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Doktorarbeit.pdfcalculation of inter-system crossing rates: Application to uracil and its derivatives
Inaugural-Dissertation
zur
der Heinrich-Heine-Universitat Dusseldorf
Jun.-Prof. Dr. Jorg Tatchen
Tag der mundlichen Prufung:
Hiermit versichere ich, die hier vorgelegte Arbeit eigenstandig und ohne unerlaubte Hilfe angefertigt zu haben. Die Dissertation wurde in der vorgelegten oder in ahnlicher Form noch bei keiner Institution eingereicht. Ich habe keine erfolglosen Promotionsver- suche unternommen.
Dusseldorf, den
(Mihajlo Etinski)
List of papers included in the thesis
• Paper 1 Electronic and vibrational spectroscopy of 1-methylthymine and its water clus- ters: The dark state survives hydration Matthias Busker, Michael Nispel, Thomas Haber, Karl Kleinermanns , Mihajlo Etinski, and Timo Fleig, Chem. Phys. Chem., 9 (2008) 1570-1577
• Paper 2 Intersystem crossing and characterization of dark states in the pyrimidine nucle- obases uracil, thymine, and 1-methylthymine Mihajlo Etinski, Timo Fleig, and Christel M. Marian, J. Phys. Chem. A 113, (2009) 11809-11816
• Paper 3 Ab initio investigation of the methylation and hydration effects on the electronic spectrum of uracil and thymine Mihajlo Etinski and Christel M. Marian, Phys. Chem. Chem. Phys. 12, (2010) 4915 - 4923
• Paper 4 Overruling the energy gap law: Fast triplet formation in 6-azauracil Mihajlo Etinski and Christel M. Marian, submitted to Phys. Chem. Chem. Phys.
List of related papers not included in the thesis
• Paper 5 Theoretical investigation of the excited states of 2-nitrobenzyl and 4,5-methylendioxy- 2-nitrobenzyl caging groups Klaus Schaper, Mihajlo Etinski, and Timo Fleig, Photochem. Photobio. 85 (2009) 1075-1081
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I express my gratitude to Professor Dr. Christel Marian for her help to formulate the subject of my thesis, exploration of which brought me a lot of intellectual excite- ment. The collaboration with Professor Marian helped me to broaden my insights into electronic spectroscopy and photophysics. I am grateful to Junior Professor Dr. Jorg Tatchen for his support of my research. I would like to thank Professor Dr. Timo Fleig for his advice during the first part of my doctoral studies in Duesseldorf. I thank Dr. Martin Kleinschmidt for help to interface the code written in C as a subroutine to the VIBES program. Also, I am grateful to all experimentalists with whom I collabo- rated: Professor Dr. Karl Kleinermanns, Priv. Doz. Dr. Klaus Schaper, Dr. Matthias Busker, Dr. Michael Nispel and Dr. Thomas Haber. I would like to thank all col- leagues from the Institute of Theoretical and Computational Chemistry, and especially to Dr. Susanne Salzmann, Dr. Stefan Knecht, Dr. Lasse Sørensen, Dr. Vidisha Rai- Constapel, Kathleen Gollnisch, Dr. Stephan Raub, Karin Schuck and Klaus Eifert for creating a friendly and creative atmosphere. I appreciate very much all help and con- tinual support received from Professor Dr. Miljenko Peric and Professor Dr. Werner Jakubetz.
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Zusammenfassung
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Summary
The first part of this thesis is focused on the theoretical formulation of the problem how to efficiently evaluate inter-system crossing rates in molecules. The problem is addressed by time-independent and time-dependent approaches. The latter approach is presented in a more detail. The central object in time-dependent method is the correlation function. A closed-form expression for the calculation of the correlation function using spin-free Born-Oppenheimer vibronic states and the Condon approxi- mation for the spin-orbit matrix element is found. Also, the expression for the rate using a second-order cumulant expansion is presented. A particularly simple expres- sion is derived employing a short-time expansion of the cumulant expansion. All three expressions for the inter-system crossing rate are implemented in a computer code. The rates obtained for test molecules using time-dependent and time-independent ap- proaches are compared and discussed. The time-dependent approach is promising in the cases where the Franck-Condon weighted density of the vibronic states is huge. This may be due to a large adiabatic energy gap between electronic states or simply due to many normal modes. The second part of the thesis is dedicated to applications of quantum-chemical meth- ods to the electronic relaxation upon photoexcitation in uracil, its methylated deriva- tives and 6-azauracil. Time-resolved spectroscopy experiments in the molecular beam showed that methylated uracils relax on the femto, pico and nanosecond time scales. Although the first experimental results suggested that the nanosecond relaxation orig- inates from the lowest excited singlet state, in a later study we conclude that it should be due to the lowest triplet electronic state. Also, we address a controversal proposal that hydration quenches nanosecond relaxation. Our results show that hydration has a significant effect on the electronic states, so that it can modify the photostability of the pyrimidine bases. Photorelaxation of 6-azauracil is particularly interesting because the triplet quantum yield is much larger than in uracil. The aza-substitution creates additional low-lying singlet and triplet nπ∗ states. The calculation of potential energy profiles along linearly interpolated paths reveals crossings and avoided crossings between singlet and triplet electronic states. Possible electronic relaxation mechanisms are discussed.
