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University of Southern California Dissertations and Theses
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Electronic structure of ionized non-covalent dimers: methods development and applications
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Electronic structure of ionized non-covalent dimers: methods development and applications
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ELECTRONIC STRUCTURE OF IONIZED NON-COV ALENT DIMERS: METHODS DEVELOPMENT AND APPLICATIONS by Anna A. Golubeva A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMISTRY) May 2010 Copyright 2010 Anna A. Golubeva Acknowledgements I would like to mention the following people to whom I owe a great debt of gratitude. Prof. Anna Krylov, my advisor, has contributed greatly to my development as a researcher - curious, motivated and thinking - in the past four years. As a person truly inspired by science, she is a perpetuum mobile of the group, never letting the research to stop. Her motivation and enthusiasm are quite contagious. What is even more important, however, is that Anna Krylov is a great person to work with - fair, understanding, open- minded, patient and with a sense of humor. Not every scientist is gifted with such a personality, but she has it all – and I’m very happy to be a part of her group. While in graduate school, I was lucky to have some outstanding teachers. I truly enjoyed the fun and engaging lectures on Statistical Mechanics by Prof. Chi Mak. His class was the place where I first found out that one can model the stock market with statistics. Prof. Wlodek Proskurowski’s class on Numerical Analysis at the Department of Mathematics significantly broadened my knowledge of linear algebra and program- ming. Now I know exactly how the Hamiltonian is diagonalized, and that Householder matrix has little to do with running a household. I would also like to acknowledge ii Dr. Michael Quinlan. With him as the undergraduate lab director, TAing never seemed boring. My scientific work was greatly influenced by Prof. Alexander Nemukhin - my advisor at the Moscow State University (MSU). His lectures on Quantum Mechanics is where I first got interested in the subject of Computational Chemistry. Many thanks go to Evgeny Epifanovsky, Vadim Mozhayskiy, Dr. Vitalii Vanovschi, Dr. Kadir Diri, Dr. Lukasz Koziol and Dr. Kseniya Bravaya, as well as all other former and present Electronic Structure group members. Finally, I do believe that behind all my achievements, there is always my Family. My husband, Anton Zadorozhnyy, made sure I never felt left alone with the difficul- ties. He provided me with support and advice whenever I was close to collapsing. My father, Alexey Golubev, a theoretical chemist himself, advised me to join the special- ized computational chemistry group at MSU when I was only 17 years old. Back then I believed that all computational chemists do is about calculating how much grams of A is needed in order to get that much grams of B. My mother, Valentina Golubeva, an analytical chemist, was the first to show me the pH paper and to teach me how to grow a crystal. These experiments resulted in major excitement of me as a 10-year old girl and, perhaps, that was why I decided to become a chemist. My sisters, Vera and Alena, are always there for me to cheer me up. My grandparents - Galina Golubeva, Viktor iii Golubev, Lubov Vinogradova and Nikolay Vinogradov - always believed in me and sup- ported me. They also always welcomed all curious child questions from me like “Can we see atoms using a microscope?”, providing the grounds for me becoming a scientist. iv Table of Contents Acknowledgements ii List of Figures viii List of Tables xiii Abstract xvii Chapter 1: Ionized non-covalent dimers: Fascinating and challenging 1 1.1 Non-covalent interactions . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Ionized non-covalent dimers as model charge-transfer systems . . . . . 2 1.3 Methodological challenges . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Equation-of-motion coupled-cluster family of methods . . . . . . . . . 7 1.5 Bonding in ionized non-covalent dimers: The qualitative Dimer Molec- ular Orbitals and Linear Combinations of Atomic Orbitals framework . 10 1.6 Chapter 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Chapter 2: Configuration interaction approximation of equation-of-motion method for ionization potentials: A benchmark study 20 2.1 Chapter 2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 The IP-CISD method . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.1 Equilibrium geometries and electronically excited states of the uracil cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.2 Equilibrium geometries of the three isomers of the benzene dimer cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.3 Water dimer cation . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4.4 Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 Chapter 2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 v Chapter 3: The electronic structure, ionized states and properties of the uracil dimers 42 3.1 Chapter 3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3.1 Prerequisites: Electronic states and spectrum of the uracil cation 45 3.3.2 Electronic structure of the uracil dimers . . . . . . . . . . . . . 47 3.3.3 Vertical ionization energies of the monomer and the dimers . . . 49 3.3.4 The electronic spectra of dimer cations . . . . . . . . . . . . . . 57 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.5 Chapter 3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Chapter 4: Ionization-induced structural changes in uracil dimers and their spectroscopic signatures 66 4.1 Chapter 4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2 Computational detais . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.1 Molecular orbital framework . . . . . . . . . . . . . . . . . . . 70 4.3.2 Ionization-induced structural changes: Equilibrium geometries of the uracil dimer cations . . . . . . . . . . . . . . . . . . . . 73 4.3.3 Binding energies of the neutral and ionized uracil dimers: Poten- tial and free energy calculations . . . . . . . . . . . . . . . . . 81 4.3.4 The electronic spectra of the uracil dimer cations . . . . . . . . 86 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.5 Chapter 4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Chapter 5: Ionized states of dimethylated uracil dimers 99 5.1 Chapter 5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.3.1 Potential energy surface of the neutral dimers: Structures and energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.3.2 The effect of methylation on the ionized states of the monomer and the dimers . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3.3 Ionization-induced changes in the monomer and the dimers: Struc- tures and properties . . . . . . . . . . . . . . . . . . . . . . . . 111 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.5 Chapter 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Chapter 6: Ionized non-covalent dimers: Outlook and future research direc- tions 129 6.1 Chapter 6 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 vi 6.2 Conical intersections in ionized non-covalent dimers: Benzene dimer cation revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.3 The effect of substituents in ionized non-covalent dimers: Electronic structure and properties . . . . . . . . . . . . . . . . . . . . . . . . . . 140 6.4 Chapter 6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Bibliography 148 Appendix: EOM-IP optimized geometries of Bz + 2 158 vii List of Figures 1.1 The DMO-LCFMO description of the two lowest ionized states in the uracil dimer. In-phase and out-of-phase overlap between the FMOs results in the bonding (lower) and antibonding (upper) dimer’s MOs. Changes in the MO energies, and, consequently, IEs, are demonstrated by the Hartree-Fock orbital energies (hartrees). Ionization from the anti- bonding orbital changes the bonding from non-covalent to covalent, and enables a new type of electronic transitions, which are unique to the ionized dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 Definitions of the geometric parameters for uracil (upper panel) and water dimer (lower panel) at the proton-transferred geometry. . . . . . 25 2.2 Definitions of the geometric parameters for three isomers of the benzene dimer: x-displaced (top),y-displaced (middle), and t-shaped (bottom). . 26 2.3 Selected bondlengths in the five lowest electronic states of the uracil cation. The corresponding values of the neutral are shown by dashed lines. The MOs from which electron is removed are shown for each state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.4 The CNC(2) angle in the five lowest electronic states of uracil cation. Dashed line shows the corresponding value at the geometry of neutral. . 38 2.5 The CC bond lengths of the three benzene dimer cation isomers in the ground electronic state optimized with IP-CISD/6-31(+)G(d) and IP- CCSD/6-31(+)G(d). Only the values of the symmetry unique param- eters for corresponding symmetry non-equivalent fragments are shown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.6 Selected bondlengths and angles in the two lowest electronic states of the water dimer cation optimized with IP-CISD and IP-CCSD with dif- ferent bases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 viii 3.1 π -stacking and hydrogen-bonding in DNA (top) and the geometries of the stacked (a) and hydrogen-bonded (b) uracil dimers. . . . . . . . . . 43 3.2 Electronic spectrum and relvant MOs of the uracil cation at the geometry of the neutral. The MO hosting the hole in the ground state of the cation is also shown (top left). Dashed lines show the transitions with zero oscillator strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3 MOs and IEs (eV) of the ten lowest ionized states of the stacked uracil dimer. Ionization from the highest MO yields ground electronic state of the dimer cation, and ionizations from the lower orbitals result in electronically excited states. . . . . . . . . . . . . . . . . . . . . . . . 48 3.4 MOs and IEs (eV) of the ten lowest ionized states of the hydrogen- bonded uracil dimer. Ionization from the highest MO yields ground elec- tronic state of the dimer cation, and ionizations from the lower orbitals result in electronically excited states. . . . . . . . . . . . . . . . . . . 49 3.5 Basis set dependence of the five lowest IEs of uracil. The shaded areas represent the range of the expertimental values. . . . . . . . . . . . . . 51 3.6 Vertical electronic spectrum of the stacked uracil dimer cation at the geometry of the neutral. Dashed lines show the transitions with zero oscillator strength. MOs hosting the unpaired electron in final electronic state, as well as their symmetries, are shown for each transition. The MO corresponding to the initial (ground) state of the cation is shown in the middle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7 Vertical electronic spectra of the stacked uracil dimer cation at two dif- ferent geometries: the geometry of the neutral (bold lines) and the relaxed cation geometry (dashed lines). MOs hosting the unpaired electron in final electronic state are shown for each transition. . . . . . . . . . . . 61 3.8 Vertical electronic spectrum of the hydrogen-bonded uracil dimer cation at the geometry of the neutral. Dashed lines show the transitions with zero oscillator strength. MOs hosting the unpaired electron in final elec- tronic state, as well as their symmetries, are shown for each transition. The MO corresponding to the initial (ground) state of the cation is shown in the middle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.1 The ten lowest ionized states of the t-shaped uracil dimer at the neutral geometry calculated with the IP-CCSD/6-311(+)G(d,p). . . . . . . . . 72 ix 4.2 The geometries of the cations versus the respective neutrals for the three uracil dimer isomers . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3 The definitions of the intra- and inter-fragment geometric parameters for uracil dimer isomers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.4 Two highest occupied MOs of the three isomers of the uracil dimer at the neutral and cation geometry. . . . . . . . . . . . . . . . . . . . . . 79 4.5 The binding energies (kcal/mol) of the three isomers of neutral uracil dimer calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) andωB97X-D/6-311(+)G(d,p) (italic). . . . . . . . . . . . . . . . . . . 82 4.6 The binding energies (kcal/mol) of the three isomers of uracil dimer cation calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) andωB97X-D/6-311(+)G(d,p) (italic). For the proton-transfered h-bonded uracil dimer cation, the binding energies corresponding to the two dis- sociation limits are presented. . . . . . . . . . . . . . . . . . . . . . . 83 4.7 The electronic spectra (top panel) of the stacked uracil dimer cation at the neutral (solid black) and the cation (dashed blue) geometries calcu- lated with IP-CCSD/6-31(+)G(d) and the electronic states correspond- ing to the three most intense transitions (bottom panel). . . . . . . . . . 87 4.8 The electronic spectra (top panel) of the h-bonded uracil dimer cation at the neutral (solid black), symmetric transition state (dashed blue) and the proton-transferred cation (dash-dotted pink) geometries calculated with IP-CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intense transitions (bottom panel). . . . . . . . . . . . . 89 4.9 The electronic spectra (top panel) of the t-shaped uracil dimer cation at the neutral (solid black) and the cation (dashed blue) geometries calcu- lated with IP-CCSD/6-31(+)G(d) and the electronic states correspond- ing to the three most intense transitions (bottom panel). . . . . . . . . . 92 5.1 Five isomers of the stacked neutral 1,3-dimethyluracil dimer and their binding energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energy structure and other isomers are given in the paren- thesis. All values were obtained with ωB97X-D/6-311(+,+)G(2d,2p) except for the D e value of isomer 1 shown in bold, which is the IP- CCSD/6-31(+)G(d) estimate. . . . . . . . . . . . . . . . . . . . . . . . 103 x 5.2 The five lowest ionized states and the molecular orbitals of dimethylu- racil (top) and uracil (bottom) calculated by IP-CCSD/6-311(+)G(d,p). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.3 The ten lowest ionized states and the corresponding MOs of the lowest- energy isomer of the neutral stacked 1,3-dimethyluracil computed with IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.4 Five low-lying isomers of the 1,3-dimethyluracil dimer cation and the dissociation energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energy structure and other isomers are given in the paren- thesis. All values were obtained with ωB97X-D/6-311(+,+)G(2d,2p) except for the D e value of isomer 1 (shown in bold), which is the IP- CCSD/6-31(+)G(d) estimate. . . . . . . . . . . . . . . . . . . . . . . . 112 5.5 The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 1 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener- gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 115 5.6 The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 2 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener- gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 116 5.7 The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 3 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener- gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 117 5.8 The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 4 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener- gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 118 5.9 The changes in geometry, binding energies (kcal/mol) and the MOs of isomer 5 of the stacked 1,3-dimethyluracil dimer at ionization. The ωB97X-D/6-311(+,+)G(2d,2p) optimized structures, dissociation ener- gies and the HF/6-31(+)G(d) MOs are presented. . . . . . . . . . . . . 119 5.10 The electronic spectra of 1,3-dimethyluracil (left) and uracil (right) at the vertical (solid black) and the relaxed (dashed blue) geometries cal- culated by IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . 120 xi 5.11 The three most intense transitions in the electronic spectrum of the low- est isomer of stacked 1,3-dimethyluracil cation at vertical (solid black) and cation (dashed blue) geometries. The DMOs corresponding to the ground state (framed) and excited states (regular) are shown. The posi- tions of the peaks were calculated at IP-CCSD/6-31(+)G(d) level, while the intensities are from the non-methylated dimer calculations. . . . . . 123 6.1 The six optimized geometries of the benzene dimer cation and the corre- sponding energy gaps calculated at the IP-CCSD(dT)/6-31(+)G(d) (italic) and IP-CCSD/6-311(+,+)G(d,p) (bold) levels of theory. . . . . . . . . . 132 6.2 The definitions of structural parameters for the benzene dimer cation. The distance between the centers of mass of the fragmentsd COM , sepa- rationh and sliding coordinatesΔ are shown. . . . . . . . . . . . . . . 133 6.3 The evolution of the four lowest electronic states of the benzene dimer cation along thex- (top panel) andy- (bottom panel) displecement coor- dinates calculated with IP-CCSD/6-31(+)G(d). Two moderately (XD, YD) and two strongly-displaced (XSD, YSD) fully-optimized ground- state structures were employed. The blue arrows depict the CR tran- sitions at four geometries and the dashed lines interconnect the related electronic states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 xii List of Tables 2.1 The IP-CCSD bondlengths ( ˚ A) in the five electronic states of the uracil cation and absolute errors (in parenthesis) of IP-CISD relative to IP- CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 The IP-CCSD angles (degrees) in the five electronic states of the uracil cation and absolute errors (in parenthesis) of IP-CISD relative to IP- CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3 IP-CCSD and IP-CISD permanent dipole moments (a.u.) of the five lowest electronic states of the uracil cation computed at the respective optimized geometries relative to the center of mass. . . . . . . . . . . . 29 2.4 The IP-CCSD and IP-CISD excitation energies (eV) and transition dipole moments (a.u.) of the uracil cation at the equilibrium geometries of the neutral and the cation. . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5 The bondlengths ( ˚ A), angles (degrees), interfragment distances and slid- ing displacements ( ˚ A) in the ground state of thex-displaced,y-displaced and t-shaped benzene dimer cations calculated with IP-CISD/6-31(+)G(d). For thex- andy-displaced structures, geometric parameters for only one of the benzene fragments are provided (the fragments are equivalent by symmetry). Absolute errors of IP-CISD relative to IP-CCSD are pre- sented in parenthesis. Average absolute errors are calculated using the data for symmetry unique parameters. . . . . . . . . . . . . . . . . . . 31 2.6 The IP-CCSD bondlengths ( ˚ A) and angles (degrees) in the two elec- tronic states of the water dimer cation and absolute errors (in parenthe- sis) of IP-CISD relative to IP-CCSD calculated with different bases. . . 33 3.1 Five lowest verical IEs (eV) of the uracil monomer calculated with EOM- IP-CCSD. The number of basis functions (b.f.) is given for each basis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 xiii 3.2 Excitation energies, transition dipole moments and oscillator strengths of the electronic transitions in the uracil cation calculated with EOM-IP- CCSD with different bases. . . . . . . . . . . . . . . . . . . . . . . . 52 3.3 Ten lowest vertical IEs (eV) of the stacked uracil dimer calculated with EOM-IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4 Ten lowest verical IEs (eV) of the hydrogen-bonded uracil dimer calcu- lated with EOM-IP-CCSD. . . . . . . . . . . . . . . . . . . . . . . . . 54 3.5 Ten lowest verical IEs (eV) of the stacked dimer calculated with EOM- IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results estimated using 6-31(+)G(d). . . . . . . . . . . . . . . . . . . . . . . . 55 3.6 Ten lowest vertical IEs (eV) of the hydrogen-bonded uracil dimer calcu- lated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results estimated from 6-31(+)G(d). . . . . . . . . . . . . . . . 56 3.7 Oscillator strengths and transition dipole moments for the electronic transitions in the ionized stacked uracil dimer calculated with EOM-IP- CCSD/6-31(+)G(d) at the geometry of the neutral. . . . . . . . . . . . 59 3.8 Oscillator strengths and transition dipole moments for the electronic transitions in the ionized stacked uracil dimer calculated with EOM-IP- CCSD/6-31(+)G(d) at the equilibrium geometry of the ionized dimer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.1 The values of optimized structural parameters ( ˚ A, Degree) of the frag- ments in the stacked, h-bonded, h-transfered h-bonded and t-shaped uracil dimer cations. The differences ( ˚ A, Degree) w.r.t. the equilibrium geometry of the respective neutral complex are also given showing the ionization-induced changes in geometry. See Fig. 4.3 for the definitions of the parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2 The values of inter-fragment structural parameters ( ˚ A, Degree) of the stacked, h-bonded, h-transfered h-bonded and t-shaped uracil dimer cations. The differences ( ˚ A, Degree) w.r.t. the equilibrium geometry of the respec- tive neutral complexes are given in parenthesis. See Fig. 4.3 for the definitions of the parameters. . . . . . . . . . . . . . . . . . . . . . . . 78 xiv 4.3 Total (E tot , hartree) and dissociation (D e , kcal/mol) energies of the four isomers of the uracil dimer in the neutral and ionized states computed by CCSD/IP-CCSD with 6-311(+)G(d,p). Relevant total energies of the uracil monomer are also given. The relaxation energies (Δ E, kcal/mol) defined as the difference in total energies of the cation at the neutral and relaxed cation geometries are also shown. For HU + 2 (PT) dissociation energies corresponding to the U 0 + U + / (U - H) 0 + UH + channels are given. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.4 The dissociation energies (kcal/mol) and standard thermodynamic quan- tities of the neutral and the cation uracil dimers calculated at theωB97X- D/6-311(+)G(d,p) level. For the proton-transfered cation the values cor- responding to the two different dissociation limits are given. . . . . . . 84 4.5 The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the stacked dimer cation at the geom- etry of the neutral and cation, IP-CCSD/6-31(+)G(d). . . . . . . . . . . 88 4.6 The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the symmetric h-bonded dimer cation at the geometry of the neutral and cation, IP-CCSD/6-31(+)G(d). . . . 90 4.7 The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the h-bonded dimer cation at the optimized proton-transferred geometry, IP-CCSD/6-31(+)G(d). . . . . 91 4.8 The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the t-shaped dimer cation at the geometry of the neutral and cation, IP-CCSD/6-31(+)G(d). . . . . . . . 93 5.1 The total (hartree) and dissociation energies (kcal/mol) of the neutral and ionized 1,3-dimethyluracil monomer and dimers calculated at the ωB97X-D/6-311(+,+)G(2d,2p) level of theory. . . . . . . . . . . . . . 104 5.2 The total (hartree) and dissociation energies (kcal/mol) of the neutral and ionized 1,3-dimethyluracil and its dimer (lowest energy isomer) calcu- lated at the IP-CCSD/6-31(+)G(d) level of theory. For the monomer and the dimer cations, the relaxation energy (Δ E CCSD relax , kcal/mol) is provided. a The uracil and uracil dimer IP-CCSD/6-31(+)G(d) results b are included for comparison. . . . . . . . . . . . . . . . . . . . . . . . 105 xv 5.3 The five lowest ionized states and the corresponding IEs (eV) of the 1,3- dimethyluracil at the vertical geometry calculated by IP-CCSD with the 6-31(+)G(d) and 6-311(+)G(d,p) bases. The IE shifts (eV) with respect to the uracil values are given in parenthesis. . . . . . . . . . . . . . . . 108 5.4 The electronic spectrum of the 1,3-dimethyluracil cation at the vertical and relaxed geometries calculated at the IP-CCSD/6-31(+)G(d) level. . 121 5.5 The ionization energies (eV) and the DMO character a corresponding to the ten lowest ionized states of the stacked 1,3-dimethyluracil dimer at the vertical geometry (isomer 1) calculated at the IP-CCSD/6-31(+)G(d) level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.1 The ground state total energies (in hartree) of the six isomers of Bz + 2 cal- culated at three levels of theory: IP-CCSD/6-31(+)G(d), IP-CCSD(dT)/6- 31(+)G(d) and IP-CCSD/6-311(+,+)G(d,p)+FNO(99.25%) . . . . . . . 131 6.2 The characteristic geometric parameters of the six ground-state struc- tures of the benzene dimer cation. The distances between the centers of mass of the fragments d COM (in ˚ A), separation h (in ˚ A) and sliding coordinateΔ (in ˚ A) values are presented. . . . . . . . . . . . . . . . . 134 6.3 The six lowest symmetry-allowed transitions in the electronic spectrum of the benzene dimer cation at the XD and XSD optimized geometries. Calculated with IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . 138 6.4 The six lowest symmetry-allowed transitions in the electronic spectrum of the benzene dimer cation at the YD and YSD optimized geometries. Calculated with IP-CCSD/6-31(+)G(d). . . . . . . . . . . . . . . . . . 139 6.5 Theoretical estimates of the lowest VIE (in eV) of the nucleobase monomers andπ -stacked dimers. . . . . . . . . . . . . . . . . . . . . . . . . . . 