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

Abstract

We present first-principle calculations on the vertical ionization potentials (IPs), electron affinities (EAs), and singlet excitation energies on an aromatic-molecule test set (benzene, thiophene, 1,2,5-thiadiazole, naphthalene, benzothiazole, and tetrathiafulvalene) within the GW and BetheSalpeter equation (BSE) formalisms. Our computational framework, which employs a real-space basis for ground-state and a transition-space basis for excited-state calculations, is well-suited for high-accuracy calculations on molecules, as we show by comparing against G0W0 calculations within a plane-wave-basis formalism. We then generalize our framework to test variants of the GW approximation that include a local-density approximation (LDA)-derived vertex function (ΓLDA) and quasiparticle-self-consistent (QS) iterations. We find that ΓLDA and quasiparticle self-consistency shift IPs and EAs by roughly the same magnitude, but with opposite sign for IPs and same sign for EAs. G0W0 and QSGW ΓLDA are more accurate for IPs, while G0W0ΓLDA and QSGW are best for EAs. For optical excitations, we find that perturbative GW -BSE underestimates the singlet excitation energy, while self-consistent GW -BSE results in good agreement with previous best-estimate values for both valence and Rydberg excitations. Finally, our work suggests that a hybrid approach, where G0W0 energies are used for occupied orbitals and G0W0ΓLDA for unoccupied orbitals, also yields optical excitation energies in good agreement with experiment but at a smaller computational cost.

Green Functions and Self-Consistency: Insights From the Spherium Model

“…where Z (ω) is given by Eq. (19). In a weakly or moderately correlated regime, one can clearly distinguish dominant quasiparticle peaks from satellites, whereas this scenario can break down in the strongly correlated regime.…”

On the possibility of singlet fission in crystalline quaterrylene

“…28,119 PBE+TS used here, has provided reliable predictions for the structure of PAH crystals, 27,75,[120][121][122] however somewhat larger deviations from experiment are obtained for HB perylene, as discussed in the SI. Errors in the G 0 W 0 step may stem from the G 0 W 0 approximation itself (i.e., neglecting the vertex, lack of selfconsistency, and the diagonal approximation), [123][124][125][126][127][128] numerical settings, pseudopotentials, 129,130 the mean-field starting point (e.g., self-interaction errors in DFT functionals), 111,[131][132][133] and approximations used in the self-energy evaluation, such as the Hybertsen-Louie generalized plasmon-pole model. 89 GW+BSE only considers particlehole interactions and cannot describe states with multi-exciton character 134,135 (it has been postulated based on multi-reference calculations that one of the low-lying excitons of the quaterrylene molecule in the gas phase may have a fraction of double-excitation character, 136,137 however such calculations cannot be performed for molecular crystals with periodic boundary conditions).…”

“…42 Several recent benchmarks for molecular systems, using different codes, have shown that G 0 W 0 +BSE@PBE systematically underestimates both singlet and triplet excitation energies. 123,[112][113][114] It is presently unknown whether the same trends persist in molecular solids, in part owing to lack of high-level reference data for periodic systems. From here on, we restrict the discussion to qualitative trends.…”

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

“…[9][10][11][12][13][14][15][16][17][18][19][20][21] It now stands as a cost-effective computational method that can model excited states 22,23 with a typical error of 0.1-0.3 eV for spin-conserving transitions according to large and systematic benchmarks. [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).…”