Simple many-body based screening mixing ansatz for improvement of GW /Bethe-Salpeter equation excitation energies of molecular systems

Abstract

We propose a simple many-body based screening mixing strategy to considerably enhance the performance of the Bethe-Salpeter equation (BSE) approach for prediction of excitation energies of molecular systems. This strategy enables us to closely reproduce results of highly correlated equation of motion coupled cluster singles and doubles (EOM-CCSD) through optimal use of cancellation effects. We start from the Hartree-Fock (HF) reference state and take advantage of local density approximation (LDA) based random phase approximation (RPA) screening, denoted as ${W}_{0}$-RPA@LDA with ${W}_{0}$ as the dynamically screened interaction built upon LDA wave functions and energies. We further use this ${W}_{0}$-RPA@LDA screening as an initial screening guess for calculation of quasiparticle energies in the framework of ${G}_{0}{W}_{0}$@HF. The ${W}_{0}$-RPA@LDA screening is further injected into the BSE. By applying such an approach on a set of 22 molecules for which the traditional $GW$/BSE approaches fail, we observe good agreement with respect to EOM-CCSD references. The reason for the observed good accuracy of this mixing ansatz (scheme A) lies in an optimal damping of HF exchange effect through the ${W}_{0}$-RPA@LDA strong screening, leading to substantial decrease of typically overestimated HF electronic gap, and hence to better excitation energies. Further, we present a second multiscreening ansatz (scheme B), which is similar to scheme A with the exception that now the ${W}_{0}$-RPA@HF screening is used in the BSE in order to further improve the overestimated excitation energies of carbonyl sulfide (COS) and disilane $({\mathrm{Si}}_{2}{\mathrm{H}}_{6})$. The reason for improvement of the excitation energies in scheme B lies in the fact that ${W}_{0}$-RPA@HF screening is less effective (and weaker than ${W}_{0}$-RPA@LDA), which gives rise to stronger electron-hole effects in the BSE.