Combining localized orbital scaling correction and Bethe–Salpeter equation for accurate excitation energies

Abstract

We applied localized orbital scaling correction (LOSC) in Bethe-Salpeter equation (BSE) to predict accurate excitation energies for molecules. LOSC systematically eliminates the delocalization error in the density functional approximation and is capable of approximating quasiparticle (QP) energies with accuracy similar or better than the GW Green's function approach and with much less computational cost. The QP energies from LOSC instead of commonly used G0 W0 and ev GW are directly used in BSE. We show that the BSE/LOSC approach greatly outperforms the commonly used BSE/ G0W0 approach for predicting excitations with different characters. For the calculations for Truhlar-Gagliardi test set containing valence, charge transfer (CT) and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/ev GW. For the calculations of Stein CT test set and Rydberg excitations of atoms, BSE/LOSC considerably outperforms both BSE/ G0W0 and TDDFT approaches with a reduced starting point dependence. BSE/LOSC is thus a promising and efficient approach to calculate excitation energies for molecular systems.

Combining Renormalized Singles GW Methods with the Bethe–Salpeter Equation for Accurate Neutral Excitation Energies

“…In BSE/G 0 W 0 , the dependence on the DFA starting point is in the range of 0.5 eV for predicting valence excitation energies and can even exceed 1.0 eV for predicting CT excitation energies. 59 It has been shown that BSE/G 0 W 0 based on range-separated functionals and tuned hybrid functionals provides more accurate excitation energies 32,60 than BSE/ G 0 W 0 based on GGA functionals. This dependence can be largely reduced by introducing self-consistency into the GW calculations, such as the eigenvalue-self-consistent GW (evGW) method, where the eigenvalues are iterated in G and W, the quasiparticle-self-consistent GW (qsGW) scheme,c 61,62 or the fully self-consistent GW (scGW) approach.…”

“…63,64 It has been shown that the BSE/evGW approach provides an accuracy comparable to TDDFT for predicting valence excitations and significantly outperforms BSE/G 0 W 0 and TDDFT for predicting CT and Rydberg excitations. 38,59,65 The DFA dependence in BSE/evGW is largely washed out. 38,59,65 In practice, evGW calculations can converge within a few steps by using the linear mixing method.…”

Renormalized Singles with Correlation inGWGreen’s Function Theory for Accurate Quasiparticle Energies

“…29 G RS W RS provides consistent improvements over G 0 W 0 29 and has been combined with the Bethe−Salpeter equation to compute accurate excitation energies. 64 The concept of RS has also been successfully applied in the multireference DFT approach 65 to describe the static correlation in strongly correlated systems. The RS Green function shares similar thinking as the renormalized singleexcitation (rSE) in the random phase approximation (RPA) calculation for accurate correlation energies.…”

“…G RS W 0 outperforms G 0 W 0 for predicting IPs with a small starting point dependence but fails to provide the unique solution to the QP equation for core states and has been combined with the Bethe–Salpeter equation to compute accurate excitation energies . The concept of RS has also been successfully applied in the multireference DFT approach to describe the static correlation in strongly correlated systems.…”

“…It can be seen that dipole moments predicted by DFT calculations depend on the choice of the DFA and that the errors are relatively large. It has been shown in ref that using localized orbitals provides improved accuracy for predicting dipole moments of small molecules. As shown in refs and , qs GW that also provides more localized orbitals outperforms DFAs for predicting dipole moments.…”