143 xvi Abstract Several prototypical ionized non-covalent dimers - the uracil, 1,3-dimethylated uracil and benzene dimer cations - are studied by high-level ab initio approaches including the equation-of-motion coupled cluster method for ionization potentials (EOM-IP-CC). The qualitative Dimer Molecular Orbitals as Linear Combinations of Fragment Molecular Orbitals (DMO-LCFMO) framework is used to interpret the results of calculations. As the simplest model systems, the neutral and ionized non-covalent dimers, such as π -stacked and H-bonded nucleobase dimers, can shed some light on the complex mech- anism of the charge transfer in DNA. The correct treatment of non-covalent interactions is challenging to the ab initio methodology, therefore the special attention is given to the development and benchmarking of the new methods. First, we introduce and benchmark the cost-saving configuration-interaction variant of the EOM-IP-CCSD method: EOM-IP-CISD. The computational scalling of EOM- IP-CISD in N 5 , as opposed to the N 6 scalling of EOM-IP-CCSD. The EOM-IP-CISD structures for the open-shell systems are of a similar quality as the HF geometries of xvii well-behaved closed-shell molecules, while the excitation energies are of a semiquanti- tative value. The performance of promising Density Functional Theory developments, i.e. the novel long-range and dispersion-corrected functionals, is also assessed through- out this work. Next, the potential energy surfaces, electronic structure and properties of uracil dimer and 1,3-dimethylated uracil dimer cations are investigated. The electronic struc- ture of dimers is explained by DMO-LCFMO. Non-covalent interactions lower the ver- tical ionization energies by up to 0.35 eV , the largest red-shift is observed for the stacked and t-shaped structures. Ionization induces significant changes in bonding patterns, structures and binding energies. In the cations the interaction between the fragments becomes more covalent and the binding energies are 1.5-2.0 times larger than in the neutrals. The relaxation of the cation structures is governed by two different mecha- nisms: the hole delocalization and the electrostatic stabilization. The electronic spectra of dimer cations exhibit significant changes upon relaxation, which can be exploited to experimentally monitor the ionization-induced dynamics. The position and inten- sity of the charge-resonance transitions can be used as spectroscopic probes in such experiments. Finally, we investigate the effect of substituents on the electronic struc- ture of non-covalent dimers. For weak perturbations, i.e. the CH 3 group, the effect of substituents can be incorporated into the qualitative DMO-LCFMO picture as constant shifts of the dimers and the monomers levels. xviii Future research topics, such as the conical intersections in the benzene dimer cations and the electronic structure of the chemically-modified nucleobase dimers, are discussed in the last chapter. xix Chapter 1 Ionized non-covalent dimers: Fascinating and challenging 1.1 Non-covalent interactions From the chemist’s perspective, there are two types of molecular interactions - cova- lent and non-covalent. Covalent interactions giving rise to chemical bonds arise when two atoms share the electrons. In the electronic structure terms, covalent interaction originate in the atomic orbital overlap, which increases the electron delocalization and, thus, lowers electronic energy. Non-covalent interactions are everything beyond the covalent definition. They include the electrostatic, induction and dispersion intermolec- ular forces, the latter being also known as van der Waals interactions. Hydrogen bond straddles the two domains, as it includes partial electron sharing, but also a degree of electrostatic interaction. The non-covalent interactions are weak relative to the covalent or pure ionic ones. Typical stabilization energies for a chemical bond are of the order 1 of hundred kilocalories per mole, whereas the hydrogen-bonded and dispersion inter- acting systems are bound by tenth to several kilocalories per mole, respectively. Nev- ertheless, the importance of non-covalent interactions for chemistry cannot be overes- timated. Condensed-phase chemistry, biochemistry, surface chemistry, catalysis, poly- mer science - these are just several fields of modern chemistry that are defined by the non-covalent interactions to a considerable degree [1–3]. For instance, the 3D structure of one of the most important molecules in biochemistry - the DNA double helix - is a result of a network of hydrogen-bonding and π -stacking interactions that are of the non-covalent nature. Other examples include protein secondary and tertiary structure, enzyme-substrate binding, and more. 1.2 Ionized non-covalent dimers as model charge- transfer systems In recent years, significant efforts were directed towards investigating charge transfer (CT) in DNA, which is related to the DNA damage processes. The DNA’s photo- and oxidizing damage is of great importance to the biology and medicine, as it is likely to be realted to some of the serious deseases [4]. Under the oxidizing or photoionizing conditions, the hole is injected in the DNA molecule, in particular, in its easiest-to-ionize guanine site. The hole then migrates 2 through the DNA strand over large distances of more than 100 ˚ A, which was experi- mentally observed for both pure DNA/DNA [5, 6] and mixed DNA/RNA duplexes [7]. In addition to the biological significance of this process, this nano-scale conductivity of DNA and RNA is attractive for the molecular electronics applications [8–10]. Despite its importance, the CT phenomenon is not yet fully understood and the progress requires joint experimental and theoretical efforts. Several mechanisms of CT in DNA have been proposed [11–16], but none of them offers a complete description of the process. Different factors were shown to be impor- tant: the DNA sequence and composition (in particular, the percentage of GC and AT Watson-Crick base pairs), thermally-induced chain fluctuations, the presence of Na + counterions [17]. Moreover, the non-covalent interactions between the bases, especially theπ -stacking, appear to be crucial for this process [18–20]. The study of ionized nucle- obase dimers - the simpliest model systems for the CT in DNA - can shed some light at this complex phenomenon. While ionization energies (IEs) of nucleic acid bases in the gas phase have been characterized both experimentally [21–27] and computationally [28–31], much less is known about the effects of interactions present in realistic environments, likeπ -stacking and h-bonding, on the ionized states of nucleobases. We characterized the electronic structure of the ionized uracil dimers [32, 33] and dimethylated uracil dimers [34]. Other ionized nucleobase dimers, like the adenine and thymine homo- and hetero-dimers [35] and cytosine dimers [36] were also investigated 3 recently. Calculations [32–36] and VUV measurements [35,36] demonstrated that non- covalent interactions lower vertical ionization energies (VIEs) by as much as 0.7 eV (in cytosine dimers). Interestingly, the magnitude and origin of the effect are different for different isomers. The largest drop in IEs was observed in the symmetric stacked and non-symmetric h-bonded dimers. In the former case, the IE is lowered due to the hole delocalization over the two fragments, while in the latter case the stabilization is achieved by the electrostatic interaction of hole with the “neutral” fragment. Therefore, non-covalent interactions seem to reduce the gaps in IEs of purines and pyrimidines, which may play an important role in hole migration through DNA. Earlier studies of the effects of π -stacking on IEs of nucleobases include Hartree- Fock and DFT estimates using Koopmans theorem [37–41], MP2 (Møller-Plesset per- turbation theory) and CASPT2 (perturbatively-correcte d complete active space self- consistent field) calculations [28, 30, 42]. 1.3 Methodological challenges The correct treatment of non-covalent interactions is difficult for ab initio methodology [1, 3, 43], especially for the systems dominated by dispersion interactions. Dispersion forces originate in correlated motion of the electrons, so highly-correlated approaches, such as coupled cluster methods, are required for reliable results. However, theN 6 -N 8 scalling of these methods quickly rules out their application to large systems (i.e., more 4 than 40-50 atoms). A less expensive alternative to the traditional correlated wave func- tion based methods, Density Functional Theory (DFT), fails to account for dispersion interaction when used with standard functionals [44, 45]. The reason is the local and semi-local character of the approximate exchange-correlation functional ( XC ). For a cluster AB, where charge densities on A and B fragments do not overlap: XC (AB)= XC (A)+ XC (B), (1.1) where XC (A) and XC (B) depend solely on the densities (or the density and its gra- dient) on fragments A and B, respectively. Such model cannot account for the long- range attractive dispersion and fails to adequately describe non-covalent systems at large separations, when the dispersion forces dominate. Moreover, the situation is far from prefect at short-range where the attractive dispersion interaction is underestimated by DFT due to the incorrect asymptotic behavior of standard functionals [44]. The latest developements of the semi-empirical dispersion-corrected functionals [46,47], where an empiricalR − 6 term is included to account for the long-range dispersion interaction, are promising; however, they do not provide a universal solution. Other problems include the shallow potential energy surfaces (PES) of non-covalent complexes and technical issues such as Basis Set Superposition Error (BSSE) [1]. Thus, even a closed-shell system is a challenge for modern computational chemistry when it is dominated by non- covalent interactions. 5 With the open-shell systems such as ionized non-covalent dimers additional issues emerge. The single-reference post-HF approaches, e.g. MP2 and CCSD, are plagued by the spin-contamination, symmetry-breaking and imbalanced description of the closely- lying multiple electronic states. The former follows from the fact that the HF variational solution (i.e., the unrestricted HF solution) is generally not an eigenfunction of thehS 2 i operator. Consequently, the UHF wave function is a mixture of states of different multi- plicity. The correct spin symmetry can be enforced in HF by restricting the spatial parts of the orbitals to be equal for the electrons with different spin (the restricted open-shell HF). However, this solution problem is not optimal from variational principle point of view, as it is higher in energy. The imbalance originates in the multi-configurational character of the open-shell wave functions, which can be accounted for by correlated multi-reference (MR) approaches, like CASPT2 or MR-CISD. However, some of the imbalance is still present in the MR wave function, because the configurations of similar importance are not treated on the same footing. Other disadvantages that limit the applications of MR meth- ods are the high cost and inconvenience resulting from the need to choose the relevant configurations manually. The DFT description of the ionized non-covalent systems suffers from self- interaction erorrs (SIE) in addition to the issues mentioned previously [48]. Because of the approximate character of the exchange-correlation functional, the exchange and repulsion terms do not cancel out for one electron in DFT. This results in unphysical 6 situation when the electron interacts with itself. The SIE is responsible for the incorrect behavior at the dissociation limit for the symmetric dimer cations, for instance, the ion- ized rare gas and nucleobase dimers [48]. The total energy of the dissociating system becomes much lower than the sum of the total energies of the products. The resulting potential energy profiles instead of levelling off at infinite separations exhibit a char- acteristic downward curve. This behaviour is suppressed if the Hartree-Fock exchange is used, which is exploited in the long-range corrected (LC) functionals. One of the promising functionals isωB97X-D [49], which includes both LR Hartree-Fock and dis- persion correction. TheωB97X-D shows significant improvement over traditional DFT functionals when applied to non-covalent systems. 1.4 Equation-of-motion coupled-cluster family of meth- ods The equation-of-motion coupled-cluster (EOM-CC) methods [50–60] offer an original solution to open-shell problems. Instead of dealing with the symmetry-broken and spin- contaminated wave function of the open-shell state of interest, the EOM-CC accesses the target states via a well-behaved reference state employing various excitation oper- ators. The reference state is chosen such that it is free from spin-contamination and symmetry-breaking at the Hartree-Fock level. Thus, the EOM methods do not suffer from these common flaws of traditional wave function approaches. When used properly, 7 they yield balanced wave functions that include all the important configurations from the target manifold. Other advantages of the EOM approach include embedded dynamical correlation effects and elegant formalism. The EOM-CC methods are universal and can be successfullly applied to diverse open-shell situations, including the open-shell cations, anions, di- and tri-radicals, bond-breaking, exactly and nearly-degenerate elec- tronic states. The wave function of the target state in EOM-CC is represented as follows: Ψ EOM− CC = ˆ Re ˆ T Φ 0 , (1.2) where Φ 0 is Hartree-Fock determinant of the closed-shell reference state, ˆ T is the coupled-cluster operator and ˆ R is the appropriate excitation operator generating the tar- get configurations from the reference CCSD wave function. Depending on an EOM-CC model, different excitation operators are used. For instance, in the EOM model for ionization potentials (EOM-IP) [58], which is an appropriate choice for ionized non- covalent systems, the operator ˆ R is ionizing and generates all 1h (one hole) and 2h1p (two hole one particle) determinants from the reference configuration. This model is capable of accessing the doublet states of the radical cations from the neutral reference. The second-quantization expressions for ˆ R and ˆ T operators for one of the extensions of the EOM-IP model with single and double substitutions (EOM-IP-CCSD) are: ˆ R= ˆ R 1 + ˆ R 2 (1.3) 8 ˆ R 1 = X i r i i (1.4) ˆ R 2 = 1 2 X ija r a ij a + ji (1.5) ˆ T = ˆ T 1 + ˆ T 2 (1.6) ˆ T 1 = X ia t a i a + i (1.7) ˆ T 2 = 1 4 X ijab t ab ij a + b + ij (1.8) where t a i , t ab ij and r i , r a ij are the unknown amplitudes of the coupled-cluster and EOM excitation operators. The EOM-CC solutions are obtained in a two-step procedure. First, the coupled-cluster equations for the reference state are solved and the amplitude vector for the operator ˆ T is obtained in a procedure that scales asN 6 . Second, the EOM states (or equivalently the left and right amplitude vectors of operator ˆ R for EOM states) are found by the diagonalization of the similarity-transformed Hamiltonian ¯ H = e − ˆ T He ˆ T at theN 5 cost. ¯ HR=ER (1.9) L ¯ H =ER (1.10) L I R J =δ ij (1.11) Other EOM-CC models include the electron atachment (EA) [57], spin flip (SF) [55, 56] and electron excitations (EE) [54] variants. These ideas can be implemented 9 within the CI approach [61] and one of the methods, EOM-IP-CISD, is described in Section 2.2. 1.5 Bonding in ionized non-covalent dimers: The qual- itative Dimer Molecular Orbitals and Linear Com- binations of Atomic Orbitals framework The DMO-LCFMO (Dimer Molecular Orbital Linear Combination of Fragment Molec- ular Orbitals) framework [62] enables the qualitative prediction of the bonding and properties of non-covalent dimers. Within this framework, the electronic structure of the dimer is described in terms of the fragment (i.e. monomer) molecular orbitals (FMOs). Symmetric and non-symmetric dimers are treated analogously to the famil- iar MO-LCAO approach to of homo- and hetero-nuclear diatomics [63]. 10 ν(F1) = π CC (F1) ν(F2) = π CC (F2) ψ + (ν) -0.361 -0.384 -0.372 -0.372 ψ - ( ν) Figure 1.1: The DMO-LCFMO description of the two lowest ionized states in the uracil dimer. In-phase and out-of-phase overlap between the FMOs results in the bonding (lower) and antibonding (upper) dimer’s MOs. Changes in the MO energies, and, con- sequently, IEs, are demonstrated by the Hartree-Fock orbital energies (hartrees). Ioniza- tion from the antibonding orbital changes the bonding from non-covalent to covalent, and enables a new type of electronic transitions, which are unique to the ionized dimers. As illustrated in Figure 1.1, the dimer molecular orbitals (DMOs) are symmetric and antisymmetric linear combinations of the FMOs: ψ + (ν )= 1 q 2(1+s νν ) (ν (F1)+ν (F2)) (1.12) ψ − (ν )= 1 q 2(1− s νν ) (ν (F1)− ν (F2)) (1.13) where ν (F1) and ν (F2) are the FMOs centered on two equivalent fragments F1 and F2, ψ + (ν ) and ψ − (ν ) denote the bonding and antibonding orbitals with respect to the 11 interfragment interaction ands νν = hν (F1) | ν (F2)i is the overlap integral. Folowing the MO-LCAO reasoning, the energy splitting between the bonding and antibonding orbitals is proportional to the overlap s νν [63]. Therefore, the dimer system ionizes at lower ionization energies relative to the monomer and the decrease in dimer IE is proportional to the FMO overlap. From Figure 1.1 we can also predict the behaviour of the ionization-induced changes in the dimer system. As the electron is ejected from the dimer, the formal bond order changes from0 to 1 2 and the interfragment interaction increases. Twice as many ionized states appear in dimer relative to the monomer. In the elec- tronic spectrum of the dimer cation, all transitions can be classified into two categories: the charge resonance (CR) and the local excitations (LE). The CR transitions are defined as transitions between the ionized states corresponding to the in- and out-of-phase com- bined FMOs of the same character, i.e. ψ − (ν ) → ψ + (ν ). The LE are the transitions between the DMOs combined out of FMOs of different character, i.e. ψ − (ν ) → ψ + (ζ ) orψ − (ν )→ψ − (ζ ). The CR transitions are unique to the dimer, whereas LE are similar to the transitions present in the electronic spectrum of monomer cation. It can be shown that the intensity of the CR transitions is sensitive to the FMO overlap and interfragment separation: I(ψ − (ν )→ψ + (ν ))∝ R F1··· F2 √ 1− s νν (1.14) 12 where s νν = hν (F1) | ν (F2))i. When the cation relaxes from the vertical geometry, the FMO overlap increases (s ν (F1)ν (F2) → 1), and the CR band intensity rises in the electronic spectrum. Therefore, the CR transitions can be used to probe the structural changes occuring in the dimer cation. In non-symmetric dimers, the transitions corresponding to charge-transfer between the fragments become important. 13 1.6 Chapter 1 References [1] K. M¨ uller-Dethlefs and P. Hobza. Noncovalent interactions: A challenge for exper- iment and theory. Chem. Rev., 100:143–167, 2000. [2] J. ˘ Cern´ y and P. Hobza. Non-covalent interactions in biomacromolecules. Phys. Chem. Chem. Phys., 9:5291–5303, 2007. [3] C.D. Scherrill. 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The formal introduction of IP-CISD is given in Section 2.2, its performance and errors for structural parameters and excitation energies are discussed in Section 2.4.1, 2.4.2 and 2.4.3. 20 2.2 The IP-CISD method The IP-CISD wave function for state can be written as: Ψ IP− CISD = ˆ RΦ 0 , (2.1) In this equationΦ 0 is the Hartree-Fock determinant of the reference closed-shell system and the operator ˆ R= ˆ R 1 + ˆ R 2 is the familiar EOM-IP excitation operator: ˆ R 1 = X i r i i (2.2) ˆ R 2 = 1 2 X ija r a ij a + ji (2.3) (2.4) In other words, ˆ R 1 and ˆ R 2 generate the linear combinations of all possible ionized (i.e., 1h) and ionized-excited (2h1p) determinants with appropriate spin-projection (either Ms=1 2 orM s =− 1 2 ) from the reference HF wave function. The equations for the amplitudes of ˆ R of the electronic state K are derived by apply- ing the variational principle to the CI energy functional: E K = <Ψ IP− CISD (K)|H|Ψ IP− CISD (K)> <Ψ IP− CISD (K)|Ψ IP− CISD (K)> (2.5) 21 and are: (H− E 0 )R=RΩ , (2.6) whereH is the matrix of the Hamiltonian in the basis of the1h and2h1p determinants, matrixR contains the amplitudes,Ω is a matrix composed of the energy differences with respect to the reference state,ω k = E K − E 0 , andE 0 =< Φ 0 |H|Φ 0 >. Thus, the amplitudes and target states’ energies are found by diagonalization of the Hamiltonian in the{1h,2h1p} space. H SS − E 0 H SD H DS H DD − E 0 R 1 (K) R 2 (K) =ω K R 1 (K) R 2 (K) (2.7) (2.8) whereH SS ,H DS , andH DD denote1h− 1h,2h1p− 1h, and2h1p− 2h1p blocks of the Hamiltonian matrix, respectively. The key advantages of a more correlated EOM-IP-CCSD method are common to its less-expensive configuration-interaction approximation. For the closed-shell refer- ences, the set of ionized and ionized-excited determinants is spin-complete and multiple ionized states are treated on the same footing in IP-CISD. 22 2.3 Computational details Equilibrium geometries of the five lowest ionized states of uracil were optimized using analytic gradients under C s constraint at the IP-CCSD and IP-CISD levels with the 6- 31+G(d) basis set [1]. The cation excitation energies and transition properties were computed at the neutral uracil geometry optimized with RI-MP2/cc-pVTZ [2] and at the optimized geometry of the lowest electronic state of the cation using the 6-31+G(d) and 6-311+G(d,p) bases [1, 3], with the core electrons frozen. Permanent dipole moments were computed at the respective optimized geometries using fully relaxed IP-CCSD and IP-CISD one-particle density matrices. Since the dipole moments of charged systems are not origin-invariant, all the dipoles were com- puted relative to the center of mass of the cations. In water dimer calculations, we employed the optimized geometries of the neutrals available in the literature [4]. The cation geometries were optimized by IP-CISD and IP-CCSD with the 6-311(+,+)G(d,p), 6-311(2+,+)G(d,p), 6-311(2+,+)G(2df) and aug- cc-pVTZ basis sets [1, 3, 5] with symmetry constraint. Benzene dimer calculations were carried out with IP-CISD and IP-CCSD with 6- 31(+)G(d) basis and under symmetry constraint, as in Ref. 8. The wave functions for the t-shaped were analyzed using the Natural Bond Orbitals (NBO) [6] procedure and the charge of the individual fragments was calculated. 23 All optimizations were conducted using defaultQ-CHEM optimization thresholds: the gradient and energy tolerance were set to3· 10 − 4 and1.2· 10 − 3 respectively; maxi- mum energy change was set to1· 10 − 6 . The IP-CCSD geometries of the benzene dimer isomers were computed using tighter thresholds [7]. All electrons were correlated in the uracil, water dimer and benzene dimer geometry optimizations and properties calculations. Figs. 2.1 and 2.2 provide the definitions of the geometric parameters for uracil, water dimer and three benzene dimer isomers. 