Developing quantum field theoretical computational methods for quantum dynamics and statistical mechanics simulations in quantum chemistry

Abstract

This thesis presents the development of two approaches—thermal normal-ordered exponential (TNOE) and thermofield coupled cluster (TFCC)—for simulating quantum dynamics and statistical mechanics in quantum chemistry, grounded in quantum field theoretical formulations. The TNOE approach employs a normal-ordered exponential ansatz to parameterize the thermal density operator, allowing the calculation of thermal properties through cluster expansions and imaginary time integration of equations of motion (EOMs). The TFCC approach introduces a fictitious space and Bogoliubov transformation to express the thermal density operator as a "pure state," similarly enabling thermal property calculations through imaginary time integration. The two approaches are verified to be mathematically equivalent and they are applied to two specific problems: the electronic structure problem and the vibronic coupling problem. The application on the thermal electronic structure problems encounters challenges due to N-representability issues. Modifications to the TNOE approach lead to the vibrational electronic coupled cluster (VECC) method, effectively simulating the quantum dynamics of vibronic coupling systems with impressive efficiency and accuracy. The statistical mechanics formulation of the VECC method, vibrational electronicthermofield coupled cluster (VE-TFCC), utilizes imaginary time integration to successfully calculate thermal properties of vibronic coupling systems with enhanced efficiency and accuracy compared to conventional methods. Overall, the VECC and VE-TFCC approaches, in combination with vibronic models, provides a robust framework for simulating quantum dynamics and thermal equilibrium properties of vibronic coupling systems.