
TDA/TDDFT errors. The MR dyes generally feature ΩSF-TDDFT values closer to 1 compared to the
BODIPYs suggesting a greater extent of double excitation character in the BODIPYs which
therefore leads to the larger TDA/TDDFT errors observed for the BODIPYs relative to the MR
dyes. Additionally, this may also indicate the only marginal improvement in accuracy of SF-
TDDFT over TDA/TDDFT for the MR-dyes may be the result of the inability of SF-TDDFT to
capture double-excitation configurations that do not involve the LUMO which may be crucial for
these dyes. The Δ-SCF based ROKS approach on the other hand is not subject to the same
limitations plaguing the linear response-based methods that rely on excitations from a reference
and offers better flexibility in describing such problematic states by variationally optimizing all
orbitals for the target state (S1). This may be the reason for the improved accuracy of the ROKS
method over the linear response methods.
We also computed the Ω value for the S0→S1 and S0→T1 transitions using the ADC(3)
method using the VDZ basis set for a sub-set of the considered dyes for which such calculations
were feasible. The ADC(3) method is a wave-function based approach that is capable of handling
double-excitations and is not subject to the SF-TDDFT limitation of only being able to access
double excitations involving the LUMO. As in the case of SF-TDDFT, the separation between
E(S1) values computed with TDDFT and ADC(3) (∆
𝐴𝐷𝐶 ( 3)
𝑇𝐷𝐷𝐹𝑇 ) trends inversely with ΩADC(3) and is
shown in Figure 4.5 (b). It can also be seen that the T1 states have significantly lower double-
excitation character compared to the S1 states of the dyes and could be the reason why
TDA/TDDFT methods accurately predict E(T1) but significantly overestimate E(S1) of these dyes.
109

4.4. Conclusion
In this work, we assessed the performance of ROKS and SF-TDDFT across a range of DFT
functionals in predicting the transition energies of two important classes of dyes: BODIPY and
MR dyes for which traditional TDA/TDDFT approaches fail dramatically. We found that the
B3LYP functional offered the best accuracy for both ROKS (MAE = 0.085 eV) and SF-TDDFT
(MAE = 0.126) across both classes of dyes vastly outperforming TDA/TDDFT (MAE =
0.484/0.323 eV) in predicting E(S1). However, TDA/TDDFT and SF-TDDFT showed similar
accuracies in predicting E(T1) for these dyes and were found to be in good agreement with
experimental values unlike E(S1). This was attributed to relatively smaller extent of double-
excitation character of the T1 states compared to the S1 states of these dyes. We hope that accurate
predictions based on the prescriptions reported in this work would inform and guide the discovery
of novel BODIPY and MR dyes for wide-ranging applications.

Table 4.2. Summary of ROKS, TDA, TDDFT, SF-TDDFT calculations at the B3LYP/6-
31G(d,p) level. (All energies in eV).

Ref. Exptl. ROKS TDA TDDFT SF-TDDFT
E(S1) E(T1) E(S1) E(S1) E(T1) E(S1) E(T1) f(S1) E(S1) E(T1)
B1
19
2.460 - 2.451 3.457 1.714 3.172 1.588 0.354 2.405 1.682
B2
19
2.252 - 2.206 3.169 1.313 2.901 1.107 0.259 2.322 1.248
B3
19
3.259 - 3.190 3.344 2.457 3.227 2.382 0.095 3.401 2.698
B4
19
3.278 - 3.317 3.394 2.553 3.285 2.489 0.104 3.551 2.881
B5
19
3.712 - 3.588 4.197 2.834 3.953 2.754 0.475 3.744 2.957
B6
19
2.583 - 2.434 3.534 1.641 3.113 1.491 0.589 2.578 1.592
B7
19
2.995 - 2.709 3.530 1.906 3.227 1.741 0.576 2.815 1.878
B8
19
2.479 - 2.258 3.399 1.314 2.952 1.095 0.569 2.394 1.259
B9
19
2.963 - 2.935 3.701 2.373 3.467 2.305 0.372 3.098 2.471
B10
19
2.109 - 2.020 2.778 1.254 2.581 1.087 0.279 2.167 1.244
110

B11
19
2.755 - 2.778 3.347 2.369 3.184 2.329 0.236 2.976 2.437
B12
19
2.412 - 2.344 3.242 1.689 2.923 1.582 0.497 2.478 1.653
B13
19
2.353 - 2.365 3.154 1.661 3.039 1.544 0.281 2.504 1.639
B14
19
2.422 - 2.349 3.172 1.685 2.925 1.573 0.391 2.474 1.648
B15
19
2.317 - 2.258 3.181 1.611 2.863 1.507 0.535 2.395 1.590
B16
19
2.331 - 2.227 2.825 1.499 2.745 1.353 0.003 2.357 1.456
B17
19
2.206 - 2.072 2.617 1.379 2.530 1.221 0.081 2.197 1.312
B18
19
2.049 - 1.950 2.760 1.342 2.506 1.209 0.873 2.067 1.306
B19
19
1.922 - 1.819 2.592 1.265 2.313 1.138 1.112 1.928 1.233
B20
19
1.907 - 1.739 2.498 1.074 2.205 0.908 0.719 1.840 0.998
B21
19
1.884 - 1.711 2.430 1.066 2.149 0.903 0.775 1.809 0.991
B22
19
1.802 - 1.637 2.368 1.018 2.069 0.866 0.738 1.731 0.959
B23
19
1.732 - 1.556 2.249 0.960 1.963 0.816 0.719 1.650 0.917
B24
23
2.58 2.15 2.540 3.313 2.194 3.153 2.138 0.238 2.826 2.185
B25
23
2.38 1.94 2.380 2.971 1.923 2.776 1.863 0.469 2.478 1.920
B26
23
2.48 1.98 2.436 3.057 1.965 2.858 1.900 0.602 2.532 1.950
B27
39
3.11 2.67 3.046 3.784 2.702 3.603 2.658 0.304 3.276 2.702
B28
39
3.03 2.68 2.873 3.463 2.537 3.311 2.492 0.186 3.072 2.529
B29
39
3.11 2.66 2.983 3.415 2.531 3.273 2.486 0.159 3.053 2.521
B30
39
2.86 2.56 2.849 3.321 2.439 3.173 2.394 0.480 2.905 2.448
B31
39
2.81 2.51 2.796 3.239 2.388 3.094 2.343 0.585 2.852 2.402
B32
39
2.83 2.54 2.884 3.350 2.478 3.206 2.434 0.523 2.940 2.486
B33
39
2.8 2.52 2.818 3.382 2.521 3.242 2.480 0.571 2.976 2.528
B34
39
2.86 2.47 2.752 3.368 2.482 3.227 2.421 0.590 2.974 2.507
B35
39
2.93 2.49 2.899 3.373 2.463 3.228 2.397 0.539 2.963 2.481
M1
26
2.838 2.594 2.980 3.213 2.665 3.136 2.644 0.203 3.108 2.713
M2
26
2.793 2.557 2.869 3.039 2.589 2.982 2.568 0.429 2.963 2.641
M3
40
3.298 2.967 3.273 3.506 2.926 3.423 2.904 0.122 3.414 3.006
M4
41
2.851 2.480 2.929 3.237 2.594 3.151 2.548 0.143 3.078 2.644
M5
42
2.713 2.436 2.824 3.051 2.520 2.977 2.501 0.235 2.926 2.556
M6
27
2.633 2.350 2.670 2.862 2.416 2.795 2.398 0.395 2.734 2.450
M7
27
2.655 2.400 2.706 2.890 2.448 2.824 2.429 0.398 2.763 2.482
M8
27
2.638 2.390 2.722 2.901 2.462 2.837 2.444 0.400 2.776 2.496
M9
43
2.831 2.541 2.916 3.085 2.674 3.038 2.632 0.070 3.030 2.676
M10
43
2.884 2.661 2.981 2.974 2.717 2.962 2.648 0.001 3.077 2.857
M11
43
2.818 2.611 2.885 2.920 2.677 2.899 2.643 0.072 2.940 2.723
M12
44
3.062 - 2.959 3.575 2.738 3.452 2.697 0.105 3.369 2.786
M13
44
2.039 - 1.874 2.304 1.627 2.177 1.579 0.089 2.128 1.676
M14
44
2.988 - 3.009 3.205 2.754 3.157 2.705 0.039 3.225 2.845
M15
44
2.371 - 2.245 2.724 1.968 2.589 1.921 0.099 2.525 1.999
M16
45
3.272 2.805 3.287 3.494 2.998 3.452 2.923 0.073 3.543 3.129
M17
46
2.799 2.422 2.843 3.108 2.521 3.032 2.477 0.150 3.000 2.589
M18
46
2.780 2.436 2.787 3.126 2.480 3.036 2.441 0.130 2.962 2.532
M19
47
3.221 2.904 3.380 3.631 3.087 3.572 3.057 0.111 3.567 3.134
M20
29
2.713 2.622 2.826 2.943 2.592 2.904 2.581 0.715 2.848 2.661
111

Table 4.3. Summary of ADC(3)/6-31G(d,p) calculations. (All energies in eV).

E(S1) Ω (S1) E(T1) Ω (T1)
B1 2.533 0.780 1.644 0.853
B2 2.179 0.755 1.139 0.851
B3 3.458 0.798 2.737 0.855
B4 3.701 0.803 3.001 0.853
B5 4.499 0.813 3.509 0.862
B7 2.756 0.795 1.602 0.860
B8 3.347 0.799 1.941 0.867
B9 2.560 0.787 1.224 0.856
B10 3.277 0.808 2.601 0.854
B11 2.099 0.755 - -
B12 2.945 0.792 2.493 0.840
B14 2.463 0.778 1.596 0.849
B16 2.388 0.774 1.411 0.841
B17 - - 1.245 0.831
B24 2.804 0.780 2.271 0.845
B25 2.609 0.776 - -
B26 2.679 0.784 - -
B27 3.351 0.790 2.885 0.844
B30 3.122 0.783 2.689 0.832
B35 3.213 0.789 - -
M3 3.808 0.802 3.410 0.837
M4 3.451 0.791 2.945 0.837

112

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Beljonne, D.; Buck, M.; Olivier, Y .; Kohler, A.; Zysman-Colman, E., A Deep Blue B,N-Doped
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118

Chapter 5. Accurately predicting transition dipole vectors of phosphors to
understand outcoupling in thin films

5.1. Introduction
As mentioned in Chapter 1, the external quantum efficiency (EQE) of an OLED device is
given by the expression, 𝜂 𝑒𝑥𝑡 = 𝜂 𝑖𝑛𝑡 𝜂 𝑜𝑢𝑡 . The internal quantum efficiency (𝜂 𝑖𝑛𝑡 ) can be
maximized to unity by using high efficiency phosphorescent/TADF emitters in a properly
optimized device architecture. The outcoupling efficiency (𝜂 𝑜𝑢𝑡 ) on the other hand which refers to
the fraction of light electrogenerated within the device that makes it to the external world, is the
limiting factor due to dissipation into different optical loss channels within the device. There are
three main optical modes that lead to losses within the device: substrate modes which refer to light
that is trapped by total internal reflection at the substrate-air interface, wave-guided modes that
refer to dissipation losses across the high-index organic layers/anode and finally losses due to
near-field coupling to surface-plasmon polaritons (SPPs) at the metallic cathode-organic layer
interface.
1

The outcoupling losses are dependent on several factors including refractive indices and
thicknesses of individual layers, distance of the emissive layer from the metallic cathode and
critically the orientation of the transition dipole vectors (TDVs) of the dopant molecules relative
to the substrate.
1
It is highly desirable to have the TDVs oriented parallel to the substrate as this
would result in maximum emission normal to the substrate consistent with the transverse nature
of electromagnetic radiation. The orientation of the TDVs in the amorphous emissive layer can be
measured by performing angle-dependent photoluminescence/electroluminescence experiments
2-
4
and the net orientation is often quantified by a metric referred to as the anisotropy factor (Θ)
which is defined as:
119

Θ =
∑ 𝑝 𝑧 2
∑ 𝑝 ⃗
2
= 〈cos
2
𝜃 〉 ( 5.1)
Here, ∑ 𝑝 𝑧 2
refers to the radiative power emitted in the direction normal to the substrate
and ∑ 𝑝 ⃗
2
is the total power emitted by all the emissive dipoles. 〈cos
2
𝜃 〉 is the average projection
of the TDVs normal to the substrate. Therefore Θ ranges from 0 for the special case where all the
TDVs are aligned horizontal to the surface to 1 when all TDVs are perpendicularly oriented and
at Θ = 0.33, the TDVs would be randomly oriented.

Figure 5.1. Dissipation of radiation via different optical modes in OLEDs for 3 TDV alignment
scenarios: (a) 𝚯 = 0.33 (isotropic) (b) 𝚯 = 0 (horizontal), and (c) 𝚯 = 1 (vertical). (Taken from
Ref.
1
)

The dissipation of light to different optical modes for the three scenarios: Θ = 0 (horizontal),
0.33 (isotropic) and 1 (vertical) were simulated by Schmidt et al.
1
and are shown in Figure 5.1. It
120

should be noted that the light coupled to substrate modes can be easily extracted by simple
modifications to the substrate like attaching a half-ball lenses to the substrate etc. It is evident from
the simulations that the scenario where all the TDVs are parallel to the substrate (Θ = 0) would
result in maximum outcoupling efficiency while the scenario where Θ = 1 yields the worst
outcome.
Several factors like molecular shape, intermolecular interactions, orientation of TDV
within molecular frame and film growth kinetics affect the alignment behavior of dopants.
1
A
couple of fluorescent and TADF dopants with linear rod-like shapes and TDVs oriented along the
long axis have been reported to show near perfect horizontal alignment (Θ ≈ 0) in doped films.
5, 6

Achieving such linear rod-like shapes with high aspect ratios is a challenge in the case of most Ir
phosphors due to their preferred octahedral coordination geometries. Several heteroleptic
bis-cyclometallated diketonate Ir complexes have been known to show modest preferential
horizontal alignment in vacuum deposited doped films with Θ values in the range 0.22-0.25.
1

Tris-cyclometallated homoleptic Ir complexes like Ir(ppy)3 on the other hand prefer to align
isotropically (Θ = 0.33), although few that show preferential horizontal alignment have been
reported.
1, 7, 8