2.4 Numerical results 2.4.1 Equilibrium geometries and electronically excited states of the uracil cation Uracil has eight different bonds between heavy atoms, as depicted in Fig. 2.1. Fig. 2.3 shows the values of the CC(1), CO(1), CO(2), and CN(2) bondlengths for the five low- est electronic states of the cation, as well as the corresponding values in the neutrals. The MOs hosting the unpaired electron are also shown. In agreement with molecular orbital considerations, ionization results in significant changes in some bond lengths, which vary from state to state. For example, the CC(1) bond becomes much longer in the first ionized state derived by ionization from theπ CC orbital, whereas the CO bonds 24 CC(1) CN(1) NC(1) CN(2) NC(2) CC(2) CO(1) CO(2) CCN(1) CNC(1) NCN(1) CNC(2) NCC(1) CCC(1) H 1 O 1 H 2 O 2 H 3 H 4 O 1 O 2 Figure 2.1: Definitions of the geometric parameters for uracil (upper panel) and water dimer (lower panel) at the proton-transferred geometry. undergo significant changes in the states derived by ionization from the respective oxy- gen lone pairs. As one can see from Fig. 2.3, IP-CISD systematically underestimates the bond lengths, probably because of the uncorrelated Hartree-Fock reference. However, it reproduces the trends, such as structural differences between the states, very well. 25 C 1 C 2 C 3 C 4 C 5 C 6 C 1 C 2 C 3 C 4 C 5 C 6 Fragment 2 C 2h x-displaced isomer Fragment 1 Fragment 1 Fragment 2 C 2h y-displaced isomer C 1 C 2 C 3 C 4 C 5 C 6 C 1 C 2 C 3 C 4 C 5 C 6 Fragment 1 Fragment 2 C 2v t-shaped isomer C 1 C 2 C 3 C 4 C 5 C 6 C 1 C 2 C 3 C 4 C 5 C 6 Figure 2.2: Definitions of the geometric parameters for three isomers of the benzene dimer: x-displaced (top),y-displaced (middle), and t-shaped (bottom). The absolute errors of IP-CISD versus IP-CCSD are summarized in Table 2.1. For the bondlengths, the IP-CISD errors are always negative. The table also presents average absolute errors and standard deviations for each state, which are around 0.014- 0.016 ˚ A and 0.007-0.010 ˚ A, respectively. Absolute average error and standard deviation for these eight bonds in five electronic states are 0.015 ˚ A and 0.008 ˚ A, respectively. The results for six bond angles are summarized in Table 2.2. The results are similar to the bondlengths behavior — IP-CISD reproduces the trend in structural changes very well. Average absolute error and standard deviation for all angles in the five states are 26 Table 2.1: The IP-CCSD bondlengths ( ˚ A) in the five electronic states of the uracil cation and absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD. Bonds 1 2 A 00 1 2 A 0 2 2 A 00 2 2 A 0 3 2 A 00 CC(1) 1.403 (0.017) 1.365 (0.009) 1.352 (0.014) 1.345 (0.014) 1.375 (0.013) CN(1) 1.321 (0.005) 1.357 (0.013) 1.390 (0.012) 1.392 (0.010) 1.471 (0.028) NC(1) 1.460 (0.027) 1.386 (0.009) 1.358 (0.011) 1.351 (0.010) 1.371 (0.017) CN(2) 1.386 (0.011) 1.427 (0.021) 1.416 (0.032) 1.351 (0.013) 1.398 (0.009) NC(2) 1.403 (0.016) 1.341 (0.003) 1.426 (0.029) 1.387 (0.007) 1.425 (0.009) CC(2) 1.469 (0.012) 1.423 (0.010) 1.444 (0.001) 1.459 (0.003) 1.473 (0.005) CO(1) 1.215 (0.020) 1.286 (0.024) 1.231 (0.018) 1.236 (0.028) 1.204 (0.027) CO(2) 1.199 (0.021) 1.199 (0.024) 1.226 (0.017) 1.272 (0.025) 1.230 (0.023) average abs. error 0.016 0.014 0.017 0.014 0.016 standard deviation 0.007 0.008 0.010 0.009 0.009 0.343 and 0.266 degrees, respectively. Fig. 2.4 visualizes changes in CNC(2) angle upon ionization. The computed permanent dipole moments in the center of mass frame are given in Table 2.3. The IP-CCSD and IP-CISD values are very similar indicating that IP-CISD reproduces well both the equilibrium structures and electron distributions. IP-CISD values are systematically 0.1-0.2 a.u. too large. Thus, IP-CISD wave func- tions inherit limitations of the uncorrelated Hartree-Fock reference and are too ionic, as compared to more correlated IP-CCSD ones. Table 2.4 presents vertical excitation energies and transition dipole moments of the uracil cation at two different geometries, i.e., the geometry of the neutral and the equilibrium geometry of the lowest ionized state. IP-CISD errors are 0.1-0.3 eV and they are consistently larger for the low-lying states. Overall, the order of states is reproduced correctly, however, IP-CISD excitation energies are of semi-quantitative accuracy only. Intensities of transitions are in qualita- 27 Table 2.2: The IP-CCSD angles (degrees) in the five electronic states of the uracil cation and absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD. Bonds 1 2 A 00 1 2 A 0 2 2 A 00 2 2 A 0 3 2 A 00 CCN(1) 119.217 (0.156) 122.529 (0.078) 122.648 (0.280) 121.826 (0.223) 120.745 (0.728) CNC(1) 125.636 (0.152) 124.334 (0.232) 123.333 (0.621) 121.309 (0.101) 122.446 (0.027) NCN(1) 113.077 (0.496) 112.381 (0.584) 113.977 (1.260) 118.079 (0.225) 114.018 (0.215) CNC(2) 126.733 (0.533) 124.291 (0.383) 126.224 (0.556) 124.315 (0.099) 129.409 (0.318) NCC(2) 115.214 (0.463) 120.781 (0.046) 114.481 (0.644) 116.352 (0.105) 113.365 (0.222) CCC(1) 120.123 (0.429) 115.684 (0.093) 119.337 (0.447) 118.120 (0.145) 120.016 (0.430) average abs. error 0.372 0.236 0.635 0.150 0.323 standard deviation 0.172 0.212 0.334 0.060 0.239 28 Table 2.3: IP-CCSD and IP-CISD permanent dipole moments (a.u.) of the five lowest electronic states of the uracil cation computed at the respective optimized geometries relative to the center of mass. 1 2 A 00 1 2 A 0 2 2 A 00 2 2 A 0 3 2 A 00 IP-CCSD 2.509 1.474 1.144 1.384 2.641 IP-CISD 2.632 1.602 1.279 1.511 2.759 tive agreement. Most importantly, both methods agree which states are dark and which are bright, indicating that the underlying wave functions are qualitatively similar. Other important trends, e.g., the lowering of the transition dipoles for the two highest states upon geometric relaxation (from the neutral to the cation), are also reproduced. The basis set dependence of the errors is small, as evidenced by the results in two different bases. 2.4.2 Equilibrium geometries of the three isomers of the benzene dimer cation Geometrical parameters (see Fig. 2.2) for the three isomers of the benzene dimer cation are summarized in Table 2.5 and visualized in Fig. 2.5. On this example, we investigate how well IP-CISD reproduces the structures of the ionized non-covalent dimers. Ioniza- tion of such systems changes the bonding from non-covalent to covalent, which results in significant structural changes, in particular the interfragment distance. For example, the interfragment distance shrinks from 3.9 to 3.3 ˚ A in the sandwich isomers. IP-CISD 29 Table 2.4: The IP-CCSD and IP-CISD excitation energies (eV) and transition dipole moments (a.u.) of the uracil cation at the equilibrium geometries of the neutral and the cation. neutral cation 6-31(+)G(d,p) IP-CCSD IP-CISD IP-CCSD IP-CISD E μ 2 E μ 2 E μ 2 E μ 2 1 2 A 0 0.668 0.000 0.367 0.000 1.175 0.000 0.820 0.000 2 2 A 00 1.063 0.000 0.867 0.000 1.809 0.000 1.577 0.000 2 2 A 0 1.647 0.790 1.427 0.819 2.385 0.611 2.156 0.613 3 2 A 00 3.566 1.342 3.627 0.955 4.209 0.940 4.223 0.611 average abs. error 0.195 0.208 neutral cation 6-311(+)G(d,p) IP-CCSD IP-CISD IP-CCSD IP-CISD E μ 2 E μ 2 E μ 2 E μ 2 1 2 A 0 0.642 0.000 0.335 0.000 1.144 0.000 0.785 0.000 2 2 A 00 1.037 0.000 0.848 0.000 1.779 0.000 1.557 0.000 2 2 A 0 1.614 0.786 1.388 0.820 2.349 0.603 2.112 0.611 3 2 A 00 3.543 1.358 3.613 0.968 4.187 0.952 4.209 0.620 average abs. error 0.198 0.211 overestimates the interplanar separation in the displaced sandwich isomers by approxi- mately 0.2 ˚ A, while the sliding displacement is reproduced quite accurately. Similarly, the separation between the rings in the t-shaped structure is overestimated. In the t-shaped structure the two fragments are nonequivalent, and the charge is unevenly distributed between the rings. The degree of charge distribution determines the intensity of charge resonance bands, which can be used to probe the structure and dynamics of the system. The NBO analysis of the IP-CISD densities for the states involved in this transition yields an 0.888 and 0.101 partial charge on fragment 1 (stem), 30 Table 2.5: The bondlengths ( ˚ A), angles (degrees), interfragment distances and sliding displacements ( ˚ A) in the ground state of the x-displaced, y-displaced and t-shaped benzene dimer cations calculated with IP-CISD/6-31(+)G(d). For the x- and y- displaced structures, geometric parameters for only one of the benzene fragments are provided (the fragments are equivalent by symmetry). Absolute errors of IP-CISD relative to IP-CCSD are presented in parenthesis. Average absolute errors are calculated using the data for symmetry unique parameters. Parameter (number) x-displaced y-displaced t-shaped (fragment 1) t-shaped (fragment 2) CH bond range 1.075 (0.013) - 1.076 (0.014) 1.074 (0.014) - 1.076 (0.013) 1.073 (0.009) - 1.077 (0.012) 1.075 (0.014) C 1 C 2 1.373 (0.010) 1.385 (0.011) 1.419 (0.010) 1.393 (0.012) C 2 C 3 1.408 (0.011) 1.414 (0.011) 1.376 (0.001) 1.387 (0.012) C 3 C 4 1.400 (0.011) 1.384 (0.011) 1.414 (0.011) 1.393 (0.012) C 4 C 5 1.379 (0.010) 1.384 (0.011) 1.414 (0.011) 1.393 (0.012) C 5 C 6 1.400 (0.011) 1.414 (0.011) 1.376 (0.001) 1.387 (0.012) C 6 C 1 1.408 (0.011) 1.385 (0.011) 1.419 (0.010) 1.393 (0.012) Average abs. error 0.011 0.011 0.007 0.012 C 1 C 2 C 3 119.569 (0.032) 120.473 (0.009) 119.428 (0.018) 119.933 (0.009) C 2 C 3 C 4 120.807 (0.026) 120.307 (0.010) 119.282 (0.096) 119.933 (0.009) C 3 C 4 C 5 119.607 (0.012) 119.301 (0.041) 121.514 (0.120) 120.133 (0.015) C 4 C 5 C 6 119.607 (0.012) 120.307 (0.010) 119.282 (0.096) 119.933 (0.009) C 5 C 6 C 1 120.807 (0.026) 120.472 (0.010) 119.428 (0.018) 119.933 (0.009) C 6 C 1 C 2 119.569 (0.032) 119.092 (0.051) 121.065 (0.108) 120.133 (0.015) Average abs. error 0.023 0.020 0.078 0.011 interfr. distance 3.31 / 3.08 3.31 / 3.07 4.81 / 4.58 sl. displacement 1.04 / 1.07 1.03 / 1.10 - 31 which is in excellent agreement with the IP-CCSD values [8] of 0.880 and 0.099, respec- tively. Charge-resonance transition energies are 0.71 and 0.81 eV for EOM-IP-CCSD and IP-CISD, respectively. The changes in intramolecular parameters are reproduced by IP-CISD very well — average absolute error in bond lengths for all three isomers is 0.01 ˚ A. Note that Jahn-Teller displacements in the t-shaped isomer are also accurately described. The contraction of the interfragment distance is reproduced correctly, however, the distance is overestimated. We interpret this by the absence of dispersion in uncorrelated Hartree- Fock reference employed by IP-CISD. The absolute error is slightly larger owing to the larger distance. 2.4.3 Water dimer cation Table 2.6 summarizes geometrical parameters (see Fig. 2.1) for the two lowest electronic states of the water dimer cation. Selected bondlengths and angles are visualized in Fig. 2.6. The errors for the intramolecular parameters are similar to those in uracil and benzene dimers. The trends in intramolecular distances are similar to the benzene dimer cations, however, in this case ionization introduces even stronger perturbation to electronic structure and leads to the proton-transfer and formation of OH··· H 3 O + complex, as evident from the value of O 1 H 2 distance in Table 2.6. The OO bondlength shortens by about 0.3 ˚ A in the lowest ionized state relative to the neutral. The values of the OO distance between the two lowest ionized states differ by about 0.06 ˚ A. IP-CISD 32 Table 2.6: The IP-CCSD bondlengths ( ˚ A) and angles (degrees) in the two electronic states of the water dimer cation and absolute errors (in parenthesis) of IP-CISD relative to IP-CCSD calculated with different bases. 6-311(+,+)G(d,p) 6-311(2+,+)G(d,p) 6-311(2+,+)G(2df) aug-cc-pVTZ Parameter 1 2 A 00 1 2 A 0 1 2 A 00 1 2 A 0 1 2 A 00 1 2 A 0 1 2 A 00 1 2 A 0 H 1 O 1 0.978(0.012) 0.973(0.010) 0.978(0.012) 0.973(0.010) 0.977(0.012) 0.973(0.010) 0.975(0.010) 0.970(0.008) O 1 H 2 1.425(0.127) 1.525(0.081) 1.423(0.128) 1.522(0.083) 1.526(0.082) 1.592(0.083) 1.429(0.115) 1.519(0.079) H 3 O 2 0.970(0.014) 0.971(0.015) 0.970(0.014) 0.971(0.015) 0.972(0.016) 0.973(0.015) 0.968(0.013) 0.970(0.014) O 2 H 4 0.970(0.014) 0.971(0.015) 0.970(0.014) 0.971(0.015) 0.972(0.016) 0.973(0.015) 0.968(0.013) 0.970(0.014) O 1 O 2 2.475(0.082) 2.532(0.060) 2.474(0.082) 2.529(0.062) 2.549(0.054) 2.592(0.062) 2.478(0.074) 2.524(0.061) H 1 O 1 H 2 123.713(6.795) 176.809(0.522) 123.485(6.881) 176.520(0.671) 126.141 (2.966) 176.858 (0.671) 120.553(6.235) 177.434(0.169) H 3 O 2 H 4 109.874(2.495) 111.259(2.279) 109.816(2.517) 111.187(2.287) 110.256 (1.302) 111.250 (2.287) 109.902(2.287) 111.147(1.976) Average abs. errors Bonds 0.050 0.036 0.050 0.037 0.036 0.037 0.045 0.035 Angles 4.645 1.400 4.699 1.479 2.134 1.479 4.198 1.073 33 reproduces these trends and structural differences between the different ionized states correctly. The absolute errors for the intermolecular parameters are slightly larger, e.g., 0.05- 0.06 ˚ A for the OO distance, however, one should keep in mind that the value of this bond is about 2.5 ˚ A. As in the benzene dimer example, IP-CISD overestimates the intramolec- ular distances. An important result is that the errors of IP-CISD relative to IP-CCSD are not very sensitive to the basis set, as one might expect in view of different amount of correlation included in the latter. The absolute average errors in bondlengths for two electronic states are 0.043, 0.044, 0.037 and 0.040 ˚ A in the 6-311(+,+)G(d,p), 6-311(2+,+)G(d,p), 6-311(2+,+)G(2df) and aug-cc-pVTZ bases, respectively. 2.4.4 Timings To demonstrate gains in computational cost, we present timings for IP-CCSD and IP- CISD calculations of the uracil dimer on a Xeon 3.2 GHz Linux machine using parallel version (threaded over two processors) of the CCSD and EOM code (the Hartree-Fock and integral transformation modules were not parallelized). The symmetry of the dimer is C 2 , and two lowest states in each irrep were requested. In 6-31+G(d) basis (320 basis functions), the wall time for total (including SCF and integral transformation) IP- CCSD and IP-CISD calculations was 5.82 and 1.50 hours, respectively. The IP-CISD calculation in 6-311+G(2d,p) basis (480 basis functions) took only 10.5 hours. 34 2.5 Conclusions The benchmark study of the novel configuration-interaction variant of EOM-IP-CCSD method is reported. The method is naturally spin-adapted, variational, and size- intensive. The computational scaling is N 5 , in contrast to the N 6 scaling of EOM- IP-CCSD, which results in significant computational savings. The performance of the method was tested on the uracil cation (five electronic states), water dimer cation (two electronic states), and three isomers of the benzene dimer cation (ground electronic state). The results demonstrate that the equilibrium geometries of the ionized states are reproduced reasonably well. Using symmetry unique parameters from these ten struc- tures optimized in a modest basis set, we computed average absolute error and standard deviation for bond lengths and angles relative to the IP-CCSD values. For bondlengths, average absolute error and standard deviation are 0.014 and 0.007 ˚ A, respectively, and for angles — 0.255 and 0.264 degrees. It is informative to compare these numbers with mean absolute errors and standard deviations of the HF and CCSD methods for well- behaved closed-shell molecules relative to the experiment [9]. For bondlengths, the CCSD/cc-pVTZ and CCSD/cc-pVDZ values are 0.0064/0.0066 and 0.0119/0.0076 ˚ A, respectively [9]. The HF errors and standard deviations in cc-pVTZ and cc-pVDZ are 0.0263/0.0223 and 0.0194/0.0225 ˚ A, respectively [9]. Thus, IP-CISD structures are of similar quality as HF geometries of closed-shell molecules. Inheriting limitations of the underlying Hartree-Fock reference, IP-CISD systematically underestimates bondlengths 35 and overestimates interfragment distances. Most importantly, IP-CISD correctly repro- duces structural changes induced by ionization and structural differences between dif- ferent ionized states. Molecular properties such as permanent and transition dipole moments and charge distributions are reproduced very well demonstrating that IP-CISD wave functions are qualitatively correct. Ionization energies cannot be computed by IP-CISD because of the use of uncorrelated Hartree-Fock description of the neutral, however, energy differences between the ionized states are of semi-quantitative accuracy (errors of about 0.3 eV relative to IP-CCSD). Our results suggest that IP-CISD is most useful as an economical alternative for geometry optimization in the ionized systems. Using IP-CISD structures, more accurate energy differences can be computed with more expensive IP-CCSD. Moreover, IP-CISD wave functions may be employed as zeroth-order wave functions in subsequent pertur- bative treatment. 36 Figure 2.3: Selected bondlengths in the five lowest electronic states of the uracil cation. The corresponding values of the neutral are shown by dashed lines. The MOs from which electron is removed are shown for each state. 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 CC(1) bond length, Angstrom Electronic State IP-CISD IP-CCSD 1 2 A˝ 1 2 A´ 2 2 A´ 2 2 A˝ 3 2 A˝ 1.18 1.20 1.22 1.24 1.26 1.28 1.30 CO(1) bond length, Angstrom Electronic State IP-CISD IP-CCSD 1 2 A˝ 1 2 A´ 2 2 A´ 2 2 A˝ 3 2 A˝ 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 IP-CISD IP-CCSD CO(2) bond length, Angstrom Electronic State 1 2 A˝ 1 2 A´ 2 2 A´ 2 2 A˝ 3 2 A˝ 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 CN(2) bond length, Angstrom Electronic State IP-CISD IP-CCSD 1 2 A˝ 1 2 A´ 2 2 A´ 2 2 A˝ 3 2 A˝ 37 123.0 123.5 124.0 124.5 125.0 125.5 126.0 126.5 127.0 127.5 128.0 128.5 129.0 129.5 130.0 CNC(2) angle, Degree Electronic State IP-CISD IP-CCSD 1 2 A˝ 1 2 A´ 2 2 A´ 2 2 A˝ 3 2 A˝ Figure 2.4: The CNC(2) angle in the five lowest electronic states of uracil cation. Dashed line shows the corresponding value at the geometry of neutral. 38 Figure 2.5: The CC bond lengths of the three benzene dimer cation isomers in the ground electronic state optimized with IP-CISD/6-31(+)G(d) and IP-CCSD/6-31(+)G(d). Only the values of the symmetry unique parameters for corresponding sym- metry non-equivalent fragments are shown 1.370 1.375 1.380 1.385 1.390 1.395 1.400 1.405 1.410 1.415 1.420 CC bond length, Angstrom Parameter x-displaced isomer, IP-CISD/6-31(+)G* x-displaced isomer, IP-CCSD/6-31(+)G* C 1 C 2 C 2 C 3 C 3 C 4 C 4 C 5 1.380 1.385 1.390 1.395 1.400 1.405 1.410 1.415 1.420 1.425 CC bond length, Angstrom Parameter y-displaced isomer, IP-CISD/6-31(+)G* y-displaced isomer, IP-CCSD/6-31(+)G* C 1 C 2 C 2 C 3 C 3 C 4 1.370 1.380 1.390 1.400 1.410 1.420 1.430 CC bond length, Angstrom Parameter t-shaped isomer, fragment 1, IP-CISD/6-31(+)G* t-shaped isomer, fragment 1, IP-CCSD/6-31(+)G* C 1 C 2 C 2 C 3 C 3 C 4 12 1.380 1.382 1.384 1.386 1.388 1.390 1.392 1.394 1.396 1.398 1.400 1.402 1.404 CC bond length, Angstrom Parameter t-shaped, fragment 2, IP-CISD/6-31(+)G* t-shaped, fragment 2, IP-CCSD/6-31(+)G* C 1 C 2 C 2 C 3 39 60 80 100 120 140 160 180 200 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Bond length, Angstrom Number of basis functions O 1 H 2 / 1 2 A'' / IP-CISD O 1 O 2 / 1 2 A" / IP-CISD O 1 H 2 / 1 2 A' / IP-CISD O 1 O 2 / 1 2 A' / IP-CISD O 1 H 2 / 1 2 A" / IP-CCSD O 1 O 2 / 1 2 A" / IP-CCSD O 1 H 2 / 1 2 A' / IP-CCSD O 1 O 2 / 1 2 A' / IP-CCSD 60 80 100 120 140 160 180 200 110 120 130 140 150 160 170 180 Angle, Degree Number of basis functions H 1 O 1 H 2 / 1 2 A" /IP-CISD H 3 O 2 H 4 / 1 2 A" /IP-CISD H 1 O 1 H 2 / 1 2 A' /IP-CISD H 3 O 2 H 4 / 1 2 A' /IP-CISD H 1 O 1 H 2 / 1 2 A" / IP-CCSD H 3 O 2 H 4 / 1 2 A" / IP-CCSD H 1 O 1 H 2 / 1 2 A' / IP-CCSD H 3 O 2 H 4 / 1 2 A' / IP-CCSD Figure 2.6: Selected bondlengths and angles in the two lowest electronic states of the water dimer cation optimized with IP-CISD and IP-CCSD with different bases. 40 2.6 Chapter 2 References [1] W.J. Hehre, R. Ditchfield, and J.A. Pople. Self-consistent molecular orbital meth- ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Phys., 56:2257, 1972. [2] A.A. Golubeva and A.I. Krylov. The effect of π -stacking and H-bonding on ion- ization energies of a nucleobase: Uracil dimer cation. Phys. Chem. Chem. Phys., 11:1303–1311, 2009. [3] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople. Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys., 72:650, 1980. [4] P.A. Pieniazek, J. VandeV ondele, P. Jungwirth, A.I. Krylov, and S.E. Bradforth. Electronic structure of the water dimer cation. J. Phys. Chem. A, 112:6159–6170, 2008. [5] T.H. Dunning. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys., 90:1007–1023, 1989. [6] E.D. Glendening, J.K. Badenhoop, A.E. Reed, J.E. Carpenter, J.A. Bohmann, C.M. Morales, and F. Weinhold. NBO 5.0. Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2001. [7] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov. Charge localization and Jahn-Teller distortions in the benzene dimer cation. J. Chem. Phys., 129:074104, 2008. [8] P.A. Pieniazek, S.A. Arnstein, S.E. Bradforth, A.I. Krylov, and C.D. Sherrill. Benchmark full configuration interaction and EOM-IP-CCSD results for proto- typical charge transfer systems: Noncovalent ionized dimers. J. Chem. Phys., 127:164110, 2007. [9] T. Helgaker, P. Jørgensen, and J. Olsen. Molecular electronic structure theory. Wiley & Sons, 2000. 41 Chapter 3 The electronic structure, ionized states and properties of the uracil dimers 3.1 Chapter 3 Overview The electronic structure and spectral properties of ionized uracil and π -stacked and h- bonded uracil dimers are characterized by EOM-IP-CCSD. In Sections 3.3.1 and 3.3.2 we discuss the electronic structure of uracil and uracil dimers, respectively. Section 3.3.3 presents the calculated vertical ionization energies for five lowest electronic states of the monomer and ten lowest electronic states of the dimers. Special attention is given to the monomer basis set effect (Section 3.3.3) as well as the proposed cost-saving energy- additivity scheme (Section 3.3.3). Lastly, we present the electronic spectra of the two uracil dimer cations calculated at the neutral and relaxed geometries (Section 3.3.4). 3.2 Computational details In all calculations of vertical IEs, we employ the uracil dimer structures presented in Fig. 3.1 from the S22 set of Hobza and coworkers [1]. The monomer calculations are 42 C 2h C 2 (a) (b) Figure 3.1: π -stacking and hydrogen-bonding in DNA (top) and the geometries of the stacked (a) and hydrogen-bonded (b) uracil dimers. carried out using the RI-MP2/cc-pVTZ optimized neutral’s geometry. For the calcula- tions of IEs and electronic spectrum of the stacked uracil dimer at the cation geometry, its structure was relaxed with DFT/6-311(+)G(d,p) with 50-50 functional (i.e., equal 43 mixture of the following exchange and correlation parts: 50% Hartree-Fock + 8 % Slater + 42 % Becke for exchange, and 19% VWN + 81% LYP for correlation). Differ- ent isomers were located on the cation potential energy surface, e.g., the t-shaped and stacked-like structures. Here we focus on just one of the stacked uracil dimer isomers. The optimized structures and relative energies of the other isomers will be discussed elsewhere [2]. IEs of the dimers and the monomer were calculated at the EOM-IP-CCSD level using several Pople bases [3, 4], i.e., 6-31(+)G(d), 6-311(+)G(d,p), and others. In the monomer calculations, we also employed the 6-31G(d) and 6-31+G(d) bases with a modifiedd-function exponent (0.2 instead of 0.8) as in Ref. 11. The core orbitals were frozen in the IE calculations. Electronic spectra of the cations were computed at the EOM-IP-CCSD/6-31(+)G(d) level. The monomer spectrum was also calculated with a bigger cc-pVTZ basis set [5]. The molecular structures and relevant total energies are provided in the Supplemen- tary Materials [6]. All calculations were conducted using theQ-CHEM electronic struc- ture package [7]. 44 3.3 Results and Discussion 3.3.1 Prerequisites: Electronic states and spectrum of the uracil cation We begin with a brief overview of the electronic structure of uracil. It is a planar closed- shell molecule of C s symmetry. The five lowest electronic states of the uracil cation correspond to ionizations from the five MOs shown in Fig. 3.2. Among these orbitals, there are two π orbitals of a 00 symmetry corresponding to the C—C and C—O double bonds of uracil; two orbitals of a 0 symmetry corresponding to the oxygen lone pairs, and one a 00 orbital of a mixed character. The highest occupied molecular orbital is π CC . Vertical IEs of the five lowest ionized states of uracil are presented in Table 3.1, and the corresponding electronic spectrum of the uracil cation is shown in Fig. 3.2. The ground state of the cation corresponds to π CC (or 1a 00 ) orbital being singly occu- pied (the corresponding orbital is shown in the picture). Four excited cation states are derived from ionization from the 1a 0 , 2a 00 , 2a 0 or 3a 00 orbitals. All four electron tran- sitions are symmetry allowed, but their intensity is different: the parallel (allowed in x,y-direction) A 00 → A 00 transitions are intense and the perpendicular (allowed in z- direction)A 00 →A 0 transitions are weak due to unfavorable orbital overlap. Overall, the calculated vertical IEs (e.g., with cc-pVTZ) for the monomer are in agreement with the experimentally determined values [8–10], with the exception of the3 2 A 00 transition, for which the calculated IE value at 13 eV is outside the experimental range of 12.5-12.7 eV . 45 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Oscillator Strength Energy, eV π CC / a'' lp(O 2 ) / a' lp(O) + lp(N) / a'' lp(O 1 ) / a' lp(N) + π CC + π CO / a'' Figure 3.2: Electronic spectrum and relvant MOs of the uracil cation at the geometry of the neutral. The MO hosting the hole in the ground state of the cation is also shown (top left). Dashed lines show the transitions with zero oscillator strength. This difference is within the EOM-IP-CCSD error bars (0.2-0.3 eV). The absolute dif- ferences between EOM-IP-CCSD/cc-pVTZ and CASPT2 IEs from Ref.11 are within 0.13-0.49 eV range and are slightly larger than the discrepancies between the EOM-IP- CCSD and the experimental values. Note that the CASPT2 results shown in Table 3.1 are obtained using the empirical IPEA correction [11], which improves the agreement with the experiment (e.g., not IPEA corrected CASPT2 value [11] for the lowest IE is 9.22 eV , which is 0.23 eV below the experimental range). 46 Table 3.1: Five lowest verical IEs (eV) of the uracil monomer calculated with EOM-IP- CCSD. The number of basis functions (b.f.) is given for each basis. Basis b.f. 1 2 A 00 1 2 A 0 2 2 A 00 2 2 A 0 3 2 A 00 6-31G(d) 128 9.13 9.75 10.17 10.75 12.71 6-31G(d) a 128 9.11 9.72 10.11 10.69 12.73 6-31(+)G(d) 160 9.38 10.05 10.44 11.03 12.95 6-31(+)G(d) a 160 9.28 9.92 10.30 10.92 12.88 6-31(2+)G(d) 192 9.39 10.05 10.45 11.03 12.95 6-311(+)G(d,p) 200 9.48 10.11 10.51 11.09 13.02 6-31(2+)G(d,p) 204 9.41 10.07 10.47 11.04 12.97 6-31(+)G(2d) 208 9.45 10.13 10.52 11.10 12.99 6-31(+)G(2d,p) 220 9.46 10.13 10.53 11.11 13.00 6-311(2+,+)G(d) 224 9.43 10.09 10.47 11.07 12.97 6-311(+)G(2d) 228 9.49 10.20 10.57 11.16 13.02 6-311(2+)G(d,p) 232 9.48 10.12 10.52 11.09 13.02 6-311(2+,+)G(d,p) 236 9.48 10.12 10.52 11.09 13.02 6-31(+)G(2df) 284 9.60 10.30 10.69 11.26 13.13 cc-pVTZ 296 9.55 10.21 10.62 11.17 13.08 Exp. b 9.45-9.6 10.02-10.13 10.51-10.56 10.90-11.16 12.50-12.70 CASPT2 c 9.42 9.83 10.41 10.86 12.59 a Modified d-orbital exponent. b Experimental results are from Refs. 8–10 c Empirically corrected (IPEA=0.25) CASPT2/ANO-L 431/21 from Ref. 11 3.3.2 Electronic structure of the uracil dimers Fig. 3.3 displays the calculated Hartree-Fock MOs corresponding to the ten lowest ion- ized states of the stacked uracil dimer and the corresponding ionization energies (IEs) calculated with EOM-IP-CCSD/6-311(+)G(d,p). The ten highest occupied orbitals of the stacked dimer are symmetric and antisymmetric combinations of the five highest occupied FMOs. The biggest splitting (0.53 eV) is between the states derived from bonding and antibonding combinations of theπ -like FMOs, whereas the combinations 47 of FMOs of the lone pair character are almost degenerate. As Fig. 3.4 shows, the elec- 9.14 9.66 10.14 10.20 10.52 10.47 11.07 11.02 12.96 12.67 Orbital energy State energy Figure 3.3: MOs and IEs (eV) of the ten lowest ionized states of the stacked uracil dimer. Ionization from the highest MO yields ground electronic state of the dimer cation, and ionizations from the lower orbitals result in electronically excited states. tronic structure of hydrogen-bonded dimer exhibits similar trends, i.e., the FMOs of the same character are combined to produce bonding and anti-bonding DMOs. The important difference is that the overlap between the FMOs is the biggest for the in- plane orbitals, resulting in the biggest splitting for the DMOs formed from FMOs cor- responding to the lone pairs on the two neighboring oxygens. Overall, the splittings are smaller than in theπ -stacked dimer, i.e., the largest splitting is 0.35 eV , and the splittings between the two lowest states is only 0.10 eV . Note that the orbital splitting does not change state ordering in the dimers relative to the monomer. 