A simplified GW/BSE approach for charged and neutral excitation energies of large molecules and nanomaterials

Abstract

Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [S. Grimme, J. Chem. Phys. 138, 244104 (2013)], we describe a simplified approach to excited state calculations within the GW approximation to the self-energy and the Bethe-Salpeter equation (BSE), which we call sGW/sBSE. The primary simplification to the electron repulsion integrals yields the same structure as with tensor hypercontraction, such that our method has a storage requirement that grows quadratically with system size and computational timing that grows cubically with system size. The performance of sGW is tested on the ionization potential of the molecules in the GW100 test set, for which it differs from ab intio GW calculations by only 0.2 eV. The performance of sBSE (based on sGW input) is tested on the excitation energies of molecules in the Thiel set, for which it differs from ab intio GW/BSE calculations by about 0.5 eV. As examples of the systems that can be routinely studied with sGW/sBSE, we calculate the band gap and excitation energy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in 4678 spatial orbitals and the absorption spectra of two large organic dye molecules with hundreds of atoms.

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods

“…Using a semiempirical ground-state reference, sTDA errors were found to be slightly larger with mean absolute deviations in the range of 0.3–0.5 eV. Most importantly, accuracy was found to be consistent for both the low-energy valence as well as the high-energy Rydberg transitions. , Simplified approaches were also suggested for the Bethe–Salpeter equation (BSE) and the GW approximation . These methods provided sGW ionization potentials within the GW100 test set differing only by 0.2 eV while improving the cubic scaling with system size.…”

“…Deviations in sBSE excitation energies amount up to 0.5 eV and are thus in an error range comparable to those of sTDA and sTDDFT. 30 A closely related TDDFT+TB approach has been suggested by Visscher et al that relies on the same monopole approximation for the electron repulsion integrals but is, in contrast to sTDA and sTDDFT, not designed for hybrid but rather pure density functionals. 31,32 The mentioned advantages of ADMM and sTDA regarding their physically correct description of exact exchange qualify both approaches as promising for an efficient calculation of excited-state properties.…”

“… 21 , 22 Simplified approaches were also suggested for the Bethe–Salpeter equation (BSE) and the GW approximation. 30 These methods provided sGW ionization potentials within the GW100 test set differing only by 0.2 eV while improving the cubic scaling with system size. Deviations in sBSE excitation energies amount up to 0.5 eV and are thus in an error range comparable to those of sTDA and sTDDFT.…”

“…Deviations in sBSE excitation energies amount up to 0.5 eV and are thus in an error range comparable to those of sTDA and sTDDFT. 30 A closely related TDDFT+TB approach has been suggested by Visscher et al that relies on the same monopole approximation for the electron repulsion integrals but is, in contrast to sTDA and sTDDFT, not designed for hybrid but rather pure density functionals. 31 , 32 …”