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Inspired by Grimme's simplified Tamm-Dancoff density functional theoryapproach [S. Grimme, J. Chem. Phys. \textbf{138}, 244104 (2013)], we describe asimplified approach to excited state calculations within the GW approximationto the self-energy and the Bethe-Salpeter equation (BSE), which we callsGW/sBSE. The primary simplification to the electron repulsion integrals yieldsthe same structure as with tensor hypercontraction, such that our method has astorage requirement that grows quadratically with system size and computationaltiming that grows cubically with system size. The performance of sGW is testedon the ionization potential of the molecules in the GW100 test set, for whichit differs from \textit{ab intio} GW calculations by only 0.2 eV. Theperformance of sBSE (based on sGW input) is tested on the excitation energiesof molecules in the Thiel set, for which it differs from \textit{ab intio}GW/BSE calculations by about 0.5 eV. As examples of the systems that can beroutinely studied with sGW/sBSE, we calculate the band gap and excitationenergy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in4678 spatial orbitals and the absorption spectra of two large organic dyemolecules with hundreds of atoms.

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