48 9.35 9.47 10.20 10.69 10.25 10.72 11.55 11.19 12.83 12.95 Orbital energy State energy Figure 3.4: MOs and IEs (eV) of the ten lowest ionized states of the hydrogen-bonded uracil dimer. Ionization from the highest MO yields ground electronic state of the dimer cation, and ionizations from the lower orbitals result in electronically excited states. 3.3.3 Vertical ionization energies of the monomer and the dimers Monomer ionization energies, transition dipoles, and the basis set effects We investigate the basis set effects using monomer IEs to choose an optimal basis set for the dimer calculations. Basis set convergence is illustrated in Fig. 3.5. The range of the experimental IEs is shown by the shaded areas. As one can see, beyond the 6-311(+)G(d,p) basis the variations in IEs are less than 0.12 eV . The analysis of 49 the data in Table 3.1 leads to the following conclusions. Firstly, the triple-ζ qual- ity basis is desirable, as double-ζ and triple-ζ IEs differ by up to 0.07 eV — com- pare, for example, 6-31(2+)G(d,p) vs. 6-311(2+)G(d,p), and 6-31(+)G(2d) vs. 6- 311(+)G(2d) results. Secondly, the polarization on hydrogens and additional polar- ization on heavy atoms have a noticeable effect on IEs: for example switching from 6-31(2+)G(d) to 6-31(2+)G(d,p) results in a just 0.02 eV change; yet the difference between 6-311(2+,+)G(d) and 6-311(2+,+)G(d,p) values is 0.05 eV . Difference between the 6-31(+)G(2df) and 6-31(+)G(2d) values is 0.17 eV . Lastly, adding diffuse func- tions on hydrogens and extra diffuse functions on heavy atoms has a negligible effect on IEs — compare, for example, 6-31(+)G(d) vs. 6-31(2+)G(d); 6-311(+)G(d,p) vs. 6-311(2+)G(d,p); and 6-311(2+)G(d,p) vs. 6-311(2+,+)G(d,p). Thus, we choose 6- 311(+)G(d,p) as an optimal basis for the dimers. The results with the modified d-orbital exponent [11] do not show systematic improvement over the values obtained with the standard polarization function. Overall, calculated vertical IEs for the monomer are in agreement with the experimentally determined values, with the exception of the 3 2 A 00 transition, for which the calculated IE value at 13 eV is outside the experimental range of 12.5-12.7 eV . The difference is within the EOM-IP-CCSD error bars (0.2-0.3 eV). Another observation is that both the state ordering and the energy gaps between the states do not depend on the basis set, i.e., the curves in Fig. 3.5 are almost parallel. This suggests that cost-reducing energy-additivity schemes can be employed for the IE calculations. 50 6-31G* 6-31(+)G* 6-311(+)G** 6-31(+)G(2d) 6-31(+)G(2df) cc-pVTZ 6-311G(2+,+)** 120 140 160 180 200 220 240 260 280 300 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 X 2 A '' 1 2 A ' 2 2 A '' 3 2 A ' 4 2 A '' Ionization energy, eV Number of basis functions Figure 3.5: Basis set dependence of the five lowest IEs of uracil. The shaded areas represent the range of the expertimental values. Finally, Table 3.2 contains monomer excitation energies and oscillator strengths calculated with different bases ranging from 6-31(+)G(d) to cc-pVTZ. Interestingly, the energies, transition dipole values and oscillator strengths change only slightly with the basis set increase, and the 6-31(+)G(d) basis set appears to be sufficient for the transition property calculations. Dimer IEs and the energy additivity scheme The monomer results from Sec. 3.3.3 suggest to employ the 6-311(+)G(d,p) basis for the dimer IE calculations together with energy-additivity schemes. Here we investi- gate whether these results apply for the dimers, whose description may require a basis 51 Table 3.2: Excitation energies, transition dipole moments and oscillator strengths of the electronic transitions in the uracil cation calculated with EOM-IP-CCSD with different bases. Property Basis 1 2 A 0 2 2 A 00 2 2 A 0 3 2 A 00 Δ E, eV 6-31(+)G(d) 0.668 1.647 1.063 3.566 6-311(+)G(d,p) 0.642 1.614 1.037 3.543 cc-pVTZ 0.664 1.627 1.069 3.533 <μ 2 >, a.u. 6-31(+)G(d) 0.0003 0.0000 0.7888 1.3419 6-311(+)G(d,p) 0.0003 0.0000 0.7859 1.3586 cc-pVTZ 0.0002 0.0000 0.7378 1.3306 f 6-31(+)G(d) 0.0000 0.0000 0.0205 0.1172 6-311(+)G(d,p) 0.0000 0.0000 0.0200 0.1180 cc-pVTZ 0.0000 0.0000 0.0193 0.1152 larger than 6-311(+)G(d,p), i.e., augmented by additional diffuse functions, to accurately describe theπ -stacking or hydrogen-bonding interaction. Tables 3.3 and 3.4 contain calculated IEs for the ten lowest ionized states of the stacked and hydrogen-bonded complexes, respectively. The IE data in Table 3.3 exhibit similar basis set effects as in the monomer. Additional sets of diffuse functions on heavy atoms or hydrogens have negligible effect on IEs, whereas extra polarization leads to noticeable changes in IEs. Overall, the results from Tables 3.3 and 3.4 confirm that the 6-311(+)G(d,p) basis is indeed an optimal choice for the stacked dimer in terms of accu- racy versus computational cost. Surprisingly, a single set of diffuse functions is suf- ficient for adequate representation of the ionized π -stacked dimer, although additional diffuse functions might become more important at shorter interfragment distances. 52 Table 3.3: Ten lowest vertical IEs (eV) of the stacked uracil dimer calculated with EOM-IP-CCSD. State 6-31G(d) 6-31(+)G(d) 6-31(2+)G(d) 6-31(2+)G(d,p) 6-311(+)G(d,p) 6-311(++)G(d,p) 6-311(2+)G(d,p) X 2 B 8.81 9.03 9.04 9.06 9.14 9.14 9.14 1 2 A 9.31 9.56 9.56 9.59 9.66 9.66 9.66 2 2 B 9.77 10.06 10.06 10.07 10.14 10.14 10.14 2 2 A 9.81 10.12 10.12 10.13 10.20 10.19 10.19 3 2 B 10.11 10.38 10.39 10.41 10.47 10.47 10.47 3 2 A 10.15 10.44 10.44 10.46 10.52 10.52 10.52 4 2 B 10.67 10.94 10.94 10.96 11.02 11.02 11.02 4 2 A 10.72 10.99 10.99 11.00 11.07 11.06 11.06 5 2 B 12.38 12.61 12.61 12.63 12.67 12.69 12.68 5 2 A 12.65 12.88 12.88 12.91 12.96 12.96 12.96 b.f. 256 320 384 408 416 424 480 53 Table 3.4: Ten lowest verical IEs (eV) of the hydrogen-bonded uracil dimer calculated with EOM-IP-CCSD. State 6-31G(d) 6-31(+)G(d) 6-311(+)G(d,p) X 2 A u 9.01 9.26 9.35 1 2 B g 9.11 9.37 9.47 1 2 B u 9.84 10.13 10.20 1 2 A g 9.89 10.17 10.25 2 2 B g 10.37 10.62 10.69 2 2 A u 10.35 10.65 10.72 2 2 B u 10.85 11.12 11.19 2 2 A g 11.20 11.49 11.55 3 2 A u 12.53 12.76 12.83 3 2 B g 12.63 12.87 12.95 The stacked dimer IEs from Table 3.3 demonstrate that, similarly to the monomer, the energy spacing between the ionized states remains almost constant in different bases, thus suggesting that energy-additivity schemes can be employed. IEs for the hydrogen-bonded dimer are collected in Table 3.4 and exhibit the same trends as in the stacked dimer. Finally, we describe a simple energy-additivity scheme for the dimer IE calculations. As the IE curves remain parallel both in the monomer and dimer, we approximate the target dimer IEs calculated with a large basis, IE D,large EOM− IP− CCSD , using the dimer IEs calculated with a smaller basis,IE D,small EOM− IP− CCSD , and the monomer IEs calculated with the large and small bases (IE M,large EOM− IP− CCSD andIE M,small EOM− IP− CCSD , respectively): 54 IE D,large EOM− IP− CCSD ≈ IE D,small EOM− IP− CCSD +(IE M,large EOM− IP− CCSD − IE M,small EOM− IP− CCSD ) (3.1) As follows from the data from Tables 3.5 and 3.6, this scheme yields the results that are very close to the exact calculation. All IEs estimated from the dimer 6-31(+)G(d) values are within 0.01-0.02 eV from the full EOM-IP-CCSD/6-311(+)G(d,p) dimer results for both complexes. This difference is negligible compared to the 0.2-0.3 eV error bars of EOM-IP-CCSD. To rationalize the excellent performance of the energy- Table 3.5: Ten lowest verical IEs (eV) of the stacked dimer calculated with EOM-IP- CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results estimated using 6- 31(+)G(d). State IE D 6− 31(+)G(d) Δ IE M 6− 311(+)− 6− 31(+)G(d) IE D,estimated 6− 311(+)G(d,p) IE D 6− 311(+)G(d,p) Abs. Error X 2 B 9.03 0.10 9.13 9.14 0.01 1 2 A 9.56 0.10 9.66 9.66 0.00 2 2 B 10.06 0.07 10.13 10.13 0.00 2 2 A 10.12 0.07 10.19 10.19 0.00 3 2 B 10.38 0.07 10.45 10.46 0.01 3 2 A 10.44 0.07 10.51 10.52 0.01 4 2 B 10.94 0.06 11.00 11.00 0.00 4 2 A 10.99 0.06 11.05 11.05 0.00 5 2 B 12.61 0.08 12.69 12.67 0.02 5 2 A 12.88 0.08 12.96 12.96 0.00 55 Table 3.6: Ten lowest vertical IEs (eV) of the hydrogen-bonded uracil dimer calculated with EOM-IP-CCSD/6-311(+)G(d,p) versus the energy-additivity scheme results esti- mated from 6-31(+)G(d). State IE D 6− 31(+)G(d) Δ IE M 6− 311(+)− 6− 31(+)G(d) IE D,estimated 6− 311(+)G(d,p) IE D 6− 311(+)G(d,p) Abs. Error X 2 A u 9.26 0.10 9.36 9.35 0.01 1 2 B g 9.37 0.10 9.47 9.47 0.00 1 2 B u 10.13 0.06 10.19 10.20 0.01 1 2 A g 10.17 0.06 10.23 10.25 0.02 2 2 B g 10.62 0.07 10.69 10.69 0.00 2 2 A u 10.65 0.07 10.72 10.72 0.00 2 2 B u 11.12 0.06 11.18 11.19 0.01 2 2 A g 11.49 0.06 11.55 11.55 0.00 3 2 A u 12.76 0.07 12.83 12.83 0.00 3 2 B g 12.87 0.07 12.94 12.95 0.01 additivity scheme, let us rewrite Eq. (3.1) separating the dimer and monomer terms as follows: IE D,large EOM− IP− CCSD − IE D,small EOM− IP− CCSD ≈ IE M,large EOM− IP− CCSD − IE M,small EOM− IP− CCSD (3.2) Eq. (3.2) thus implies that the basis set correction is the same for the monomer, stacked or hydrogen-bonded dimer and the splitting between the overlapping FMOs is well reproduced even in a relatively small basis set, i.e., 6-31(+)G(d). 56 3.3.4 The electronic spectra of dimer cations This Section compares the electronic spectra of the monomer and the dimer cations calculated by EOM-IP-CCSD. The transitions are between the states of the cation cor- responding to different orbitals being singly-occupied. Our best estimates, i.e., EOM- IP-CCSD/6-311(+)G(d,p), show that stacking and hydrogen-bonding interactions lower the first ionization energy of the dimer by 0.34 and 0.13 eV , respectively, relative to uracil. The magnitude of the IE decrease in the stacked dimer is remarkably close to that in benzene. Thus, the uracil dimers are ionized more easily than the monomer. Another interesting observation is a relationship between the drop in IE and the degree of initial hole localization. Since a larger IE drop is a consequence of better orbital over- lap, the dimer configurations that ionize easier would feature more extensive initial hole delocalization. This might have mechanistic consequences for the ionization-induced processes in DNA, where different relative nucleobase configurations are present due to structural fluctuations. Electronic transitions in the dimers belong to the two different types, namely, CR (charge resonance) and LE (local excitations). The former are derived from the transitions between the bonding and anti-bonding DMOs, e.g., see Fig. 1.1 and Eqns. (1.12),(1.13), and are unique for the ionized dimers. The latter are the transi- tions between DMOs formed from different FMOs, and resemble the monomer transi- tions. Another difference between the CR and LE transitions is that the transition dipole moment of the former increases linearly with the fragment separation, whereas the LE 57 bands decay [12]. The strong sensitivity of the CR bands to the dimer geometry sug- gests to employ these transitions as a spectroscopic probe of structure and dynamics in ionizedπ -stacked and h-bonded systems. Stacked uracil dimer cation The calculated electronic spectrum of stacked dimer cation at the neutral’s geometry is shown in Fig. 3.6; the corresponding excitation energies, transition dipoles and oscillator strengths are provided in Table 3.7. 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.00 0.02 0.04 0.06 0.08 0.10 Oscillator Strength Energy, eV b a bab a ba b a Figure 3.6: Vertical electronic spectrum of the stacked uracil dimer cation at the geom- etry of the neutral. Dashed lines show the transitions with zero oscillator strength. MOs hosting the unpaired electron in final electronic state, as well as their symmetries, are shown for each transition. The MO corresponding to the initial (ground) state of the cation is shown in the middle. 58 Table 3.7: Oscillator strengths and transition dipole moments for the electronic transi- tions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) at the geometry of the neutral. Transition Δ E, eV <μ 2 >, a.u. f X 2 B →1 2 A 0.523 7.2917 0.0935 X 2 B →2 2 B 1.027 0.0028 0.0000 X 2 B →2 2 A 1.081 0.1503 0.0039 X 2 B →3 2 B 1.349 0.1141 0.0037 X 2 B →3 2 A 1.406 0.5170 0.0178 X 2 B →4 2 B 1.906 0.0023 0.0001 X 2 B →4 2 A 1.952 0.0052 0.0002 X 2 B →5 2 A 3.844 0.3530 0.0332 X 2 B →5 2 B 3.573 0.9990 0.0874 The ground electronic state of the cation is 1 2 B (the respective singly-occupied orbital is shown). All nine arising transitions are allowed by symmetry: the transi- tions of theB → A type are perpendicular, whereas theB → B transitions are parallel with respect to the inter-fragment axis. The four most intense bands correspond to the final electronic states1 2 A, 3 2 A, 5 2 B and5 2 A, the first one giving rise to the CR band. Note that the intensity of the LE transitions between the lone-pair like andπ -like orbitals remains very small. To estimate the effect of geometry relaxation of the cation on the spectrum, we also computed the excitation spectrum at the relaxed dimer cation geometry. The correspond- ing excitation energies, transition dipoles, and oscillator strengths are given in Table 3.8. As in the benzene dimer cation, the optimized geometry of the uracil dimer cation fea- tures shorter interfragment distance that facilitates more efficient orbital overlap. 59 Table 3.8: Oscillator strengths and transition dipole moments for the electronic transi- tions in the ionized stacked uracil dimer calculated with EOM-IP-CCSD/6-31(+)G(d) at the equilibrium geometry of the ionized dimer. Transition Δ E, eV <μ 2 >, a.u. f X 2 B →1 2 A 1.60 6.6438 0.2601 X 2 B →2 2 B 2.08 0.0006 0.0000 X 2 B →2 2 A 2.10 0.0075 0.0003 X 2 B →3 2 B 2.48 0.0721 0.0044 X 2 B →3 2 A 2.63 0.4591 0.0295 X 2 B →4 2 B 3.09 0.0011 0.0000 X 2 B →4 2 A 3.09 0.0008 0.0000 X 2 B →5 2 A 4.88 0.1995 0.0238 X 2 B →5 2 B 4.60 0.7477 0.0842 Fig. 3.7 compares the spectra calculated at the neutral geometry and at the opti- mized geometry of the cation. The intensity pattern is similar to the spectrum at the neutral geometry: the most intense bands correspond to the final electronic states1 2 A, 3 2 A, 5 2 B and5 2 A. A significant increase (approximately threefold) in intensity of the CR band is observed; LE band intensity increases for some electronic states (3 2 A ) and slightly decreases for the others (5 2 B and 5 2 A). Overall, the excitation energies uni- formly increase, with the shift being around 1.1 eV . Hydrogen-bonded uracil dimer cation The spectrum of the hydrogen-bonded dimer at the geometry of neutral is presented in Fig. 3.8. Comparison of this spectrum with the stacked dimer example instantly reveals an important difference, i.e., smaller number of peaks with non-zero intensity owing to 60 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 Oscillator Strength Energy, eV Figure 3.7: Vertical electronic spectra of the stacked uracil dimer cation at two different geometries: the geometry of the neutral (bold lines) and the relaxed cation geometry (dashed lines). MOs hosting the unpaired electron in final electronic state are shown for each transition. higher symmetry of hydrogen-bonded complex. The ground electronic state of cation isX 2 A u and theA u → A u andA u → B u transitions are now forbidden by symmetry. Two transitions derived from the allowed parallel transitions,A u →A g , are also of zero intensity in the spectrum. Three transitions of theA u → B g type are the most intense, among them the X 2 A u → 1 2 B g CR band. The CR band in h-bonded dimer appears at 0.11 eV , which is 0.4 eV below that of the π -stacked dimer, however, its oscillator strength is only slightly smaller (0.076 vs. 0.094). The intensity of the CR transition is lower than the most intense LE transition, i.e.,X 2 A u →3 2 B g . 61 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Oscillator Strength Energy, eV b u a g b g a u b u a g a u a u b g b g Figure 3.8: Vertical electronic spectrum of the hydrogen-bonded uracil dimer cation at the geometry of the neutral. Dashed lines show the transitions with zero oscillator strength. MOs hosting the unpaired electron in final electronic state, as well as their symmetries, are shown for each transition. The MO corresponding to the initial (ground) state of the cation is shown in the middle. 3.4 Conclusions We charactarized the electronic structure of the π -stacked and hydrogen-bonded uracil dimer cations by EOM-IP-CCSD. We computed IEs corresponding to the ground and electronically excited states of the cations and calculated transition dipoles and oscilla- tor sthengths for the electronic transions between the cation states. The results of the calculations are rationalized within DMO-LCFMO framework. Similarly to the benzene dimer, the π -stacking lowers the first IE by about 0.4 eV vertically. The magnitude of the IE decrease correlates with the degree of initial hole 62 localization, as both depend on orbital overlap. Thus, the dimer configurations that ionzie easier would feature a more delocalized hole. Ionization changes the bonding from non-covalent to covalent, which induces sig- nificant geometrical changes, e.g., fragments move closer to each other to maxmize the orbital overlap. The electronic spectra of the ionized dimers feature strong CR bands whose position and intensity is very sensitive to the structure: geometrical relaxation in the π -stacked dimer blue-shifts the CR band by more than 1 eV and results in the three-fold intensity increase. These properties of the CR transitions may be exploited in pump-probe experiments targeting the ionization-induced dynamics in systems with π -stacking interactions, e.g., DNA or RNA strands. The perturbation in the LE bands in the dimer is also described. The hydrogen-bonded dimer features slightly less intense CR bands at lower energies. Benchmark calculations in a variety of basis sets show that 6-311(+)G(d,p) basis yields sufficiently converged IEs, and that energy-additivity scheme based on dimer calculations in a small 6-31(+)G(d) basis allows efficient and accurate evaluation of the dimer IEs. 63 3.5 Chapter 3 References [1] P. Jureˇ cka, J. ˇ Sponer, J. ˇ Cern´ y, and P. Hobza. Benchmark database of accurate (MP2 and CCSD(T) compl ete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys., 8:1985, 2006. [2] A.A. Zadorozhnaya and A.I. Krylov. Ionization-induced structural changes in uracil dimers and their spectroscopic signatures. J. Chem. Theory Comput., 2010. In press. [3] W.J. Hehre, R. Ditchfield, and J.A. Pople. Self-consistent molecular orbital meth- ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Phys., 56:2257, 1972. [4] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople. Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys., 72:650, 1980. [5] T.H. Dunning. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys., 90:1007–1023, 1989. [6] A.A. Golubeva and A.I. Krylov. The effect of π -stacking and H-bonding on ion- ization energies of a nucleobase: Uracil dimer cation. Phys. Chem. Chem. Phys., 11:1303–1311, 2009. [7] Y . Shao, L.F. Molnar, Y . Jung, J. Kussmann, C. Ochsenfeld, S. Brown, A.T.B. Gilbert, L.V . Slipchenko, S.V . Levchenko, D.P. O’Neil, R.A. Distasio Jr, R.C. Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y . Lin, T. Van V oorhis, S.H. Chien, A. Sodt, R.P. Steele, V .A. Rassolov, P. Maslen, P.P. Koram- bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen, A. Drew, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S. Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z. Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y .M. Rhee, J. Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. Woodcock III, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel, W.J. Herhe, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon. Advances in methods and algorithms in a modern quantum chemistry program package. Phys. Chem. Chem. Phys., 8:3172–3191, 2006. [8] D. Dougherty, K. Wittel, J. Meeks, and S. P. McGlynn. Photoelectron spectroscopy of carbonyls. Ureas, uracils, and thymine. J. Am. Chem. Soc., 98:3815, 1976. 64 [9] S. Urano, X. Yang, and P.R. LeBrenton. UV photoelectron and quantum mechani- cal characterization of DNA and RNA bases: Valence electronic structures of ade- nine, 1,9-dimethylguanine, 1-methylcytosine, thymine and uracil. J. Mol. Struct., 214:315, 1989. [10] G. Lauer, W. Sch¨ afer, and A. Schweig. Functional subunits in the nucleic acid bases uracil and thymine. Tetrahedron Lett., 16(45):3939, 1975. [11] D. Roca-Sanju´ an, M. Rubio, M. Merch´ an, and L. Serrano-Andr´ es. Ab initio deter- mination of the ionization potentials of DNA and RNA nucleobases. J. Chem. Phys., 125:084302, 2006. [12] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth. Electronic structure of the benzene dimer cation. J. Chem. Phys., 127:044317, 2007. 65 Chapter 4 Ionization-induced structural changes in uracil dimers and their spectroscopic signatures 4.1 Chapter 4 Overview Ionization-induced structural changes and properties of the three representative isomers of the ionized uracil dimer, i.e. the stacked, t-shaped and h-bonded, are characterized by high-level electronic structure calculations. First we discuss the electronic structure of the t-shaped isomer (Section 4.3.1). Then, the equilibrium geometries (Section 4.3.2), energetics (Section 4.3.3), and electronic spectroscopy (section 4.3.4) are considered. Finally, the benchmark results for density functional theory (DFT) with long-range cor- rected functionals are presented in the Postscript. 66 4.2 Computational detais We used EOM-IP-CCSD in calculations of IEs, electronic spectra, and dissociation ener- gies of the dimers, whereas for geometry optimizations and frequencies we employed IP-CISD andωB97X-D. IP-CISD with the 6-31(+)G(d) basis [1] was used to optimize the SU + 2 and HU + 2 (TS) structures. The TU + 2 and HU + 2 (PT) structures were optimized withωB97X-D and the 6-311(+)G(d,p) basis set [2]. For both the IP-CISD and DFT-D optimizations, tight convergence criteria were enforced: the gradient and energy tolerance were set to3· 10 − 5 and1.2· 10 − 4 respec- tively; maximum energy change was set to1· 10 − 7 . To ensure the accuracy of the DFT-D optimizations we employed the extra-fine EML(99,590) grid. We use the best available geometries for calculations of energy differences. The choice of the geometries is described below. In calculations of vertical properties (i.e., at the equilibrium geometries of the neutral dimers) we used the geometries from the S22 set of Hobza and coworkers [3]. The geometry of the t-shaped isomer was opti- mized with the DFT-D as described above. To assess possible effect of the BSSE on the structures, our study of adenine and thymine dimers [4] compared the B3LYP-D/6- 31+G(d,p) optimized structure of the stacked AT dimer versus the one from the S22 set [3]. We found that the interfragment distance differs from the BSSE-corrected RI- MP2/TZVPP value [3] by only 0.076 ˚ A. The increase of the basis set from 6-31+G(d,p) to 6-311++G(2df,2pd) results in 0.004 ˚ A increase in inter-fragment separation. Thus, we do not expect significant BSSE effects on our optimized structures. 67 In monomer calculations, we used the structures of the uracil cation and the neutral optimized by IP-CISD/6-31(+)G(d) and RI-MP2/cc-pVTZ, respectively, with the stan- dard convergence thresholds (the gradient and energy tolerance3· 10 − 4 and1.2· 10 − 3 and maximum energy change1· 10 − 6 ). In all optimizations of the symmetric structures (i.e., all isomers, except for the TU 0 2 , TU + 2 , and HU + 2 (PT)) the symmetry was enforced. For the stacked dimer cation we carried out an additional DFT-D optimization without the C 2 symmetry constraint that showed that the minimum indeed corresponds to the symmetric structure. In addition, vibrational analysis was also performed. For the accurate energy estimates, single-point calculations were carried out at the geometries obtained as described above. The IP-CCSD method with the 6- 311(+)G(d,p) basis was employed. For benchmark purposes, we also present ωB97X- D/6-311(+)G(d,p)/EML(99,590) estimates calculated at the respective DFT-D minima. The performance of different methods is discussed in the Postscript. While the BSSE corrections can be substantial for weakly-bound systems when compact basis sets are employed [3, 5, 6], using augmented triple-zeta bases reduces the BSSE considerably. Moreover, empirical dispersion correction in DFT-D methods mitigates the BSSE. For example, the counterpoise correction for binding energy in the stacked adenine-thymine dimer at the B3LYP-D/6-311+G(2df) is only 1.4 kcal/mol [4, 7]. For the neutral stacked uracil dimer, theωB97X-D and CCSD values ofD e are 10.5 and 11.1 kcal/mol (with the 6-311(+)G(d,p) basis set), in a good agreement with the 68 CCSD(T)/CBS value of 9.7 kcal/mol [8]. Thus, the BSSE effects are relatively small at the ωB97X-D/6-311(+)G(d,p) level even for the most problematic neutral stacked dimers. In the ionized systems, which are much stronger bound, the effect of BSSE on the binding energy should be even smaller. To quantify this, we computed the counter- poise correction for the stacked uracil dimer cation. The computed BSSE is 1.3 kcal/mol as estimated at theωB97X-D level with 6-311(+)G(d,p) basis set. To obtain the standard thermodynamic quantities and the ZPE corrections, we per- formed the vibrational analysis at theωB97X-D/6-311(+)G(d,p)/EML(99,590) level for all complexes at the respective reoptimized geometries. The electronic spectra of the dimer cations were obtained with IP-CCSD/6- 31(+)G(d) at the cation and neutral geometries described above. All open-shell DFT-D calculations employed the spin-unrestricted references. In these calculations, the spin-contamination of the doublet Kohn-Sham determinant was low with the typicalhS 2 i values of 0.76 - 0.78. All electrons were correlated in all the optimizations; in the single-point energy and spectra calculations the core electrons were frozen unless otherwise stated. The optimized geometries, corresponding reference energies and frequencies are provided in the Supplementary Materials [9]. 