Accuracy Assessment of GW Starting Points for Calculating Molecular Excitation Energies Using the Bethe–Salpeter Formalism

Abstract

The performance of the Bethe-Salpeter equation (BSE) approach for the first-principles computation of singlet and triplet excitation energies of small organic, closed-shell molecules has been assessed with respect to the quasiparticle energies used on input, obtained at various levels of GW theory. In the corresponding GW computations, quasiparticle energies have been computed for all orbital levels by means of using full spectral functions. The assessment reveals that, for valence excited states, quasiparticle energies obtained at the levels of eigenvalue-only self-consistent (ev GW) or quasiparticle self-consistent theory (qs GW) are required to obtain results of comparable accuracy as in time-dependent density-functional theory (TDDFT) using a hybrid functional such as PBE0. In contrast to TDDFT, however, the BSE approach performs well not only for valence excited states but also for excited states with Rydberg or charge-transfer character. To demonstrate the applicability of the BSE approach, computation times are reported for a set of aromatic hydrocarbons. Furthermore, examples of computations of ordinary photoabsorption and electronic circular dichroism spectra are presented for (C) and C, respectively.

The Quest for Highly Accurate Excitation Energies: A Computational Perspective

“…64,65 One of the main advantage of BSE compared to TD-DFT (with a similar computational cost) is that it allows a faithful description of charge-transfer states and, when performed on top of a (partially) self-consistently GW calculation, BSE@GW has been shown to be weakly dependent on its starting point (i.e., on the functional selected for the underlying DFT calculation). 66,67 However, due to the adiabatic (i.e., static) approximation, doubly excited states are completely absent from the BSE spectrum.…”

Pros and Cons of the Bethe–Salpeter Formalism for Ground-State Energies

“…[24][25][26][27][28][29][30] One of the main advantages of BSE compared to TD-DFT is that it allows a faithful description of charge-transfer states. [31][32][33][34][35][36] Moreover, when performed on top of a (partially) self-consistent evGW calculation, [37][38][39][40][41][42][43] BSE@evGW has been shown to be weakly dependent on its starting point (e.g., on the exchange-correlation functional selected for the underlying DFT calculation). 24,43 However, similar to adiabatic TD-DFT, [44][45][46][47] the static version of BSE cannot describe multiple excitations.…”

“…[31][32][33][34][35][36] Moreover, when performed on top of a (partially) self-consistent evGW calculation, [37][38][39][40][41][42][43] BSE@evGW has been shown to be weakly dependent on its starting point (e.g., on the exchange-correlation functional selected for the underlying DFT calculation). 24,43 However, similar to adiabatic TD-DFT, [44][45][46][47] the static version of BSE cannot describe multiple excitations. [48][49][50] A significant limitation of the BSE formalism, as compared to TD-DFT, lies in the lack of analytical nuclear gradients (i.e., the first derivatives of the energy with respect to the nu-clear displacements) for both the ground and excited states, 51 preventing efficient studies of excited-state processes (e.g., chemoluminescence and fluorescence) associated with geometric relaxation of ground and excited states, and structural changes upon electronic excitation.…”

Unphysical Discontinuities in GW Methods

“…8,13,47,93 For larger systems, hybrid functionals 94 might be the ideal compromise, thanks to the increase of the HOMO-LUMO gap via the addition of (exact) HF exchange. 8,35,38,46,95 4 Concluding remarks e GW approximation of many-body perturbation theory has been highly successful at predicting the electronic properties of solids and molecules. [2][3][4] However, it is also known to be inadequate to model strongly correlated systems.…”