5.2. SOC-TDDFT calculations
To study the net orientation of the optical TDVs of dyes in a host matrix, it is essential to
know the orientation of the TDV of the concerned optical transition with respect to the molecular
frame of the dye in addition to knowing how the molecule is oriented against the substrate. The
TDVs for transitions between electronic states having the same spin can be computed often quite
accurately within the framework of conventional quantum chemistry methods that do not account
121

for spin-orbit interactions. Therefore, the TDV of the emissive transition (typically S1→S0 in
accordance with Kasha’s law) in a fluorescent dye can be calculated using conventional excited
state quantum chemistry methods that do not include spin-orbit coupling (SOC) like traditional
TD-DFT (Time-dependent Density Functional Theory) methods. However, emission from
phosphorescent systems (usually heavy metal complexes) involve transitions from triplet states
into the singlet ground state which are strictly forbidden in the absence of SOC and hence the
TDVs of such transitions and other phosphorescent properties cannot be computed within such a
framework. Several approaches to incorporate SOC within TDDFT and other quantum chemistry
methods have been developed and implemented
9-22
. Among these, TD-DFT with the relativistic
ZORA (zero-order regular approximation) Hamiltonian
17-19
has been used in several studies to
compute phosphorescent properties of heavy metal complexes with high accuracy
23-27
. In a recent
study, J.J. Kim et al.
28
used the ZORA approach within the TD-DFT framework to compute the
(T1→S0) TDVs for a number of phosphorescent emitters. The ZORA equation is an approximation
to the relativistic Dirac equation and is written as:
𝐻 𝑍𝑂𝑅𝐴 𝛹 = (𝑉 + 𝐩
𝑐 2
2𝑐 2
− 𝑉 𝐩 +
𝑐 2
( 2𝑐 2
− 𝑉 )
2
𝛔 . ( 𝛁 𝑉 × 𝐩 ) )𝛹 = 𝐸𝛹 ( 5.2)
In the above expression, 𝑉 contains the nuclear and electronic coulombic potentials and exchange-
correlation potential, 𝐩 is the momentum operator, 𝛔 denotes the Pauli matrices and 𝑐 is the speed
of light. It can be seen that SOC enters in the third term of the Hamiltonian. The ZORA
Hamiltonian approach can be used to compute the TDVs involved in the transition from triplet
states to the singlet ground state in phosphorescent dyes at a tractable cost.
We used the ZORA TDDFT approach (henceforth referred to as SOC-TDDFT) to compute
the TDVs associated with the phosphorescent emission of several complexes and the results are
122

summarized in Figure 5.2. The ground state geometry of all complexes reported here were
calculated at the B3LYP/LACVP** level. Starting from the ground state optimized geometry,
unrestricted DFT was employed to optimize the triplet state geometry without any symmetry
restrictions at the same level. SOC-TDDFT calculations using the ZORA Hamiltonian were
performed on the triplet optimized geometries of the complexes using the B3LYP functional and
the DYALL-2ZCVP-ZORA-J-PT-GEN basis set to compute the TDVs. All calculations were
performed using the Materials Science Suite developed by Schrödinger
29
.It should also be noted
that a consequence of SOC is the loss of degeneracy of the three sub-levels of the triplet states
even in the absence of a magnetic field and therefore in phosphorescent emitters which often
exhibit large SOC effects, the phosphorescent emission is a consequence of transitions from all 3
sub-levels of the T1 state to the ground S0 state with different oscillator strengths at slightly
different energies (usually <200 cm
-1
apart from each other). It is most often the case that the
transition from one of the 3 triplet sub-levels to the ground state has an oscillator strength that is
orders of magnitude larger than the other two and, thus, dictate the photophysical properties. Hence
for the sake of simplicity, the TDVs for emission from the other two sublevels are ignored.

5.3. Understanding orientation of TDVs in homoleptic Ir complexes
From Figure 5.2 we see that the TDV computed using the ZORA approach for the
transition between the most emissive triplet (T1) sub-level and the S0 state of Re(ppy)CO4 is at an
angle 17.3
0
w.r.t. Re-N bond and is in very good agreement with the experimentally measured
TDV orientation at ~18
0
w.r.t. the Re-N bond.
30
Note that this is one of the few phosphorescent
systems for which the spatial orientation of the TDV with respect to the molecular frame has been
verified experimentally from measurements on a single crystal. In the absence of any further
123

experimental data, these calculations can be an invaluable tool in studying the alignment of
phosphorescent emitters and can complement experimental methods.

Emitter δ (
0
) Emitter δ (
0
)
Re(ppy)(CO) 4 17.3 (~18*) Ir(1F-ppy) 3 33.86
Ir(ppy) 3 37.84 Ir(2F-ppy) 3 30.28
Ir(chpy) 3 26.23 Ir(3F-ppy) 3 41.48
Ir(1-bzppy) 3/Ir(phq) 3 3.29 Ir(4F-ppy) 3 33.70
Ir(2-bzppy) 3 10.69 Ir(7F-ppy) 3 33.36
Ir(3-bzppy) 3/Ir(piq) 3 42.61 Ir(8F-ppy) 3 35.97
Ir(4-bzppy) 3 38.09 Ir(9F-ppy) 3 32.81
Ir(5-bzppy) 3 31.94 Ir(10F-ppy) 3 34.65
Ir(6-bzppy) 3 44.51

Ir(7-bzppy) 3 30.95

Figure 5.2. The values of δ calculated using SOC-TDDFT for the Ir complexes studied here.
*Experimentally observed δ reported in
30
.
124

We herein demonstrate the utility of such calculations in aiding experimental methods in
understanding alignment in a set of closely related facial homoleptic Iridium complexes, namely,
Ir(ppy)3, Ir(phq)3, Ir(chpy)3 and Ir(piq)3. Among these complexes, Ir(piq)3 and Ir(chpy)3 exhibit
non-isotropic orientation with anisotropy factors (Θ) of 0.22 and 0.23 respectively while the other
two complexes have been reported to show isotropic orientation of the TDVs.

Figure 5.3. Orientation of Ir(ppy)3, Ir(chpy)3, Ir(piq)3 and Ir(phq)3 (clockwise from left) with C3
axis perpendicular to the substrate. (Substrate is assumed to lie perpendicular to the plane of the
paper)

An analysis of the geometry of Ir(chpy)3 indicates that when viewed across the C3 axis,
one end of the structure is aromatic in nature while the other end is aliphatic as seen in Figure 5.3.
During vapor deposition, the molecule would prefer to orient such that the aromatic end is facing
the aromatic host molecules that have already been deposited (due to favorable intermolecular π-
π interactions) with the aliphatic end facing vacuum resulting in the C3 axis being aligned
perpendicular to the substrate. Therefore, a large proportion of the molecules would be aligned

125

with the C3 axis perpendicular to the substrate which is the most energetically favorable
arrangement. The TDV associated with the phosphorescent emission of Ir(chpy)3 computed using
SOC-TDDFT is found to lie on one of the chpy ligands making an angle (δ) of 26.2
0
w.r.t. Ir-N
bond. The angle can now be compared with results of the anisotropy factor simulations reported
for homoleptic complexes with vertical C3 axis alignment
31
(shown in Figure 5.4) which predicts
non-isotropic net TDV orientation for the given δ. A similar case can be made for the observed
non-isotropic TDV alignment exhibited by Ir(piq)3. While Ir(piq)3 does not possess aliphatic
groups like those seen in Ir(chpy)3, one end of the structure is susceptible to more aromatic
interaction than the other owing to the clustering of the three isoquinoline (2 fused aromatic rings)
moieties on one end affording stronger aromatic interactions with host molecules compared to the
other end which only exposes three phenyl moieties. This being the most energetic favorable
arrangement, a majority of the molecules would be oriented with the C3 axis lying perpendicular
to the substrate. The computed TDV for Ir(piq)3 lies on one of the piq ligands subtending a δ angle
of 42.6
0
. The anisotropy factor simulations (Figure 5.4) predict that with this δ value, Ir(piq)3 is
predicted to show a much smaller anisotropy factor than Ir(chpy)3 with almost perfect horizontal
overall TDV alignment (i.e. Θ ≈ 0) in contrast to the observed Θ at 0.22. It should be noted that
the anisotropy factor simulation is based on the assumption that all the dopants are aligned with
the C3 axis lying perpendicular to the substrate. In reality, however, such a picture is highly
unlikely and we expect to see a dispersion of different possible molecular orientations with a large
proportion of them being oriented with their C3 axis perpendicular or close to perpendicular to the
substrate. The anisotropy factor simulations therefore represent the maximum achievable value of
Θ for a given value of δ and the deviation from this maximum value is a measure of disorder in
the system. It can also be argued that Ir(chpy)3 has a stronger propensity to orient with its C3 axis
126

perpendicular to the substrate compared to Ir(piq)3 on account of the fact that the aromatic/aliphatic
interface in Ir(chpy)3 offers a much stronger motivation for perpendicular (C3 axis) alignment than
the aromatic/less aromatic interface of Ir(piq)3 and therefore a larger proportion Ir(chpy)3
molecules are expected to be aligned perpendicularly against a vacuum/aromatic interface
compared to Ir(piq)3 which could explain why we observe only a 0.1 decrease in Θ value for
Ir(piq)3 compared to Ir(chpy)3 in spite of the simulation predicting a much larger drop in Θ. Like
Ir(piq)3, the structure of Ir(phq)3 also exposes naphthalene-like moieties in one direction with
phenyl moieties in the opposite direction and therefore a large proportion of Ir(phq)3 molecules
would preferentially exhibit perpendicular (C3 axis) orientation when deposited on the host matrix.
The TDV calculated for this complex lies along one of the phq ligands with a δ angle of 3.3
0
and
the anisotropy simulations for this δ predicts isotropic TDV alignment which is exactly what has
been reported experimentally. Unlike the other 3 complexes, Ir(ppy)3 exhibits a somewhat
isotropic structure with no preferred molecular orientation and hence the molecules are expected
to be randomly oriented in the host matrix. As a consequence, irrespective of the orientation of the
TDV w.r.t. the molecular frame, Ir(ppy)3 would show isotropic overall TDV alignment.
It is now clear that in addition to having an inherent asymmetry in the molecular structure,
the orientation of the TDV with respect to the molecular frame is an important factor that
influences Θ. It would therefore be beneficial to understand how the direction of the TDV can be
modulated by chemical modifications which could then lead us to the realm of rational design of
dopants with favorable anisotropy factors. Of the complexes discussed above Ir(piq)3 and Ir(phq)3
are benzoderivatives of Ir(ppy)3 with the benzo group attached at the 1 and 3 positions respectively
and these complexes have distinctly different δ values. We therefore embarked upon
systematically studying how addition of benzo groups at different positions on the parent Ir(ppy)3
127

complex affect the direction of the TDV. The δ values computed for the homoleptic Ir complexes
based on all possible benzoderivatives of the ppy ligand is shown in Figure 5.2. Based on the
calculated TDVs and the anisotropy simulations for homoleptic complexes with perpendicular
molecular (C3 axis) alignment, Ir(piq)3 and Ir(6-bzppy)3 can be expected to show better TDV
alignment compared to the other structures. It should be noted that despite having a favorable δ
angle, Ir(4-bzppy)3 is unlikely to exhibit low anisotropy factors owing to lack of structural
asymmetry as in the case of Ir(ppy)3. We also explored the influence of fluorine substitutions at
different positions of the ppy ligand on the direction of the TDV and we see that Ir(3F-ppy)3 is
expected to show the lowest value of Θ among all the fluoro-substituted derivatives (Figure 5.2).
We hope that this work has helped develop a better understanding of factors that influence
alignment of phosphors, ultimately paving the way for rational design of emitters with low Θ
values.

Figure 5.4. Dependence of 𝚯 on δ for bis-cyclometallated and homoleptic facial tris-
cyclopetallated Ir complexes when their respective C2 and C3 axes are oriented perpendicular to
the substrate based on anisotropy factor simulations. (Taken from Ref.
31
)

Recently, a new class of homoleptic Ir complexes with varied molecular shape and
chemical asymmetry were developed in our lab.
32
The structures of the complexes are shown in
128

Figure 5.5 along with the δ values computed using the ZORA approach. The δ values of the Ir(mi)3
and Ir(mip)3 complexes were calculated to be 33
o
while Ir(miF)3 shows a slightly larger δ value of
38
o
owing to the CF3 groups that pull the TDV closer towards them. Therefore, the TDVs in these
complexes lie more or less perpendicular (84-90
o
) to the C3 axis ideal for low Θ values provided
the complexes preferentially align with the C3 axis perpendicular to the substrate.

Figure 5.5. Structures of newly developed complexes
32
along with calculated δ values. (Ir(ppy)3
and Ir(ppyCF3)3 are shown for reference)

The asymmetric shape of the complexes indicate that they would in fact likely prefer to
align in such a fashion. To quantify the extent of shape asymmetry, the aspect ratios of the
complexes were computed using the following procedure. First, the 3D moments matrix of each
complex was computed by taking the Ir atom as the center. The moments matrix (𝑀 ) is then
computed as:
𝑀 =
[

∑( 𝑥 𝑖 − 𝑥 𝐼𝑟
)
2
𝑖 ∑( 𝑥 𝑖 − 𝑥 𝐼𝑟
) ( 𝑦 𝑖 − 𝑦 𝐼𝑟
)
𝑖 ∑( 𝑥 𝑖 − 𝑥 𝐼𝑟
) ( 𝑧 𝑖 − 𝑧 𝐼𝑟
)
𝑖 ∑( 𝑥 𝑖 − 𝑥 𝐼𝑟
) ( 𝑦 𝑖 − 𝑦 𝐼𝑟
)
𝑖 ∑( 𝑦 𝑖 − 𝑦 𝐼𝑟
)
2
𝑖 ∑( 𝑦 𝑖 − 𝑦 𝐼𝑟
) ( 𝑧 𝑖 − 𝑧 𝐼 𝑟 )
𝑖 ∑( 𝑥 𝑖 − 𝑥 𝐼𝑟
) ( 𝑧 𝑖 − 𝑧 𝐼𝑟
)
𝑖 ∑( 𝑦 𝑖 − 𝑦 𝐼𝑟
) ( 𝑧 𝑖 − 𝑧 𝐼𝑟
)
𝑖 ∑( 𝑧 𝑖 − 𝑧 𝐼𝑟
)
2
𝑖 ]

( 5.3)
129

where, 𝑥 𝑖 , 𝑦 𝑖 , 𝑧 𝑖 are the positional coordinates of an atom i in the molecule and 𝑥 𝐼𝑟
, 𝑦 𝐼𝑟
,
𝑧 𝐼𝑟
are the coordinates of the central Ir atom. The matrix 𝑀 is then diagonalized to obtain the
corresponding eigenvalues, λ1, λ2 and λ3. Then, √λ
1
, √λ
2
and √λ
3
represent the relative length of
the principal semi-axes of a hypothetical ellipsoid hull that represents the molecule (i.e. 𝑎 ∝ √λ
1
,
𝑏 ∝ √λ
2
,𝑐 ∝ √λ
3
).
In our case, since we are dealing with homoleptic octahedral complexes, the lengths of at
least two of the semi-axes are expected to be similar (𝑎 ≈ 𝑏 ). The aspect ratio can then be
computed as the ratio between 𝑎 and 𝑐 . The DFT (B3LYP/LACVP*) ground state optimized
geometries were used to compute the aspect ratios in all cases.

