Connecting Density Functional Theory and Green's Function Theory

Abstract

Developing accurate and efficient theoretical approaches to describe the electronic structure has been a long-standing task in quantum chemistry. The main workhouse in quantum chemistry, density functional theory (DFT), has been widely used because of the good accuracy and the affordable computational cost. However, the applicability of commonly used density functional approximations (DFAs) is limited by intrinsic problems such as the delocalization error. Green's function theory that recently has gained increasing attention is shown to outperform the Kohn-Sham DFT approach on many aspects but is also computationally demanding. In this work, DFT and Green's function theory are connected to develop accurate and robust approaches for describing both ground state and excited state properties. For ground state calculations, the renormalized singles (RS) Green's function that captures all singles contributions from the KS Green's function is applied in the GW and the T-matrix approximation to predict accurate quasiparticle (QP) energies. GRSWRS and GRSTRS are shown to outperform over commonly used G0W0 and G0T0 for predicting ionization potentials (IPs) and core-level binding energies (CLBEs). The RS with correlation (RSc) Green's function that also includes higher order contributions in GW is shown to provide further improvements over GRSWRS. The concept of RS has also been used in the multireference DFT approach, which describes strongly correlated systems. We also provide an analytical approach to calculate QP energies of DFAs that can be expressed as a functional of the non-interacting Green's function. For excited state calculations, we combine localized orbital scaling correction (LOSC) with Bethe-Salpeter equation (BSE) to calculate excitation energies of molecular systems. QP energies from LOSC that systematically eliminates the delocalization error are used in BSE, which bypasses the expensive GW calculations. BSE/LOSC is shown to predict accurate excitation energies of valence, charge transfer and Rydberg excitations. We also combine the RS Green's function with BSE. BSE/GRSWRS is shown to provide a comparable accuracy to the computationally expensive BSE/evGW. We show that combining the merit of DFT and Green's function theory leads to accurate and efficient theoretical approaches for describing both the ground state and the excited state.