Accurate excited states with quantum Monte Carlo: looking beyond conventions

The development of accurate computational methods for the predictive modeling of excited states is a very active field of research in quantum chemistry. Despite significant progress, there still exists a serious theoretical vacuum in the availability of efficient techniques that can provide a reliable description, particularly when one is interested in features of the potential energy surface outside the Franck-Condon region. In this thesis, we explore the use of the highly-correlated quantum Monte Carlo (QMC) methods in this direction. In particular, we assess the predictive power of QMC methods in obtaining robust and accurate estimates of excitation energies as well as ground- and excited-state geometries. To this aim, we investigate these properties for a range of small prototypical molecules in the gas phase, which have been found to be challenging for standard electronic structure methods.

Here, we propose two novel strategies to systematically construct QMC wave functions of increasing quality thereby truly assessing the impact of the ingredients put into them. On one hand, we explore the choice of expansions built using an automated configuration-interaction (CI) approach called CIPSI which performs a smart selection of the most relevant determinants necessary to describe a given state from the full CI space and provide clear strategies to do so for multiple states in a balanced manner. On the other hand, we devise an alternative formulation of the many-body wave function by employing different local orbital descriptions and a correlation scheme based on the concept of orbital domains of local coupled-cluster methods. Next, we capitalize on recent methodological advances in variational Monte Carlo (VMC: the simplest QMC technique) that have rendered it a self-consistent method to optimize not only these wave functions but also molecular geometries in an efficient manner, even when involving over tens of thousands of variational parameters. We demonstrate that: (a) VMC is already sufficient to yield chemically accurate estimates of excitation energies and optimal geometries, circumventing the need to further employ the more sophisticated diffusion MC technique, and (b) When optimized in VMC, relatively compact wave functions can already produce these estimates
compatible with best theoretical benchmarks.