Electronic Excitations from Density Functional Theory, Time-Dependent Linear Response and Many-Body Green’s Functions

Abstract

The accurate theoretical description of electronic excitations is of crucial importance for understanding many important processes in various areas of science and technology, including specific problems such as photocatalysis, spectroscopy as well as various biochemical reactions. While the current state of the art for an accurate quantum chemistry description of the electronic ground state is relatively mature, the accurate and efficient treatment of electronic excited states is still teeming with both challenges and opportunities. In this treatise, the following different yet related methodologies have been employed to tackle this problem. Firstly, the orbitals and orbital energies obtained with ground state Kohn-Sham density functional theory calculations are adopted to describe the electron addition excitation, offering valuable qualitative insight into the photocatalytic mechanism and product selectivity of CO2 reduction with rhodium nanoparticles. Secondly, the development of the T-matrix method based on the time-dependent pairing density linear response and the particle-particle random phase approximation (pp-RPA) takes the leap from qualitative correctness to quantitative reliability for describing electron addition and removal excitations. Thirdly, the pp-RPA has been used to study neutral excitations, particularly the excited state potential energy surfaces and geometry optimization. Also, an active orbital selection approach has been developed which enables ~100-fold computational time savings and the application of the pp-RPA to large systems including polyacetylenes and polydiacetylenes. Lastly, a generalized theoretical framework from the superconductive Gorkov Green’s function perspective has been proposed which unifies the pp-RPA with the conventional particle-hole (ph) RPA, allowing for a systematic improvement of electron correlation treatment by incorporating higher-order self energy contributions in the respective ph and pp Bethe-Salpeter equations (BSEs). Initial numerical results in the ph channel demonstrate a significant accuracy improvement compared with conventional methods such as time-dependent density functional theory (TDDFT) within the adiabatic approximation.