Figure 5.6. Structures of complexes reported by Kim et al.
8

The aspect ratios computed for the complexes are shown in Figure 5.7 along with aspect
ratios of a closely related class of phenyl-imidazole based Ir cyclometallated compounds reported
by Kim et al.
8
Plotting the measured anisotropy factors (Θ) against the calculated aspect ratios
(Figure 5.7) for the complexes reveals the strong correlation between the two. Interestingly, the
complexes cluster neatly into groups depending on the kind of polar pendant substituents on the
cyclometallating ligands. The complexes bearing CN substituents exhibit the lowest Θ values,
followed by the ones bearing CF3 groups and the complexes with no polar groups showing the
highest Θ values among the complexes considered. The electrostatic surface potential (esp) plots
for the complexes shown in Figure 5.7 reveal that the polar groups are concentrated on one end of
130

the complex when viewed across the C3 axis. Therefore, in addition to the shape anisotropy, the
chemical asymmetry by virtue of the polar substituents lowers the Θ values of the complexes
bearing polar groups relative to ones that lack them. Further, the DFT computed partial charge on
the N atom in the CN group of D3 (-0.53) is larger than that of the F atoms on CF3 groups of
Ir(miF)3 (-0.27) and this may perhaps be the reason for the CN-substituted complexes showing Θ
values lower than their CF3-substituted counterparts.
1 1.5 2 2.5 3 3.5
0.1
0.2
0.3
0.4
Ir(ppy)
3
, Ir(mi)
3
, Ir(mip)
3
Ir(miF)
3
, Ir(ppyCF
3
)
3
D1-D5
Q
Aspect ratio
(a)

(c)
Complex Aspect ratio
Ir(ppy)3 1.2
Ir(ppyCF)3 1
Ir(mi)3 2.2
Ir(mip)3 3
Ir(miF)3 1.9
D1 1.3
D2 1.9
D3 2.1
D4 2.7
D5 2.9

Figure 5.7. (a) Observed trend between Θ and aspect ratio for the complexes studied here.
32
(b)
Esp plots of the Ir complexes calculated at the B3LYP/LACVP* level. (c) Computed aspect
ratios.
131

5.4. TDVs of Pt complexes
The TDVs for several Pt complexes developed in our lab
33
were also calculated using the
ZORA approach and the results were used to help understand their alignment behavior in thin
films. The structures of the Pt complexes are shown in Figure 5.8 along with the computed TDVs.
The measured Θ values of these complexes in doped CBP films reported in Ref.
33
indicate that all
complexes, except the bis-Pt complex, (dbx)(Pt(dpm)) show net vertical alignment. A similar
mechanism like the one detailed above for the Ir complexes can be used for these Pt complexes as
well. The complexes in Figure 5.8 possess two distinct regions: an aromatic part featuring the
chromophoric ligand and an aliphatic part due to the diketonate ancillary ligand. During vapor
deposition, the complexes would prefer to align in such a way that the aromatic part (chromophoric
ligand) points towards the substrate due to favorable π-π interactions with host matrix and the
aliphatic groups on the other hand would prefer to be pointing away towards the vacuum end.
Now, factoring in the orientation of the TDVs of the mono-Pt complexes resulting from the MLCT
transition, a net vertical alignment of the TDVs is expected for these films. The TDV of the bis-Pt
complex on the other hand lies along the Pt-Pt axis consistent with observed net horizontal TDV
alignment.

Figure 5.8. Computed TDVs and measured Θ of Pt complexes reported in Ref.
33
.
δ = 10.6
0
Θ = 0.23
δ = 23.8
0
Θ = 0.38
δ = 32.6
0
Θ = 0.54
δ = 36.1
0
Θ = 0.46
132

Recently, the alignment behavior of a pyridylazolate Pt complex, PtD (Figure 5.9) as neat
films was reported by our group.
34
It was found that the neat PtD films exhibited excimeric
emission. The XRD-derived crystal structure of the neat PtD films was used to compute the TDV
associated with excimeric emission. On close inspection of the crystal structure of PtD (Figure
5.9 (b)), it can be seen that there are two unique dimer configurations that could potentially lead
to excimeric/dimeric emission – one with a Pt-Pt separation of 3.35 Å and the other with a 3.41 Å
separation, henceforth referred to as 3.35-dimer and 3.41-dimer respectively. To simulate T1 state
relaxation of the PtD excimers/dimers (3.41-dimer and 3.35-dimer) within the crystalline matrix,
T1 state geometry optimization was performed on each dimer constrained by a molecular shell
consisting of all its immediate neighbors (based on the crystal structure packing data) modelled as
a rigid classical force-field. This was done using a 2-layer hybrid QM/MM ONIOM (our own n-
layered integrated molecular orbital and molecular mechanics) scheme in which the central dimer
was treated at the B3LYP/LanL2Dz level while the UFF molecular mechanics force-field was used
to model the surrounding molecular shell which was kept frozen during the optimization. All
ONIOM calculations were performed using the Gaussian 09 program.
35
Subsequently,
SOC-TDDFT calculations were performed on the T1 (ONIOM:B3LYP/LanL2Dz:UFF) optimized
structure of both dimers to obtain the TDVs associated with dimeric/excimeric emission. The
surrounding molecular shell was ignored for the SOC-TDDFT calculations.
The DFT calculations predict that the energy of the excimeric/dimeric T1 state of the
3.35-dimer (2.25 eV) is lower than that of the 3.41-dimer (2.27 eV). Also, the oscillator strength
computed for the most emissive T1 sub-level (i.e., sub-level with the largest oscillator strength
among the three sub-levels) of the former is found to be almost twice that of the latter further
indicating that emission in neat crystalline PtD films originates predominantly from the 3.35-dimer
133

sites. The arrow in Figure 5.9 (c) indicates the direction of the computed TDV (for the T1 sub-
level with largest oscillator strength) associated with excimeric/dimeric emission from 3.35-dimer
sites. The TDV subtends a polar angle of 10
°
with the z-axis chosen to lie along the Pt-Pt axis and
an azimuthal angle of 99° with the x-axis that passes through the Pt-N(pyrazole-ring) bond of one
of the monomers. The computed TDV along with the XRD data were used to explain the alignment
behavior of the neat PtD films as reported in J. Kim et al.
34

(d)

3.35-dimer (PtD) 3.41-dimer (PtD)
Energy f Energy f
T1 (I)
2.2515
(550.67)
0.25 x 10
-5

2.2682
(546.61)
0.17 x 10
-5

T1 (II)
2.2519
(550.57)
0.16 x 10
-4

2.2689
(546.45)
0.85 x 10
-4

T1 (III)
2.2533
(550.22)
0.15 x 10
-3

2.2698
(546.24)
0.75 x 10
-4

Figure 5.9. (a) Chemical structure of PtD. (b) Crystal structure of PtD. (c) Computed TDV of
emission from the 3.35-dimer. (d) Computed energies and oscillator strengths of the triplet
sublevels for both PtD dimers.

5.5. References

134

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138

Chapter 6. Modeling the effects of solvation on the photophysical properties
of chromophores

6.1. Introduction
Recently, our lab reported several 2-coordinate coinage metal (Cu, Ag, Au) complexes that
exhibit strong solvatochromic effects both in their absorption and emission spectra.
1-3
The
complexes contain an electron-donating carbazolide ligand and an electron-withdrawing carbene
coordinating to a monovalent coinage metal ion in a collinear arrangement as shown in Figure
6.1. It was found that their absorption spectra exhibited strong negative solvatochromism (up to
50 nm) i.e., blue shift with increase in polarity of the medium. The emission spectra on the other
hand showed positive solvatochromism (red-shift with increased medium polarity) albeit to a
lesser extent (15-20 nm). A similar trend was also observed for a recently reported class of
tetradentate pyridyl-carbazole Pt complexes
4
(Figure 6.1).

Figure 6.1. Chemical structures of a sampling of complexes studied here.

It is clear from the solvatochromic absorption/emission data that intramolecular charge-
transfer states (CT) states are at play. Commonly used hybrid DFT functionals, such as B3LYP
and PBE0, have been reported to severely underestimate the energies of charge transfer states.
5-7

These errors stem from the incorrect description of long-range exchange interactions by the hybrid
139

DFT functionals. Range-separated hybrid (RSH) functionals, such as CAM-B3LYP, ωPBE,
ωB97xD, etc. can remedy this situation by treating short-range and long-range interactions
separately and introducing 100% Hartree Fock (HF) exchange for the long-range interactions.
8-11

This is achieved by splitting the 1/𝑟 electron-electron interaction operator using error functions as
shown below:
1
𝑟 = 𝑅 ̂
𝑆𝑅
+ 𝑅 ̂
𝐿𝑅
=
∫ 𝑒 −𝑡 2 ∞
ω𝑟 𝑑𝑡 𝑟 +
∫ 𝑒 −𝑡 2 ω𝑟 0
𝑑𝑡 𝑟 ( 6.1)

The first term is the short-range interaction term that decays to 0 over a length scale of 1/ω
and the second term kicks in for long-range interactions. ω is usually referred to as the
range-separation parameter. Depending on the functional, the ω value can be either universally
fixed by fitting to empirical data or by tuning it to satisfy certain conditions that would be satisfied
by the exact functional like the Koopman’s condition i.e., for an N-electron system, 𝐸 𝐻𝑂𝑀𝑂 ( 𝑁 )=
𝐸 ( 𝑁 )− 𝐸 ( 𝑁 − 1) .
12
The general form of an RSH XC functional can then be expressed as:
𝐸 𝑋𝐶
𝑅𝑆𝐻 = 𝑐 𝑋 ,𝑆𝑅
𝐸 𝑋 ,𝑆𝑅
𝐻𝐹
+ 𝑐 𝑋 ,𝐿𝑅
𝐸 𝑋 ,𝐿𝑅
𝐻𝐹
+ ( 1− 𝑐 𝑋 ,𝑆𝑅
) 𝐸 𝑋 ,𝑆𝑅
𝐷𝐹𝑇 + ( 1− 𝑐 𝑋 ,𝐿𝑅
) 𝐸 𝑋 ,𝐿𝑅
𝐷𝐹𝑇 + 𝑐 𝐶 𝐸 𝐶 𝐷𝐹𝑇 ( 6.2)
The coefficients in the above equation are often empirically derived for different
functionals. The excitation energies of one of the complexes (CAAC-Cu-Cz) described above,
computed using TDDFT with the B3LYP hybrid functional and the CAM-B3LYP RSH functional
are shown in Figure 6.2. While the energies of the LE (local excitation) states are predicted with
reasonable accuracy by both functionals, the energies of the CT states computed using the
CAM-B3LYP functional was found to be in very good agreement with the experimental values
while the B3LYP functional was found to grossly underestimate them due to the reasons described
above. We therefore relied on RSH functionals to model the excited states of the complexes.
140

Further, implicit and explicit solvation modeling procedures are used to understand the effects of
solvation on the excited states of these complexes as described below.

B3LYP/LACVP*
CAM-
B3LYP/LACVP*
Exptl.
1
ICT 2.21 3.25 2.96
3
ICT 1.97 2.99 -
3
LE 3.08 3.02 2.88

Figure 6.2. Comparison of vertical excitation energies (in eV) of CAAC-Cu-Cz predicted by
TDDFT using the B3LYP and CAM-B3LYP functionals with experimental data.
1

6.2. CAAC-Cu-Cz complex
The CAAC-Cu-Cz complex recently reported by our lab is a highly luminescent
chromophore with a reported quantum yield of nearly 100% and fast emission in the microsecond
regime.
1
It is also highly solvatochromic with strong negative solvatochromism observed in its
absorption spectra and slightly weaker positive solvatochromism in emission. It features a broad
emission profile at room temperature in both MeCy (non-polar) and 2-MeTHF (polar) solvents
(Figure 6.3). However, upon cooling to 77 K, narrow, vibronic and long-lived emission (ms
regime) was observed.
1

DFT/TDDFT calculations were performed to get a better understanding of the observed
phenomena. All DFT and TDDFT calculations reported here were performed using the Q-Chem
5.0 package.
13
Ground state geometry optimization was performed at the B3LYP/LACVP** level.
3
LE ICT
141

Single-point TDDFT calculations were performed on the ground state optimized structure at the
ωPBEh/6-31G** level to compute excited state properties. The value of the range separation
parameter () in the ωPBEh RSH functional was tuned to satisfy the global density-dependent
(GDD) criterion
14
to get a balanced description of CT and LE states and the tuned value was found
to be 0.263 bohr
-1
for CAAC-Cu-Cz.

Figure 6.3. (left) Excitation and emission spectra of CAAC-Cu-Cz in different media. (right)
Emission spectra in 77 K and room temperature (RT). (Adapted from Ref.
1
)

In vacuum, the TDDFT calculations predicted the presence of three closely lying states: a
pair of inter-ligand CT (ICT) states of the same orbital parentages but different spin multiplicity
(
3
ICT and
1
ICT) and a Cz-ligand localized (
3
Cz) triplet state. We have further modeled the effects
of solvation on the excited states at 77 K and room temperature (300 K) using a multi-scale hybrid
approach that employed classical Molecular Dynamics (MD) simulations in conjunction with
TDDFT as detailed below.
A simulation cell was built with 128 2-MeTHF solvent molecules around the copper
complex. First, to approximate the response of the solvent molecules to the
3
ICT excited state at
300 K, the atomic charges of the forcefield for the complex were replaced with the electrostatic
350 400 450 500 550 600
0
0.5
1

Normalized Intensity (a. u.)
Wavelength (nm)
Em, MeCy
Ex, MeCy
Em, toluene
Ex, toluene
Em, 2-MeTHF
Ex, 2-MeTHF
Em, CH
2
Cl
2
Ex, CH
2
Cl
2
400 500 600
0
0.5
1
2-MeTHF, RT
2-MeTHF, 77 K
MeCy, RT
MeCy, 77 K
Wavelength (nm)
0
0.5
1
Normalized Intensity (a. u.)
142

potential-fitted (esp) point charges of the
3
ICT state derived from UDFT (ωPBEh/6-31G**) while
those of the solvent molecules were replaced by the corresponding ground state esp point charges,
calculated at the B3LYP/6-31G** level. A 200 ns NPT MD simulation (P = 1 atm, T = 300 K)
was performed using the OPLS2005 forcefield.
15
. 50 snapshots were extracted from the last 100 ns
of the MD run, and TDDFT (ωPBEh/6-31G**) calculations were performed on each snapshot with
atoms of all the solvent molecules replaced by the corresponding esp-fitted point charges to serve
as a polarizing influence on the complex. It was thus found that the lowest triplet state in all cases
was
3
CT due to stabilization by the solvent molecules (the distribution of T1 energies is reported
in Figure 6.4). Next, to study the effect of solvation at 77 K a similar procedure was followed
where the atomic charges of the OPLS2005 forcefield were now replaced by the ground state
esp-fitted charges computed at the ωPBEh/6-31G** level. A series of 10 ns NVT runs were
performed on the 300 K equilibrated cell in steps of decreasing temperatures (300–200–100–77 K)
followed by a 200 ns NPT simulation (P = 1 atm, T = 77 K). The simulation resulted in a frozen
rigid equilibrated cell which was used to perform a single point TDDFT calculation as done in the
previous case. It was found that the
3
Cz state becomes the lowest lying triplet in accordance with
the experimental observation of
3
Cz emission in 2-Me-THF at 77 K (Figure 3). The destabilization
of the
3
ICT state can be attributed to its corresponding dipole (4.25 D) which is opposite in
direction to the large ground state and
3
Cz dipole calculated to be 11.80 D and 11.27 D
respectively. Hence, the solvent molecules in a frozen matrix are expected to be arranged in such
a configuration so as to stabilize the high ground state dipole, whereas the dipole of the
3
CT state,
being in the opposing direction, would be destabilized. Negative solvatochromic effects observed
in absorption can be explained using the same rationale.
143

Figure 6.4. Histogram of T1 energies computed for 50 snapshots of the NPT MD run at 300K.

6.3. MAC-Cu-Amines and DAC-Cu-Amine complexes
The MAC/DAC-Cu-Amine complexes reported by Shi et al.
3
are very closely related to
CAAC-Cu-Cz and their structures are shown in Figure 6.5. They were also reported to exhibit
strong solvatochromism and excellent luminescent properties featuring high PLQY and
microsecond emission lifetimes.
2, 3

Figure 6.5. Structures of MAC/DAC-Cu-Cz complexes (Taken from Ref.
3
).

