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Vibronic Coupling, Symmetry and Dynamics in Unsaturated Hydrocarbons

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Vibronic Coupling, Symmetry and Dynamics in Unsaturated Hydrocarbons Vibronic coupling, symmetry and dynamics in unsaturated hydrocarbons by Christopher Robertson A thesis submitted to the University of Birmingham for the degree of DOCTOR OF PHILOSOPHY School of Chemistry University of Birmingham 2014 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Abstract This theoretical work looks at excited state photochemistry - the study of the molecular processes triggered by the absorption/emission of light to/from electronically excited states. Although the Born-Oppenheimer has been often called the most successful approximation in theoretical Chemistry, when studying the excited state surfaces of most molecular systems, one quickly reaches an impasse. Excited states exhibit high-dimensional cross- ings through conical intersections where the adiabatic approximation gives rise to discontinuities and where population transfer between states occurs. We therefore need to resort to more careful considerations of the system that take into account the interactions of the electronic and nuclear wave- functions. The approach taken here is that of using approximate vibronic coupling models, as well as extending the methods and algorithms to con- struct them. These models are then used in quantum dynamic calculations to obtain time-dependent properties, compute spectra and calculate dissoci- ation cross-sections. A Genetic Algorithm which aids to the fitting of diabatic model param- eters is described in detail and tested in two systems. A speciation routine performs multiple local optimizations of all possible subsets of inter-state coupling parameters to prepare the initial guess population. A covariance matrix constructed from the population is then used to generate moderate adaptive mutations on members. The neutral and cationic surfaces of cyclo- butadiene is one of the systems for which this fitting algorithm was used. A 10-dimensional model was fitted along important geometries using normal coordinates and the photo-electron spectrum was then calculated to compare with the experimentally recorded one. The diabatic coupling is typically in- 0.0 ferred from topological features exhibited between states. A more powerful way of constraining the coupling relationship between nuclei and electrons is the use of symmetry. We show how one can generate polynomial func- tions which are invariant with respect to the non-Abelian point groups D h ∞ and O. These polynomials are then calculated and listed to fourth and third order respectively. These D h invariant polynomials are then used for the ∞ construction of an acetylene model, where they reduce the number of fitted polynomials entering the construction of the model by an order of magnitude. Acetylene is a linear system which exhibits Renner-Teller (RT) and pseudo Jahn-Teller (pJT) interactions between states. The spectra of normal coor- dinate model systems which either explicity contain these RT-interactions or are ‘folded’ into the diabatic model are compared to help understand these non-adiabatic effects. A more rigorous 10-state full-dimensional model of acetylene is then constructed using curvilinear coordinates which allow us to use D h constraints and which result in a remarkably simple kinetic energy ∞ operator. A pulse polarized laser field is modeled as a Gaussian enveloped sinusoidal function and used to model the experimental technique of vibra- tionally mediated dissociation (VMD) of acetylene. Dissociation cross sec- tions are calculated for all possible angles. A bigger system Tolan (di-Phenyl acetylene), the monomial of a family of a photo-active dendritic antenna, is under study. Standard Geometry optimization methods locate the S1 minima far from the Franck-Condon (FC) region towards a trans-stilbene geometry. Comparison between the experimental and calculated absorption spectra val- idates the model and is subsequently used to model the first few picoseconds of population transfer, to qualitatively match the experimentally observed fluorescence decay lifetimes of the FC optically active bright state. 