Simplified GW/BSE Approach for Charged and Neutral Excitation Energies of Large Molecules and Nanomaterials

Abstract

Inspired by Grimmeʼs simplified Tamm−Dancoff density functional theory approach [Grimme, S. J. Chem. Phys. 2013, 138, 244104], 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 initio GW calculations by only 0.2 eV. The performance of sBSE (based on the sGW input) is tested on the excitation energies of molecules in Thielʼs set, for which it differs from ab initio 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.

Quasiparticle Self-Consistent GW-Bethe–Salpeter Equation Calculations for Large Chromophoric Systems

“…So far, applications of the GW -BSE method have been limited to rather small molecules. ,, We presented here a new implementation of the method, which enables its routine application to much larger systems. As opposed to a recently developed simplified GW -BSE scheme, our implementation does not introduce any empirical approximations to the matrix elements of the BSE Hamiltonian. Our implementation allowed us to calculate the 12 lowest excited states of the complete complex of 6 chromophores in the PSII RC with almost 2000 correlated electrons on the qs GW -BSE/TZP level.…”

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules

“…The final class uses the first-principles Kohn–Sham (KS) ground state and only introduces approximations to the linear response matrix; that is, a semiempirical linear response is performed on top of a first-principles ground state. Examples of this class include the simplified Tamm–Dancoff (sTDA) and simplified TDDFT (sTDDFT) models, , the TDDFT plus tight-binding (TDDFT+TB) model, and the simplified GW (sGW) and simplified Bethe–Salpheter equation (sBSE) models . More recently, a minimal auxiliary basis model for TDDFT (TDDFT-as) was proposed for semilocal density functionals in which the linear response kernel is approximated using RI where the fitting basis for each atom includes only one s -type Gaussian function .…”

“…Examples of this class include the simplified Tamm−Dancoff (sTDA) and simplified TDDFT (sTDDFT) models, 45,46 the TDDFT plus tight-binding (TDDFT+TB) model, 47 (sGW) and simplified Bethe−Salpheter equation (sBSE) models. 48 More recently, a minimal auxiliary basis model for TDDFT (TDDFT-as) was proposed for semilocal density functionals in which the linear response kernel is approximated using RI where the fitting basis for each atom includes only one s-type Gaussian function. 49 TDDFT-as was applied to silver nanoparticles where an average error of only 12 meV was found.…”

“…We attribute the excellent performance of TDDFT-ris for both excitation energies and spectra to the explicit description of transition densities using the minimal auxiliary basis. By contrast, tight-binding approaches ,, describe transition densities implicitly with Löwdin charge densities, which have numerical as opposed to physical definitions. , The TDDFT-ris model therefore opens up the possibility of computing accurate absorption spectra and optical properties for organic molecules with many hundreds of atoms using hybrid density functionals that may not be affordable otherwise.…”

Energies and spectra of solids from the algorithmic inversion of localized $GW$

“…[13,44,45]. Related approaches have also appeared recently to efficiently compute the GW self-energy and solve the Bethe-Salpeter equation [46,47].…”