Development of a Hierarchy of Theoretical Methods towards In Silico Photochemistry

Computational investigation of the processes occurring in molecules upon absorption of light has been of great interest throughout the years. Several methods have been developed with the goal to provide insight into the time evolution of molecules upon excitation. Usually for these methods increased accuracy comes at the cost of increased computational effort, which renders exact dynamics unfeasible. This project will be centered around three main challenges: testing an efficient method that still provides the proper description of decoherence effects, expanding the framework of nonadiabatic dynamics to also account for the decay through spontaneous emission of photons, and finally furthering the theoretical concept of introducing a time-dependent potential energy surface (PES) as an alternative to the usually used concept of the evolution of a time-dependent wavefunction on time-independent PES.
One widely used approach for the simulation of nonadiabatic dynamics consists of mixed quantum/classical methods. At the lower end of these methods surface hopping is found, which is computationally feasible even for larger, high-dimensional systems, but comes with a known problem: The phenomenon of decoherence does not arise naturally in this framework leading to "overcoherence". This obstacle has only been circumvented by introducing different ad hoc corrections.
In contrast, ab-initio multiple spawning (AIMS) presents a method that correctly predicts decoherence effects during nonadiabatic processes. In AIMS the classical trajectories are substituted by coupled gaussian trajectory basis functions (TBF), which enables an accurate description of quantum effects. However, the increase in accuracy comes at the cost of computational efficiency. An approach has recently been proposed to alleviate this computational bottleneck, where uncoupled groups of coupled TBFs are detected and reduced to only one group, based on a stochastic selection process, the stochastic selection- (SS-) AIMS.
In the first part of the project, the surface hopping dynamics of several molecules will be investigated with and without using decoherence corrections. In comparison, the dynamics of the same molecules will be studied employing AIMS as well as SS-AIMS, to get insight into the performance of SS-AIMS, as compared to surface hopping and AIMS.
Despite the high accuracy of AIMS simulations, there are still processes that cannot be described by the method, e.g., there does not yet exist a framework of AIMS that would be able to take spontaneous emission of an excited atom into account. The description of spontaneous transitions from an excited state to the ground state while emitting a photon, necessitates the presence of a quantized electromagnetic field. However, the framework of the Schrödinger equation only accounts for the quantisation of electronic energy levels. Hence, it has to be extended to a quantum field theory where the electromagnetic field is quantised, and the Hamiltonian includes the atoms as well as the field and the coupling between them. The next part of the project consists of the development and implementation of an extension of AIMS to quantum electrodynamics with the goal to enable the consideration of spontaneous emission.
The above-stated methods for describing nonadiabatic dynamics are all based on the so-called Born-Huang ansatz, where the molecular wavefunction is expressed into a basis of electronic eigenstates. An alternative to this representation of the wavefunction is provided by the exact factorisation, where the molecular wavefunction is expressed as a single product of a nuclear wavefunction and an electronic factor. The resulting concept of a time-dependent PES can be used as a starting point for the development of simpler ways to simulate nonadiabatic processes. The final part of the project would be dedicated to further theoretical approaches based on the exact factorisation of the wavefunction.