2.50 2.55 2.60 2.65 2.70 2.75
0
5
10
Counts
T
1
(eV)
144

Ground state geometries of all the MAC/DAC-Cu-Amine complexes studied here were
optimized at the B3LYP/LACVP** level. TDDFT calculations were performed on the optimized
structures at the CAM-B3LYP/LACVP** level. The CAM-B3LYP RSH functional was chosen to
achieve an accurate description of ICT states and was found to be in good agreement with
experimental results. These calculations were performed using Schrodinger’s Materials Science
Suite.
16

TDDFT calculations were used to predict the lowest energy excited states for these complexes.
Compounds 1 and 2 show two closely spaced but quite different excited states, one is essentially
an intramolecular charge transfer (ICT) transition, involving electron transfer from the carbazole
to the carbene. The singlet and triplet ICT levels (
1
ICT and
3
ICT) are predicted to be quite close
in energy. The second excited state is one that is a triplet localized completely on the carbazole
ligand,
3
Cz. Both the
3
Cz and
1,3
ICT states are seen for compounds 3-6, but the ICT states fall well
below the
3
Cz state.
Ground and excited state dipole moments were estimated using DFT and TDDFT calculations
(vide infra) and are given in Table 6.1 for compounds 1-6. The dipole moments were calculated
based on the optimized structures of the ground,
3
Cz,
1
ICT and
3
ICT states at the
CAM-B3LYP/LACVP** level.
17
In all complexes, the linear geometry in addition to a large
separation between the donor and the acceptor imparts a large ground-state molecular dipole
moment. From MAC to DAC analogues, the addition of one carbonyl group decreases the
ground-state dipole by ~2 D. The ICT transitions involve a redistribution of the electron density
away from the Cz towards the carbene, which effectively gives rise to excited state (
1
ICT and
3
ICT) dipole moment that is much smaller (1 and 4) or even in the opposite direction to the ground
state dipole(2, 3, 5 and 6). The singlet and triplet ICT states have slightly different dipole moments
145

because the
1
ICT is nearly all HOMO LUMO transition whereas the
3
ICT has multiple triplet states
mixed in which alters the dipole. For example, the
3
ICT state of 2 has significant contribution from
3
Cz transitions (20%) while the
1
ICT state is predominantly a HOMO-LUMO (ICT) transition
(94%). In all of compounds except 6, the
3
Cz state has a dipole moment very similar to that of the
ground state since the transition involves only the redistribution of electron density within the
carbazole ligand. However, in 6, the
3
Cz was found to have a significant mixing in of the HOMO-
LUMO ICT transition (26%) leading to a marked reduction in the dipole moment.
Table 6.1. Dipole moment () of complexes 1-6 in ground state (S0), lowest ligand-excited state
(
3
Cz) and excited ICT states.

 ( Cu-N)*
Complex  gs
S 0
 es
3
Cz
 es

1
ICT
 es

3
ICT
1
19.1
(18.9)
19.1
(18.8)
5.5
(-4.3)
4.5
(3.0)
2
14.9
(14.8)
12.5
(12.4)
8.6
(-8.6)
1.2
(0.4)
3 10.6 (10.2)
9.9
(9.4)
13.7
(-13.2)
11.6
(-11.1)
4
17.2
(17.2)
16.7
(16.7)
8.9
(-8.9)
6.6
(-6.6)
5
13.7
(13.0)
11.4
(10.3)
13.5
(-12.8)
11.8
(-11.0)
6
8.3
(8.3)
0.60
(0.5)
17.0
(-17.0)
15.4
(-15.4)
*
Obtained from TD-DFT calculations (CAM-B3LYP/LACVP**) using geometry optimized structures.
μ Z is the projection of μ along the Cu–N bond axis. Negative values indicate dipole moments are opposite
in direction from the dipole moments in the ground state. All dipole moment values are reported in
Debye.

Natural transition orbitals (NTOs) of complexes 1-6 are shown in the Table 6.2. The lowest
singlet excited states (S1) for all complexes are ICT transitions from HOMO (carbazoles) to
LUMO (carbenes) with little orbital contribution from the metal, which leads to a small exchange
interaction between the involved electrons and hence a small ΔE(S1-T1). A small oscillator strength
146

of the S1→S0 is normally observed when the HOMO-LUMO overlap is small, leading to a small
kr(S1→S0). However, high kr is obtained for all of these linear complexes, which is likely achieved
through strong coupling between the filled 2pz orbital of the Cz ligand (donor) and the empty 2pz
orbital of the carbene (acceptor). The d orbitals of the Cu center, whereas gives a small ΔE(S1-T1)
due to the small metal contribution, serves as an electronic bridge between the two parallel 2pz
orbitals of the two ligands. The calculated high oscillator strength (𝑓 = 0.11 – 0.14) are consistent
with the high kr obtained experimentally. The calculated energy of S1 correlates well with the
experimental absorption peak at the lowest energy.
The lowest triplet transitions (T1) of the complexes are strongly temperature- and
medium-dependent. As detailed earlier, in 2-MeTHF solution, all complexes exhibit broad ICT
emission at RT whereas vibronically resolved
3
Cz emission is observed in the frozen 77 K matrices
for complexes 1-3. In order to help understand this phenomenon, TDDFT calculations were
performed for complexes 1-4 using the IEF-PCM solvation model in the non-equilibrium limit
using the ptSS (perturbative state-specific) approach as implemented in Q-Chem 5.1. This scheme
accounts for the relaxation of the fast-electronic degrees of freedom in response to the excited state
charge distribution while the slower (nuclear) degrees of freedom are considered to be in
equilibrium with the ground state charge distribution. Therefore, the scheme can be used to model
in an albeit approximate way, the rigidochromic effect in frozen polar matrices (77 K) which
primarily arises due to the inability of the solvent molecules to reorient in response to the excited
state charge distribution. The dielectric constant (6.97) and ε∞ (1.97) values were set based on the
experimentally reported values for 2-MeTHF. The predicted energies of the
3
Cz and
3
ICT states at
room temperature and 77K are in good qualitative agreement with the values observed
experimentally. The theory predicts that in all cases, the ICT states get destabilized to a large
147

extent in the non-equilibrium limit (77 K) relative to the gas phase energies (RT) whereas the
3
Cz
state remains largely unperturbed. The reason for the destabilization of the ICT states can be
understood by comparing the dipole moments of the
3
ICT and
3
Cz states relative to the ground
states. The ICT states are found to have a much smaller or even opposite dipole moment relative
to the ground

state, leading to the destabilization of the ICT states in the non-equilibrium limit.
The
3
Cz state is unperturbed due to the comparable dipole moments with the ground state.
Table 6.2. Natural transition orbitals (NTO) of complex 1-6 in gas phase.

Natural Transition Orbitals (NTOs)
S1 T1 T2
1

3.52 eV (352 nm) 2.90 eV (427 nm) 3.13 eV (396 nm)
2

3.24 eV (383 nm) 2.94 eV (422 nm) 3.05 eV (406 nm)
3

2.93 eV (423 nm) 2.73 eV (454 nm) 3.02 eV (410 nm)
4

2.78 eV (446 nm) 2.58 eV (480 nm) 2.89 eV (429 nm)
5

148

2.48 eV (500 nm) 2.26 eV (549 nm) 2.86 eV (434 nm)
6

2.20 eV (564 nm) 1.92 eV (646 nm) 2.79 eV (444 nm)

The orbitals are shown as solid (hole) and mesh (particle).

Per the TDDFT calculations, for complex 1 the T1 (2.90 eV) and T2 (3.13 eV) are both
3
Cz
states, with the T3 (3.41 eV) being the first
3
ICT state. The emission of 1 at 77 K shows vibronic
line structure in all matrices since the ICT states are further destabilized and the
internal-conversion (IC) process from the
3
Cz state to
3
ICT state is thermodynamically unfavorable
at low temperature. For complex 2, the lowest triplet state is mainly
3
Cz state at RT as well but
only slightly below the
3
ICT state. In the rigid polystyrene matrix that has a small dipole and is
highly polarizable, the matrix could quickly respond to the changing dipole upon excitation.
Therefore, the
3
ICT state is still thermodynamically accessible at 77 K, hence leading to broad ICT
emission. However, the
3
ICT state is significantly destabilized in the frozen polar 2-MeTHF matrix
and the thermal promotion from the
3
Cz to
3
ICT state becomes unfavorable. Therefore, the
emission in 2-MeTHF at 77 K shows vibronically resolved
3
Cz emission. The lowest triplet state
of complex 3 at RT is the
3
ICT state and the energy of the lowest
3
Cz state is slightly higher, which
explains why the emission is broad and featureless at 77 K in both polystyrene films. The
3
ICT
state is significantly destabilized in 2-MeTHF from RT to 77 K and becomes higher than the
3
Cz
state, which explains the mixed
3
ICT and
3
Cz character of the emission of 3 in 2-MeTHF at 77 K.
The
3
ICT state of complex 4 is much lower than the
3
Cz state even in frozen 2-MeTHF, leading to
broad and featureless ICT emission at 77 K. Complexes 5 and 6 behave similar as complex 4.
149

1 2 3 4
1.5
2.0
2.5
3.0
3.5
4.0

3
Cz

3
CT RT

3
CT 77 K
Energy (eV)
Complex

Figure 6.6. Energy diagram of the
3
Cz states (black),
3
CT states at RT (red) and 77 K (blue) of
complexes 1-4 in 2-MeTHF.

6.4. Tetradentate Pyridyl-Carbazole Platinum Complexes
Recently, an interesting tetradentate pyridyl-carbazole platinum complex referred to as
PtNON (Figure 6.7) was reported to achieve high efficiency blue phosphorescence with an
operational lifetime of 600h at 1000 cd/m
2
when incorporated into an OLED device.
18-21
Like the
previous discussed 2-coordinate complexes, PtNON was shown to exhibit strong solvatochromism
and temperature dependent emission profile ranging from broad featureless emission in 2-MeTHF
at room temperature to narrow vibronic emission at 77 K as shown in Figure 6.7.
4

Figure 6.7. Emission spectra of PtNON in different media. (Adapted from Ref.
22
)
400 450 500 550 600 650 700
0.0
0.5
1.0
77K
PMMA
MeCyHex
2-MeTHF
DCM
MeCN

Normalized PL Intensity
Wavelength (nm)
solvent polarity
150

To elucidate the origin of the narrow emission and solvatochromism in pyridyl-carbazole
based tetradentate Pt complexes, four PtNON derivatives with different substitutions at the
4-position of the pyridine were modeled (i.e. PtNON, PtNON-CF3, PtNON-Me, and PtNON-OMe
in Scheme 1) via DFT at the B3LYP / LACVP** level of theory. As can be seen from the DFT
calculations, the lowest unoccupied molecular orbital (LUMO) densities are localized on the
pyridine rings in all cases, and the highest occupied molecular orbital (HOMO) densities are
localized predominantly on the platinum and the platinum-adjacent rings of the carbazole moieties.
Consequently, the HOMO energies are minimally influenced by the pyridine substitutions,
whereas the LUMO energies vary dramatically from -2.0 eV for PtNON-CF3 to -1.11 eV for
PtNON-OMe upon this single site-substitution.

Figure 6.8. Top row: molecular structure of PtNON derivatives. Middle row: LUMO densities
and energies. Bottom row: HOMO densities and energies. DFT calculations were performed at
the B3LYP / LACVP** level.

LUMO = -1.36 eV
LUMO = -1.34 eV
LUMO = -1.11 eV
HOMO = -5.01 eV HOMO = -5.01 eV
HOMO = -4.98 eV
E
T
= 2.80 eV E
T
= 2.87 eV
E
T
= 2.89 eV
LUMO = -2.0 eV
HOMO = -5.15 eV
E
T
= 2.32 eV
LUMO = -1.36 eV
LUMO = -1.34 eV
LUMO = -1.11 eV
HOMO = -5.01 eV HOMO = -5.01 eV
HOMO = -4.98 eV
E
T
= 2.80 eV E
T
= 2.87 eV
E
T
= 2.89 eV
LUMO = -2.0 eV
HOMO = -5.15 eV
E
T
= 2.32 eV
-2.00 eV -1.36 eV -1.34 eV -1.11 eV
-5.15 eV -5.01 eV -5.01 eV -4.98 eV
HOMO LUMO
151

It can be seen in Figure 6.9 that the lowest energy triplet, T1, in PtNON-OMe, PtNON-Me,
and PtNON is a locally excited (LE) state centered on the carbazole moiety, where both the hole
and the electron comprising the triplet state are localized predominately on the carbazole, with
some character of the electron extending onto the pyridine in the case of PtNON. The higher lying
triplet, T2, involves a charge transfer transition, CT, with relatively little metal character. In
contrast, PtNON-CF3 shows a pyridine-centered LUMO that is significantly lower in energy than
the comparable pyridine based MO in the other three derivatives, due to the strong electron
withdrawing effect of the trifluoromethyl group, and thus the T1 state is CT in character, wherein
the hole is delocalized across the platinum carbazole and extended onto the pyridine, and the
electron is confined to the pyridine. The T2 in PtNON-CF3 is an LE state, similar to the LE states
observed for the other PtNON complexes. In PtNON-OMe, the difference in energy between the
T1 (LE) and T2 (CT) energies was calculated to be 90 meV, nearly fourfold greater than kT at room
temperature; in PtNON-Me and PtNON, the difference between T1 and T2

was calculated to be
much smaller (40 and 50 meV, respectively), closer to kT and indicating that temperature and
solvation effects may have a greater effect on the emitting state in these species than in
PtNON-OMe (electron rich) and PtNON-CF3 (electron poor). Together, these data suggest that
destabilizing the carbazole-pyridine CT state relative to the ligand-centered carbazole LE state
could be accomplished by a single site-substitution affecting the pyridine-centered LUMO energy,
leading to a relative rearrangement of the two lowest energy triplet states and inducing a narrowing
and blue-shifting of the emitting state.
To study the effects of solvation on the energies of the excited states, TD-DFT calculations
were performed on each of the derivatives using the IEF-PCM solvation model both in the
equilibrium and non-equilibrium limit. The non-equilibrium scheme accounts for the relaxation of
152

the solvent’s fast-electronic degrees of freedom in response to the excited state charge distribution
while the slower (nuclear) degrees of freedom are considered to be in equilibrium with the ground
state charge distribution. Therefore, the scheme can be used to model the rigidochromic effect in
frozen polar matrices (77 K) which primarily arises due to the inability of the solvent molecules
to reorient in response to the excited state charge distribution. The equilibrium solvation
calculation accounts for both electronic and nuclear relaxation of the solvent in response to the
excited state of interest and can therefore be used to model the effect of solvation in a fluid
environment. Based on the TD-DFT results, it was found that in the three more electron-rich
derivatives (PtNON, PtNON-Me, and PtNON-OMe) the T1 and T2 states have predominantly LE
and CT character respectively, whereas in the electron-poor PtNON-CF3 derivative, both the T1
and T2 states are found to be CT in character. In all cases, the CT states are destabilized in the non-
equilibrium limit relative to the equilibrium, while the LE states remain largely unperturbed. This
is due to the orientation of CT transitions opposing the inherent ground state dipole moment in
each of the complexes as shown in Table 6.3. In such a case, the CT state is hence destabilized in
the non-equilibrium limit due to the inability of the frozen medium to effectively stabilize the new
electronic distribution. Meanwhile, in the equilibrium limit, both electronic and nuclear degrees of
freedom of the solvent can respond to the electronic configuration of the CT state and can hence
stabilize it, as is the case in a fluid medium. The LE states, on the other hand, result in no significant
change in dipole moment upon photoexcitation relative to the ground state, and hence remain
largely unperturbed by the solvent. In the equilibrium solvation limit, the stabilization of the CT
state in PtNON and PtNON-Me brings it close in energy to the LE state (to within about 50 meV).
Therefore, in these derivatives, the CT and the LE states are expected to be in thermal equilibrium
at room temperature. In the frozen 77 K case, however, the widening of the CT-LE gap brought
153

about by the relative destabilization of the CT state along with the decreased temperature renders
thermal equilibration to the CT state unfavorable. In the extreme example, there is a large CT-LE
separation in PtNON-OMe both in the equilibrium and non-equilibrium limit, leading to the
expectation that in this system, narrow LE emission will dominate at both cryogenic and room
temperatures. In the case of PtNON-CF3, where both lowest energy triplet states are CT in nature,
broad CT emission is expected in all media. All the computational predictions reported above for
these complexes were found to be consistent with experimental findings as reported in our recent
paper (Fleetham et al.
4
).