69 Throughout this work, we use the following notations for the isomers: HU 2 , SU 2 and TU 2 refer to the h-bonded, stacked and t-shaped isomers, respectively. For the hydrogen- bonded cations, we distinguish between the symmetric structure, which is a transition state (TS), and a proton-transferred one (PT) corresponding to the true minimum. 4.3 Results and discussion 4.3.1 Molecular orbital framework The character of electronic states and the bonding patterns in ionized non-covalent dimers depend strongly on the relative orientation of the fragments [4, 10–13]. Orbital overlap and electrostatic interactions are the most important factors determining the degree of hole delocalization, changes in bond strength due to ionization, and subse- quent nuclear dynamics. When the two fragments are equivalent by symmetry, as in sandwich benzene dimers [10] or stacked C 2 nuclear base dimers [4, 12], the dimer states are derived from in-phase (bonding) and out-of-phase (antibonding) combination of the fragments MOs, and the initial hole is equally delocalized between the two frag- ments. The changes in IE due to dimerization depend on the orbital overlap, e.g., larger changes are observed for the states derived from ionizations of π orbitals [4, 10, 12]. Ionizations from anti-bonding orbitals increase formal inter-fragment bond order, and produce tighter-bound structures, whereas ionizations from the bonding orbitals result in dissociative states. 70 Orbital picture, changes in vertical IEs and initial hole delocalization are similar in symmetric hydrogen bonded dimers, however, the ionization-induced dynamics is more complex and involves proton transfer [4, 14]. The changes in vertical IEs are smaller for most of the states due to a less favorable overlap. In dimers with non-equivalent fragments, the MOs (and, consequently, the initial hole) become more localized, how- ever, changes in IEs and wave functions can also be explained by overlap considerations within DMO-LCFMO framework [11, 13]. Finally, in non-symmetric h-bonded dimers electrostatic interactions become more important than orbital overlap. For example, we observed large changes (0.4-0.7 eV) in IEs and binding energies in some non-symmetric hydrogen-bonded dimers of thymine and cytosine [4,14]. In these dimers, the hole local- ized on one of the fragments is stabilized by the dipole moment of the neutral fragment. The electronic structure of the stacked and symmetric h-bonded uracil dimers at the respective neutral geometries was discussed in detail in Ref. 12. Below we focus on the t-shaped isomer. The principal difference between the t-shaped and the stacked or h- bonded structures is that in the former the two fragments are not equivalent by symmetry, which affects its electronic structure. The ten lowest ionized states of the t-shaped uracil dimer and the corresponding MOs are presented in Figure 4.1. As in the stacked and h-bonded systems, the dimer MOs are formed from the MOs of the fragments, and the ionized states of the dimer correlate well with the states of the monomer (i.e., no mixing of the MOs of different character is observed). For example, the two highest-lying MOs are the linear combinations of the π CC MOs of the fragments. However, the MOs of 71 Ionization Energy, eV 9.13 9.24 9.83 9.94 10.14 10.28 10.71 10.87 12.67 12.72 Figure 4.1: The ten lowest ionized states of the t-shaped uracil dimer at the neutral geometry calculated with the IP-CCSD/6-311(+)G(d,p). the t-shaped dimer are more localized. For example, the lp(O) MO of the dimer is a localizedlp(O) orbital of one of the fragments. For the four delocalized dimer orbitals (formed by the π CC and lp(O)+lp(N) fragment orbitals) the distribution of electron density is also uneven. Owing to a less favorable overlap between the fragment MOs, the splittings between the pairs of ionized states in the t-shaped dimer is smaller. The largest splitting of 0.14 eV was observed for the dimer states derived from from the π -likelp(O)+lp(N) fragment orbitals. Despite less efficient overlap and smaller splittings between the pairs of states derived from the same FMOs, the absolute changes in IEs in this isomer are similar to those in the stacked dimer. For example, the lowest IE of this isomer is 9.13 eV . 72 This value is red-shifted by 0.35, 0.22 and 0.01 eV relative to the 1 st IE of the monomer, symmetric h-bonded andπ -stacked dimers, respectively. This is similar to large changes in IEs observed in the non-symmetric h-bonded dimers of thymine and cytosine, where lowering of IE was due to electrostatic stabilization of the localized hole by the dipole moment of the “neutral” fragment. The dipole moment of uracil is 4.19 D, which is comparable to the dipole moment of thymine (4.11 D). 4.3.2 Ionization-induced structural changes: Equilibrium geome- tries of the uracil dimer cations Ionization induces significant structural changes in the dimers, as can be seen from Fig- ure 4.2. In the analysis below, we distinguish between the changes in the structures of the fragments (and compare those to ionization-induced changes in the monomer) and the inter-fragment relaxation. The definitions of parameters are given in Figure 4.3, and their values are summarized in Tables 4.1 and 4.2. Only the symmetry-unique parameters are given. First, let us consider the effect of ionization on intra-fragment parameters (see Table 4.1) and compare the monomer and the symmetric dimer cations data. The magnitude of relaxation in the monomer is larger than in the stacked and h-bonded dimers. For instance, the C 5 C 6 bond increases by 0.043 ˚ A in the monomer versus 0.018 ˚ A and 0.002 ˚ A in the stacked and h-bonded dimers, respectively. The sign of the change in the monomer and the symmetric dimers is the same for all the parame- ters, which is consistent with the DMO-LCFMO picture. The magnitude of the changes 73 Figure 4.2: The geometries of the cations versus the respective neutrals for the three uracil dimer isomers . SU 2 0 C 2 C 2 SU 2 + TU 2 + TU 2 0 C 1 C 1 C s HU 2 + C 2h HU 2 0 C 2h 74 Figure 4.3: The definitions of the intra- and inter-fragment geometric parameters for uracil dimer isomers. N 1 2 3 4 5 6 1 C 2 N 3 C 4 C 5 C 6 O 1 O 2 H 2 H 1 O 2 N 1 C 5 C 6 F2 F1 O 2 H 1 O 1 H 1 F2 H 2 O 2 O 2 C 5 O 2 C 6 F1 is smaller in the dimers because the hole is delocalized over the two fragments. In the non-symmetric dimers, the fragments are not equivalent and the orbital picture is more complicated. The hole is distributed unevenly between the two fragments, such that the positive charge is localized on one of them. Comparing the data presented in Table 4.1 for the h-bonded proton-transfered and the t-shaped dimer cations with the monomer, we observe that the structural changes of Fragment 1 of HU + 2 (PT), Fragment 2 of TU + 2 and the monomer cation are very similar. For instance, the C 5 C 6 bond increases by 0.057, 0.050 and 0.043 ˚ A in Fragment 1 of HU + 2 (PT), Fragment 2 of TU + 2 and the monomer 75 Table 4.1: The values of optimized structural parameters ( ˚ A, Degree) of the fragments in the stacked, h-bonded, h-transfered h-bonded and t-shaped uracil dimer cations. The differences ( ˚ A, Degree) w.r.t. the equilibrium geometry of the respective neutral complex are also given showing the ionization-induced changes in geometry. See Fig. 4.3 for the definitions of the parameters. Parameter SU + 2 HU + 2 (TS) HU + 2 (PT), F1 HU + 2 (PT), F2 TU + 2 , F1 TU + 2 , F2 U + C 4 C 5 1.461 +0.010 1.461 +0.011 1.461 +0.011 1.458 +0.008 1.431 -0.026 1.475 +0.024 1.457 +0.011 C 5 C 6 1.367 +0.018 1.352 +0.002 1.407 +0.057 1.337 -0.013 1.353 +0.011 1.392 +0.050 1.386 +0.043 C 6 N 1 1.330 -0.038 1.352 -0.017 1.310 -0.059 1.391 +0.022 1.357 -0.012 1.324 -0.045 1.316 -0.049 N 1 C 2 1.405 +0.023 1.379 +0.012 1.411 +0.044 1.332 -0.035 1.389 -0.002 1.429 +0.044 1.433 +0.053 C 2 N 3 1.368 -0.014 1.349 -0.022 1.363 -0.008 1.331 -0.040 1.401 +0.023 1.377 -0.003 1.357 -0.017 N 3 C 4 1.384 -0.017 1.399 -0.008 1.400 -0.007 1.438 +0.031 1.365 -0.032 1.384 -0.007 1.387 -0.010 C 4 O 2 1.198 -0.024 1.190 -0.028 1.204 -0.014 1.194 -0.024 1.257 +0.041 1.206 -0.014 1.195 -0.020 C 2 O 1 1.182 -0.034 1.208 -0.023 1.216 -0.015 1.287 +0.056 1.195 -0.012 1.190 -0.017 1.178 -0.034 C 4 C 5 C 6 119.3 -0.5 119.5 -0.1 119.4 -0.2 120.4 +0.7 118.4 -1.1 119.5 +0.3 119.7 -0.1 C 5 C 6 N 1 121.0 -0.9 121.1 -1.5 123.1 +0.6 121.8 -0.7 121.9 +0.2 120.1 -1.8 119.4 -2.6 C 6 N 1 C 2 124.3 +0.8 123.4 +0.9 120.1 -2.4 121.0 -1.5 123.7 +0.2 124.9 +1.4 125.5 +2.0 N 1 C 2 N 3 113.8 +0.8 115.4 +1.1 118.2 +3.9 118.8 +4.5 112.9 -0.6 113.5 +0.4 113.6 +0.8 C 2 N 3 C 4 126.9 -1.2 126.3 -1.8 125.5 -2.6 125.5 -2.6 126.2 -1.1 127.0 -0.4 126.2 -2.4 N 3 C 4 C 5 114.7 +1.3 114.3 +1.4 113.7 +0.8 112.5 -0.4 116.9 +2.5 114.7 +0.2 115.7 +2.4 Σ (angle) 719.9 +0.3 – – – 720.0 +0.0 719.7 +0.1 720.0 +0.0 76 cation, respectively. Thus, one of the fragments in non-symmetric dimers relaxes simi- larly to the monomer cation, while the other adjusts accordingly. This is similar to the t-shaped benzene dimer [11]. The ionization-induced changes in the inter-fragment parameters (given in Table 4.2) and the MOs (shown in Fig. 4.4) are consistent with the DMO-LCFMO predictions — the fragments adjust their relative orientation to maximize the overlap between their HOMOs (π CC ). The change in the MOs is illustrated in Figure 4.4 depicting HOMOs at the neutral and the cation geometries. In the stacked dimer, the twoπ CC FMOs give rise to the efficient overlap lending a partial covalent character to the ionized dimer. In the t-shaped dimer, the changes in HOMO are different. Upon relaxation, the hole becomes more localized on the lower fragment, and the only contribution to the overlap is due to the the oxygen lone pair of the top fragment pointing towards theπ CC MO of the lower one. The magnitude of the relaxation is quantified by Table 4.3, which presents the dif- ferences in the total energies between the relaxed and vertical structures of the dimer cations calculated by EOM-IP-CCSD/6-311(+)G(d,p). For the t-shaped, stacked and h-bonded isomers,Δ E CCSD is -12.71, -6.48 kcal/mol, and -0.64 kcal/mol respectively. Such a large relaxation effect in the t-shaped cation is somewhat surprising, as from Figure 4.4 the FMOs overlap more efficiently in the stacked dimer. The reason is the electrostatic interaction of the lone pair on oxygen of Fragment 1 and the hole on the Fragment 2, which stabilizes the t-shaped structure [4]. The inter-fragment parame- 77 Table 4.2: The values of inter-fragment structural parameters ( ˚ A, Degree) of the stacked, h-bonded, h-transfered h-bonded and t-shaped uracil dimer cations. The differences ( ˚ A, Degree) w.r.t. the equilibrium geometry of the respective neutral complexes are given in parenthesis. See Fig. 4.3 for the definitions of the parameters. SU + 2 HU + 2 (TS) HU + 2 (PT) TU + 2 C 5 C 6 3.299 (-0.451) O 1 H 1 1.828 (+0.053) O 1 H 1 1.749 (-0.026) H 2 O 2 2.000 (+0.072) O 2 N 1 3.116 (-0.175) O 2 H 1 1.828 (+0.053) O 2 H 1 1.018 (-0.757) O 2 C 5 2.178 (-1.099) O 2 C 6 2.701 (-0.950) α 18.4 (+5.6) – – – d 3.51 (+0.34) – – – 78 Figure 4.4: Two highest occupied MOs of the three isomers of the uracil dimer at the neutral and cation geometry. SU 2 0 SU 2 + HU 2 0 HU 2 + (TS) HU 2 + (HT) TU 2 0 TU 2 + 79 Table 4.3: Total (E tot , hartree) and dissociation (D e , kcal/mol) energies of the four isomers of the uracil dimer in the neutral and ionized states computed by CCSD/IP- CCSD with 6-311(+)G(d,p). Relevant total energies of the uracil monomer are also given. The relaxation energies (Δ E, kcal/mol) defined as the difference in total energies of the cation at the neutral and relaxed cation geometries are also shown. For HU + 2 (PT) dissociation energies corresponding to the U 0 + U + / (U - H) 0 + UH + channels are given. Complex E CCSD tot D CCSD e Δ E CCSD U 0 -413.882 346 – – U + -413.542 383 – -5.41 UH + -414.209 422 – – (U-H) 0 -413.212 558 – – SU 0 2 -827.782 419 11.1 – SU + 2 -827.456 874 20.2 -6.48 HU 0 2 -827.793 226 17.9 – HU + 2 (TS) a -827.450 565 16.2 -0.64 HU + 2 (PT) b -827.475 648 32.0/33.7 – TU 0 2 -827.779 232 9.1 – TU + 2 -827.463 991 24.6 -12.71 a Transition state. b Proton-transferred structure, UH + (U–H)˙. ters presented in Table 4.2 are consistent with the MO changes. In the stacked dimer cation, the fragments slide with respect to each other, so the overlap of FMOs centered on C 5 , C 6 , N 1 and O 2 atoms increases (see Figure 4.4). The C 5 C 6 and O 2 N 1 distances decrease by 0.451 and 0.175 ˚ A, respectively. Surprisingly, the distance between the centers-of-masses of the fragments increases by 0.34 ˚ A in the cation with respect to the neutral. This illustrates that the average geometric parameters in polyatomic systems can be misleading. 80 In the t-shaped cation, the fragments move to minimize the distance between the lone pair on O 2 of the top fragment and the π CC MO of the bottom one. The characteristic parameters in this case are the O 2 C 5 and O 2 C 6 distances, which decrease by 1.099 and 0.950 ˚ A, respectively. In the symmetric h-bonded dimer, the structural changes and, consequently, relax- ation energy are small. As one can see from Figure 4.4, there is also no significant changes in MOs upon relaxation due to unfavorable orbital overlap. Moreover, this symmetric structure is a transition state, as shown by the vibrational analysis discussed later. Much larger stabilization is achieved by a proton transfer, which lowers the total energy by 15.7 kcal/mol making the proton-transfered h-bonded isomer the lowest- energy structure on the cation’s PES. 4.3.3 Binding energies of the neutral and ionized uracil dimers: Potential and free energy calculations Potential energy profile Figures 4.5 and 4.6 present the relative ordering and binding energies of the neutral and ionized uracil dimers calculated by IP-CCSD and ωB97X-D with the 6-311(+)G(d,p) basis. In the neutral, the symmetric h-bonded uracil dimer is the minimum energy isomer, with the stacked and t-shaped dimers lying 6.8 and 8.8 kcal/mol higher in energy. Excluding the proton-transferred dimer, the lowest-energy cation structure is the 81 HU 2 0 SU 2 0 TU 2 0 C 1 C 2h C 2 -D e , kcal/mol D e = 17.9 / 19.4 D e = 11.1 / 10.5 D e = 9.1 / 8.3 Figure 4.5: The binding energies (kcal/mol) of the three isomers of neutral uracil dimer calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) and ωB97X-D/6- 311(+)G(d,p) (italic). t-shaped one. The energy spacing between the t-shaped and the stacked and h-bonded cations is 4.4 and 8.4 kcal/mol, respectively. Upon the proton transfer the total energy of the h-bonded cation is lowered by 15.8 kcal/mol, so that it lies 7.4 kcal/mol below than the t-shaped cation. The calculated binding energies for the h-bonded, stacked and t-shaped neutral dimers are 17.9, 11.1 and 9.1 kcal/mol, respectively. The DFT-D and CCSD values are within 1 kcal/mol from each other. TheD e for the stacked and h-bonded isomer are also in good agreement with the recent CCSD(T)/CBS values of 20.4 and 9.7 kcal/mol from Ref. 8. Note that the interaction of the fragments in the neutral uracil dimers is much stronger than in the benzene dimers, where the typical interaction energies lie in range 82 TU 2 + C 1 SU 2 + C 2 HU 2 + (TS) C 2h HU 2 + (PT) Cs -D e , kcal/mol D e = 24.6 / 27.0 D e = 20.2 / 24.2 D e = 16.2 / 20.2 D e = 32.0 / 31.2 D e ′ = 33.7 / 38.2 Figure 4.6: The binding energies (kcal/mol) of the three isomers of uracil dimer cation calculated at two levels of theory: IP-CCSD/6-311(+)G(d,p) (bold) and ωB97X-D/6- 311(+)G(d,p) (italic). For the proton-transfered h-bonded uracil dimer cation, the bind- ing energies corresponding to the two dissociation limits are presented. of 1.5-3.0 kcal/mol for all isomers [15, 16]. The binding energies increase upon ion- ization, in agreement with the DMO-LCFMO predictions. In the t-shaped, stacked and symmetric h-bonded cations the fragments are bound by 24.6, 20.2 and 16.2 kcal/mol, respectively. For comparison, in the benzene dimer cation the binding energies are 20 and 12 kcal/mol for the sandwich and t-shaped isomers, respectively [10,11]. However, the strongest interaction is observed in the proton-transfered h-bonded cation, where the binding energy corresponding to the U 0 +U + dissociation channel is 32.0 kcal/mol (this channel lies 1.8 kcal/mol below an alternative (U-H) 0 +UH + channel). In conclusion, when the uracil dimer is ionized the interaction between the fragments increases almost two-fold for the stacked and h-bonded isomers and more than two-fold 83 for the t-shaped isomer. Such a strong increase in interaction in the t-shaped structure is very different from the benzene dimer cation and can be explained by electrostatic interactions rather than orbital overlap considerations. The h-bonded isomer is stabilized by the proton transfer. Free energy profile It has been argued that the entropy contribution to the stability can be important in the nucleobase dimer systems favoring stacked isomers over h-bonded ones [17]. Thus, we performed the vibrational analysis using ωB97X-D. Moreover, we wanted to quantify the zero point energy (ZPE) corrections to the dissociation energies. The calculated dissociation energies and the standard thermodynamic quantities for the dissociation of the neutral and the ionized dimers are given in Table 4.4. Table 4.4: The dissociation energies (kcal/mol) and standard thermodynamic quantities of the neutral and the cation uracil dimers calculated at the ωB97X-D/6-311(+)G(d,p) level. For the proton-transfered cation the values corresponding to the two different dissociation limits are given. Reaction D e D 0 Δ H 0 , kcal/mol Δ S 0 , cal/mol× K Δ G 0 , kcal/mol SU 0 2 →U 0 +U 0 10.5 9.8 8.4 31.5 -1.0 SU + 2 →U 0 +U + 24.4 22.7 20.9 40.4 8.8 HU 0 2 →U 0 +U 0 19.4 18.2 16.8 38.1 5.4 HU + 2 (TS)→U 0 +U + 20.2 21.8 23.2 40.5 11.1 HU + 2 (TS)→HU + 2 (PT) 11.0 13.1 -8.8 2.7 -9.6 HU + 2 (PT)→U 0 +U + 31.2 30.6 -0.7 37.7 18.7 HU + 2 (PT)→(U − H) 0 +UH + 38.2 37.0 -1.3 38.6 24.2 TU 0 2 →U 0 +U 0 8.3 7.6 6.2 29.6 -2.6 TU + 2 →U 0 +U + 27.0 25.1 23.0 38.8 11.4 84 Among the neutral uracil dimers, only the h-bonded isomer is predicted to be stable under the standard conditions (Δ G 0 = 5.4 kcal/mol). Standard Gibbs free energies, Δ G 0 , of the stacked and t-shaped are -1.0 and -2.6 kcal/mol, respectively. The data in Table 4.4 shows that the entropy contribution is similar for all three isomers: Δ S 0 of dissociation is 31.5, 38.1 and 29.6 cal/mol× K for the stacked, h-bonded and t-shaped isomers, respectively. However, more appropriate treatment including anharmonicities may discriminate between the isomers more. The enthalpy contribution is different: for the h-bonded uracil dimer the enthalpy of dissociation is 16.8 kcal/mol, whereas the corresponding values for the stacked and t-shaped isomers are 8.4 and 6.2 kcal/mol, respectively. Unlike neutrals, all of the dimer cation isomers are stable under the standard con- ditions. The most stable isomer is the proton-transfered h-bonded cation with Δ G 0 of 18.7 kcal/mol. In order of the decreasing stability, the proton-transferred dimer is fol- lowed by the t-shaped, symmetric h-bonded (TS) and the stacked isomers. Again, the Δ S 0 values are very close for all of the isomers being 40.4, 40.5, 37.7 and 38.8 for SU + 2 , HU + 2 (TS), HU + 2 (PT) and TU + 2 , respectively, whereas the Δ H 0 contributions are different. Thus, we conclude that the enthalpy determines the relative stability of the neutral and ionized uracil dimers to a high degree, while the entropy contribution has a less pronounced effect. 85 Lastly, the ZPE corrections lower the dissociation energy estimates by 0.6–1.9 kcal/mol for all the neutral and ionized dimers, except for the symmetric h-bonded dimer. In the symmetric h-bonded dimer, the ZPE correction has the opposite sign and increases the dissociation energy by 1.6 kcal/mol, which is because this structure is a transition state with one imaginary frequency. 4.3.4 The electronic spectra of the uracil dimer cations This section presents the calculated electronic spectra of the uracil dimer cations. The spectra of the stacked and h-bonded isomers at the geometry of the neutral were described in a detail in the previous work [12], therefore, we focus on the effect of geom- etry relaxation on the spectroscopic properties. For the h-bonded dimer, we present the spectra of both the symmetric (TS) and the proton-transfered structures. Figures 4.7-4.9 present the electronic spectra of the stacked, h-bonded and t-shaped uracil dimers, respectively, calculated by IP-CCSD/6-31(+)G(d) at the neutral and the cation geometries. Figures 4.7-4.9 also show the character of the electronic states cor- responding to the three most intense transitions in each spectra. The transition energies, transition dipole moments and oscillator strengths are provided in Tables 4.5– 4.8. The spectrum of the stacked dimer at the neutral geometry is dominated by the three intense lines at 0.5, 3.5 and 3.8 eV (see Fig. 4.7). The first peak is the CR band, which is unique to the dimer, while the others are the local excitations (LE) between the states of cation with the various π -orbitals singly occupied. Upon geometric relaxation, the 86 spectrum shifts to the higher energies by approximately 0.8 eV , so the lines appear at 1.2, 4.4, and 4.6 eV . The intensity of the charge resonance band increases more than two-fold upon relaxation. The h-bonded dimer cation spectra at the geometry of the 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 Oscillator Strength Energy, eV Energy, eV SU 2 0 SU 2 + Energy, eV ΔE = 0.524 ΔE = 3.573 ΔE = 3.844 ΔE = 1.248 ΔE = 4.390 ΔE = 4.622 Figure 4.7: The electronic spectra (top panel) of the stacked uracil dimer cation at the neutral (solid black) and the cation (dashed blue) geometries calculated with IP- CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intense transitions (bottom panel). 87 Table 4.5: The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the stacked dimer cation at the geometry of the neutral and cation, IP-CCSD/6-31(+)G(d). neutral cation Transition Δ E <μ 2 > f Δ E <μ 2 > f X 2 B →1 2 A 0.524 7.2918 0.0935 1.248 7.4212 0.2269 X 2 B →2 2 B 1.023 0.0028 0.0000 1.799 0.0010 0.0000 X 2 B →2 2 A 1.081 0.1503 0.0040 1.809 0.0197 0.0009 X 2 B →3 2 B 1.349 0.1141 0.0038 2.190 0.0709 0.0038 X 2 B →3 2 A 1.406 0.5171 0.0178 2.362 0.4090 0.0237 X 2 B →4 2 B 1.906 0.0024 0.0001 2.798 0.0010 0.0000 X 2 B →4 2 A 1.952 0.0053 0.0003 2.800 0.0016 0.0001 X 2 B →5 2 B 3.573 0.3531 0.0333 4.390 0.7613 0.0819 X 2 B →5 2 A 3.844 0.9990 0.0875 4.622 0.2323 0.0263 neutral (see Fig. 4.8) features two intense lines at 0.1 and 3.6 eV and a small peak at 1.3 eV . As in the stacked cation, these lines are the CR band and two local excitations (LE) corresponding to the transition between theπ -orbitals of cation (see Fig. 4.8). The CR band is less intense than in the stacked cation and the most intense transition is the LE at 3.6 eV . The spectrum at the transition state structure exhibits only minor differ- ences, i.e, 0.1 eV blue shifts in peak positions with the intensities remaining the same. However, the spectrum and the character of states changes dramatically upon proton transfer. A new band appears at 2.5 eV . The localized character of the states and C s symmetry make the proton-transfered h-bonded cation spectrum very similar to that of the uracil cation. In the t-shaped cation spectra at the neutral geometry, the CR and 88 0.00.5 1.01.5 2.02.5 3.03.5 4.04.5 5.05.5 6.06.