Generalized Quantum Master Equations for Simulating Electronic Dynamics in Molecular Systems

Abstract

Simulating the inherently quantum-mechanical electronic energy and charge transfer in complex molecular system poses a challenge because of the exponential scaling of the computational cost with system size and/or complexity. While approximate mixed quantum-classical and semiclassical methods can reduce said cost, they also give rise to a significant loss of accuracy. Quantum rate theory approaches based on restricting the use of the use of those approximate methods to the calculation of memory kernels and correlation functions enhance the accuracy while not sacrificing computational efficiency. Some of these approaches are perturbative in that they treat the coupling between the electronic and nuclear degrees of freedom or the coupling between the electronic states as a small perturbation. In contrast, the Generalized Quantum Master Equation (GQME) approach is nonperturbative and thereby accounts for couplings of arbitrary size.

The effect of the nuclear degrees of freedom on the electronic dynamics is described by the GQME's memory kernel superoperator which holds all relevant information of the effects of the nuclear degrees of freedom on the electronic degrees of freedom. Because it is typically short-lived compared to the electronic dynamics it describes, calculating the memory kernel via approximate methods, such as the Mean-Field (Ehrenfest method) which is the focus of this dissertation, can still accurately determine the electronic dynamics.

The recently introduced M-GQME (Modified GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Excitonic Hamiltonians are often used for describing electronic energy and charge transfer dynamics in complex molecular systems such as photosynthetic and organic photovoltaic systems of biological and technological interests.

The robustness and accuracy of the M-GQME has previously been demonstrated on the two-state spin-boson benchmark model. In this thesis, we extended the range of applicability of M-GQME to energy transfer in the seven-state FMO benchmark model system, with projection-free inputs obtained via the Ehrenfest method. The main result is that the M-GQME with Ehrenfest-based inputs was found to yield accurate results across a wide parameter range. It was also found to dramatically outperform the direct application of the Ehrenfest method and to produce electronic population results that converge by a finite memory time. This should be contrasted with the Shi-Geva implementation of the GQME, which gives rise to electronic population results that oscillate asymptotically.

Another novel application of the M-GQME approach reported in this thesis is to the spin-boson model when the initial state involves entanglement between the nuclear and electronic degrees of freedom. The main outcome of this M-GQME based study is a proof of concept demonstration of the ability to use initial state entanglement as a resource for controlling electronic energy and charge transfer.

This dissertation also reports word on advancing a novel pedagogical project called Compute-to-Learn (C2L). This pedagogy was implemented in the University of Michigan as an honors-option studio offered to students participating in various physical chemistry courses and is designed to simulate a laboratory/research environment so that students can acquire a more hands-on approach towards understanding abstract physical chemistry concepts. The program uses four main pillars: student-led projects, peer learning, programming as a tool for learning, and having a publishable deliverable for teaching.