Benchmarking the Bethe–Salpeter Formalism on a Standard Organic Molecular Set

Abstract

We perform benchmark calculations of the Bethe–Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel’s set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe–Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G0W0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average −0.59 eV redshift compared to reference calculations for Thiel’s set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe–Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe–Salpeter implementation may differ significantly for states implying a large multiple excitation character.

molgw 1: Many-body perturbation theory software for atoms, molecules, and clusters

“…1. The optimal choice of gKS starting point, whether Hartree-Fock, a semi-local approximation, or a hybrid functional within density-functional theory (DFT), is not trivial for a given system and is currently an active area of research [41,39,42,38,43,44]. In any case, the wavefunctions and eigenvalues that result from the gKS calculation are used to produce the screened Coulomb interaction W which is an ingredient in both the GW approximation to the self-energy and in the BSE.…”

“…Some authors [42,43,47] advocate for iterating further the GW equations by updating the eigenvalues in Eq. (1) to those from Eq.…”

Excitation spectra of aromatic molecules within a real-spaceGW-BSE formalism: Role of self-consistency and vertex corrections

“…In several examples with atom-centered basis sets, the accuracy of selfconsistent GW is competitive with G 0 W 0 predictions using Hartree-Fock and hybrid functional mean-field starting points. [2][3][4][5]10,13,15,17,22,24,52,55 However, recent results for fully self-consistent GW on a plane-wave basis set report slightly larger errors. 19 Overall, self-consistent GW pushes the IPs upward compared to G 0 W 0 with a DFT starting point, and it shifts IPs slightly downward when using a Hartree-Fock starting point.…”

Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

“…3, we compare the first lowest optical singlet excitations predicted by TDSX with the revised best theoretical estimates for Thiel's test set, as obtained from reference literature values and quantum chemistry calculations, e.g., coupled cluster [88]. Thiel's test set consists of 28 molecules and was recently used for benchmarking state-of-the-art many-body perturbation theory techniques based on the Bethe-Salpeter-equation (BSE) and the GW approximation [89,90]. Jacquemin et al [91] found TDPBE0 (timedependent density functional calculations with the PBE0 functional) to be exceptionally accurate for this set, with the lowest mean absolute error compared to 28 exchange correlation functionals.…”

“…(10)], TDPBE0 and PBE0 with many-body perturbation theory corrections (BSE@G 0 W 0 @PBE0) TDPBE0 and BSE@G 0 W 0 @PBE0 are taken from Ref. [89].…”