Electronic transitions, statistics and digital tools for quantum chemistry (PhD. thesis)
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This thesis concerns two main topics: i) molecular electronic excited states and ii) digital tools for theoretical quantum chemistry. The present thesis starts with a study of the GW family of approximations. These are known to be accurate and relatively cheap methodologies for the computation of charged excitations such as ionization potentials and electronic affinities in molecules and band gaps in solids. These methods can be perturbative, partially or fully self-consistent and are able to provide chemically accurate properties for weakly correlated systems. However, as discussed in details, discontinuities can be observed for several key properties, particularly in potential energy surfaces even in the weakly correlated regime. These discontinuities are due to poles in the self-energy — a key quantity of the GW formalism — as each of its branch is associated with a distinct solution of the quasiparticle equation. We show that, in diatomic molecules, multisolution behavior in frontier orbitals is more likely if the energy gap between these orbitals is small. The central part of this thesis deals with the QUEST project, a large database of more than 600 vertical excitations energies of various natures. The aim of this open-source and easily-modifiable database is to provide highly-accurate reference excitations energies for benchmarking and cross comparisons of computational models. These reference excitations energies are divided into six subsets depending on the size of the molecules and the types of excitations. In order to gather the huge amount of data of the QUEST project, we have created a website where one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the type of basis set, etc. The next part is about digital tools and, in particular, the implementation of a web demo of Quantum Package, an open-source software developed primarily by our research group, which has been designed to be easy to use by quantum chemists, whether they are users or developers. The possibility of testing the software without the need to install it is a real opportunity to make Quantum Package more popular in our community. The containerization technology provided by Docker and the Linux kernel allow us to quickly start a clean demo environment for each user and stop it easily with interesting performance. Finally, pursuing the recent work of our team on the benzene molecule, we report reference frozen-core correlation energies for the twelve five- and six-membered ring molecules of the QUEST project using the Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI) algorithm in the standard correlation-consistent double-ζ Dunning basis set (cc-pVDZ). These correspond to Hilbert spaces with sizes ranging from 10²⁸ to 10³⁶. The performance and convergence properties of several series of methods are investigated. In particular, we study the convergence properties of the Møller-Plesset perturbation series up to fifth-order as well as various single-reference coupled-cluster models which include up to quadruple excitations.