Accurate excited states with quantum monte carlo: Looking beyond conventions
Due to the COVID-19 crisis measures the PhD defence of Monika Dash will take place (partly) online in the presence of an invited audience.
The PhD defence can be followed by a live stream.
Monika Dash is a PhD student in the research group Computational Chemical Physics (CCP). Her supervisor is prof.dr. C. Filippi from the Faculty of Science and Technology (TNW).
The development of accurate computational methods for the predictive modelling of excited states is a very active field of research in quantum chemistry. Despite significant progress in the past decade, there still exists a serious theoretical vacuum in the availability of efficient techniques that can provide a reliable description of excited states. The scarcity is more profound when one is interested in exploring features of a potential energy surface (PES) outside the so-called Franck-Condon region. For instance, one might ask: What happens to the geometry of a molecule when it absorbs light? Is the equilibrium structure in this excited state significantly different from the ground-state geometry? What chemical processes can these modifications facilitate?
In this thesis, we explore the somewhat unconventional use of the quantum Monte Carlo (QMC) methods to answer some of these questions. These are a class of highly accurate wave function based techniques that solve the electronic Schrodinger equation in a stochastic manner. This involves performing a random walk of the electrons, computing (say) energies corresponding to different electronic distributions and finally averaging them to estimate the net energy of a molecule. QMC methods have primarily been employed to calculate the total ground-state energies of molecules, even for systems containing over a hundred atoms. However through some key efforts made within our group and in this thesis, we have realized that they also hold potential to model excited states also in fairly complicated situations where standard quantum chemical approaches fail to provide an appropriate description. Furthermore, being embarrassingly parallel in nature, these methods can truly exploit the use of modern day supercomputers. To establish the proficiency of QMC as a reliable approach for the robust and predictive modelling of excited states, we investigate the gas phase properties i.e. ground and excited-state geometries as well as excitation energies, for a range of small, yet theoretically challenging prototypical molecules.
In doing so, we propose two novel strategies to systematically construct QMC wave functions of increasing quality while 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. We capitalize on recent methodological advances in variational Monte Carlo (VMC: the simplest QMC technique) which 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 thus allowing us to truly ascertain the predictive power of QMC. Our most important findings are: (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 (particularly those obtained with the CIPSI scheme) can already produce these estimates compatible with theoretical benchmarks of the highest quality.