Figure 6.9. Natural transition orbitals for the CT (bottom) and LE (top) states in PtNON
derivatives. Blue and red plots refer to hole and electron densities respectively for each
transition.

3
LE
3
CT
3
LE
3
CT
3
LE
3
CT
3
LE
3
CT
PtNON-CF
3
PtNON-Me PtNON-OMe
PtNON
154

Table 6.3. Excited triplet state energies and dipole moments of the complexes computed using
TDDFT. (T1 and T2 energies were obtained from TD-DFT (CAM-B3LYP/LACVP**) using the
IEFPCM solvation model for THF in the equilibrium and non-equilibrium limit.)

Equilibrium
solvation
Non-equilibrium
solvation
µ (D)
T1 T2 T1 T2 S0 T1 T2
PtNON-CF3
2.26/CT 2.57/CT 2.38/CT 2.64/CT
4.44
(1.15, -4.27, -0.39)
6.58
(4.49, 3.59, 3.20)
7.54
(5.22, 4.26, 3.37)
PtNON
2.76/LE 2.81/CT 2.77/LE 2.84/CT
8.39
(-0.84, -8.34, 0.47)
6.47
(-1.25, -6.32, -0.53)
4.42
(-2.80, -1.93, -2.82)
PtNON-Me
2.80/LE 2.84/CT 2.80/LE 2.87/CT
9.46
(-0.72, -9.41, 0.63)
8.36
(-2.17, -8.07, 0.11)
5.31
(-3.45, -2.96, -2.75)
PtNON-OMe
2.83/LE 2.91/CT 2.83/LE 2.93/CT
11.58
(-0.84, -11.54,
0.36)
10.95
(-1.47, -10.84,
0.34)
7.13
(-3.50, -5.67, -2.51)
* Dipole moment vectors are reported for a coordinate system with Pt as the origin and the y-axis
intercepts the O atom connecting the two carbazoles and the z-axis goes through the plane of the
ligands.

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158

Chapter 7. Kinetics of TADF and phosphorescent molecular systems

Emission from TADF and heavy metal based phosphorescent systems involve multiple
states unlike simple fluorescent dyes which only involve the S1 state. Consequently, the kinetics
of the latter systems are more complicated and often exhibit strong dependence on temperature.
The kinetics of these systems are discussed in detail below.

7.1. Simplified kinetic picture of TADF (PL ~100%)
In our recently published paper
1
, we discussed the kinetics of TADF systems by classifying
them into 3 distinct cases based on the relative magnitudes of the radiative rate of the S1 state and
the ISC rate. We start by discussing the kinetics of TADF emitters with the potential to achieve an
electroluminescence efficiency (
EL
) of 100%. A luminescence efficiency near 100% is a
prerequisite for achieving a near-unity value for 
EL
. This requires that the emission efficiency
from T1 and S1 be ~ 100%, allowing us to simplify the kinetic scheme significantly by ignoring
the nonradiative channels, which consequently are much slower than the radiative rates, as
illustrated in Figure 7.1. The triplet sublevels in the simplified picture are considered to be
degenerate, consistent with the zero-field splitting (ZFS) of these levels being markedly lower in
energy than the energy difference between the singlet and triplet, EST. It is important to include
the rate constants for ISC between the T1 and S1 states. These rate constants are often referred to
as reverse ISC (kRISC) for endergonic ISC (T1→S1) and ISC (kISC) for exergonic ISC (S1→T1)
2, 3

but the simpler labels of 𝑘 1
for T1→S1 and 𝑘 −1
for S1→T1 will be used here. Using 𝑘 1
and 𝑘 −1

eliminates the need for a “reverse” ISC to promote a “forward” TADF. The phosphorescent
channel (from T1) can be neglected since 𝑘 𝑇 1
is much smaller than 𝑘 𝑆 1
, kISC, and 𝑘 𝑇𝐴𝐷𝐹 for TADF
159

emitters. For T1
∆
→ S1 to outcompete phosphorescence or nonradiative decay from the T1 state, a
small exchange energy (EST < 2000 cm
-1
, 0.25 eV) is required, which becomes an upper limit for
the efficient TADF emitters. A common signature of TADF is emission spectra that redshift upon
cooling due to the lower T1 energy. Emission due to TADF originates from the S1 state at room
temperature, whereas at 77 K, there is insufficient thermal energy to promote the T1→S1 ISC
process and thus emission is from the T1 state, i.e. phosphorescence, albeit with a much longer
lifetime. Therefore, estimates of EST are often made by comparing emission spectra measured at
room temperature and at 77 K. While this simple approach is a good qualitative measure,
temperature effects on the line shape and rigidochromic solvent shifts make this method of
estimating EST unreliable. Thus, the best method to determine EST and directly measure the
energy difference between the two states is to perform variable temperature photophysical
measurements (vide infra).
4-9

Figure 7.1. The full kinetic scheme for emission via TADF is shown to the left, where 𝒌 𝟏 , 𝒌 −𝟏
, 𝒌 𝑻 𝟏 and kTnr characterize ISC transitions. The rate constant for TADF (𝒌 𝑻𝑨𝑫𝑭 ) is for the
process illustrated by the green arrow. The simplified scheme to the right was generated
assuming PL>0.9 (kr >> knr) and 𝒌 𝑻 𝟏 << 𝒌 𝟏 , 𝒌 −𝟏 , 𝒌 𝑺 𝟏 . (Taken from Ref.
1
)

𝑘 −1

T
1

S
1

𝒌 𝑻 𝟏
𝒌 𝑺 𝟏
𝒌 𝑻𝑨𝑫𝑭
S
0

𝑘 1

𝒌 𝑻𝒏𝒓
𝒌 𝑺𝒏𝒓
T
1

S
1

𝒌 𝑺 𝟏
𝒌 𝑻𝑨𝑫𝑭
S
0

𝑘 1

𝑘 −1
 E
ST

160

Using the simplified three level model of Figure 7.1, one only needs to consider three rate
constants to evaluate the rate constant and radiative lifetime for TADF, i.e. 𝑘 1
, 𝑘 −1
and 𝑘 𝑆 1
. As
we will show below, the relative values of 𝑘 1
, 𝑘 −1
can be determined from the energy difference
between S1 and T1, EST. Using this simple model gives the kinetic scheme in equation (7.1) and
the rate expression in equation (7.2).
(7.1)
𝑘 𝑇𝐴𝐷𝐹 =
𝑘 1
𝑘 𝑆 1
𝑘 −1
+𝑘 𝑆 1
(7.2)
Here, we will consider three cases: 𝑘 𝑆 1
>> kISC , 𝑘 𝑆 1
<< kISC and 𝑘 𝑆 1
~ kISC, where kISC = 𝑘 1
,
𝑘 −1
. Compounds whose kinetics correspond to each of these cases will henceforth be referred to
as Case 1, 2 and 3 materials, respectively.

7.1.1. Case 1: 𝒌 𝑺 𝟏 >> kISC
This is the simplest case to consider. If we assume that 𝑘 1
is slower than phosphorescence
(𝑘 𝑇 1
), there will be no interconversion between singlet and triplet channels and the S1 and T1 states
prior to radiative or nonradiative decay, thus both states will relax independently. Emission will
be from fluorescence (with the lifetime given by 𝜏 𝑆 1
= 1/ 𝑘 𝑆 1
); the T1 will decay nonradiatively.
This condition is often the situation found in fluorescence-based OLEDs, and for devices
optimized to harvest triplet excitons by TTA.
10
Highly efficient fluorescent dyes are designed to
have very slow ISC rates since this process can be an efficient nonradiative channel for excited
state decay. In fluorescent OLEDs the dopant gives rise to singlet emission while the triplets reside
on the host material and nonradiatively decay to the ground state. Thus, in this case the OLED
161

efficiency is 25% if the triplets do not lead to net emission and 62.5% for fluorescence plus TTA
collection of the triplets.
10
An alternative is to use two different emitting materials, one that
fluoresces with high efficiency and the other phosphoresces at high efficiency, collecting the S 1
excitons exclusively at the fluorophore and the T1 excitons at the phosphor. This approach allows
for highly efficient, parallel fluorescent and phosphorescent processes.
11-14

7.1.2. Case 2: kISC >> 𝒌 𝑺 𝟏
Rapid ISC is the common situation for TADF based emitters that include transition metal
ions, particularly those with monovalent Group 11 metals. There has been a great deal of recent
interest in monovalent copper, silver and gold complexes for TADF.
6, 7, 15-17
Their d
10

configuration prevents the nonradiative decay though ligand field states that is prevalent for
complexes with metal ions with d
1
-d
9
configurations. The closed shell configuration for the d
10

ions does not preclude strong SOC in these complexes, leading to fast ISC rates. TADF emitters
built around Group 11 metal ions have achieved 
TADF
as short as 0.5 s and PL ~ 1.0.
7
If 𝑘 1
and
𝑘 −1
are both >> 𝑘 𝑆 1
, a rapid preequilibrium approximation can be used to simplify the rate law
given in equation (7.2), giving equation (7.3), where Keq is the equilibrium constant for 𝑇 1
⇄ 𝑆 1
.
It is important to stress that once the ISC rate exceeds 𝑘 𝑆 1
by a factor of 50 or more, no further
benefit accrues from increasing this rate; i.e. making a rapid preequilibrium even more rapid does
not change the kinetics of the overall process.
𝑘 𝑇𝐴𝐷𝐹 =
𝑘 1
𝑘 𝑆 1
𝑘 −1
= 𝐾 𝑒𝑞
𝑘 𝑆 1
⟹ 𝜏 𝑇𝐴𝐷𝐹 =
𝜏 𝑆 1
𝐾 𝑒𝑞
⁄ (7.3)
It is important to stress that the individual values of 𝑘 1
and 𝑘 −1
are unimportant in this rapid
preequilibrium limit, all that matters is their ratio, which gives Keq. This feature leads to an
162

interesting conclusion: if the TADF efficiency is 100%, it becomes possible to determine Keq from
time-resolved emission data at short lifetimes. Large SOC constants of the central ion in metal
complexes typically push 𝑘 −1
values into the 1-200 ps regime, allowing for a direct measure of
this rate constant from the initial emission decay times. After a few hundred ps, the emission rate
settles to the rate given by equation (7.3), which is on the 0.5-5 s time scale. Thus, the ratio of
the emission intensity at earliest time (pure S1 emission) to the intensity at long time (> 500 ps) is
equal to Keq.
7
Note that this situation is only true in cases where PL ~ 1.0, so nonradiative decay
can be neglected. Thus, with Keq and 
TADF
in hand one can easily determine 𝑘 𝑆 1
. One can also
use the value of K eq to calculate EST as given in equation (7.4). The factor of ⅓ in this equation
accounts for the three-fold degeneracy of the triplet state.
18
Figure 7.2 shows the luminescence
decay traces for two TADF emitters, one with a silver ion and the other a copper ion. These decay
traces were generated using time correlated single photon counting methods with a 20 ps excitation
source. The two complexes have similar 𝑘 −1
values (160 and 220 ps, respectively), but very
different Keq values (0.13 and 0.02, respectively). These Keq values correspond to EST values of
190 cm
-1
for the silver complex and 570 cm
-1
for the copper complex (both at 300 K). The EST
values obtained this way are comparable to values found using a detailed variable temperature
kinetic analysis of the photoemission lifetimes.
7

𝐾 𝑒𝑞
=
𝑘 1
𝑘 −1
=
1
3
𝑒𝑥𝑝 ( −
∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ) ⇒ ∆𝐸 𝑆𝑇
= −𝑘 𝐵 𝑇 ∙ ln( 3𝐾 𝑒𝑞
) (7.4)
The emission behaviour of heavy metal phosphorescent materials, such as those commonly
used in OLEDs, can also be treated by a similar analysis to the one given here for Case 2. The
emission is well fit to an equation similar to equation 7.3, where 𝑘 1
and 𝑘 −1
are rates of internal
163

conversion between triplet sublevels, and 𝑘 𝑆 1
is replaced with 𝑘 𝑇 𝐼𝐼𝐼
, the decay rate constant for the
highest lying triplet sublevel (discussed in section 7.3).

