Computational Modelling of Excited State Decay in Polyatomic Molecules
Creators: name: Mendive Tapia, David
Publisher: name: Imperial College London
Year: 2013

description: The introduction of general numerical methods in the form of widely available software can have a dramatic effect on the development of a scientific field. In electronic structure theory, for example, general-purpose programs (such as Gaussian, ADF, MOLPRO,. . . ) combined with better computational resources have in part led to molecular electronic structure calculations becoming a ubiquitous tool in chemical research. Similarly, quantum dynamics methods based on coupled time-evolving Gaussian basis sets and molecular potential energy surfaces calculated on-the-fly hold out similar promise in the study of non-adiabatic processes, because of their generality and freedom from ad hoc assumptions. Therefore, the aim of this thesis is to investigate the convergence and applicability of quantum dynamics calculations with a fully variational coupled Gaussian basis set description, termed variational Multi-Con guration Gaussian (vMCG). It is suggested that the vMCG approach provides a way to balance accuracy against computational cost for molecules of comparable size by choosing the number of coupled Gaussian product basis functions and a middle way forward between grid-based and trajectory surface hopping approaches to non-adiabatic molecular quantum dynamics calculations. In order to prove the suitability of vMCG we show its application to three problems of chemical interest: the study of fulvene excited state decay, the prediction of a coherent control mechanism for the same system and the benchmarking of an electronic population dynamics model for electronic transitions when occurring through a conical intersection. In the long term, the development of vMCG is expected to have a major impact, allowing nonadiabatic dynamics simulations to be made not only by theoreticians, but also by non-specialists and experimentalists in both industry and academia.Chapter 1: Modelling Excited State Decay [Diagrams appear here. To view, please open pdf attachment] This chapter introduces and reviews the current state-of-the-art modelling of non-adiabatic processes in molecular systems. This is a challenging topic since the simulation must treat simultaneously the motion of the nuclei and the electrons, which are coupled together. It is concluded that a wide range of methodologies are available. However, when looking for a general tool for the study of non-adiabatic processes, quantum dynamics methods based on coupled time-evolving Gaussian basis sets such as the Direct Dynamics variational Multi-Con guration Gaussian (DD-vMCG) wavepacket method, as well as to other related methods - such as Ab Initio Multiple Spawning (AIMS, FMS)[1, 2] and Multi-Con gurational Ehrenfest (MCE)[3, 4] - seem to be an especially suitable choice because of their generality and freedom from ad hoc assumptions. Chapter 2: variational Gaussian nuclear wavepackets [Diagrams appear here. To view, please open pdf attachment] This chapter describes three possible time-evolving Gaussian basis sets for use in non-adiabatic quantum dynamics based on the Direct Dynamics variational Multi-Con guration Gaussian (DD-vMCG) wavepacket method. These general model representations are compared using model calculations in a simple harmonic oscillator and describing their connections to other work. It is suggested that the fully variational nuclear wavefunction, termed vMCG (variational Multi-Con guration Gaussian) is a very convenient formulation leading towards a realistic sampling of the phase space without the initial conditions (i.e. initial disposition and momentum) being so important when using a su cient amount of coupled Gaussian basis functions. Chapter 3: Fulvene S1/S0 Excited State Decay [Diagrams appear here. To view, please open pdf attachment] The vMCG (variational Multi-Con guration Gaussian) approach described in Chapter 2 is benchmarked in a realistic system by modelling the radiationless decay from an electronic excited state through an extended conical intersection seam. As a benchmark system, we model the radiationless decay of fulvene from its rst electronic excited state and monitor two associated properties: the spatial extent to which the conical intersection seam is sampled and the timescale and stepwise nature of the population transfer. We illustrate how the use of a fully variational nuclear wavefunction provides a way to balance accuracy against computational cost for molecules of comparable size by choosing the number of coupled Gaussian product basis functions. Chapter 4: Controlling Fulvene S1/S0 Decay [Diagrams appear here. To view, please open pdf attachment] Direct quantum dynamics simulations using the vMCG (variational Multi- Con guration Gaussian) approach were performed in order to model the control of the stepwise population transfer in fulvene. As shown in Chapter 3, ultra-fast internal conversion takes place centred on the higher-energy planar/sloped region of the S1/S0 conical intersection seam. Therefore, two possible schemes for controlling whether stepwise population transfer occurs or not | either altering the initial geometry distribution or the initial momentum composition of the photo-excited wavepacket - were explored. In both cases, decay took place instead in the lower-energy twisted/peaked region of the crossing seam, switching o the stepwise population transfer. This absence of re-crossing is a direct consequence of the change in the position on the intersection at which decay occurs and its consequences should provide an experimentally observable fingerprint of this system. Chapter 5: A population transfer model for intramolecular electron transfer [Diagrams appear here. To view, please open pdf attachment] The aim of this chapter is to further prove the applicability of the vMCG (variational Multi-Con guration Gaussian) approach by benchmarking an approximate population dynamics model in Jahn-Teller systems. The socalled Density Matrix Non-Equilibrium Fermi Golden Rule (DM-NFGR) can be seen as a simpli ed version of vMCG, in which the nite Gaussian basis set and on-the-fly evaluation of the nuclear Hamiltonian are eliminated via use of the density matrix formalism and a perturbational treatment of the equations. This has three clear advantages: firstly, it allows us to extend the maximum molecular size considerably; secondly, we can relate the population dynamics to an analytical time-dependent rate expression; and finally, temperature effects can be included in the simulations. Benchmark calculations for the 2,6-bis(methylene) adamantyl (BMA) radical cation support the reliability of the results.