Proceedings of nanoGe Fall Meeting 2021 (NFM21)
DOI: https://doi.org/10.29363/nanoge.nfm.2021.153
Publication date: 23rd September 2021
The GW approximation to the self-energy and the corresponding Bethe-Salpeter equation (BSE) together provide a state-of-the-art computational framework for the study of charged and neutral excitations in molecules and materials. However, their computational cost can be prohibitive for the description of certain electronic phenomena or large systems. In this talk, I'll describe two new directions that aim to lower the cost of GW/BSE calculations. The first direction addresses full-frequency implementations of GW/BSE including dynamical screening. I'll show that the requisite frequency-dependent eigenvalue problems of GW and BSE calculations can be exactly recast as frequency-independent eigenvalue problems in an enlarged space. Combined with the density fitting approximation to electron repulsion integrals, this reformulation leads to reduced scaling implementations of both methods. Moreover, it allows us to quantitatively study double excitations, including their energies and wavefunction character. In a second direction, I'll consider GW/BSE calculations on very large systems, with thousands of electrons or more. Here, we have used a simplifying approximation to the electron repulsion integrals with the same structure as in methods based on tensor hypercontraction. This approximation leads to GW/BSE calculations with storage and execution times that scale quadratically and cubically with the system size, respectively, and typically exhibit errors of only about 0.5 eV with respect to fully ab initio calculations. These methods can be applied to study systems containing thousands of electrons in only a few hours on commodity hardware.
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