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Contents
List of Tables 3
List of Figures 7
1 Introduction 9 1.1 Photochemistry of nucleic acids . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 The molecular Hamiltonian and its approximations 13 2.1 Separation of electron and nuclear coordinates . . . . . . . . . . . . . . 14 2.2 The solution of the electronic Schrodinger equation . . . . . . . . . . . 15
2.2.1 The Hartree-Fock method . . . . . . . . . . . . . . . . . . . . . 15 2.2.2 The coupled-cluster method . . . . . . . . . . . . . . . . . . . . 17
2.3 The nuclear Schrodinger equation and the normal mode Hamiltonian . 19 2.4 Coupling of the electron spin and angular momentum . . . . . . . . . . 23
3 Decay of the excited electronic state 25 3.1 Weak vibronic coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Strong vibronic coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 The time-independent method for the calculation of the inter-system
crossing rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4 The time-dependent method for the calculation of the inter-system cross-
ing rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.1 The correlation function . . . . . . . . . . . . . . . . . . . . . . 33 3.4.2 Cumulant expansion . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.3 Short-time approximation . . . . . . . . . . . . . . . . . . . . . 37
4 Implementation and testing of the time-dependent method for inter-system crossing rates 39 4.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2 Test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 Absorption spectrum of thioxanthone . . . . . . . . . . . . . . . 43 4.2.2 Inter-system crossing rates . . . . . . . . . . . . . . . . . . . . . 44
4.2.2.1 Thymine . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.2.2 Phenalenone . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.2.3 Flavone . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2.2.4 Free base porphyrin . . . . . . . . . . . . . . . . . . . 53
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Contents
5 Applications 57 5.1 Dark electronic state in the pyrimidine bases uracil, thymine, and their
methylated derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Overview of the experimental and theoretical results . . . . . . 58 5.1.2 Electronic spectroscopy of 1-methylthymine and its water clusters 61 5.1.3 Effects of hydration and methylation on the electronic states of
uracil and thymine . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.1.4 Inter-system crossing in uracil, thymine and 1-methylthymine . 66
5.2 Formation of the triplet electronic state in 6-azauracil . . . . . . . . . . 71
6 Conclusions and outlook 77
Bibliography 79
List of Tables
1.1 Relative induction frequencies of the major photoproducts induced by UV radiation. Adapted from reference [1] . . . . . . . . . . . . . . . . . 10
3.1 Typical time scales of molecular photophysical processes [2, 3]. . . . . . 26
4.1 Calculated inter-system crossing rates S1 T1y for phenalenone in s−1 . 51 4.2 Calculated inter-system crossing rates S1 T1x for flavone in s−1 . . . . 53 4.3 Calculated inter-system crossing rates S1 T1x for porphyrin in s−1 . . 55
5.1 Wavelengths of the pump and probe pulses, resolution and relaxation time constants obtained in femtosecond pump-probe experiments in molecular beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Spin-orbit matrix elements S1|HSO|T1 in cm−1 calculated at the S1
state geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.3 Spin-orbit matrix elements in cm−1 calculated at the TDDFT optimized
S2 geometry of uracil using the DFT/MRCI/TZVP method for gener- ating the wave function . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Calculated rate constants kISC [s−1] for the (S1 T1) ISC channels in uracil, thymine and 1-methylthymine. ΔEad [cm−1] denotes the adia- batic electronic energy difference. . . . . . . . . . . . . . . . . . . . . . 69
5.5 Rate constants kISC [s−1] for the (S2 T2) and (S2 T3) ISC channels in uracil calculated at the DFT/MRCI/TZVP//DFT B3-LYP/TZVP level. ΔEad [cm−1] denotes the adiabatic electronic energy difference. . 69
5.6 Spin-orbit matrix elements calculated at the respective singlet minimum geometry of 6-azauracil . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.1 Comparison of calculated inter-system crossing rates with time-dependent and time-independent approach (VIBES) in s−1. . . . . . . . . . . . . . 77
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List of Figures
1.1 UV action spectra for human cell killing and mutagenesis and carcino- genic action spectrum for mouse skin. Figure taken from reference [4] . 10
1.2 Nucleic bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 Schematic two-dimensional (Q1, Q2) ground (lower, blue) and excited (upper, red) state PES. Left panel: Displaced-distorted harmonic po- tential energy surfaces with (i) D = 0 , (ii) d′
Q1 = d′′
Q2
, and (iii) J = 1, i. e. the excited state PES is (i) displaced, (ii) dis- torted, but (iii) not rotated relative to the ground state PES. Right panel: Displaced-distorted-rotated harmonic potential energy surfaces with (i) D = 0 (ii) d′
