Cubic-Scaling All-Electron GW Calculations with a Separable Density-Fitting Space–Time Approach

• Published in: Journal of chemical theory and computation Vol. 17; no. 4; pp. 2383 - 2393
• Main Authors: Duchemin, Ivan, Blase, Xavier
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 13.04.2021
• Subjects: Chemical Sciences; Condensed Matter; Coulomb potential; Crossovers; Electrons; Flakes (defects); Mathematical analysis; or physical chemistry; Physics; Scaling; Spectroscopy and Excited States; Theoretical and
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.1c00101

We present an implementation of the GW space–time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization or sparsity considerations. The independent-electron susceptibility is constructed in a time representation over a nonuniform distribution of real-space locations {r k } optimized within a separable resolution-of-the-identity framework to reproduce standard Coulomb-fitting calculations with meV accuracy. The compactness of the obtained {r k } distribution leads to a crossover with the standard Coulomb-fitting scheme for system sizes below a few hundred electrons. The needed analytic continuation follows a recent approach that requires the continuation of the screened Coulomb potential rather than the much more structured self-energy. The present scheme is benchmarked over large molecular sets, and scaling properties are demonstrated on a family of defected hexagonal boron-nitride flakes containing up to 6000 electrons.