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Oscillator Strength Energy, eV HU 2 0 HU 2 + (TS) HU 2 + (HT) Energy, eV Energy, eV Energy, eV ΔE = 0.113 ΔE = 1.358 ΔE = 3.615 ΔE = 0.121 ΔE = 1.632 ΔE = 3.835 ΔE = 2.475 ΔE = 3.650 ΔE = 3.984 Figure 4.8: The electronic spectra (top panel) of the h-bonded uracil dimer cation at the neutral (solid black), symmetric transition state (dashed blue) and the proton-transferred cation (dash-dotted pink) geometries calculated with IP-CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intense transitions (bottom panel). the two intense LE transitions appear at 0.1, 3.5 and 3.6 eV (see Fig. 4.9). The spec- trum is very similar to that of the h-bonded isomer at the neutral geometry. As in the stacked and h-bonded cations, the transitions between the π -like orbitals are the most 89 Table 4.6: The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the symmetric h-bonded dimer cation at the geometry of the neutral and cation, IP-CCSD/6-31(+)G(d). neutral cation Transition Δ E <μ 2 > f Δ E <μ 2 > f X 2 A u →1 2 B g 0.113 27.4607 0.0763 0.121 28.7406 0.0849 X 2 A u →1 2 B u 0.871 0.0000 0.0000 1.064 0.0000 0.0000 X 2 A u →1 2 A g 0.915 0.0003 0.0000 1.123 0.0003 0.0000 X 2 A u →2 2 B g 1.358 0.2527 0.0084 1.632 0.3048 0.0122 X 2 A u →2 2 A u 1.391 0.0000 0.0000 1.683 0.0000 0.0000 X 2 A u →2 2 B u 1.867 0.0000 0.0000 1.954 0.0000 0.0000 X 2 A u →2 2 A g 2.232 0.0000 0.0000 2.381 0.0000 0.0000 X 2 A u →3 2 A u 3.501 0.0000 0.0000 3.740 0.0000 0.0000 X 2 A u →3 2 B g 3.615 1.3026 0.1154 3.835 1.2053 0.1133 intense. However, the character of the states is different — the states are more local- ized. Upon relaxation, the spectrum changes completely, as does the character of the states. The maximum intensity increases 2.5 times, new intense lines appear in the 1.7-3.0 eV and 4.5-5.0 eV regions. The orbital picture is now much more complex — the DMOs become combinations of several FMOs. Thus, the electronic transitions can no longer be described as CR or LE excitations. The most intense bands correspond to the transitions between the cation states with the π CC orbital and the lp(O) orbital singly occupied and are of charge-transfer character. To summarize, the three isomers have distinctly different spectra, which can be used to distinguish between them exper- imentally. Moreover, significant changes upon relaxation may be exploited to monitor 90 Table 4.7: The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the h-bonded dimer cation at the optimized proton- transferred geometry, IP-CCSD/6-31(+)G(d). Transition Δ E <μ 2 > f X 2 A 00 →1 2 A 0 1.702 0.0004 0.0000 X 2 A 00 →2 2 A 00 2.475 0.7690 0.0466 X 2 A 00 →2 2 A 0 2.782 0.0040 0.0003 X 2 A 00 →3 2 A 0 3.325 0.0024 0.0002 X 2 A 00 →3 2 A 00 3.650 0.0605 0.0054 X 2 A 00 →4 2 A 00 3.984 1.1704 0.1142 X 2 A 00 →4 2 A 0 4.493 0.0001 0.0000 X 2 A 00 →5 2 A 00 5.343 0.0162 0.0021 X 2 A 00 →5 2 A 0 6.082 0.0039 0.0006 ionization-induced dynamics in a pump-probe experiment. Immediately upon the ion- ization, the isomers will exhibit the intense lines in the three regions: 0.0-0.7 eV , 1-1.5 eV and 3.0-4.0 eV . While the spectra of the h-bonded and t-shaped dimers at the neu- tral geometry are similar, the stacked cation can be distinguished by the two peaks of moderate intensity in the 0.5-0.7 eV 3.5-4.0 eV regions. Upon the relaxation, the most intense CR band of the stacked isomer shifts to 1.2 eV and acquires additional intensity. The relaxation of the t-shaped cation manifests itself by significant growth of intensity in the 2.5-3.0 eV region. The hydrogen-bonded complex is more difficult to distinguish because of the overlap of its spectral lines with the stacked and t-shaped spectra. Still, the signature of proton transfer is the 0.3-0.4 eV blue shift of the intense transition in the 3.5-4.0 eV region. 91 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 Oscillator Strength Energy, eV TU 2 0 TU 2 + Energy, eV ΔE = 0.108 ΔE = 3.561 Energy, eV ΔE = 3.613 ΔE = 2.622 ΔE = 2.945 ΔE = 4.757 Figure 4.9: The electronic spectra (top panel) of the t-shaped uracil dimer cation at the neutral (solid black) and the cation (dashed blue) geometries calculated with IP- CCSD/6-31(+)G(d) and the electronic states corresponding to the three most intense transitions (bottom panel). 4.4 Conclusions We characterized the electronic structure of the three representative isomers of the ion- ized uracil dimers: h-bonded, stacked, and t-shaped. The interactions 92 Table 4.8: The excitation energies (Δ E, eV), transition dipole moments (< μ 2 >, a.u.) and oscillator strengths (f) of the t-shaped dimer cation at the geometry of the neutral and cation, IP-CCSD/6-31(+)G(d). neutral cation Transition Δ E, eV <μ 2 >, a.u. f Δ E, eV <μ 2 >, a.u. f X 2 A 1 →2 2 A 1 0.108 18.4996 0.0488 1.866 0.5715 0.0261 X 2 A 1 →3 2 A 1 0.725 0.1761 0.0031 2.384 0.7506 0.0438 X 2 A 1 →4 2 A 1 0.841 0.0436 0.0009 2.622 1.8376 0.1180 X 2 A 1 →5 2 A 1 1.031 0.1376 0.0035 2.750 0.0428 0.0029 X 2 A 1 →6 2 A 1 1.176 0.5961 0.0172 2.945 1.1927 0.0861 X 2 A 1 →7 2 A 1 1.609 0.0095 0.0004 3.324 0.0042 0.0003 X 2 A 1 →8 2 A 1 1.776 0.0261 0.0011 3.584 0.3711 0.0326 X 2 A 1 →9 2 A 1 3.561 0.6475 0.0565 4.757 0.6759 0.0788 X 2 A 1 →10 2 A 1 3.613 0.6276 0.0555 5.539 0.0295 0.0040 between the fragments lower vertical IEs by 0.13-0.35 eV , the largest drop in IE being observed for the stacked and t-shaped isomers. Interestingly, the character of the ionized states and the origin of the IE change is different in these two isomers. In the stacked dimer, the hole is delocalized between the two fragments, and orbital overlap determines the change in IE. In the t-shaped isomer, the hole is localized, and the change in IE is due to electrostatic interactions between the “ionized” and the “spectator” frag- ment. The change in IE for the symmetric h-bonded dimer is small, because neither overlap nor electrostatic interactions can stabilize the hole, however, larger changes are expected for the non-symmetric h-bonded dimers [4]. The geometric relaxation is also different for the three isomers. The stacked isomer relaxes to tighter structure with more efficient overlap between the FMOs, and the hole 93 remains delocalized between the fragments. The h-bonded isomer undergoes proton transfer forming lowest-energy structure on the cation’s surface in which the charge and the unpaired electron are localized on different moieties. Finally, the t-shaped dimer relaxes to the structure with the localized hole. The respective binding energies of the cation isomers are 20.2, 32.0 and 24.6 kcal/mol. Finally, we characterized the electronic spectra of the cations at the neutral and the relaxed geometries. At the neutral geometry, the h-bonded and stacked isomers feature intense CR bands at 0.1 and 0.5 eV , respectively. The CR band in the t-shaped isomer is less intense, and appears at the same energy as in the h-bonded dimer (0.1 eV). For all three isomers, the spectra change dramatically upon relaxation. In the stacked isomer, the intense CR band shifts to higher energies (i.e., from 0.5 to 1.3 eV) and becomes even more intense. In the h-bonded isomer, the CR bands (present at the neutral geometry at 0.1 eV) disappears upon proton transfer, and the spectrum becomes very similar to that of the monomer. In the t-shaped isomer, new intense lines corresponding to the charge- transfer transitions develop at 2.5-3.0 eV . Thus, the spectra evolution in these isomers is rather different, which may be exploited for their experimental determination. Postscript: Performance ofωB97X-D for the structures and energet- ics of non-covalent neutral and ionized dimers Self-interaction corrected functionals provide more reliable (although not fully satis- factory) description of the ionized non-covalent dimers than the standard non-corrected 94 functionals. To investigate the performance of theωB97X-D functional [18] as an inex- pensive alternative to more reliable wave function methods, we benchmarked this func- tional using the stacked uracil isomer. We compared the intra and inter-fragment struc- tural parameters of the ωB97X-D/6-311(+)G(d,p) optimized geometries of the neutral and cation to the best available geometries. For the neutral system, the geometry from the S22 set of Hobza and coworkers was used as a benchmark [3]. For the cation, we used the IP-CISD/6-31(+)G(d) optimized geometry for comparison. The average abso- lute errors and the standard deviations for the bond lengths and angles in the DFT-D optimized geometries were calculated. In the neutral, the average absolute error and the standard deviation for bond lengths were 0.004 and 0.003 ˚ A, respectively; the average absolute error and standard deviation for angles were 0.247 and 0.182 Degree. In the cation, the corresponding values were 0.010 and 0.005 ˚ A, 0.377 and 0.233 Degree. As of the inter-fragment parameters, in the neutral the DFT-D parameters (C 5 C 6 and O 2 N 1 ) differ by less than 0.05 ˚ A from the geometry from the S22 set, while in the cation the DFT-D overestimated them by 0.15 ˚ A comparing to the IP-CISD/6-31(+)G(d) value. Given the tendency of IP-CISD to overestimate the inter-fragment distances in weakly bound systems by 0.2-0.3 ˚ A (as compared to more accurate IP-CCSD [19]), the DFT-D geometry of the cation may be more accurate than the IP-CISD one. We conclude that theωB97X-D structures are reasonably accurate, which validates the use of this method for geometry optimizations of our system. 95 To assess the performance of the ωB97X-D functional for the energetics, we com- puted the dissociation energies for all isomers of the neutral and cation dimers and com- pared them to the IP-CCSD/6-311(+)G(d,p) values. The results are summarized in Fig- ures 4 and 5. ωB97X-D predicts the correct relative ordering of the neutral and cation isomers. Quantitatively, the DFT-D errors in dissociation energies with respect to the IP- CCSD values are in 1-2 kcal/mol range for the neutral dimers and in 1-5 kcal/mol range for the cations. The errors inD e are non-systematic. Therefore, DFT-D withωB97X-D functional provides a correct qualitative picture for energetics; the quantitative predic- tions are of moderate accuracy, so a more reliable approach should be employed. 96 4.5 Chapter 4 References [1] W.J. Hehre, R. Ditchfield, and J.A. Pople. Self-consistent molecular orbital meth- ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Phys., 56:2257, 1972. [2] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople. Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys., 72:650, 1980. [3] P. Jureˇ cka, J. ˇ Sponer, J. ˇ Cern´ y, and P. Hobza. Benchmark database of accurate (MP2 and CCSD(T) compl ete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys., 8:1985, 2006. [4] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov. The effect of π -stacking, h-bonding, and electrostatic interactions on the ionization energies of nucleic acid bases: Adenine-adenine, thymine-thymine and adenine-thymine dimers. Phys. Chem. Chem. Phys., 2010. in press, DOI:10.1039/b919930f. [5] D. Roca-Sanju´ an, M. Merch´ an, and L. Serrano-Andr´ es. Modelling hole-transfer in DNA: Low-lying excited states of oxidized cytosine homodimer and cytosine- adenine heterodimer. Chem. Phys., 349:188–196, 2008. [6] G. Olaso-Gonz´ ales, D. Roca-Sanju´ an, L. Serrano-Andr´ es, and M. Merch´ an. Toward understanding of DNA fluorescence: The singlet excimer of cytosine. J. Chem. Phys., 125:231002, 2006. [7] K. Bravaya. Private communication. [8] M. Pitoˇ n´ ak, K.E. Riley, P. Neogr´ ady, and P. Hobza. Highly accurate CCSD(T) and DFT-SAPT stabilization energies of H-bonded and stacked structures of the uracil dimer. Comp. Phys. Comm., 9:1636–1644, 2008. [9] A.A. Zadorozhnaya and A.I. Krylov. Ionization-induced structural changes in uracil dimers and their spectroscopic signatures. J. Chem. Theory Comput., 2010. In press. [10] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth. Electronic structure of the benzene dimer cation. J. Chem. Phys., 127:044317, 2007. [11] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov. Charge localization and Jahn- Teller distortions in the benzene dimer cation. J. Chem. Phys., 129:074104, 2008. 97 [12] A.A. Golubeva and A.I. Krylov. The effect of π -stacking and H-bonding on ion- ization energies of a nucleobase: Uracil dimer cation. Phys. Chem. Chem. Phys., 11:1303–1311, 2009. [13] P.A. Pieniazek, J. VandeV ondele, P. Jungwirth, A.I. Krylov, and S.E. Bradforth. Electronic structure of the water dimer cation. J. Phys. Chem. A, 112:6159–6170, 2008. [14] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed. Ionization of cytosine monomer and dimer studied by VUV photoionization and electronic structure cal- culations. Phys. Chem. Chem. Phys., 2010. In press, DOI: 10.1039/B921498D. [15] M.O. Sinnokrot and C.D. Sherrill. Highly accurate coupled cluster potential energy curves for the benzene dimer: Sandwich, t-shaped, and parallel-displaced config- urations. J. Phys. Chem. A, 108:10200–10207, 2004. [16] M.O. Sinnokrot and C.D. Sherrill. High-accuracy quantum mechanical studies of pi-pi interactions in benzene dimers. J. Phys. Chem. A, 110:10656–10668, 2006. [17] M. Kratochvil, O. Engkvist, J. Sponer, P. Jungwirth, and P. Hobza. Uracil dimer: Potential energy and free energy surfaces. Ab initio beyond Hartree-Fock and empirical potential studies. J. Phys. Chem. A, 102(35):6921–6926, 1998. [18] J.-D. Chai and M. Head-Gordon. Long-range corrected hybrid density function- als with damped atom-atom dispersion interactions. Phys. Chem. Chem. Phys., 10:6615–6620, 2008. [19] A.A. Golubeva, P.A. Pieniazek, and A.I. Krylov. A new electronic structure method for doublet states: Configuration interaction in the space of ionized 1h and 2h1p determinants. J. Chem. Phys., 130(12):124113, 2009. 98 Chapter 5 Ionized states of dimethylated uracil dimers 5.1 Chapter 5 Overview Electronic structure, equillibrium geometries and properties of 1,3-dimethyluracil and its dimer are characterized by electronic structure calculations. Section 5.3.1 discusses the structures and binding energies of several low-lying neutral isomers. We investigate the effect of methylation on the ionized states of the monomer and the dimers, and quantify the changes in IEs due toπ -stacking interactions (Section 5.3.2). The structural relaxation in the ionized systems and the binding energies of the cations are discussed in Section 5.3.3, as well as the electronic spectra of the monomer and the lowest-energy dimer isomer. 99 5.2 Computational details In this study, we employed a variety of ab initio techniques. The structures were obtained as follows. For the monomer, we employed the RI-MP2/cc-pVTZ and IP- CISD/6-31(+)G(d) methods [1, 2] in the neutral and the cation optimizations, respec- tively. Different starting geometries were used in optimizations including theC s andC 1 conformers with different angles of rotation of the CH 3 groups. We found that both the neutral and the ionized 1,3-dimethyluracil haveC s structures in which only the hydro- gens of the CH 3 groups lie out of plane. By considering the two main factors contributing to the stability of the stacked dimers, i.e., electrostatic interactions and steric repulsion, five starting geometries were generated for the optimization, which employed a DFT-D method with the ωB97X-D functional [3], the 6-311(+,+)G(2d,2p) basis set [4], and the EML(75,302) grid. The basis set and grid combination was chosen based on the numerical tests, which showed that calculations with smaller bases, e.g., 6-311(+,+)G(d,p), and smaller grids fail to reproduce the degeneracy of enantiomeric structures. Tight convergence criteria were enforced in all optimizations, with the gradient and energy tolerance set to3· 10 − 5 and 1.2· 10 − 4 , respectively, and the maximum energy change 1· 10 − 7 . For the only sym- metric isomer we carried out additional optimization without the symmetry constraint, which proved that the minimum-energy structure is indeedC i symmetric. The same level of theory was used in the dimer cation optimizations. We used the neutral structures as the starting geometries. All cation optimizations employed the 100 spin-unrestricted references. The spin-contamination of the doublet Kohn-Sham deter- minant was low with the typical hS 2 i values within the 0.76 - 0.77 range. Just like in the neutrals, the C i symmetry of the only symmetric isomer was tested by additional optimizations without theC i constraint. The dissociation and ionization energies and the electronic spectra of the cations were then calculated with the IP-CCSD method and a moderate 6-31(+)G(d) basis set. In the monomer calculations, we also employed a larger 6-311(+)G(d,p) basis to investigate the basis set effect on ionization energies. Core electrons were frozen in the single-point IP-CCSD energy and spectra calculations. Optimized geometries, relevant total energies, and harmonic frequencies are given in the Supplementary Materials [5]. The data on the non-methylated uracil monomer and dimer to which we frequently refer in this work are from Refs. 10, 18. All calculations were performed using theQ-CHEM electronic structure program [6]. 101 5.3 Results and Discussion 5.3.1 Potential energy surface of the neutral dimers: Structures and energetics Nucleobase dimers form numerous isomers [7–9], which can be described as the stacked, t-shaped and h-bonded structures. Three representative isomers from each man- ifold have been characterized in our recent study of the uracil dimer [10]. The h-bonded structure corresponds to the global energy minimum in non-methylated species. Methylation at nitrogens reduces polarity of the molecule, eliminates hydrogens that can participate in h-bonding, and introduces bulky groups. These factors destabilize the t-shaped and h-bonded structures of the 1,3-dimethyluracil dimers. The molecular dynamics study by Hobza and coworkers [11] showed that the potential energy sur- face (PES) of the 1,3-dimethyluracil dimers is dominated by the stacked structures, the t-shaped isomers lying 5-6 kcal/mol higher in energy and h-bonded isomers being unsta- ble. Our calculations usingωB97X-D/6-311(+)G(d,p) found an h-bonded-like structure (which is better described as a van der Waals dimer) about 10 kcal/mol above the stacked manifold. Thus, we focus on the stacked isomers of the 1,3-dimethyluracil dimer. The five optimized structures of the neutral stacked 1,3-dimethyluracil are shown in Figure 5.1; the corresponding binding and relative energies calculated withωB97X- D/6-311(+,+)G(2d,2p) and CCSD/6-31(+)G(d) are summarized in Tables 5.1 and 5.2, respectively. The lowest-energy structure of the dimethylated uracil dimer is non- 102 Isomer 1 (0) D e =13.8 / 15.9 Isomer 2 (+1.2) D e =12.6 C i C 1 D e =12.4 Isomer 3 (+1.5) D e =11.7 Isomer 4 (+2.2) C 1 C 1 D e =10.9 Isomer 5 (+2.9) C 1 Figure 5.1: Five isomers of the stacked neutral 1,3-dimethyluracil dimer and their bind- ing energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energy structure and other isomers are given in the parenthesis. All values were obtained with ωB97X-D/6-311(+,+)G(2d,2p) except for theD e value of isomer 1 shown in bold, which is the IP-CCSD/6-31(+)G(d) estimate. symmetric isomer 1, which is similar to the minimum-energy stacked uracil structure from the S22 set by Hobza and coworkers [12]. This isomer is followed by isomers 2 (C i ), 3 (C 1 ), 4 (C 1 ) and 5 (C 1 ) lying 1.2, 1.5, 2.2, and 2.9 kcal/mol higher in energy, respectively. The energy gaps between the isomers are very small: the five isomers lie in just 2.9 kcal/mol range, and some of them are nearly degenerate, i.e., separated by 0.3 kcal/mol. These energy differences are of the order of kT(298.18 K) = 0.6 kcal/mol, which suggests significant populations of all these isomers at the standard conditions. The dense π -stacked manifold and structural motifs are similar to stacked thymine 103 Table 5.1: The total (hartree) and dissociation energies (kcal/mol) of the neutral and ionized 1,3-dimethyluracil monomer and dimers calculated at the ωB97X-D/6- 311(+,+)G(2d,2p) level of theory. Complex E tot DFT− D D DFT− D e mU 0 -493.431022 – mU + -493.111429 – S(mU) 0 2 , isomer 1 -986.884084 13.8 S(mU) 0 2 , isomer 2 -986.882142 12.6 S(mU) 0 2 , isomer 3 -986.881741 12.4 S(mU) 0 2 , isomer 4 -986.880611 11.7 S(mU) 0 2 , isomer 5 -986.879409 10.9 S(mU) + 2 , isomer 1 -986.587029 28.0 S(mU) + 2 , isomer 2 -986.570893 17.9 S(mU) + 2 , isomer 3 -986.578185 22.4 S(mU) + 2 , isomer 4 -986.576570 21.4 T(mU) + 2 , isomer 5 -986.572944 19.1 dimers [13], where five isomers lie within 2.2 kcal/mol. Interestingly, no low-energy stacked isomers were identified for dimers of another pyrimidine, cytosine dimer [14]. The binding energies of the neutral stacked 1,3-dimethyluracil dimers lie in the range of 10.9-13.8 kcal/mol, as computed by DFT-D. For the lowest-energy isomer we also computed the CCSD/6-31(+)G(d) value. The resulting binding energy of 15.9 kcal/mol is in a good agreement with 13.8 kcal/mol computed with ωB97X-D/6-311(+)G(d,p). Based on our results for uracil [10], using larger basis set in CCSD calculations lowers the CCSD binding energy and improves the agreement between the methods. The binding energy of the lowest energy isomer (13.8 kcal/mol) is larger than that of the stacked non-methylated uracil dimer for which D e = 10.5 kcal/mol (these are 104 Table 5.2: The total (hartree) and dissociation energies (kcal/mol) of the neutral and ionized 1,3-dimethyluracil and its dimer (lowest energy isomer) calculated at the IP- CCSD/6-31(+)G(d) level of theory. For the monomer and the dimer cations, the relax- ation energy (Δ E CCSD relax , kcal/mol) is provided. a The uracil and uracil dimer IP-CCSD/6- 31(+)G(d) results b are included for comparison. Complex E tot CCSD D CCSD e Δ E CCSD relax mU 0 -492.032033 – – mU + -491.715681 – -3.8 S(mU) 0 2 , isomer 1 -984.089466 15.9 – S(mU) + 2 , isomer 1 -983.798612 31.9 -11.2 U 0 -413.683919 – – U + -413.345482 – -4.1 SU 0 2 -827.387312 12.2 – SU + 2 -827.069011 24.9 -8.7 a The difference between the total energies of the cation at the vertical and the relaxed geometries. b For these estimates, we employed same structures as in Ref. 10 For the stacked uracil dimer cation, the DFT-D/ωB97X-D/6-311(+)G(d,p) optimized geometry was used. DFT-D values, but the similar trend is observed for the CCSD/6-31(+)G(d) binding energies, which are 15.9 and 12.2 kcal/mol). For comparison, the binding energy of the lowest stacked thymine and adenine homodimers are 12.5 kcal/mol and 10.6 kcal/mol, respectively [13]. An increase in binding energy upon methylation is somewhat surprising, as methy- lated uracil is less polar than uracil (the RI-MP2/cc-pVTZ dipole moments are 4.19 D versus 4.02 D) and, therefore, one may expect weaker electrostatic interaction between the fragments in the 1,3-dimethyluracil dimer. However, this difference appears to be too small, and local electrostatic interactions play a more important role. The anal- ysis of the structures reveals that the (NCH 2 )H δ + ··· O δ − (C) distance in the stacked 105 1,3-dimethyluracil dimer is shorter than the (N)H δ + ··· O δ − (C) distance in the stacked uracil dimer, which results in stronger electrostatic interaction between the fragments in the former complex. A tighter structure of the methylated dimer is also counterin- tuitive because of the presence of the bulky methyl groups. The observed increase in binding energy upon substitution is consistent with the results of Sherrill and cowork- ers [15, 16], who demonstrated that the electrostatic considerations alone are not suffi- cient to explain the changes in binding inπ -stacked systems upon substitution and that differential changes in dispersion interactions play an important role. 5.3.2 The effect of methylation on the ionized states of the monomer and the dimers 1,3-dimethyluracil Figure 5.2 presents the five highest occupied MOs of 1,3-dimethyluracil and uracil and the corresponding VIEs calculated at the IP-CCSD/6-311(+)G(d,p) level. The shapes of the MOs are similar in the two molecules, except for the σ CH electronic density on the CH 3 groups of 1,3-dimethyluracil. Another minor difference can be seen in the lp(N)+π CC +π CO orbital, which is more localized in dimethylated uracil. The order of the ionized states in methylated uracil is the same as in uracil. The HOMO is the π -like MO centered at the C–C double bond, and the corresponding IE is 8.87 eV . This state is followed by ionization from the two lone pair and two π -like 106 8.87 9.77 9.74 10.66 12.16 π CC / a´´ lp(N)+lp(O) / a´´ lp(O 1 ) / a´ lp(O 2 ) / a´ lp(N)+ π CC + π CO / a´´ Ionization Energy, eV 9.48 10.51 10.11 11.09 13.02 π CC / a´´ lp(N)+lp(O) / a´´ lp(O 1 ) / a´ lp(O 2 ) / a´ lp(N)+ π CC + π CO / a´´ Ionization Energy, eV Figure 5.2: The five lowest ionized states and the molecular orbitals of dimethyluracil (top) and uracil (bottom) calculated by IP-CCSD/6-311(+)G(d,p). orbitals with VIEs of 9.74 (lp(O 1 )), 9.77 (lp(O)+lp(N)), 10.66 (lp(O 2 )) and 12.16 eV (lp(N)+π CC +π CO ). However, the values of IEs and the spacings between the ionized states are different. Methylation lowers the first IE by 0.6 eV relative to uracil. Similar effect is observed 107 for other states: the VIEs of 1 2 A 0 , 1 2 A 00 , 2 2 A 0 and 2 2 A 00 states decrease by 0.37, 0.74, 0.43 and 0.86 eV , respectively. Note that for the oxygen lone-pair states, the magnitude of the effect is smaller than for the states derived from ionization from π -like orbitals. The largest shifts are observed for the states with large contributions from lone pairs of nitrogens, which are primary substitution sites. As a result, the1 2 A 0 and1 2 A 00 states that are separated by 0.4 eV in uracil become almost degenerate in 1,3-dimethyluracil. The Table 5.3: The five lowest ionized states and the corresponding IEs (eV) of the 1,3- dimethyluracil at the vertical geometry calculated by IP-CCSD with the 6-31(+)G(d) and 6-311(+)G(d,p) bases. The IE shifts (eV) with respect to the uracil values are given in parenthesis. Basis X 2 A 00 1 2 A 0 1 2 A 00 2 2 A 0 2 2 A 00 6-31(+)G(d) 8.77 (-0.61) 9.67 (-0.38) 9.69 (-0.75) 10.58 (-0.45) 12.07 (-0.88) 6-311(+)G(d,p) 8.87 (-0.61) 9.74 (-0.37) 9.77 (-0.74) 10.66 (-0.43) 12.16 (-0.86) IEs are lowered due to electron-donating CH 3 groups increasing electron density in the ring (destabilization of the respective MOs) and due to a larger size of the methylated species contributing to hole stabilization. The effect is larger in the states derived from ionization from delocalized π orbitals, in which the CH 3 group donates the electron density to the π system via the lp(N) component, whereas the in-plane lp(O) orbitals are affected less. Dimethyluracil dimers Similarly to other π -stacked dimers [10, 13, 17, 18], the electronic structure and ion- ized states of the 1,3-dimethyluracil dimer can be described within the DMO-LCFMO 108 framework [17]. The molecular orbitals of the dimer (DMOs) shown in Figure 5.3 are the in- and out-of-phase combinations of the FMOs. Figure 5.3 also presents the cor- responding IEs. Because of the lower symmetry, some of the electronic states of the methylated uracil dimer are localized on individual fragments. The first IE of the 1,3- Ionization Energy, eV 9.42 9.66 9.69 9.85 10.51 10.46 11.88 11.67 8.40 8.81 Figure 5.3: The ten lowest ionized states and the corresponding MOs of the lowest- energy isomer of the neutral stacked 1,3-dimethyluracil computed with IP-CCSD/6- 31(+)G(d). dimethyluracil dimer corresponds to ionization from the π CC (F1)− π CC (F2) DMO. Stacking interaction lowers it by 0.37 eV relative to the monomer, i.e, 8.40 eV versus 8.77 eV as calculated at the IP-CCSD/6-31(+)G(d) level. Thus, the magnitude of the effect is comparable to that in the non-methylated stacked uracil dimer and the stacked thymine dimer (both have 0.35 eV decrease in IE), whereas the shift in adenine dimer is smaller (0.2 eV) [13]. 