Q1 = d′′
Q2 , and (iii) J = 1. For an
explanation of the terms see text. Taken from ref. [5] . . . . . . . . . . 21 2.2 Duschinsky matrix J for thymine: It is an orthogonal matrix close to a
unit matrix with the dimension equal to the number of normal modes (for discussion about translation and rotation see text); nondiagonal elements clearly show coupling between normal modes . . . . . . . . . . 22
3.1 Photophysical (left) and photochemical path (right) in configuration space 25 3.2 Jablonski diagram: radiative processes - absorption (A), fluorescence (F)
phosphorescence (P); radiationless processes: internal conversion (IC), intersystem crossing (ISC), vibrational relaxation (VR) . . . . . . . . . 27
3.3 Level coupling scheme for the Wigner-Weisskopf model . . . . . . . . . 28 3.4 The singlet |S and triplet |T potential energy surfaces . . . . . . . . . 31
4.1 An example input file to start a time-dependent calculation of an inter- system crossing rate with the VIBES program . . . . . . . . . . . . . . 40
4.2 The pseudocode of the program. For explanation see text. . . . . . . . 41 4.3 Chemical structure of thioxanthone . . . . . . . . . . . . . . . . . . . . 43 4.4 Graphical representation of the Duschinsky matrix for the S0 → S2 tran-
sition in thioxanthone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.5 Real part of the correlation function related to the absorption spectrum
of thioxanthone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.6 Absorption spectrum for the S2 ←S0 transition in thioxanthone obtained
from the time-dependent and the time-independent (VIBES) approaches 45 4.7 The ground state structures of the test molecules. . . . . . . . . . . . . 45 4.8 Duschinsky matrix related to the transition between the S1 and T1 states
of thymine. In order to visualize the normal mode mixing, absolute values of the matrix elements Jij are shown. . . . . . . . . . . . . . . . 46
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List of Figures
4.9 The real parts of the correlation function, second-order cumulant expan- sion and short-time approximation as functions of time for thymine . . 47
4.10 Dependence of the inter-system crossing rate on the adiabatic electronic energy gap in thymine . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.11 Duschinsky matrix related to transition between the S1 and T1 states of phenalenone. In order to visualize the normal mode mixing, absolute values of the matrix elements Jij are shown. . . . . . . . . . . . . . . . 49
4.12 The real parts of the correlation function, the second-order cumulant expansion and the short-time approximation as functions of time for phenalenone (presented only the first 50 fs) . . . . . . . . . . . . . . . . 49
4.13 Duschinsky matrix related to transition between the S1 and T1 states of flavone. In order to visualize the normal mode mixing, absolute values of the matrix elements Jij are shown. . . . . . . . . . . . . . . . . . . . 52
4.14 The real parts of the correlation function, the second-order cumulant expansion and the short-time approximation as functions of time for flavone (presented only the first 50 fs) . . . . . . . . . . . . . . . . . . . 52
4.15 Duschinsky matrix related to transition between the S1 and T1 states of porphyrin. In order to visualize the normal mode mixing, absolute values of the matrix elements Jij are shown. . . . . . . . . . . . . . . . 54
4.16 The real parts of the correlation function, the second-order cumulant expansion and the short-time approximation as functions of time for porphyrin (presented only the first 50 fs) . . . . . . . . . . . . . . . . . 55
5.1 Proposed potential energy surfaces and processes for the pyrimidine bases. Ionization from the S1 state and the dark state Sd sample dif- ferent Franck-Condon regions of the ionic state, resulting in different ionization energies for these two states. From reference [6] . . . . . . . 59
5.2 Lifetimes of 1-methyluracil, 1,3-dimethyluracil, 1,3-dimethylthymine, and thymine at different excitation wavelengths. From reference [6] . . . . . 60
5.3 Geometries of the conical intersection in 1-methylthymine: 1ππ/1nπ
(CI1), 1ππ/S0 (CI2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4 Potential energy profiles of the ground (squares), 1nπ∗ (triangles) and 1ππ∗ state (circles) of 1-methylthymine, calculated at the CASSCF(10,8)/6- 31G* level of theory along the LIIC reaction path. A: from the equilib- rium geometry of the ground state to the CI1; B: from the equilibrium geometry of the ground state to the minimum of the 1ππ∗ state and to the CI1; C: from the CI1 to the minimum of the 1nπ∗ state; D: from the CI1 to the CI2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.5 Chemical structures of methylated uracils and thymines. Atom labels are given for uracil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.6 Density distribution of the Hartree-Fock frontier molecular orbitals which contribute to the lowest excited electronic states of methylated uracils and thymines (aug-cc-pVDZ basis set, isovalue=0.03). . . . . . . . . . . 65
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