Modelisation of London dispersion forces by random phase approximation: methodological developments

TL;DR

This thesis advances the formalism and computational methods of the random phase approximation (RPA) for modeling London dispersion forces, including developments in the dielectric matrix formulation, localized orbitals, and gradient calculations.

Contribution

It introduces new formal developments and computational tools for RPA, particularly in range-separated theories, with applications to geometry optimization and visualization of correlated densities.

Findings

Developed a real-space program for RPA functions visualization

Derived analytical gradients for RPA correlation energies in range separation

Performed geometry optimizations and visualizations on molecular sets

Abstract

In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localised orbitals, especially developments of the virtual localized orbitals that are the "projected oscillatory orbitals" (POO). A program has been written to calculate functions such as the exchange hole, the response function, etc on real space grid (parallelepipedic or of the "DFT" type) ; some of those visualisations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developped in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developped here with a lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimisations at the RSH+dRPA-I and RSH+SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualisations of correlated densities at the RSH+dRPA-I level.