Figure 7.2. Emission decay traces are shown for silver (left) and copper (right) based TADF
emitters.
7
The initial decay is due to ISC (S1→T1). The τ
TADF
values for the two compounds are
500 and 1,400 ns, respectively, well outside of the window shown here. (Taken from Ref.
1
)

7.1.3. Case 3: kISC ~ 𝒌 𝑺 𝟏
When kISC and 𝑘 𝑆 1
are comparable, the situation is more complicated than the two previous
cases. The S1 and T1 states cannot be treated independently (Case 1) and cannot be simplified to
equation (7.2) using a preequilibrium approximation (Case 2), so equation (7.2) cannot be further
simplified. This situation is common for organic TADF emitters, where there are no metal atoms
to provide strong SOC. The principal approach that has been used to enhance the ISC rate in these
compounds (and move closer to Case 2) is to make the energy difference between the S1 and T1
states very small. A small EST is typically achieved in organic TADF materials by decoupling
the donor and acceptor groups involved in a charge transfer excited state.
4, 19-21
This decoupling
is accomplished by designing molecules where the donor and acceptor moieties are oriented
orthogonal to each other,
22
connected by a nonconjugated linkage
23, 24
or are on separate molecules
0 1 2 3 4
0.001
0.01
0.1
1

Normalized Intensity
Time (ns)
Raw
IRF
Fit
0 1 2 3 4
0.001
0.01
0.1
1

Normalized Intensity
Time (ns)
Raw
IRF
Fit
TADF
TADF
S
1
S
1
ISC ISC
164

(i.e. an exciplex)
25, 26
The idea of using a small EST to promote TADF makes sense when one
considers the parameters that control the TADF rate given in equation (7.5) (to a first
approximation considering only direct spin-orbit coupling),
27-31

𝑘 𝑇𝐴𝐷𝐹 ∝ ∑
⟨𝑇 𝑛 |𝐻 𝑆𝑂𝐶 |𝑆 1
⟩
𝛥 𝐸 𝑆 1
−𝑇 𝑛 𝑛 · ⟨𝑆 0
|𝑒𝑟 |𝑆 1
⟩ (7.5)
where HSOC is the SOC operator, e is the charge of an electron and r is the operator coupling S0
and S1. Here, the mixing is considered to be weak between the T1 and S1 states, because these
states have the same orbital parentage and thus their interaction will be forbidden by El Sayed’s
rule, which requires a change in angular momentum between the singlet and triplet states to offset
the change in spin angular momentum in the ISC process.
32
Thus, a high density of states is
beneficial to keep T1 and Tn close in energy for efficient ISC, which is facilitated by the multiple
closely spaced d orbitals of transition metal complexes or the use of multiple donor and acceptor
groups in a single TADF molecule to create a number of closely spaced orthogonal triplet states.
A small value of EST will enhance the rate of TADF; however, there are two other
mitigating factors. The spin-orbit coupling operator (𝐻 𝑆𝑂𝐶 ) in organic compounds is typically very
small, making the Tn/S1 mixing terms in the numerator small as well. Moreover, the approach
that is often used to promote a small EST value is to build electron donor-acceptor luminophores
where emission results from a charge transfer transition.
19
Minimizing the electronic coupling
between the donor and acceptor leads to the desired small EST values, but also markedly decreases
the oscillator strength of the S0→S1 transition, ⟨𝑆 0
|𝑒𝑟 |𝑆 1
⟩, and counteracts the effect of a small
EST. Therefore, while 
TADF
values approaching 1 s have been reported for organic TADF
compounds, these lifetimes are rarely achieved and most are longer (
TADF
= 5-100 s).
4, 20, 21

165

While the kinetics of emission from Class 3 TADF materials cannot be simplified by a
preequilibrium approximation, the kinetics can be simplified by assuming that knr can be neglected
(consistent with a high PL) and slow phosphorescence (𝑘 𝑇 1
can be ignored), leading to equation
(7.6). Emission decay traces for Class 3 emitters are bimodal, with a prompt component for decay
from S1 state (ns timescale) and a slower one for TADF (s timescale). The prompt time constant
is often erroneously ascribed to 𝑘 𝑆 1
, yet rates for emission from the S1 state (𝑘 𝑆 1
) and ISC from
S1→T1 (𝑘 −1
) are comparable, so it is not possible to unequivocally determine either rate constant
from the prompt luminescence decay.
h = 
TADF
=
𝑘 −1
+𝑘 𝑆 1
𝑘 1
𝑘 𝑆 1
= 3𝑒 ∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 (
1
𝑘 𝑆 1
+
1
𝑘 −1
) (7.6)
Even the simple treatment in equation (7.6) illustrates why decreasing EST has a positive
effect on 
TADF
. Thus, while some approaches to decreasing EST can be counterproductive (vide
supra), a small EST is clearly beneficial. Note that while increasing the already fast ISC rate for
Class 2 TADF materials does not lead to a smaller 
TADF
, the same is not true for Class 3 emitters.
Increasing 𝑘 −1
independent of EST will still lead to lower 
TADF
(as per equation (7.6)) until 𝑘 −1

reaches values much faster than 𝑘 𝑆 1
, at which point the emitter will behave like a Class 2 material.
The values for 𝑘 −1
in purely organic molecules generally vary over a wide range spanning 10
3
-
10
11
s
-1
.
33
However, those molecules that exhibit TADF typically feature rather slow ISC rates
(<10
7
s
-1
) for reasons outlined below.
Before discussing the strategies being investigated by researchers to boost the ISC rate of
organic TADF emitters, it is instructive to offer a brief discussion on the factors that influence ISC.
Within the Condon approximation assuming non-dependence of spin orbit coupling (SOC) on
166

vibrational degrees of freedom, the ISC rate (𝑘 −1
) can be simply expressed according to Fermi’s
golden rule as:
𝑘 −1
=
2𝜋 ℏ
𝜌 𝐹𝐶
|⟨Ψ
𝑇 1
|𝐻 𝑆𝑂𝐶 |Ψ
𝑆 1
⟩|
2
( 7.7)
Here, Ψ
𝑆 1
and Ψ
𝑇 1
are the electronic wavefunctions of the S1 and T1 states respectively, 𝜌 𝐹𝐶
is the
Frank Condon weighted vibrational density of states and 𝐻 𝑆𝑂𝐶 is the spin-orbit coupling operator.
As dictated by equation (7.7), the ISC rate is primarily dependent on the spin-orbit coupling matrix
elements (SOCME) between the S1 and the T1 states, which in turn is dependent on the nature of
the two states and vanishes when both states involve the same set of orbitals (El-Sayed’s rule).
34,
35
This is further exacerbated in the case of long-range singlet and triplet CT (
1,3
CT) states, which
feature limited overlap between the constituent molecular orbitals, given the short-range
dependence (1/r
3
) of the SOC operator (HSOC) on distance between the two electrons.
36
This
shortcoming is a major issue for TADF materials, especially those that usually feature S 1 and T1
states of long-range CT character mandated by the requirement of minimal EST as noted earlier.
Furthermore, pure-organic TADF materials are at a disadvantage relative to TADF emitters
featuring heavy metals since the latter can leverage the ~Z
4
scaling of the SOCME to boost ISC.
The situation in organic TADF emitters can be improved if energetically close-lying states
of different orbital character are introduced that can interact with the
1,3
CT states directly via SOC.
For such a scenario, the electronic wavefunctions of the S1 and T1 states can now be expressed in
terms of the SOC-unperturbed (spin-pure) electronic wavefunctions (Φ
𝑆𝑛 /𝑇𝑛
) according to first-
order perturbation theory:
Ψ
𝑆 1
/𝑇 1
= |Φ
𝑆 1
/𝑇 1
⟩ + ∑𝑎 𝑛 𝑆 1
/𝑇 1
𝑛 |Φ
𝑇 𝑛 /𝑆 𝑛 ⟩ ( 7.8)

167

𝑎 𝑛 𝑆 1
/𝑇 1
=
|⟨Φ
𝑆 1
/𝑇 1
|𝐻 𝑆𝑂𝐶 |Φ
𝑇 𝑛 /𝑆 𝑛 ⟩|
|𝐸 𝑆 1
/𝑇 1
− 𝐸 𝑇 𝑛 /𝑆 𝑛 |
( 7.9)

It is crucial that the new states that couple to the
1,3
CT states lie close in energy to the latter
as the strength of coupling between the states according to equation (7.9) is inversely proportional
to the energy separation between them. The short-range nature of the 𝐻 𝑆𝑂𝐶 operator indicates that
it is beneficial if these states also have significant spatial overlap with the
1,3
CT states (for instance,
CT or localized excited states featuring one of the molecular orbitals that is also involved in
1,3
CT
states). This requirement creates a situation again where transition metal ions are advantageous,
since they often have degenerate or nearly degenerate d-orbitals that give rise to closely spaced
1,3
CT states of differing orbital parentage. It should be noted that the formalism presented above
within the Condon approximation assumes that SOC is not dependent on the vibrational degrees
of freedom. However, several groups have demonstrated the pivotal role of spin-vibronic coupling
mechanisms in facilitating ISC in TADF systems, wherein the S1 and T1 states can couple with
each other through spin-orbit and spin-vibronic coupling via close-lying intermediate states (Sn
and Tn).
37-42
The total SOC interaction including both direct and spin-vibronic coupling can be
expressed through second-order perturbation theory as:
𝐻 𝑆𝑂𝐶 = ⟨Ψ
𝑇 1
|𝐻 𝑆𝑂𝐶 |Ψ
𝑆 1
⟩ + ∑
𝜕 ⟨Ψ
𝑇 1
|𝐻 𝑆𝑂𝐶 |Ψ
𝑆 1
⟩
𝜕 𝑄 𝛼 𝑄 𝛼 𝛼 +
1
2
∑∑
𝜕 2
⟨Ψ
𝑇 1
|𝐻 𝑆𝑂𝐶 |Ψ
𝑆 1
⟩
𝜕 𝑄 𝛼 𝜕 𝑄 𝛽 𝑄 𝛼 𝑄 𝛽 𝛽 𝛼 +∑
⟨Ψ
𝑇 1
|𝐻 𝑆𝑂𝐶 |Ψ
𝑆𝑚
⟩⟨Ψ
𝑆𝑚
|Τ
̂
𝑁 |Ψ
𝑆 1
⟩
|𝐸 𝑆𝑚
− 𝐸 𝑇 1
|
𝑚 + ∑
⟨Ψ
𝑇 1
|Τ
̂
𝑁 |Ψ
𝑇𝑛
⟩⟨Ψ
𝑇𝑛
|𝐻 𝑆𝑂𝐶 |Ψ
𝑆 1
⟩
|𝐸 𝑇𝑛
− 𝐸 𝑆 1
|
𝑛

168

In the above expression, the first term is the direct SOC coupling term described earlier, the
second and third summation terms refer to vibrational spin-orbit coupling terms (expanded up to
the second order) accounting for the variation of the SOCME along nuclear degrees of freedom
(QX) and most importantly the fourth and fifth summation terms refer to the spin-vibronic terms
which facilitate coupling between the S1 and T1 state through vibronic coupling via intermediate
states (Sm, Tn respectively).
Researchers have sought to improve ISC in organic TADF systems using the mechanisms
presented above, with 𝑘 −1
rates as high as 10
11
s
-1
thought to be achievable.
43
Design strategies
have included the introduction of close-lying states capable of coupling with the
1,3
CT states
through one or a combination of the following approaches: introduction of a manifold of multiple
close lying
1,3
CT states by attaching multiple donor units to an acceptor core or vice versa,
44-46

introduction of LE states (usually
3
LE) localized on the donor moieties or the acceptor moieties or
both that lie close in energy to
1,3
CT states,
47-49
and introduction of a functionalized bridging unit
between the donor and acceptor units that offers close-lying LE states localized on the bridging
unit and CT states (from the donor to bridge and bridge to acceptor).
24
Several groups have
highlighted the importance of vibrational flexibility of the molecular structure to allow for efficient
spin-vibronic coupling between states to boost ISC.
38, 40, 42
Computational tools have been used to
identify the specific vibrational modes that are most conducive to ISC among all modes for several
systems.
40, 42
Such studies may aid the rational design of performant TADF luminophores wherein
steric interactions along the modes facilitating ISC can be optimally relaxed, while steric blockades
along other modes to minimize non-radiative decay are still maintained.
Environmental factors also have a significant effect on TADF as ISC rates varying by orders
of magnitude across media of different polarity have been reported.
43, 50, 51
This apparent sensitivity
169

to solvent media has been attributed to the fact that the states of different character (e.g., charge
transfer vs. -*) that couple with each other are affected differently by the polarity of the
surrounding matrix, and that the energy separation between them varies accordingly which directly
affects the extent of coupling between them (equation 7.9). Therefore, the matrix surrounding the
emitter cannot be considered innocuous and can in fact be leveraged as a design parameter to
optimize TADF performance.

7.2. TADF kinetics of systems with PL < 100%
In section 7.1, an important limitation was made and that was that only systems with TADF
efficiencies near 100% would be considered. This led to a tremendous simplification of the kinetic
equations as we were able to ignore the non-radiative rates. A number of papers have described
the complete kinetic picture of TADF with PL  100%.
4-9
Using only the assumption that the
three triplet sublevels are degenerate, the TADF rate can be expressed according to equation
(7.10),
52

𝑘 𝑇𝐴𝐷𝐹 =
𝑘 1
𝑘 −1
Φ
𝑝 𝑘 𝑝 Φ
𝑇𝐴𝐷𝐹 (7.10)
where, 𝑘 𝑝 and 𝑘 𝑇𝐴𝐷𝐹 are the prompt and delayed fluorescence rates while Φ
p
and
Φ
TADF
are the quantum yields of prompt and delayed emission respectively.
Substituting 𝑘 1
=
𝑘 −1
3
𝑒 −
ΔΕ
𝑆 1
−𝑇 1
𝑘 𝐵 𝑇 in ( 7.10)
𝑘 −1
3
𝑒 −
ΔΕ
𝑆 1
−𝑇 1
𝑘 𝐵 𝑇 =
𝑘 𝑝 𝑘 𝑇𝐴𝐷𝐹 𝑘 −1

Φ
TADF
Φ
p
( 7.11)
Replacing Φ
TADF
in terms of the total quantum yield ( Φ
PL
= Φ
TADF
+ Φ
p
) gives ( 7.12)
𝑘 −1
3
𝑒 −
ΔΕ
𝑆 1
−𝑇 1
𝑘 𝐵 𝑇 =
𝑘 𝑝 𝑘 𝑇𝐴 𝐷 𝐹 𝑘 −1

( Φ
PL
− Φ
p
)
Φ
p
( 7.12)
170

Substituting Φ
p
= 𝑘 𝑆 1
𝜏 𝑝 in ( 7.12)
( 𝑘 −1
)
2
3
𝑒 −
ΔΕ
𝑆 1
−𝑇 1
𝑘 𝐵 𝑇 = 𝑘 𝑇𝐴𝐷𝐹 ( Φ
PL
− 𝑘 𝑆 1
𝜏 𝑝 )
𝑘 𝑆 1
( 𝜏 𝑝 )
2
( 7.13)

𝑘 𝑇𝐴𝐷𝐹 =
𝑘 𝑆 1
( 𝜏 𝑝 )
2
( Φ
PL
− 𝑘 𝑆 1
𝜏 𝑝 )

( 𝑘 −1
)
2
3
𝑒 −
ΔΕ
𝑆 1
−𝑇 1
𝑘 𝐵 𝑇 ( 7.14)
These expressions are significantly more complicated than any of the kinetic expressions in
Cases 1-3 but fitting over a sufficiently large temperature range can yield good values for the
kinetic parameters and EST. Note that in equation (7.14), Φ
PL
, 𝜏 𝑝 and 𝜏 𝑇𝐴𝐷𝐹 are temperature-
dependent variables. Therefore, by measuring 𝜏 𝑝 , 𝜏 𝑇𝐴𝐷𝐹 and 𝛷 𝑃𝐿
across a wide temperature range
and fitting the data to equation (7.14), all of the relevant TADF parameters may be obtained.
Similar approaches have been used by several research groups to obtain accurate kinetic
parameters for TADF emitters.
4-9

7.3. Emission kinetics of heavy metal based phosphors

Figure 7.3. Kinetic schemes for heavy metal-based phosphors and organic TADF emitters. Note
that the assumption here is that the emission takes place with a luminescence efficiency
approaching 100% in both cases, so nonradiative pathways are not considered. (Taken from
Ref.
1
)
171

