UC Berkeley

The accurate description of molecular excited states is an active frontier in the development of electronic structure theory. Compared to their ground state counterparts, electronic structure methods for excited states remain less well developed and many of the most widely used options struggle to provide accurate and predictive results across all varieties of excited states. This thesis presents a series of contributions to the development of variational Monte Carlo (VMC) as a broadly reliable tool for excited states, with a particular emphasis on wave function optimization algorithms.

We first present an analysis of current first and second order optimization techniques in VMC, demonstrating that each class of algorithm has strengths and weaknesses in terms of convergence and computational efficiency. The complementary nature of these traits motivates the design of a hybrid optimization algorithm, which can overcome the individual disadvantages of its constituent methods. After first developing this approach for ground state energy minimization, we extend it to the minimization of a variance-based objective function for the state-specific targeting of excited states. We demonstrate that employing VMC with the hybrid optimization algorithm can obtain highly accurate excitation energies across multiple classes of excited states, including single valence excitations, double excitations, and charge transfer. This level of reliability currently eludes all other electronic structure methods that can be applied beyond small molecules and enables VMC to serve as a widely applicable benchmark method for assessing which computationally cheaper methods are most trustworthy in various chemical contexts. We also continue our methodological work by presenting a systematic study of the issue of optimization stability in VMC and identify best practices for successful variance minimization that may aid the work of other researchers.