109 The order of the ionized states in the 1,3-dimethyluracil dimer is different from the uracil dimer. In the latter (as well as in the stacked thymine dimer, see Ref. 13), the states corresponding to the in- and out-of-phase FMO combinations appear pair by pair in the same order as the respective monomer states. In the methylated uracil dimer, the states arising from ionization from lp(O 1 ) FMOs lie in between the pair of states corresponding to thelp(O)+lp(N) FMOs. The largest splittings between the pairs of states are observed for the states derived from the π -like FMOs owing to their larger overlap. Compare, for example, the 0.41, 0.43 and 0.21 eV splittings for the states derived from ionization from theπ -like orbitals to the 0.06 and 0.03 eV splittings for the lone-pair states. Overall, the magnitude of the splittings in methylated and non-methylated dimers is similar, except for the lp(O)+lp(N) pair of states (0.43 eV vs. 0.06 eV in the 1,3-dimethyluracil and uracil dimers, respectively). Due to large weight oflp(N), these MOs are most affected by the electron-donating CH 3 groups. The increased electron density in theπ -system results in larger overlap and, consequently, larger splittings. This large splitting is responsible for different state ordering. So far, this is the first example of that type — in all other model systems we have studied (benzene, water, uracil, and adenine dimers) the stacking inter- actions did not change the relative order of the ionized states, even though the splittings in different pairs of states were quite different. 110 5.3.3 Ionization-induced changes in the monomer and the dimers: Structures and properties Ionization induces considerable structural changes. For the lowest ionized state, relax- ation pattern is consistent with the MO character. In the uracil monomer, double CC bond elongates inducing the changes in an entire bond-alternation pattern [10]. In the dimer, these changes are accompanied by the rings re-orienting to increase the over- lap between the respective FMOs [10]. Methylated species show very similar behavior. Below we discuss changes in binding energies and relative order of the isomers and characterize spectroscopic signatures of the structural relaxation. Binding energies of the dimer cations Figure 5.4 presents five relaxed structures of the 1,3-dimethyluracil dimer cations. The total and dissociation energies of the dimer cations estimated by ωB97X-D are given in Table 5.1; and the CCSD/6-31(+)G(d) estimates for the lowest-energy isomer are provided in Table 5.2. Similarly to the neutral dimers, the global minimum corresponds to isomer 1 (C 1 ). However, in all other aspects the PES of the dimer cation differs drastically from that of the neutral. The order of the isomers and the energy gaps between them change upon ionization. Following isomer 1, isomers 3, 4, 5 and 2 lie 5.6, 6.6, 8.8 and 10.1 kcal/mol higher in energy. In contrast to the neutral, the five minima on the cation PES are well-separated in energy. For example, the two lowest-energy structures are more than 5 kcal/mol 111 Isomer 1 (0) D e = 28.0 / 31.9 Isomer 2 (+10.1) D e = 17.9 C i C 1 D e = 22.4 Isomer 3 (+5.6) D e = 21.4 Isomer 4 (+6.6) C 1 C 1 D e =19.1 Isomer 5 (+8.8) C 1 Figure 5.4: Five low-lying isomers of the 1,3-dimethyluracil dimer cation and the disso- ciation energies (kcal/mol). The energy spacings (kcal/mol) between the lowest-energy structure and other isomers are given in the parenthesis. All values were obtained with ωB97X-D/6-311(+,+)G(2d,2p) except for the D e value of isomer 1 (shown in bold), which is the IP-CCSD/6-31(+)G(d) estimate. apart, whereas all five neutral isomers lie within 2.9 kcal/mol interval. Thus, we expect dominant population of the lowest-energy structure (isomer 1) of the cation under the standard conditions. Another difference is the appearance of the t-shaped dimer cation (isomer 5) among low-lying structures. It is 8.8 kcal/mol above the isomer 1 (but 1.5 kcal/mol below one of the stacked structures). The dissociation energies of 1,3-dimethyluracil cations fall within the 17.9-28.0 kcal/mol range, as computed with DFT-D. Therefore, the fragments in ionized dimers are bound 1.4 to 2.0 times stronger than in the neutral dimers with the largest and the smallest increases observed for isomers 1 and 2, respectively. The magnitude of the 112 increase is similar to that observed in the uracil dimers. Note that, similarly to the neu- tral dimers, the interaction between the fragments is stronger in the methylated dimers than in the non-methylated analogues. The best estimate of the binding energy for the lowest-energy cation structure (isomer 1) is 31.9 kcal/mol (at IP-CCSD/6-31(+)G(d) level), which is 7.0 kcal/mol larger than that of the stacked uracil dimer (24.9 kcal/mol at IP-CCSD/6-31(+)G(d) level). The binding energy of the ionized stacked thymine dimer is similar to that of uracil, i.e., 19.8 kcal/mol. The increase of binding energy upon methylation can be explained by the increased electron density in the π -system resulting in larger overlap, and is consistent with a slightly larger change of IE due to dimerization. Another contribution into the binding energy comes from the geometric relaxation, which is larger in the methylated dimer relative to the non-methylated species (11.2 versus 8.7 kcal/mol). The corresponding relaxation energies in both monomers are about 3-4 kcal/mol (see Table 5.2). Larger geometric relaxation in the methylated dimer is similar to the results for the stacked thymine and adenine homodimers [13], where the difference between VIE and AIE was 15.0 kcal/mol and 11.3 kcal/mol for TT and AA, respectively, and the corresponding monomer values were 5-6 kcal/mol. Equilibrium geometries of the cations The ionization-induced changes in geometry and the electronic structure of isomers 1-5 of the 1,3-dimethyluracil dimer are illustrated in Figures 5.5- 5.9. In each picture, the neutral and the cation geometries and the two highest MOs of the dimer are shown. The 113 analysis of these five cases reveals two distinct trends. In isomers 1,2 and 4 (Group 1), the relaxation results in the increased FMO overlap and, consequently, the delocalized DMOs at the cation geometry. Isomers 3 and 5 (Group 2) exhibit a different pattern: the DMOs are localized on one of the fragments at the cation geometry and no signifi- cant FMO overlap develops upon the relaxation. In both structureslp(O) of one of the fragments moves toward the hole centered on π CC MO of the other fragment. Thus, Group 2 cations are stabilized by the favorable electrostatic interaction of the localized hole and the negative charge on lp(O). This motif, which is similar to the t-shaped uracil dimer [10], demonstrates that electrostatic interactions can be competitive with the hole delocalization effects even in the stacked systems. Therefore, two factors are responsible for the stabilization of the ionized 1,3-dimethyluracil dimer cations: the DMO-LCFMO mechanism in which the stabilization of the ionized state is proportional to the FMO overlap [17], and the electrostatic mechanism [10, 13, 14]. The magnitude of relaxation is comparable for the two mechanisms, e.g., in Group 1 the binding energy increases 1.4 to 2.0 times relative to the neutrals, and for Group 2 the increase is 1.7 to 1.8 fold. However, one may expect that the DMO-LCFMO stabilization is more sensitive to relative orientation of the fragments than electrostatic interactions and that the constrained environments (e.g., DNA) may discriminate between the two effects, although it is clear how strong perturbation by the backbone can affect relative strengths of these interactions. 114 (mU) 2 0 isomer 1 (mU) 2 + isomer 1 D e =28.0 / 31.9 D e =13.8 / 15.9 (mU) 2 0 isomer 1 (mU) 2 + isomer 1 Figure 5.5: The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 1 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6- 311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d) MOs are presented. Let us now compare the absolute values of the binding energies for isomers 1-5. For the Group 1 isomers stabilized via DMO-LCFMO mechanism, the strongest and the weakest inter-fragment interaction is observed in isomer 1 (28.0 kcal/mol) and symmet- ric isomer 2 (17.9 kcal/mol), respectively. The difference between these two cases is 115 (mU) 2 0 isomer 2 (mU) 2 + isomer 2 D e =17.9 D e =12.6 (mU) 2 0 isomer 2 (mU) 2 + isomer 2 Figure 5.6: The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 2 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6- 311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d) MOs are presented. apparent from Figures 5.5 and 5.6. In isomer 1, the DMOs look more like a bonding orbital, whereas isomer 2 fails to develop significant FMO overlap. Isomer 4 (see Fig- ure 5.8) lies in between these two limiting cases with the moderate overlap and binding energy of 21.4 kcal/mol. In Group 2, the values of binding energies are less diverse, 116 (mU) 2 0 isomer 3 (mU) 2 + isomer 3 D e =22.4 D e =12.4 (mU) 2 0 isomer 3 (mU) 2 + isomer 3 Figure 5.7: The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 3 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6- 311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d) MOs are presented. which is consistent with the electrostatic stabilization mechanism. In isomers 3 and 5 the fragments are bound by 22.4 and 19.1 kcal/mol, respectively. 117 (mU) 2 0 isomer 4 (mU) 2 + isomer 4 D e =21.4 D e =11.7 (mU) 2 0 isomer 4 (mU) 2 + isomer 4 Figure 5.8: The ionization-induced changes in geometry, binding energies (kcal/mol) and the MOs of isomer 4 of the stacked 1,3-dimethyluracil dimer. The ωB97X-D/6- 311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d) MOs are presented. Electronic spectra of the cations 1,3-dimethyluracil The electronic spectra of the methylated uracil and uracil cations at the vertical and relaxed geometries calculated by IP-CCSD/6-31(+)(d) are shown in Figure 5.10. Table 5.4 provides the values of transition energies, dipole moments and 118 (mU) 2 0 isomer 5 D e =19.1 D e =10.9 (mU) 2 + isomer 5 (mU) 2 0 isomer 5 (mU) 2 + isomer 5 Figure 5.9: The changes in geometry, binding energies (kcal/mol) and the MOs of isomer 5 of the stacked 1,3-dimethyluracil dimer at ionization. The ωB97X-D/6- 311(+,+)G(2d,2p) optimized structures, dissociation energies and the HF/6-31(+)G(d) MOs are presented. oscillator strengths. Owing to the similarity in their structures and MOs, the spectra of methylated and non-methylated uracil cation are very similar (see Figure 5.10). In both cases, the two bright transitions correspond to the transitions between the states of the cations with theπ -orbitals singly-occupied. The methylated uracil spectrum is slightly 119 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Oscillator Strength Energy, eV π CC / a´´ lp(N)+lp(O) / a´´ lp(N)+ π CC + π CO / a´´ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Oscillator Strength Energy, eV π CC / a´´ lp(N)+lp(O) / a´´ lp(N)+ π CC + π CO / a´´ Figure 5.10: The electronic spectra of 1,3-dimethyluracil (left) and uracil (right) at the vertical (solid black) and the relaxed (dashed blue) geometries calculated by IP- CCSD/6-31(+)G(d). blue-shifted. The effect of the geometry relaxation on the spectra is larger in the uracil cation than in the 1,3-dimethyluracil cation with the line shifts of +0.7-0.8 eV for the former and +0.5-0.6 eV for the latter. This can be explained by the electron-donating properties of the CH 3 groups which reduce the effect of ionization on the structure. 120 Table 5.4: The electronic spectrum of the 1,3-dimethyluracil cation at the vertical and relaxed geometries calculated at the IP-CCSD/6-31(+)G(d) level. neutral cation Transition Δ E, eV <μ 2 >, a.u. f Δ E, eV <μ 2 >, a.u. f X 2 A 00 →1 2 A 0 0.899 0.0004 0.0000 1.269 0.0004 0.0000 X 2 A 00 →1 2 A 00 0.917 0.5222 0.0117 1.557 0.3996 0.0152 X 2 A 00 →2 2 A 0 1.809 0.0000 0.0000 2.399 0.0000 0.0000 X 2 A 00 →2 2 A 00 3.297 1.6952 0.1369 3.822 1.4258 0.1335 1,3-dimethyluracil dimer cation Table 5.5 presents IEs of isomer 1 computed at the vertical and relaxed geometries. The respective MOs are shown in Figure 5.3. Due to low symmetry and large size of the methylated dimer we only computed the exci- tation energies, as calculations of the oscillator strengths for the electronic transitions in the cation are more computationally expensive than just energy calculations. How- ever, the intensities of the peaks can be estimated based on the intensities in the uracil dimer cation [10, 18] and DMO-LCFMO analysis (see Ref. 17 for the DMO-LCFMO nomenclature), as explained below. These results are visualized in Figure 5.11. In the stacked uracil dimer cation, the ψ − (π ) → ψ + (π ) and ψ − (π ) → ψ − (π ) transi- tions (i.e. the transitions between the electronic states derived from the ionization from the DMOs composed out of π -like FMOs) are intense, whereas the ψ − (π ) → ψ + (lp) and ψ − (π ) → ψ − (lp) transitions are weak. Analogously to the stacked uracil dimer, in the methylated dimer cation spectrum at the vertical geometry, we expect at least three intense peaks: at 0.41, 1.45 and 3.27 eV . The former peak is the CR band, and the latter two are the local excitations (LE) involving other π -like DMOs, i.e. the 121 Table 5.5: The ionization energies (eV) and the DMO character a corresponding to the ten lowest ionized states of the stacked 1,3-dimethyluracil dimer at the vertical geometry (isomer 1) calculated at the IP-CCSD/6-31(+)G(d) level. neutral cation State DMO IE DMO E ex X 2 A 1 ψ − (π CC ) 8.40 (-0.63) ψ − (π CC ) 0.00 1 2 A 1 ψ + (π CC ) 8.81 (-0.75) ψ + (π CC ) 1.48 2 2 A 1 ψ − (lp(O)+lp(N)) 9.42 (-0.96) ψ − (lp(O)+lp(N)) 1.99 3 2 A 1 lp(O 1 ), F1 9.66 (-0.40) ψ − (lp(O 1 ) 2.15 4 2 A 1 lp(O 1 ), F2 9.69 (-0.43) ψ + (lp(O 1 ) 2.18 5 2 A 1 ψ + (lp(O)+lp(N)) 9.85 (-0.59) ψ + (lp(O)+lp(N)) 2.44 6 2 A 1 lp(O 2 ), F1 10.46 (-0.48) ψ − (lp(O 1 ) 3.07 7 2 A 1 lp(O 2 ), F2 10.51 (-0.48) ψ + (lp(O 1 ) 3.09 8 2 A 1 ψ − (lp(N)+π CC +π CO ) 11.67 (-0.94) ψ − (lp(N)+π CC +π CO ) 4.25 9 2 A 1 ψ + (lp(N)+π CC +π CO ) 11.88 (-1.00) ψ + (lp(N)+π CC +π CO ) 4.37 a In the DMO-LCFMO notations [17], theψ + (ν ) andψ − (ν ) represent the bonding and antibonding combinations of the MOs of fragments 1 and 2 (ν F1 andν F2 ). b The shifts of IEs (eV) of the dimethylated uracil dimer relative to the non-methylated analogue are given in parenthesis. For the relaxed cation, the excitation energies (eV) calculated at IP-CCSD/6-31(+)G(d) level are presented. ψ + (lp(O)+lp(N) andψ − (lp(N)+π CC +π CO ). The transition dipole moment is related tos ν F1 ν F2 , the overlap of the FMOs on fragments 1 and 2, by the following equation: I(ψ − (ν )→ψ + (ν ))∝ R AB √ 1− s ν F1 ν F2 , (5.1) whereR AB is the inter-fragment distance. Upon the geometry relaxation, the states of the dimer become more delocalized, as can be seen in Fig. 5.5 showing the two highest-occupied DMOs at the neutral and 122 0.00.51.01.52.02.53.03.5 4.04.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 Oscillator strength Energy, eV 1 2 A 1 5 2 A 1 X 2 A 1 8 2 A 1 Figure 5.11: The three most intense transitions in the electronic spectrum of the lowest isomer of stacked 1,3-dimethyluracil cation at vertical (solid black) and cation (dashed blue) geometries. The DMOs corresponding to the ground state (framed) and excited states (regular) are shown. The positions of the peaks were calculated at IP-CCSD/6- 31(+)G(d) level, while the intensities are from the non-methylated dimer calculations. cation geometries. The states derived from thelp(O 1 ) andlp(O 2 ) FMOs are no longer localized on one of the fragments, as they were at the vertical geometry (not shown). Thus, we expect the following changes in the spectrum. The increasing overlap between theψ + (π CC ) andψ − (π CC ) DMOs leads to the growth of the intensity of CR band, which shifts to 1.48 eV upon the relaxation. Based on the similarity of the methylated and non- methylated systems, we expect the intensity of the CR band to (at least) double at the relaxed geometry. The position of the LE band that appears at 1.45 eV at the vertical geometry shifts to 2.44 eV; however, as follows from the FMO overlaps and splittings 123 no considerable increase of intensity is expected. Finally, the LE transition at 3.27 eV in the vertical spectrum shifts by +1.0 eV and its intensity decreases upon relaxation. 5.4 Conclusions The structures, binding energies, properties of several isomers of the neutral and ionized 1,3-dimethylated uracil dimers are characterized using ab initio methods. The methyla- tion suppresses the formation of hydrogen-bonded and t-shaped neutral structures, how- ever, the π -stacked manifold is rather dense. Five lowest isomers of the stacked dimer lie within the 2.9 kcal/mol range, which suggests that all of the isomers will be present at the standard conditions. The binding energies of the neutral dimers are in the range of 10.9-13.8 kcal/mol (DFT-D). Surprisingly, in sterically-constrained and less polar methylated species the fragments are bound stronger than in the non-methylated analogs (the corresponding DFT-D estimate for the stacked uracil dimer is 10.5 kcal/mol). The MOs of the uracil are only slightly perturbed by the CH 3 group; however, the effect is significant for the values of IEs. The methylation lowers the first IE of the 1,3- dimethyluracil by 0.6 eV as compared to uracil; the higher-lying states also exhibit red shifts of a varying magnitude (0.37-0.86 eV). This IE lowering is due to the electron- donating CH 3 groups, which increase the electron density in the ring and stabilize the ionized state. The effect is bigger in the states derived from ionization from the delocal- ized π orbitals, in which the electron density is efficiently donated to the π -system via 124 thelp(N) component. The magnitude of the effect correlates with the weight oflp(N) in the leading MO, which is not surprising as nitrogens are the primary substitution sites. Similarly to uracil dimer, the electronic structure of the methylated uracil dimer is well described by DMO-LCFMO. The stacking interactions lower the first IE by 0.37 eV in the methylated dimers, which is very similar to 0.35 eV lowering in the non- methylated system (and the stacked dimer of thymine). Another important finding is the 0.6 eV lowering of the IE in the methylated dimer due to the methylation: the effect is the same as in the monomer. It implies that the effect of substitutions can be incor- porated into the qualitative DMO-LCFMO picture as a constant shifts of the dimer and monomer levels, whereas the splittings between the in-phase and out-of-phase DMOs are surprisingly insensitive to the substitution, except for the states derived from orbitals with large weights of lp(N). These states exhibit much larger splittings than in non- methylated species (i.e., 0.43 versus 0.06 eV), which ultimately results in changes in the states ordering. This is different from other model systems that we have studied (ben- zene, water, uracil, and adenine dimers) where the stacking interactions do not change the relative order of the ionized states, even though the splittings in different pairs of states are quite different. Ionization changes the bonding pattern inducing considerable changes in structures and binding energies. The energy separation between the isomers increases, so one can expect dominant population of the lowest isomer at the standard conditions. The binding energies increase 1.4-2.0 fold upon ionization and lie in 17.9-28.0 kcal/mol 125 range (DFT-D); for the lowest-energy dimer cation structure, the IP-CCSD value ofD e is 31.9 kcal/mol. This binding energy is larger than that in the non-methylated uracil and thymine dimers. Similarly to the neutrals, the methylation increases the inter-fragment interaction in the dimer. The relaxation of the cation structures is governed by two distinct mechanisms: the hole delocalization (and the FMO overlap) and the electrostatic stabilization (interaction of thelp(O) with the localized hole). Finally, we presented electronic spectra of the ionized species. Significant changes in the spectra upon relaxation can be exploited to monitor the ionization-induced dynam- ics in dimethylated uracils. At the vertical geometry, there are three intense transitions: at 0.41, 1.45 and 3.27 eV , the CR band at 0.41 eV and LE at 1.45 eV being the most intense. Upon relaxation, these bands are blue-shifted, and their intensities change to 1.48 (CR), 2.44 (LE) and 4.25(LE) eV . The CR band at 1.48 eV is expected be the most intense and can be used to monitor the relaxed stacked dimer cation formation. 126 5.5 Chapter 5 References [1] W.J. Hehre, R. Ditchfield, and J.A. Pople. Self-consistent molecular orbital meth- ods. XII. 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Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y . Lin, T. Van V oorhis, S.H. Chien, A. Sodt, R.P. Steele, V .A. Rassolov, P. Maslen, P.P. Koram- bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen, A. Drew, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S. Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z. Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y .M. Rhee, J. Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. Woodcock III, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel, W.J. Herhe, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon. Advances in methods and algorithms in a modern quantum chemistry program package. Phys. Chem. Chem. Phys., 8:3172–3191, 2006. [7] K. M¨ uller-Dethlefs and P. Hobza. Noncovalent interactions: A challenge for exper- iment and theory. Chem. Rev., 100:143–167, 2000. [8] J. Sponer, J. Leszczynski, and P. Hobza. Electronic properties, hydrogen bonding, stacking, and cation binding of DNA and RNA bases. Biopolymers, 61:3–31, 2002. 127 [9] H. Saigusa. Excited-state dynamics of isolated nucleic acid bases and their clusters. Photochem. Photobiol., 7:197–210, 2006. [10] A.A. Zadorozhnaya and A.I. Krylov. Ionization-induced structural changes in uracil dimers and their spectroscopic signatures. J. Chem. Theory Comput., 2010. In press. [11] M. Kratochv´ ıl, O. Engkvist, J. Vacek, P. Jungwirth, and P. Hobza. Methylated uracil dimers: Potential energy and free energy surfaces. Phys. Chem. Chem. Phys., 2:2419–2424, 2000. [12] P. Jureˇ cka, J. ˇ Sponer, J. ˇ Cern´ y, and P. Hobza. Benchmark database of accurate (MP2 and CCSD(T) compl ete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys., 8:1985, 2006. [13] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov. The effect of π -stacking, h-bonding, and electrostatic interactions on the ionization energies of nucleic acid bases: Adenine-adenine, thymine-thymine and adenine-thymine dimers. Phys. Chem. Chem. Phys., 2010. in press, DOI:10.1039/b919930f. [14] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed. Ionization of cytosine monomer and dimer studied by VUV photoionization and electronic structure cal- culations. Phys. Chem. Chem. Phys., 2010. In press, DOI: 10.1039/B921498D. [15] M.O. Sinnokrot and C.D. Sherrill. Unexpected substituent effecst in face-to-face π -stacking interactions. J. Phys. Chem. A, 107:8377–8379, 2003. [16] M.O. Sinnokrot and C.D. Sherrill. Substituent effects inπ − π interactions: Sand- wich and t-shaped configurations. J. Am. Chem. Soc., 126:7690–7697, 2004. [17] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth. Electronic structure of the benzene dimer cation. J. Chem. Phys., 127:044317, 2007. [18] A.A. Golubeva and A.I. Krylov. The effect of π -stacking and H-bonding on ion- ization energies of a nucleobase: Uracil dimer cation. Phys. Chem. Chem. Phys., 11:1303–1311, 2009. 128 Chapter 6 Ionized non-covalent dimers: Outlook and future research directions 6.1 Chapter 6 Overview The non-covalent ionized clusters pose a challenge to theory; at the same time, this very complexity makes them an exicting and rewarding research topic. Closely-lying elec- tronic states result in multi-configurational wave functions and rich electronic structure with large number of states and multiple conical intersections. Weak dispersion inter- actions and large number of degrees of freedom together make the geometry search dif- fucult, but produce potential energy surfaces with a variety of distinct structures, both minima and transition states. In this chapter, two of the numerous possible research directions will be explored. 