As discussed earlier, a similar scheme presented for Case 2 TADF materials (where kISC >>
𝑘 𝑆 1
) can be used for heavy metal complexes. The kinetic scheme for high efficiency emitters of
either molecular heavy metal based phosphorescent or TADF compounds is shown in Figure 7.3.
Yersin et al. have shown that the scheme illustrated here is common for heavy metal phosphors,
where the upper triplet has a markedly higher emission rate the lower two levels.
53
The lifetimes
for the triplet sublevels and the overall phosphorescence lifetime for the heavy metal scheme
shown here are for facial-tris(2-phenylpyridinato-C2,N)iridium.
54
Note that the principal
differences in the schemes are that the phosphor case emits from an upper triplet level (not a
singlet) and the lower level is comprised of two triplet sublevels rather than three. The emission
in both cases involves thermal population of a higher lying, short lived state from a long-lived
triplet. The thermally assisted emission process dramatically outcompetes emission
(phosphorescence) from the lower triplet sublevels. Thus, equations (7.1-7.3) used to describe
TADF emission transform into equations (7.15-7.17) for a heavy metal based phosphor (assuming
that the kISC >> 𝑘 𝑇 III
).
(7.15)
𝑘 𝑝 ℎ
=
𝑘 1
𝑘 𝑇 III
𝑘 −1
+𝑘 𝑇 III
(7.16)
𝑘 𝑝 ℎ
=
𝑘 1
𝑘 𝑇 III
𝑘 −1
= 𝐾 𝑒𝑞
𝑘 𝑇 III
⟹ 𝜏 𝑝 ℎ
=
𝜏 𝑇 𝐼𝐼𝐼
𝐾 𝑒𝑞
⁄ (7.17)
The energy spacing between the upper TIII and lower TI, TII levels is the zero-field splitting
(ZFS) energy, which is analogous to EST for TADF emitters. Thus, the same sort of thermal
activation described for TADF based emission is seen for molecular heavy metal phosphors. This
172

energy difference sets up the same sort of equilibrium between the lower (long-lived) and upper
(emissive) states as seen in TADF. An analogous expression to equation (7.4) for TADF is given
in equation (7.18), which relates the ZFS energy to the equilibrium constant between the triplet
sublevels ( 𝑇 𝐼 ,𝐼𝐼
⇄ 𝑇 𝐼𝐼𝐼
) . Here the factor of 2 account for the doubly degenerate lower triplet
sublevels.
𝐾 𝑒𝑞
=
𝑘 1
𝑘 −1
=
1
2
𝑒𝑥𝑝 ( −
∆𝐸 𝑍𝐹𝑆 𝑘 𝐵 𝑇 ) ⇒ ∆𝐸 𝑍𝐹𝑆 = −𝑘 𝐵 𝑇 ln( 2𝐾 𝑒𝑞
) (7.18)

7.4. Kinetics of a general N-state emissive system
In the scenarios discussed above, only one state (S1 for TADF and TIII for Ir-based
phosphorescence) was assumed to be emissive while the others were considered to be dark states.
This assumption holds validity in most TADF and Ir phosphorescent systems since the lowest
states are very slow relative to the emissive state (i.e., 𝑘 𝑇 I
,𝑘 𝑇 II
,𝑘 𝑇 III
≪ 𝑘 𝑆 1
for TADF and
𝑘 𝑇 I
,𝑘 𝑇 II
≪ 𝑘 𝑇 III
for Ir phosphors). Even for such systems, the assumption breaks down at lower
temperatures since the emission becomes more dominated by the lower lying states. Therefore, a
generalized Boltzmann scheme that is valid at all temperatures and for a general system with
multiple close-lying emissive states irrespective of their relative rates is given below.
For a general system of N different emissive states each with emission rates, 𝑘 i
, assuming
rapid thermalization, the overall rate of the system at a given temperature (T) can be given by the
following:
𝑘 = ∑𝑘 𝑖 𝑝 𝑖 𝑁 𝑖 ( 7.19)
173

where, 𝑝 𝑖 is the partition function i.e., 𝑝 𝑖 =
𝑛 𝑖 ∑ 𝑛 𝑖 𝑁 𝑖 =
𝑒 −∆𝐸 𝑖 𝑘 𝐵 𝑇 ⁄
∑ 𝑒 −∆𝐸 𝑖 𝑘 𝐵 𝑇 ⁄
𝑁 𝑖
The overall rate is therefore given by the following expression,
𝑘 =
∑𝑘 𝑖 𝑒 −∆𝐸 𝑖 𝑘 𝐵 𝑇 ⁄
𝑁 𝑖 ∑𝑒 −∆𝐸 𝑖 𝑘 𝐵 𝑇 ⁄
𝑁 𝑖 ( 7.20)
For a TADF system with the assumption of 3 degenerate triplet sublevels, the above
expression becomes:
𝑘 𝑇𝐴𝐷𝐹 =
3 𝑘 𝑇 1
+ 𝑘 𝑆 1
𝑒 −∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ⁄
3 + 𝑒 −∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ⁄
⇒ 𝜏 𝑇𝐴𝐷𝐹 =
3 + 𝑒 −∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ⁄
3(
1
𝜏 𝑇 1
)+ (
1
𝜏 𝑆 1
) 𝑒 −∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ⁄
( 7.21)

Similarly for a phosphorescent system with the 3 distinct triplet sublevels, equation (7.20)
becomes:
𝑘 𝑝 ℎ
=
𝑘 𝑇 𝐼 + 𝑘 𝑇 𝐼𝐼
𝑒 −∆𝐸 𝑇 𝐼𝐼
𝑘 𝐵 𝑇 ⁄
+ 𝑘 𝑇 𝐼𝐼𝐼
𝑒 −∆𝐸 𝑇 𝐼𝐼𝐼
𝑘 𝐵 𝑇 ⁄
1 + 𝑒 −∆𝐸 𝑇 𝐼𝐼
𝑘 𝐵 𝑇 ⁄
+ 𝑒 −∆𝐸 𝑇 𝐼𝐼𝐼
𝑘 𝐵 𝑇 ⁄

⇒ 𝜏 𝑝 ℎ
=
1 + 𝑒 −∆𝐸 𝑇 𝐼𝐼
𝑘 𝐵 𝑇 ⁄
+ 𝑒 −∆𝐸 𝑇 𝐼𝐼𝐼
𝑘 𝐵 𝑇 ⁄
(
1
𝜏 𝑇 𝐼 )+ (
1
𝜏 𝑇 𝐼𝐼
) 𝑒 −∆𝐸 𝑇 𝐼𝐼
𝑘 𝐵 𝑇 ⁄
+ (
1
𝜏 𝑇 𝐼𝐼𝐼
) 𝑒 −∆𝐸 𝑇 𝐼𝐼𝐼
𝑘 𝐵 𝑇 ⁄
( 7.22)

In the above expression, ∆𝐸 𝑇 𝐼𝐼
and ∆𝐸 𝑇 𝐼𝐼𝐼
denote the energy separation respectively of 𝑇 𝐼𝐼

and 𝑇 𝐼𝐼𝐼
relative to 𝑇 𝐼 .

7.5. Extent of spatial overlap in electronic transitions
As noted earlier, two key factors that determine the rate of emission in a TADF system are
the transition dipole moment of the S0→S1 transition (𝜇 𝑆 0
𝑆 1
) and the energy gap between the S1 and
174

T1 states (∆𝐸 𝑆𝑇
). For a simple purely HOMO→LUMO transition, these parameters can be
expressed according to the following equations:
𝜇 𝑆 0
𝑆 1
= ⟨ϕ
𝑆 0
|𝐫 |ϕ
𝑆 1
⟩ = ∫𝜒 𝐻 ( 𝐫 ) 𝐫 𝜒 𝐿 ( 𝐫 ) 𝑑 𝐫 ( 7.23)
∆𝐸 𝑆𝑇
= 2𝐾 𝐻𝐿
= 2∫𝜒 𝐻 ( 𝐫 ) 𝜒 𝐿 ( 𝐫 )
1
|𝐫 − 𝐫 ′
|
𝜒 𝐻 ( 𝐫 ′
) 𝜒 𝐿 ( 𝐫 ′
) 𝑑 𝐫 𝑑 𝐫 ′
( 7.24)
In the above expressions, 𝜒 𝐻 and 𝜒 𝐿 represent the HOMO and LUMO orbitals respectively
and 𝐾 𝐻𝐿
is the exchange integral associated with the 2 orbitals. It is clear that for symmetry allowed
transitions, increasing the extent of spatial overlap between the HOMO and LUMO orbitals would
simultaneously increase 𝜇 𝑆 0
𝑆 1
and ∆𝐸 𝑆𝑇
. In the context of TADF, increasing 𝜇 𝑆 0
𝑆 1
is favorable while
increasing ∆𝐸 𝑆𝑇
is detrimental to the TADF rate as dictated by the following expression:
𝑘 𝑇𝐴𝐷𝐹 =
𝑒 −∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ⁄
3(
1
𝑘 𝑆 1
+
1
𝑘 𝐼𝑆𝐶 )
; 𝑘 𝑆 1
∝ ( 𝜇 𝑆 0
𝑆 1
)
2
( 7.25)

In the above equation, 𝑘 𝐼𝑆𝐶 is rate of ISC from the S1 state down to the T1 state. Since both
𝜇 𝑆 0
𝑆 1
and ∆𝐸 𝑆𝑇
are strongly correlated with the extent of spatial overlap (Λ) between the orbitals
involved in the transition, it can be useful to calculate this metric to gauge TADF performance
especially for systems with 𝑘 𝐼𝑆𝐶 ≫ 𝑘 𝑆 1
(i.e., case 2 compounds discussed in section 7.1.2). In this
case, the TADF rate is now no longer limited by 𝑘 𝐼𝑆𝐶 and only depends on 𝜇 𝑆 0
𝑆 1
and ∆𝐸 𝑆𝑇
as equation
(7.25) reduces to the following:
𝑘 𝑇𝐴𝐷𝐹 =
1
3
𝑘 𝑆 1
𝑒 −∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ⁄
; 𝑘 𝑆 1
∝ ( 𝜇 𝑆 0
𝑆 1
)
2
⟹ 𝑘 𝑇𝐴𝐷𝐹 ∝ ( 𝜇 𝑆 0
𝑆 1
)
2
𝑒 −∆𝐸 𝑆𝑇
𝑘 𝐵 𝑇 ⁄
( 7.26)
However, electronic transitions are seldom represented by a single pair of MOs like a
HOMO→LUMO transition and often involve transitions involving multiple MOs. In such cases,
175

it would be easier to calculate Λ for a given electronic transition in the NTO (natural transition
orbital) space rather than in the MO space according to the following expression:
Λ =
∑𝜎 𝑘 𝑘 ∫
| 𝜙 𝑘 𝑒 | | 𝜙 𝑘 ℎ
| 𝑑 𝜏 ∑𝜎 𝑘 𝑘 ( 7.27)
where, 𝜙 𝑘 𝑒 and 𝜙 𝑘 ℎ
are the electron and hole NTO pairs and 𝜎 𝑘 is the amplitude of the
corresponding NTO pair. The value of Λ would be bounded below by 0 for purely CT transitions
with no spatial overlap and bounded above by ≈1 for strongly localized excitations. Peach et al.
55

used a similar scheme to quantify the extent of spatial overlap, however the integrals were
computed in the MO space which can become cumbersome for transitions involving a large
number of MOs.
The integrals in equation (7.27) were computed numerically for each NTO pair using the
ORBKIT
56
and Cubature
57
python libraries. An in-house python code was used to compute Λ from
the NTOs generated by Q-Chem in the Molden format. The source code is available on GitHub
(https://github.com/danielsylvinson/OverlApp) and the pre-built binaries (for Windows only) can
be downloaded from SourceForge (https://sourceforge.net/projects/overlapp).
The Λ value was computed for a collection of compounds developed in our lab
6, 7, 16, 58-60

along with some from the literature
61, 62
(see Figure 7.4). The NTOs were computed using TDDFT
calculations at the B3LYP/LACVP* level for all compounds. The TDDFT calculations were
performed on the ground state optimized structures computed at the same level of theory. The
DFT/TDDFT calculations were performed using the Q-Chem software package.
63

The experimental values of ∆𝐸 𝑆𝑇
for the compounds were taken from
temperature-dependent lifetime measurements for the 2-coordinate TADF compounds
7, 58
(1-13)
and from the onsets of fluorescence and phosphorescence spectra for the remaining compounds.
59

176

It is clear from Figure 7.4 and Table 7.1 that there is a strong positive correlation (Pearson
correlation coefficient = 0.96) between the experimental value of ∆𝐸 𝑆𝑇
(logarithmic) and Λ as
would be expected by equation (7.24). Compounds that have been shown to exhibit TADF were
found to have Λ values below 0.45 with the DIPYR compounds (15-21) that have intermediate
∆𝐸 𝑆𝑇
gaps due to multi-resonance occupying a range of Λ values between 0.65 and 0.70.
Anthracene (14) which is characterized by strongly localized π-π* excitation in its S1 and T1 states
consequently has a large ∆𝐸 𝑆𝑇
gap (1.32 eV) and Λ value of 0.84. Unfortunately, experimental
values of ∆𝐸 𝑆𝑇
for compounds 8-9 and 11-13 are unavailable at this time and are therefore not
included.

Figure 7.4. Relationship between experimental kTADF, ΔEST and 𝚲 for the compounds presented
above.
177

The dependence of the experimentally observed TADF radiative rate (kTADF) at 300 K on
Λ was also investigated for the TADF (case 2) exhibiting compounds (1-13) and is shown in
Figure 7.4. kTADF was found to appreciably correlate (negatively) with Λ however with a few
outliers. It should be noted that the T1 state in compounds 8-10 were suspected to be characterized
by a π-π* local excitation within the carbazole ligand (
3
Cz) while the S1 state exhibited intra-ligand
charge transfer between the carbazole and the carbene ligands (
1
ICT).
58
Therefore, the activation
barrier for TADF (∆𝐸 𝑆𝑇
) in these compounds would be between the
3
Cz and
1
ICT states and not
between states of similar character (i.e.,
3
ICT and
1
ICT) as it would be in most cases. The Λ value
on the other hand is computed based on the NTOs of the S1 state (
1
ICT in this case) and while it is
a good descriptor for the separation between S1 and T1 states (∆𝐸 𝑆𝑇
) when they exhibit the same
character (
3
ICT and
1
ICT states), it becomes inadequate when the states have significantly different
character (
3
Cz and
1
ICT states). This is likely the reason why these compounds especially 8 and 9
are the biggest outliers in the dataset. The Pearson coefficient calculated between kTADF
(logarithmic) and Λ was -0.76 without the biggest outliers (8, 9) indicating substantial
phenomenological correlation (negative) between the two parameters for case 2 TADF compounds
(𝑘 𝐼𝑆𝐶 ≫ 𝑘 𝑆 1
) whose S1 and T1 states bear similar character. It must also be noted that there is a
likely an inflection point that could be reached at lower Λ values where further decreases in Λ
would lead to a drop in kTADF due to its adverse effect on 𝜇 𝑆 0
𝑆 1
.
Table 7.1. Values of kTADF, ΔEST and 𝚲 for the compounds considered above.
Compound 𝚲 kTADF ΔEST
1 0.37 3.5 0.07
2 0.30 20 0.02
3 0.42 8.8 0.07
5 0.36 6.4 0.07
6 0.29 24 0.02
178

7 0.40 10 0.07
8 0.32 2.5 -
9 0.26 2.2 -
10 0.37 4.4 0.11
11 0.35 17.2 -
12 0.29 22.4 -
13 0.26 40 -
14 0.84 - 1.32
15 0.68 - 0.44
16 0.65 - 0.34
17 0.63 - 0.30
18 0.61 - 0.30
19 0.66 - 0.30
20 0.66 - 0.44
21 0.68 - 0.39
22 0.29 - 0.06

7.6. Blurring the lines between TADF and phosphorescence?
A new class of Ir complexes bearing carbenic ligands (Figure 7.5) were recently reported
by our lab.
64
They were reported to feature high PLQY and radiative rates with emission in the
green-blue window making them very attractive as OLED dopant candidates. An interesting
observation for these classes of compounds is that their luminescence lifetime was found to vary
over a very small range of values across a span of temperatures from 4 K to 300 K
65
(Figure 7.5)
relative to conventional Ir complexes like Ir(ppy)3.
The measured data was initially fit to a 3-state phosphorescence kinetic model according
to equation (7.22) and the fit parameters are shown in Table 7.2. The zero-field splitting, ∆𝐸 𝑇 𝐼𝐼𝐼

calculated from the fits for the facial complexes were found to be unusually large relative to
conventional Ir complexes. Further, the radiative lifetime of the 𝑇 𝐼𝐼𝐼
sublevel was calculated to be
extremely small close to what could be expected for a singlet state. It was therefore suspected that
179

the emission in these complexes may have some contribution from the S1 state. Subsequently, the
data was also fit to a 4-state kinetic model that includes the S1 state wherein the two lowest triplet
sublevels (𝑇 𝐼 ,𝑇 𝐼𝐼
) are now assumed to be degenerate to reduce the number of fit parameters. The
overall lifetime of emission for this model is given by:
𝜏 𝑒𝑚
=
2 + 𝑒 −∆𝐸 𝑇 𝐼𝐼𝐼
𝑘 𝐵 𝑇 ⁄
+ 𝑒 −∆𝐸 𝑆 1
𝑘 𝐵 𝑇 ⁄
(
2
𝜏 𝑇 𝐼 ,𝐼𝐼
)+ (
1
𝜏 𝑇 𝐼𝐼𝐼
) 𝑒 −∆𝐸 𝑇 𝐼𝐼𝐼
𝑘 𝐵 𝑇 ⁄
+ (
1
𝜏 𝑆 1
) 𝑒 −∆𝐸 𝑆 1
𝑘 𝐵 𝑇 ⁄
( 7.28)

The ZFS (∆𝐸 𝑇 𝐼𝐼𝐼
) and singlet-triplet gap (∆𝐸 𝑆 1
) values extracted from this model are now
consistent with what would be expected for such systems (Table 7.2). However, the radiative
lifetimes of the two lowest triplet sublevels (𝜏 𝑇 𝐼 ,𝐼𝐼
) are found to be unusually small especially for
the meridional isomers (~1 μs).

