Computational Modelling of Excited State Decay in Polyatomic Molecules
Author(s)
Mendive Tapia, David
Type
Thesis
Abstract
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.
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.
Date Issued
2013
Date Awarded
2013-04
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Bearpark, Michael
Publisher Department
Chemistry
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)