2024 Theses Doctoral

The GW Approximation and Bethe-Salpeter Equation for Molecules and Extended Systems

Bintrim, Sylvia Joy

In the first two chapters, we provide a new way to think about the Green’s function-basedGW approximation and Bethe-Salpeter equation (BSE). The former is the most popular beyond-mean-field method for band structures of solids and an increasingly popular one for ionization potentials and electron affinities of molecules. The latter is widely used to compute neutral excitation energies and spectra for solids as well as, increasingly, molecules. Inspired by quantum chemistry approaches, we obtain a computational scaling reduction and avoid approximating certain dynamical quantities. The new formalism suggests further improvements to the GW and BSE methods.

In chapters four and five, we derive and test a cheap, approximate version of the GW and BSE for large molecules and then extend the strategy to periodic systems. In chapter six, we assess another Green’s function-based method, the constrained random phase approximation with exact diagonalization, usually applied to solids. This method allows one to treat electron correlation within an active space of important orbitals while also including some of the external orbital space effects. In chapters seven and eight, we implement the BSE in the PySCF software package for periodic systems using Gaussian density fitting and then apply it to a challenging system, the superatomic solid Re₆Se₈Cl₂.