2 0.0 Glossary Born–Oppenheimer MO = Molecular orbital BOA = approximation MPI = Multi-photon ionization CAP = Complex absorbing potential Multi-reference MRCI = CAS = Complete active space configuration interaction CBD = cyclo butadiene NA = Non-adiabatic Coupled-cluster (SD = Nicotinamide adenine di NADPH = CC = singles doubles) nucleotide phosphate Conical intersection/ Normal distribution CI = Configuration interaction ND = mutations (S = with Covariance matrix speciation) adaptation (S = with Principal component CMA = PCA = speciation) analysis CMF = Constant mean-field PES = Potential energy surface DFT = Density functional theory pJT = pseudo Jahn-Teller DOF = Degree of freedom Perturbation theory, PT2 = second order DPA = Di-phenyl acetylene Root mean squared Discreet variable RMSD = DVR = representation deviation Rayleigh Schrodinger EOM = Equations of motion perturbation theory, Franck-Condon RS2 = FC = second order FWHM = Full width half maximum RT = Renner-Teller GA = Genetic algorithm SCF = Self-consistent field GS = Ground state SE = Schroedinger equation HF = Hartree-Fock SPF = Single particle function Harmonic oscillator HO = Time dependent density Highest occupied molecular TDDFT = functional theory HOMO = orbital Time-dependent IR = Infra-red TDSE = Schroedinger equation IrRep = Irreducible representation Time-independent JT = Jahn-Teller TISE = Schroedinger equation KE = Kinetic energy TOF = Time of flight LED = Light emitting diode UV = Ultra-violet LIF = Laser-induced fluorescence Vibronic coupling Lowest unoccupied molecular VCHAM = hamiltonian LUMO = orbital Vibrationally mediated Multi-configurational VMD = dissociation MCTDH = time-dependent Hartree ZPE = Zero point energy Moller-Plesset perturbation Zero point vibrational MP2 = theory, second order ZPVE = energy 1 Acknowledgements As an undergraduate I remember reading a history of science book about the life of those classically ‘great scientists’ like Einstein, Maxwell and the like. Although well written, it is not the best format for any book, really. One of the chapters was dedicated to Neils Bohr and was entitled "science through conversations" or to the effect. At the time I was not impressed with Bohr’s portrayed personality; here was a great man, I thought, that needed to bounce off other peoples ideas to come up with something worthwhile. He was nothing like the those other ‘greats’, standing alone in the darkness of uncertainty, searching for that eureka moment to bring back fire from mount Olympus. Ironically, looking back at my first few steps in research, I’ve concluded that I am that sort of bouncy person! (alas, I would not draw any other similarities between myself and the great man). This is because I could honestly say that without some of the conversations I have had with colleagues, I would have stagnated for longer in those endless ditches that are the everyday condition of the computer chemist. Over these years, I felt happy to arrive in the office and start pestering my poor friends into discussions. It was an environment where I felt at liberty to display my endless ignorance in the light of scrutiny of friends. I would therefore first like to thank Graham Worth for allowing me to join his group. I would also like to thank him for his endless (albeit endless) optimism; for the space and patience with which he allowed me to explore some ideas and without which I would have had to give up some of the projects, for his good advice and his friendship. I thank the The School of Chemistry with all its characters and drama that makes life interesting and my flat-mates for their friendship and tolerance of my sharp edges. It 0.0 would feel wrong to start listing all the lovely people in the Worth group (and outside it) that I feel indebted to for my work, without making this a long and somewhat tawdry section. I hope the words above suffice to express my gratitude towards them. Having said this, I would like thank three people whom had so palpable effect on my work that deserve special mention. I thank Gareth Richings for turning around with patience and sympathy almost everyday, every time I uttered his name with a tone of helplessness. His clarity of thought and ability with the pencil consistently served as a universal acid for many of my more nebulous ideas. For similar reasons I would thank Simon Neville. He warned me of many of the caveats involved in constructing vibronic coupling models (the endless mine-fields and ideosyncrasies of the VCHAM code!) and provided several germinal ideas. I valued the heated discussions we had together and for which I must confess, because of his un-faulting rigour, I typically suffered the bigger wounds ( :P ). Finally I would also like to thank Pietro S. Oliveto that, through casual drinks in the dreaded Bratby bar, directed me towards the work of Hansen and from where I cheaply extracted some valuable ideas. Finally I would like to specially thank my parents, brother, my family in the UK and my girlfriend Elaine Yip for the un-waving love and support I required for the completion of this work. 2 This thesis and the work described in it are entirely my own, except where I have acknowledged either help from a named person or a refer- ence is given to a published source or a thesis. List of Publications C. Robertson, G. A. Worth. “Generating symmetry adapted bases for non-abelian point groups to be used in vibronic coupling models.” JT special issue of J. Chem. Phys., submitted C. Robertson, G. A. Worth. “A genetic algorithm for the optimiza- tion of multi-state multi-mode vibronic coupling model parameters.” in preparation C. Robertson, G. A. Worth.
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