Figure 7.5. Dependence of luminescence lifetime on temperature for Ir complexes considered
here. (Data for Ir carbene complexes collected by Dr. Muazzam Idris
65
; Data for fac-Ir(ppy)3
taken from Ref.
66
)

1 10 100
1
10
100
fac-Ir(ppy)
3
fac-Ir(pmp)
3
mer-Ir(pmp)
3
fac-Ir(pmpz)
3
mer-Ir(pmpz)
3
fac-Ir(tpz)
3
T (K)
 (s)
180

Table 7.2. Fit parameters for 3-state triplet model and 4-state TADF model.
3-state triplet model
∆𝑬 𝑻 𝑰𝑰
(eV, cm
-1
) ∆𝑬 𝑻 𝑰𝑰𝑰
(eV, cm
-1
)
𝝉 𝑻 𝑰
( μs)
𝝉 𝑻 𝑰𝑰

(μ s)
𝝉 𝑻 𝑰𝑰𝑰

(ns)
fac-Ir(ppy)
3
66
0.00236, 19 0.0211, 170 116 6.40 200
fac-Ir(tpz)
3

0.0121, 97.6 0.109, 879 4.72 2.06 80
fac-Ir(pmp)
3

0.0217, 175 0.0864, 697 3.59 1.30 74
fac-Ir(pmpz)
3

0.0121, 97.6 0.0929,749 6.21 2.56 114
mer-Ir(pmp)
3

0.00096, 7.74 0.0199, 161 0.94 0.95 268
mer-Ir(pmpz)
3

5.6 x 10
-7
, 0.0045
0.0135, 109 1.17 2.55 440
4-state TADF model
∆𝑬 𝑻 𝑰𝑰𝑰
(eV, cm
-1
) ∆𝑬 𝑺𝟏
(eV, cm
-1
)
𝝉 𝑻 𝑰 ,𝑻 𝑰𝑰

( μs)
𝝉 𝑻 𝑰𝑰𝑰

(μ s)
𝝉 𝑻 𝑺𝟏

(ns)
fac-Ir(tpz)
3

0.0125, 101 0.110, 888 4.73 1.52 50
fac-Ir(pmp)
3

0.0208, 168 0.0844, 681 3.59 0.88 49
fac-Ir(pmpz)
3

0.0112, 90.3 0.0925,746 6.21 1.86 74
mer-Ir(pmp)
3

0.0017, 13.6 0.0193, 156 0.94 0.96 211
mer-Ir(pmpz)
3

4.6 x 10
-6
, 0.037
0.013, 105 1.29 3.25 347

181

To get a deeper understanding of these systems, SOC-TDDFT calculations were performed
using the ZORA approach (see Chapter 5) within the perturbative scheme as implemented in the
ADF software package.
67
The T1 optimized structure of each compound computed at the
B3LYP/LACVP* level was used for the single-point SOC-TDDFT calculations. The calculations
employed the DZ basis set and the ωPBE RSH functional with the range separation parameter (ω)
tuned to satisfy the GDD criterion
68
for each compound. It was found that regular hybrid
functionals like B3LYP grossly underestimated the excitation energies while standard RSH
functionals like CAM-B3LYP overestimated them. We therefore suspected that a tuned RSH
functional may be necessary to accurately describe the transitions. The excitation energies
computed using the tuned ωPBE functional were found to be in good agreement with experimental
values as shown in Table 7.3. The calculations also predict that the lifetime of the two lowest
triplet sublevels (𝑇 𝐼 ) is significantly lower (faster) than that of a conventional phosphor like
fac-Ir(ppy)3 consistent with the temperature-dependent lifetime data. Plugging in the calculated
energy gaps and rates into the 4-state model (without assumption of degenerate 𝑇 𝐼 and 𝑇 𝐼𝐼

sublevels) again confirms the smaller range of lifetime variation as a function temperature for the
Ir carbene complexes relative to fac-Ir(ppy)3 as seen in Figure 7.6.
Table 7.3. SOC-TDDFT computed energies, f and lifetime for relevant states.

E (cm
-1
)
ƒ
 (s)
fac-Irppy
3
(expt. em = 19270)

S
1

20872 1.37E-02 1.68E-07
T
III
18732 2.08E-03 1.37E-06
T
II
18644 9.62E-04 2.99E-06
T
I
18630 2.58E-06 1.12E-03
ZFS
102

ΔE
ST

2242

182

fac-Irpmp
3
(expt. em = 23810)

S
1
25961 2.03E-02 7.32E-08
T
III

24539 1.82E-03 9.13E-07
T
II

24487 1.19E-03 1.41E-06
T
I

24476 1.33E-04 1.25E-05
ZFS 63
ΔE
ST
1485
fac-Irpmpz
3
(expt. em = 21739)

S
1
23544 3.09E-02 5.83E-08
T
III

21192 7.50E-04 2.97E-06
T
II

21165 5.51E-06 4.05E-04
T
I

21126 8.38E-04 2.67E-06
ZFS 66
ΔE
ST
2418
mer-Irpmp
3
(expt. em = 22727)

S
1
23911 4.33E-03 4.04E-07
T
III

23471 9.52E-04 1.91E-06
T
II

23428 1.71E-04 1.07E-05
T
I

23426 3.80E-04 4.79E-06
ZFS 45
ΔE
ST
485
mer-Irpmpz
3

(expt. em = 20408)

S
1
21156 3.56E-03 6.27E-07
T
III

20766 4.08E-04 5.68E-06
T
II

20734 3.60E-05 6.46E-05
T
I

20710 4.13E-04 5.65E-06
ZFS 56
ΔE
ST
446

183

1 10 100
1E-6
1E-5
1E-4
1E-3
 (s)
T (K)
fac-Irppy
fac-Irpmp
fac-Irpmpz
mer-Irpmp
mer-Irpmpz

Figure 7.6. Dependence of luminescence lifetime on temperature for Ir complexes considered
here based on the SOC-TDDFT calculations.

The singlet states (Sn) that contribute to the triplet sublevels significantly are shown in
Figure 7.7 for fac-Ir(ppy)3, fac-Ir(pmpz)3 and mer-Ir(pmpz)3. For the facial isomers, it can be seen
the singlets that strongly couple with the triplet sublevels are the MLCT states that involve the
transition between the 3 different t2g metal-based orbitals each hybridized with phenyl π orbitals
on different ligands to the same π* orbital localized on the same carbene moiety that is involved
in the T1 MLCT state. In fac-Ir(ppy)3, the 𝑇 𝐼𝐼
and 𝑇 𝐼𝐼𝐼
sublevels exhibit the strongest coupling to
the Sn states with the 𝑇 𝐼 sublevel showing minimal coupling while the 𝑇 𝐼 and 𝑇 𝐼𝐼𝐼
sublevels in
fac-Ir(pmpz)3 have the strongest coupling to the Sn states relative to 𝑇 𝐼𝐼
consistent with the
calculated rates. In mer-Ir(pmpz)3, the S1 and T1 states involve a transition from one of the t2g
orbitals hybridized with phenyl π orbitals on two of the ligands to the π* orbital localized on the
carbene moiety in the remaining ligand. The other Sn states that contribute significantly to the
triplet sublevels involve similar transitions from different configurations of hybrid t2g-π orbitals
(localized on 2 ligands) to π* orbitals on the carbene moiety in different ligands. As in the case of
184

fac-Ir(pmpz)3, the 𝑇 𝐼 and 𝑇 𝐼𝐼𝐼
sublevels of the meridional isomer exhibit the strongest coupling to
the Sn states compared to 𝑇 𝐼𝐼
.

f ac-Ir(ppy) 3
S
1
S
4
S
5
S
1
S
4
S
5

f 2.46E-02 2.49E-02 0.110

SOC-T
III

0.0138 0.0020 0.0148 44.17 12.89 105.74
SOC-T
II

0.0021 0.0286 0.0016 6.72 184.31 11.43
SOC-T
I

f ac-Ir(pmpz) 3 S
1
S
4
S
5
S
1
S
4
S
5

f 4.17E-02 9.27E-02 8.41E-02

SOC-T
III
0.0067 0.0022 0.0017 17.82 14.09 12.74
SOC-T
II

SOC-T
I

0.0027 0.0060 0.00 17.29 44.97
185

m er -Ir(pmpz) 3
S
1
S
4
S
5
S
6
S
7

f 4.78E-03 5.09E-03 1.85E-02 0.22916 0.14993
SOC-T
III

0.0008 0.0007 0.0014
SOC-T
II

0.0018

SOC-T
I

0.0115 0.0028 0.0008 0.0007

Figure 7.7. Major contributions of Sn states to triplet sublevels.

Finally, we also computed the emission contribution and occupancy of each of the states
at room temperature based on the fit parameters from the 4-state model (Table 7.4) according to
the following equations:
% 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 ( 𝑋 𝑖 )= (
1
𝑘 𝑒𝑚
𝑘 𝑖 𝑒 −( 𝐸 𝑖 −𝐸 0
)
𝑘 𝐵 𝑇 ⁄
∑𝑒 −( 𝐸 𝑗 −𝐸 0
)
𝑘 𝐵 𝑇 ⁄
𝑗 ) × 100 ( 7.29)
186

% 𝑂𝑐𝑐𝑢𝑝𝑎𝑛𝑐𝑦 ( 𝑋 𝑖 )= (
𝑒 −( 𝐸 𝑖 −𝐸 0
)
𝑘 𝐵 𝑇 ⁄
∑𝑒 −( 𝐸 𝑗 −𝐸 0
)
𝑘 𝐵 𝑇 ⁄
𝑗 ) × 100 ( 7.30)
It can be seen from Table 7.4 that both S1 and T1 states contribute significantly to the
emission with fac-Ir(pmp)3 and mer-Ir(pmpz)3 exhibiting roughly equal contributions from the S1
and T1 states. Therefore, the data seems to suggest that emission in these complexes blur the
distinction between phosphorescence and TADF per their conventional definitions.

Table 7.4. Emission contribution and occupancy of each state based on kinetic models. (Note
that fac-Ir(ppy)
3 is fit to the triplet 3-state model based on data from Ref.
66
).
% 𝑪𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 ( 𝑿 𝒊 )
@300 K % 𝑻 𝑰 ,𝑰𝑰
% 𝑻 𝑰𝑰𝑰
% 𝑺 𝟏
fac-Ir(ppy)
3

0.4, 6.0 93.6 -
fac-Ir(tpz)
3

38.0 36.4 25.6
fac-Ir(pmp)
3

29.8 22.3 47.9
fac-Ir(pmpz)
3

29.9 39.5 30.5
mer-Ir(pmp)
3

48.4 9.0 42.6
mer-Ir(pmpz)
3

35.2 17.2 47.5
% 𝑶𝒄𝒄𝒖𝒑𝒂𝒏𝒄𝒚 ( 𝑿 𝒊 )
@ 300 K % 𝑻 𝑰 ,𝑰𝑰
% 𝑻 𝑰𝑰𝑰
% 𝑺 𝟏
fac-Ir(ppy)
3

42.5, 38.7 18.8 -
fac-Ir(tpz)
3

76.0 23.4 0.54
187

fac-Ir(pmp)
3

80.5 18.0 1.54
fac-Ir(pmpz)
3

74.7 24.2 1.04
mer-Ir(pmp)
3

58.6 27.5 13.9
mer-Ir(pmpz)
3

55.5 27.7 16.8

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Abstract (if available)

Abstract The field of organic optoelectronics has garnered a lot of interest in recent decades due to rapid advances in the development of organic light-emitting diodes (OLEDs), organic photovoltaics (OPVs), optoelectronic sensors, etc. Among them, OLED technologies have advanced into the realm of commercialization and have been successfully incorporated into a wide array of color display and lighting products. While OLEDs have several favorable attributes over traditional display/lighting technologies like amenability to flexible form-factors, high color purity and contrast, they are plagued by low stability, especially for the blue component. Molecular degradation events during device operation have been identified as the main culprit for the low stability. Therefore, there is a strong desire to design molecular materials that are robust to such degradation events but can still be successfully incorporated into efficient OLED device architectures. ❧ The traditional chemical design process that relies on trial and error, human intuition and sometimes serendipity is cumbersome and highly resource-intensive. Recent advances in high-performance computing and the development of efficient and accurate molecular modeling software have led to increased utilization of computational tools in the chemical design process in several fields especially drug design, catalysis, semiconductors among others. Further, the development of data-driven approaches like machine learning has further helped accelerate the design process. However, the adoption of such approaches in the field of organic optoelectronics has remained limited and has only recently started to gain traction. Here, we present the development and application of efficient virtual screening workflows that incorporate both first principles based multi-scale materials modeling and data-driven machine learning approaches to aid the design of novel molecular materials, particularly for OLEDs. The same workflows can also be extended to other optoelectronic applications. We also employ computational approaches to gain deeper insights into the underlying mechanisms of photo-physical and electronic processes in molecular materials to further inform the design process.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Muthiah Ravinson, Daniel Sylvinson (author)

Core Title Computational materials design for organic optoelectronics

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Degree Conferral Date 2021-12

Publication Date 09/30/2021

Defense Date 07/28/2021

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

Tag density functional theory,DFT,machine learning,materials discovery,OAI-PMH Harvest,OLEDs,organic electronics

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Thompson, Mark (committee chair), Nakano, Aiichiro (committee member), Vilesov, Andrey (committee member)

Creator Email danielsylvinson@gmail.com,muthiahr@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC16011561

Unique identifier UC16011561

Legacy Identifier etd-MuthiahRav-10122

Document Type Dissertation

Format application/pdf (imt)

Rights Muthiah Ravinson, Daniel Sylvinson

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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