129 6.2 Conical intersections in ionized non-covalent dimers: Benzene dimer cation revisited It has been shown that the radiationless decay through the conical intersections between the electronic states of the nucleobase dimers contributes to the DNA’s intrinsic stabil- ity [1, 2], pariticipates in the DNA charge transfer process [3–5] and can be responsible for some mutations [5] (see Ref. 2 for the most recent review). For instance, based on the calculations Merchan and coworkers [3, 4] proposed the cooperative micro-hopping mechanism of the hole transfer in DNA. According to this mechanism, the hole migra- tion is a series of transitions between the intersecting electronic states of the nucleobase dimers facilitated by the thermal fluctuations of the flexible DNA chain. In connection with the CI theme, we revisited the familiar benzene dimer [6]. This system was a subject of extensive theoretical [6–10] and experimental [11–15] investi- gation for several decades. However, not all of the questions have been answered yet. In the previous study of the benzene dimer cation [6], the excited states and proper- ties of the three isomers of the Bz + 2 (the x-dispaced (XD) sandwich, y-displaced (YD) sandwich and t-shaped) were investigated using EOM-IP-CCSD. The minimum corre- sponds to the displaced isomers, which are nearly-degenerate, and the t-shaped cation was estimated to lie 6 kcal/mol higher in energy. The calculated electronic spectrum of the cation agrees well with the gas-phase [11–14] and condensed phase [15, 16] experi- ments: the position of the CR band at 1.35 eV was predicted with a remarkable 0.02 eV 130 accuracy. However, the theory underestimated the intensity of the secondary CR peak at 1.07 eV in the experimental spectrum by more than two orders of magnitude, and the reason for this was unclear. Based on the experimental observations [14], this feature was assigned as one of the two CR transitions corresponding to the single isomer of Bz + 2 . Motivated by discussion with Prof. Bally from the University of Fribourg, we con- sidered three alternative benzene dimer cation structures: the two strongly-displaced sandwich isomers (XSD and YSD, which are displaced along thex- andy-axis, respec- tively) and the fused structure (FD) that were proposed earlier [17]. The ground-state geometries of XSD, YSD and FD were optimized at IP-CISD/6-31(+)G(d) level; the XD, YD and TS structures were obtained previously [6] employing the IP-CCSD opti- mization with the 6-31(+)G(d) basis. The optimized ground state geometries of the Table 6.1: The ground state total energies (in hartree) of the six isomers of Bz + 2 calcu- lated at three levels of theory: IP-CCSD/6-31(+)G(d), IP-CCSD(dT)/6-31(+)G(d) and IP-CCSD/6-311(+,+)G(d,p)+FNO(99.25%) Isomer Ground State E tot CCSD/6− 31(+)G(d) E tot CCSD(dT)/6− 31(+)G(d) E tot CCSD/6− 311(+,+)G(d,p) XD X 2 B g -462.717304 -462.910464 -462.727685 YD X 2 B g -462.717660 -462.910781 -462.728058 TS X 2 B 2 -462.705866 -462.898372 -462.716231 XSD X 2 B u -462.707551 -462.901399 -462.717910 YSD X 2 B u -462.710547 -462.904717 -462.720998 FD X 2 A u -462.664903 -462.867298 -462.675027 six isomers of Bz + 2 and the estimated energy gaps are presented in Fig. 6.1. Table 6.1 provides the ground state total energies calculated at three different levels of theory. 131 YD XD XSD TS FD 0.23/ 0.20 6.37 / 5.89 7.42 / 7.79 33.28 / 27.29 E, kcal/mol YSD 4.43 / 3.80 Figure 6.1: The six optimized geometries of the benzene dimer cation and the cor- responding energy gaps calculated at the IP-CCSD(dT)/6-31(+)G(d) (italic) and IP- CCSD/6-311(+,+)G(d,p) (bold) levels of theory. Table 6.2 summarizes the characteristic geometric parameters, which are explained in Figure 6.2, for the six isomers. As follows from Table 6.2, the displacement cordi- nate values for the XSD and YSD structure are more than 2 ˚ A larger relative to the moderately-displaced XD and YD structures. Surprisingly, the separation coordinate and the distance between the centers of mass of the fragments are 0.2-0.4 ˚ A smaller for the XSD and YSD isomers relative to the XD and YD isomers, respectively. As IP-CISD tends to overestimate the intermolecular separations relative to IP-CCSD by 0.2-0.3 ˚ A the actual difference for moderately and strongly-displaced structures may be even more pronounced. In the fused structure FD, the two covalent bonds are formed, which can be seen from the smallh andd COM values. 132 d COM Δ h Figure 6.2: The definitions of structural parameters for the benzene dimer cation. The distance between the centers of mass of the fragments d COM , separation h and sliding coordinatesΔ are shown. In accord with the previous study [6], the two lowest structures of Bz + 2 are the nearly- degenerate XD and YD sandwich isomers, which lie more than 7 kcal/mol below the TS structure (see Fig. 6.1). Not surprisingly, the fused FD structure lies much higher in energy, so we omit it from further consideration. However, the two strongly-displaced structures - XSD and YSD - were found to lie in between the sandwich and t-shaped structures, the lowest one less than 4 kcal/mol apart from the XD and YD isomers. It is unclear whether the XSD and YSD are the minima or transition states. Note that the discussed energy differences are estimated at IP-CCSD/6-311(+)G(d,p) level. Our tests showed that the effect of triple contributions is almost neglegible and changes the energy differences by only 0.01-0.03 kcal/mol for four low-lying isomers and 0.17 kcal/mol for 133 Table 6.2: The characteristic geometric parameters of the six ground-state structures of the benzene dimer cation. The distances between the centers of mass of the fragments d COM (in ˚ A), separationh (in ˚ A) and sliding coordinateΔ (in ˚ A) values are presented. Isomer d COM h Δ XD 3.27 3.09 1.07 YD 3.29 3.10 1.10 TS 4.57 – – XSD 3.01 2.91 3.16 YSD 2.81 2.77 3.22 FD 1.64 1.49 3.15 FD structure. At the same time, increasing the basis set to 6-311(+)G(d,p) at IP-CCSD level results in 0.02, 0.66, 0.45, 0.39 and 5.82 kcal/mol changes in energy differences for XD, YSD, XSD, TS and FD isomers, respectively. Therefore, we expect the IP- CCSD/6-311(+)G(d,p) estimates to be of better quality than IP-CCSD(dT)/6-31(+)G(d). This finding shows that the PES of the benzene dimer cation (as well as other ionized non-covalent dimers) is shallow and rugged. What consequences does it have for the electronic structure? Consider Figure 6.3, which depicts the evolution of the four lowest electronic states of Bz + 2 along the x- (top panel) and y- (bottom panel) displacement coordinates. The corresponding singly-occupied MOs of the cation and the calculated enegy spacings (the ground state of the XD and YD structures are chosen as the zero-level) are presented. The dashed lines connect the related electronic states in moderately and strongly- displaced sandwich isomers; the blue arrows mark the CR transitions. As it appears, the electronic states change the order along thex- andy- displacement coordinate. For 134 0.27 eV 0.51eV 1.28 eV 1.40 eV 0.86 eV 1.23 eV 1.25 eV B g B u A g A u A u A g B g B u Displacement along x axis E, eV 0 eV XD XSD CI? ΔE E, eV 0.19 eV 1.07 eV 1.28 eV 1.43 eV 0.91 eV 1.25 eV 1.29 eV B g B u A g A u A u A g B g B u Displacement along y axis 0 eV ΔE CI? YD YSD Figure 6.3: The evolution of the four lowest electronic states of the benzene dimer cation along thex- (top panel) andy- (bottom panel) displecement coordinates calculated with IP-CCSD/6-31(+)G(d). Two moderately (XD, YD) and two strongly-displaced (XSD, YSD) fully-optimized ground-state structures were employed. The blue arrows depict the CR transitions at four geometries and the dashed lines interconnect the related elec- tronic states. 135 instance, in the XSD structure the states, when ordered by the increasing energy, appear as X 2 B u , 1 2 B g , 1 2 A g and 1 2 A u as opposed to the X 2 B g , 1 2 A g , 1 2 B u and 1 2 A u order in the XD isomer. This points to the presense of the conical intersections between the surfaces, for example, the1 2 B g and1 2 B u states of thex-displaced structures; moreover, the intersection point is likely to be located along the x-coordinate. Interestingly, the optimization of the geometry of the excited1 2 B g state of XSD converges to the ground state XD geometry. Analogously, in the y-displaced structures, the CI point between the X 2 B g and 1 2 B u states may exist along the y-axis. In the C 2h group the B g → B u transitions are allowed by symmetry, so the interconversion between the ground states of moderately (XD, YD) and the corresponding strongly-displaced (XSD, YSD) structures can occur. These findings suggest an alternative explanation of the origin of the broad peak at 1.07 eV observed in the gas-phase experiment. As the authors point out [14], the two-photon ionization leads to a large excess of energy in the experimental system. The estimate of the lowest IE of the benzene dimer is significantly lower than the 12 eV available to the system and is in the range of 8.59-8.79 eV for all the isomers [6]. Some of the energy dissipates in the evaporative cooling process, but it is still likely that the hot ionized dimers are produced in this experiment. If the height of the barrier for theX 2 B g → X 2 B u interconversion through the CI is significantly smaller than the energy excess, the strongly-displaced structures will be populated at the experimental conditions along with XD and YD. Therefore, four CR bands will be observed in the 136 spectrum — at 0.96, 1.10, 1.40 and 1.43 eV (see Fig. 6.3 and Tables 6.4 and 6.3) — consistently with the experimental findings. The relative intensity of the two arising features in 1.4-1.5 eV and 0.9-1.1 eV spectral regions will be determined by the ratio of moderately- and strongly-displaced structures at experimental conditions rather than the calculated intensities of the elementary transitions (which are similar for all CR bands). The 0.14 eV spacing between the two lowest CR transitions even explains the broadening of the experimental band at 1.07 eV . Quite a few questions remain unanswered. Where is the PES crossing point located and how large is the interconversion barrier? Are the XSD and YSD true minima or transition states? What is the effect of the entropic contribution on the barriers and energy gaps? The last point is particularly important when interpreting the results of finite-temperature experiments, like the one discussed above. The DFT-D vibrational analysis with the ωB97X-D functional can address the latter two questions (for the ground states). However, one should be careful as the harmonic approximation used in frequency calculations is likely to be of limited accuracy. As of the former, using the minimum-energy crossing point search procedure implemented in Q-Chem for EOM- CC family of methods [18], we can locate the PES crossing point and estimate the barrier of interconversion. 137 Table 6.3: The six lowest symmetry-allowed transitions in the electronic spectrum of the benzene dimer cation at the XD and XSD optimized geometries. Calculated with IP-CCSD/6-31(+)G(d). XD XSD Transition Δ E, eV <μ 2 >, a.u. f Transition Δ E, eV <μ 2 >, a.u. f X 2 B g →1 2 B u 1.28 0.0036 0.0001 X 2 B u →1 2 B g 0.59 0.0055 0.0000 X 2 B g →1 2 A u 1.40 6.3050 0.2168 X 2 B u →1 2 A g 0.96 11.1522 0.2619 X 2 B g →2 2 B u 3.32 0.6052 0.0493 X 2 B u →2 2 A g 3.56 0.0001 0.0000 X 2 B g →2 2 A u 3.74 0.0040 0.0004 X 2 B u →2 2 B g 3.64 0.0000 0.0000 X 2 B g →3 2 B u 3.80 0.0057 0.0005 X 2 B u →3 2 A g 4.28 0.4044 0.0424 X 2 B g →3 2 A u 5.96 0.0003 0.0000 X 2 B u →3 2 B g 6.04 0.0001 0.0000 138 Table 6.4: The six lowest symmetry-allowed transitions in the electronic spectrum of the benzene dimer cation at the YD and YSD optimized geometries. Calculated with IP-CCSD/6-31(+)G(d). YD YSD Transition Δ E, eV <μ 2 >, a.u. f Transition Δ E, eV <μ 2 >, a.u. f X 2 B g →1 2 B u 1.28 0.0029 0.0001 X 2 B u →1 2 B g 0.73 0.0115 0.0002 X 2 B g →1 2 A u 1.43 6.2174 0.2184 X 2 B u →1 2 A g 1.10 10.6157 0.2871 X 2 B g →2 2 B u 3.34 0.6055 0.0495 X 2 B u →2 2 B g 3.58 0.0000 0.0000 X 2 B g →3 2 B u 3.76 0.0069 0.0006 X 2 B u →2 2 A g 3.70 0.0024 0.0002 X 2 B g →2 2 A u 3.82 0.0034 0.0003 X 2 B u →3 2 A g 4.39 0.3794 0.0409 X 2 B g →3 2 A u 5.96 0.0005 0.0001 X 2 B u →3 2 B g 6.09 0.0002 0.0000 139 6.3 The effect of substituents in ionized non-covalent dimers: Electronic structure and properties The electronic structure and properties of the chemically-modified nucleobase dimers is another promising research direction, which is attractive from both the fundamental and the applied viewpoints. It was shown that the conductivity of the DNA decreases sufficiently with the increase of the A-T base pair’s content [19–21]. This imposes the restrictions on the sequence and composition of the DNA molecules that may be suc- cessful candidates for molecular electronics applications. Another issue is the oxidative degradation of guanine in the chain that is associated with the charge transport [22]. To overcome these difficulties, synthetic analogs of the DNA can be used in the device con- struction. In these analogs the target properties can be modified by the introduction of substituents, like alkyl, halogen groups, additional aromatic rings or heteroatoms in the ”native” nucleobase structures. The latter approach was successfully used by Majima and coworkers [23]. In their experimental study, the 7-Deazaadenine (Z) (i.e. adenine with one of the N heteroatoms replaced by the C atom) was introduced in the DNA sequence instead of the adenine. This increased the efficiency of the charge transport more than two-fold relative to the original sequence. This effect was explained by the smaller gap between the HOMOs of the ZT and GC base pairs as compared to AT and GC. Okamoto and coworkers [22] used another approach, i.e. they extended the nucle- obase aromatic system. The Benzodeazaadenine was incorporated in the DNA instead 140 of the native adenine nucleobase. The modified DNA samples exhibited a remarkably high hole transport ability. The authors indicated that the orderedπ -stacking array, low oxidation potentials of the nucleobases and suppressed oxidative degradation are the three essential factors for the successfull design of the synthetic DNA nanowire. To facilitate the search of promising synthetic DNA analogs, a systematic approach is needed. A qualitative theory, which would be able to predict the effect of chemical modifications on the electronic structure, ionization energies and states of the nucle- obase and nucleobase clusters, would be of great value. We have already investigated the effect of methylation on the ionized states and electronic structure of the monomer and dimers of one of the nucleobases. The results showed that the qualitative trends for IEs of the modified nucleobase can be predicted by classifying the introduced perturbation as stabilizing or destabilizing for the corresponding ionized state. The simple analysis of the molecular orbitals of the original nucleobase in conjuction with the qualitative organic chemistry considerations (i.e. inductive and resonance effects, electron-donor and electron-acceptor groups) can provide an insight. An interesting question is whether or not the effect of substitutions can be extrap- olated from the monomer to the dimer system. For instance, in the 1,3-dimethylated uracils, the effect of methylation on the lowest IE of the dimer was comparable to that in the monomer: -0.61 and -0.63 eV shifts in the first IE, respectively. For other states, the methylation-related shifts were also similar (see Table 5.5), unless there was an exces- sive electron density overlap in the methylated dimer attributed to the CH 3 groups, e.g. 141 as for the2 2 A 1 and5 2 A 1 states, where theσ CH MO component of one of the fragments overlapped with the lp(O) component of the other. The DMO-LCFMO splittings of states were also similar in the methylated and non-methylated dimers (0.37 vs. 0.35 eV , respectively), again excluding the2 2 A 1 and5 2 A 1 states. Thus, for most states the DMO- LCFMO overlap and the effect of substituents on the IEs are additive, so the electronic structure of the substituted dimer cation can be extrapolated from the prototype dimer using the substituted monomer results. In terms of the qualitative DMO-LCFMO frame- work, the levels of modified dimers are just shifted up or down by constants equal to the state shifts observed in the substituted monomer. Such extrapolation schemes can be useful for approximate estimates when the full calculation is too expensive. It should be noted, however, that the CH 3 groups represent a relatively small perturbation, such that the shapes of MOs and structures are similar for the methylated- and non-methylated systems. It is likely that the introduction of strong electron-acceptors, like NO 2 and halogens, or bulk aromatic rings will significantly perturb the structure, MOs and the states, so that such simplified considerations will be of limited value. Back to the DNA nanowire design, according to the micro-hopping mechnanism pro- posed by Merch´ an and coworkers [3], the hole transfer along the single DNA strand is a series of hole hops betwen the pairs of adjacentπ -stacked nucleobases, which involves the transitions through the conical intersections. How can we control the efficiency of such process? First, the low-lying ionized states of the adjacent nucleobase dimers should be nearly-degenerate. Second, there should exist a low-energy CI between the 142 PES of the two dimer systems (i.e. the CI on the tetramer surface along the separation coordinate of the dimers). Consider Table 6.5 presenting some of the available theoretical estimates of the first VIE of the DNA and RNA nucleobases and stacked nucleobase dimers. The first VIEs Table 6.5: Theoretical estimates of the lowest VIE (in eV) of the nucleobase monomers andπ -stacked dimers. Monomers Stacked dimers VIE, eV VIE, eV A 8.37 a , 8.37 b A 2 8.18 b T 9.07 a , 9.13 b AT 2 8.28 b C 8.73 a T 2 8.78 b G 8.09 a U 2 9.21 c U 9.42 a , 9.55 c a Empirically corrected (IPEA=0.25) CASPT2/ANO-L 431/21 from Ref. 24. b The EOM-IP-CCSD/cc-pVTZ from Ref. 25. For dimers, the extrapolation was used. c The EOM-IP-CCSD/cc-pVTZ from Ref. 26. For dimers, the extrapolation was used. of the DNA bases lie in the 8.1 - 9.1 eV range, with guanine and adenine ionizing at lower energies than thymine and cytosine [24, 25]. In RNA, thymine is replaced with uracil that extends this range to 9.55 eV [26]. The stacked dimer data is incomplete, and includes three homodimer (U 2 , T 2 , A 2 ) and one heterodimer (AT) structure (i.e 4 structures out of 15 possible) [25, 26]. For effective CT, we need to tighten the lowest VIE range. From the DMO-LCFMO considerations, it follows that homodimers com- posed from the hard-to-ionize thymine and uracil should affect the CT in DNA and RNA the most (because for the heterodimers, like AT or TC, VIEs are expected to be lower). The synthetic RNAs with dimethylated uracils could be one of the possible solutions. 143 However, in such case the double-helix structure of RNA could be perturbed, as the AU hydrogen-bonding interactions will be suppressed. 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Phys., 109(7):2604–2608, 1998. 157 Appendix: EOM-IP optimized geometries of Bz + 2 Comment: X-displaced isomer (XD), ground electronic state (X 2 B g ), optimized with IP-CCSD/6-31(+)G(d) underC 2h symmetry constraint,E NN =647.863144. Atom x y z C 1.577051 -0.344668 -1.391098 H 1.596237 -0.355418 -2.480441 C 2.242307 0.695416 -0.691513 H 2.753735 1.478322 -1.248242 C 2.242307 0.695416 0.691513 H 2.753735 1.478322 1.248242 C 1.577051 -0.344668 1.391098 H 1.596237 -0.355418 2.480441 C 0.955447 -1.401972 0.694504 H 0.500928 -2.220563 1.249090 C 0.955447 -1.401972 -0.694504 H 0.500928 -2.220563 -1.249090 C -2.242307 -0.695416 0.691513 H -2.753735 -1.478322 1.248242 C -1.577051 0.344668 1.391098 H -1.596237 0.355418 2.480441 C -0.955447 1.401972 0.694504 H -0.500928 2.220563 1.249090 C -0.955447 1.401972 -0.694504 H -0.500928 2.220563 -1.249090 C -1.577051 0.344668 -1.391098 H -1.596237 0.355418 -2.480441 C -2.242307 -0.695416 -0.691513 H -2.753735 -1.478322 -1.248242 158 Comment: y-displaced isomer (YD), ground electronic state (X 2 B g ), optimized with IP-CCSD/6-31(+)G(d) underC 2h symmetry constraint,E NN =648.359009. Atom x y z C -2.375370 -0.802427 0.000000 H -3.000807 -1.692604 0.000000 C -1.970007 -0.221982 1.202903 H -2.275235 -0.658658 2.152860 C -1.180373 0.964775 1.203183 H -0.923839 1.432362 2.152829 C -0.826193 1.574414 0.000000 H -0.257481 2.501418 0.000000 C -1.180373 0.964775 -1.203183 H -0.923839 1.432362 -2.152829 C -1.970007 -0.221982 -1.202903 H -2.275235 -0.658658 -2.152860 C 1.970007 0.221982 -1.202903 H 2.275235 0.658658 -2.152860 C 2.375370 0.802427 0.000000 H 3.000807 1.692604 0.000000 C 1.970007 0.221982 1.202903 H 2.275235 0.658658 2.152860 C 1.180373 -0.964775 1.203183 H 0.923839 -1.432362 2.152829 C 0.826193 -1.574414 0.000000 H 0.257481 -2.501418 0.000000 C 1.180373 -0.964775 -1.203183 H 0.923839 -1.432362 -2.152829 159 Comment: t-shaped isomer (TS), ground electronic state (X 2 B 2 ), optimized with IP-CCSD/6-31(+)G(d) underC 2v symmetry constraint,E NN =600.842133. Atom x y z C 0.000000 -1.399973 -2.278360 H 0.000000 -2.488962 -2.299023 C -1.217379 -0.699252 -2.285733 H -2.158362 -1.246985 -2.316611 C 1.217379 -0.699252 -2.285733 H 2.158362 -1.246985 -2.316611 C -1.217379 0.699252 -2.285733 H -2.158362 1.246985 -2.316611 C 1.217379 0.699252 -2.285733 H 2.158362 1.246985 -2.316611 C 0.000000 1.399973 -2.278360 H 0.000000 2.488962 -2.299023 C 0.000000 0.000000 0.907763 C 1.244445 0.000000 1.609353 H 2.172257 0.000000 1.041906 H 0.000000 0.000000 -0.174517 C 1.244368 0.000000 2.986650 H 2.173847 0.000000 3.551289 C 0.000000 0.000000 3.681626 H 0.000000 0.000000 4.770875 C -1.244368 0.000000 2.986650 H -2.173847 0.000000 3.551289 C -1.244445 0.000000 1.609353 H -2.172257 0.000000 1.041906 160 Comment: strongly x-displaced isomer (XSD), ground electronic state (X 2 B u ), optimized with IP-CISD/6-31(+)G(d) under C 2h symmetry constraint, E NN =614.903162. Atom x y z C 1.150552 0.969722 0.707571 H 0.419080 1.555055 1.234935 C 2.136379 0.279022 1.407161 H 2.149267 0.295308 2.481720 C 3.108690 -0.404995 0.705527 H 3.883640 -0.932554 1.232270 C 3.108690 -0.404995 -0.705527 H 3.883640 -0.932554 -1.232270 C 2.136379 0.279022 -1.407161 H 2.149267 0.295308 -2.481720 C 1.150552 0.969722 -0.707571 H 0.419080 1.555055 -1.234935 C -1.150552 -0.969722 -0.707571 H -0.419080 -1.555055 -1.234935 C -2.136379 -0.279022 -1.407161 H -2.149267 -0.295308 -2.481720 C -3.108690 0.404995 -0.705527 H -3.883640 0.932554 -1.232270 C -3.108690 0.404995 0.705527 H -3.883640 0.932554 1.232270 C -2.136379 -0.279022 1.407161 H -2.149267 -0.295308 2.481720 C -1.150552 -0.969722 0.707571 H -0.419080 -1.555055 1.234935 161 Comment: strongly y-displaced isomer (YSD), ground electronic state (X 2 B u ), optimized with IP-CISD/6-31(+)G(d) under C 2h symmetry constraint, E NN =617.531975. Atom x y z C -0.948544 1.036858 0.000000 H -0.094961 1.691125 0.000000 C -1.541681 0.660690 1.221958 H -1.103733 0.987375 2.147873 C -2.691245 -0.097191 1.218022 H -3.158457 -0.383562 2.142498 C -3.265501 -0.478245 0.000000 H -4.169692 -1.060908 0.000000 C -2.691245 -0.097191 -1.218022 H -3.158457 -0.383562 -2.142498 C -1.541681 0.660690 -1.221958 H -1.103733 0.987375 -2.147873 C 0.948544 -1.036858 0.000000 H 0.094961 -1.691125 0.000000 C 1.541681 -0.660690 1.221958 H 1.103733 -0.987375 2.147873 C 2.691245 0.097191 1.218022 H 3.158457 0.383562 2.142498 C 3.265501 0.478245 0.000000 H 4.169692 1.060908 0.000000 C 2.691245 0.097191 -1.218022 H 3.158457 0.383562 -2.142498 C 1.541681 -0.660690 -1.221958 H 1.103733 -0.987375 -2.147873 162 Comment: fused isomer (FD), ground electronic state (X 2 A u ), optimized with IP-CISD/6-31(+)G(d) underC 2h symmetry constraint,E NN =656.211616. Atom x y z C -0.561504 0.600372 0.764805 H -0.141109 1.492488 1.205667 C -1.817295 0.192585 1.428685 H -1.835554 0.189867 2.505310 C -2.900883 -0.171726 0.725565 H -3.807561 -0.444572 1.235457 C -2.900883 -0.171726 -0.725566 H -3.807561 -0.444572 -1.235457 C -1.817295 0.192585 -1.428685 H -1.835554 0.189867 -2.505310 C -0.561504 0.600372 -0.764805 H -0.141109 1.492488 -1.205667 C 0.561504 -0.600372 0.764805 H 0.141109 -1.492488 1.205667 C 1.817295 -0.192585 1.428685 H 1.835554 -0.189867 2.505310 C 2.900883 0.171726 0.725565 H 3.807561 0.444572 1.235457 C 2.900883 0.171726 -0.725566 H 3.807561 0.444572 -1.235457 C 1.817295 -0.192585 -1.428685 H 1.835554 -0.189867 -2.505310 C 0.561504 -0.600372 -0.764805 H 0.141109 -1.492488 -1.205667 163
Abstract (if available)
Abstract
Several prototypical ionized non-covalent dimers - the uracil, 1,3-dimethylated uracil and benzene dimer cations - are studied by high-level ab initio approaches including the equation-of-motion coupled cluster method for ionization potentials (EOM-IP-CC). The qualitative Dimer Molecular Orbitals as Linear Combinations of Fragment Molecular Orbitals (DMO-LCFMO) framework is used to interpret the results of calculations. As the simplest model systems, the neutral and ionized non-covalent dimers, such as pi-stacked and H-bonded nucleobase dimers, can shed some light on the complex mechanism of the charge transfer in DNA. The correct treatment of non-covalent interactions is challenging to the ab initio methodology, therefore the special attention is given to the development and benchmarking of the new methods.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Golubeva, Anna A.
(author)
Core Title
Electronic structure of ionized non-covalent dimers: methods development and applications
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Chemistry
Publication Date
04/05/2010
Defense Date
11/17/2009
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
benzene dimer,effect of substituents,electronic spectrum of dimer cation,electronic structure,EOM-IP,EOM-IP-CC,EOM-IP-CISD,equation-of-motion method,ionized dimers,methylated uracil dimer,non-covalent dimers,nucleobase dimers,OAI-PMH Harvest,uracil dimer
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Krylov, Anna I. (
committee chair
), Haas, Stephan (
committee member
), Mak, Chi Ho (
committee member
)
Creator Email
ane4ka.golubeva@gmail.com,golubeva@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m2878
Unique identifier
UC1293258
Identifier
etd-Golubeva-3405 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-297407 (legacy record id),usctheses-m2878 (legacy record id)
Legacy Identifier
etd-Golubeva-3405.pdf
Dmrecord
297407
Document Type
Dissertation
Rights
Golubeva, Anna A.
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
benzene dimer
effect of substituents
electronic spectrum of dimer cation
electronic structure
EOM-IP
EOM-IP-CC
EOM-IP-CISD
equation-of-motion method
ionized dimers
methylated uracil dimer
non-covalent dimers
nucleobase dimers
uracil dimer