Simulating Electronically Nonadiabatic Dynamics via the Generalized Quantum Master Equation
Ellen Mulvihill · Deep Blue (University of Michigan) · 2020
One of the greatest challenges facing computational chemistry is the simulation of electronically nonadiabatic dynamics. While there are several reduced dynamics methods for doing so, they often rely on restrictive assumptions such as weak coupling between the electronic and nuclear degrees of freedom (DOF) or between electronic states. An alternative approach for simulating nonadiabatic dynamics is via mixed quantum-classical (MQC) and quasiclassical (QC) methods which can handle strong coupling but their reliability and computational feasibility decrease with increasing simulation time. In comparison, the generalized quantum master equation (GQME) requires no approximation in its derivation and scales favorably with increasing simulation time. In the first chapter of this dissertation, two previous approaches to the GQME will be examined and a modified approach to the GQME (M-GQME) will be introduced. The two previous approaches are reliant on splitting the Hamiltonian into system, bath, and system-bath coupling terms which is neither natural nor convenient for simulating nonadiabatic dynamics. In comparison, the M-GQME is optimized for simulating nonadiabatic dynamics. Within the M-GQME, new protocols will be introduced for calculating the memory kernel via different MQC and QC methods. Through the application of the M-GQME to a spin-boson model with the memory kernel obtained via the Ehrenfest method, it will be shown that the M-GQME is more stable and robust compared to the previous approaches and that limiting the use of Ehrenfest to calculating the memory kernel enhances its accuracy in comparison to using it to directly simulate the system's dynamics. In the second chapter, two mapping Hamiltonian (MH) approaches with a QC approximation will be outlined and utilized to calculate the memory kernel of the M-GQME. These QC/MH methods have several advantages over the Ehrenfest method, including describing both the electronic and nuclear degrees of freedom as classical-like quantities and the ability to have non-Hermitian initial electronic states. By combining the QC/MH methods with the M-GQME on the spin-boson model, it will be shown that the M-GQME with the QC/MH methods outperforms both the M-GQME with Ehrenfest and the direct application of the QC/MH methods. In the third chapter, forty-four different methods for obtaining the memory kernel of the GQME are systematically explained and explored, including the three approaches previously discussed. The ability to calculate the memory kernel of the GQME is relatively new and a thorough examination of the different ways of obtaining the memory kernel has not been done. Through the study of these many approaches on the spin-boson model, the impact of the different approaches will be described and the benefits of the M-GQME compared to other approaches further solidified. In the fourth and fifth chapters, the M-GQME will be applied to models of the Fenna-Matthews-Olson (FMO) complex, a photosynthetic system, and the 2,6,-bis(methylene) adamantyl (BMA) radical cation, which contains a conical intersection. These two systems represent areas of considerable interest, given the prevalence of photosynthesis and conical intersections in biologically- and technologically-relevant systems. As will be shown, the success of the M-GQME with FMO and preliminary failure with BMA illuminates future areas where the M-GQME is expected to succeed along with the limitations of its application.