Accelerating Time-Dependent Density Functional Theory and GW Calculations for Molecules and Nanoclusters with Symmetry Adapted Interpolative Separable Density Fitting

Abstract

Computing integrals over orbital pairs is one of the most costly steps in many popular first-principles methods used by the quantum chemistry and condensed matter physics community. Here, we employ a recently proposed interpolative separable density fitting method (ISDF) to significantly reduce the cost of steps involving orbital pairs in linear response time-dependent density functional theory and GW calculations. In our implementation, we exploit the symmetry property of a system to effectively reduce the number of interpolation points and thus the computational cost. The performance of ISDF is illustrated with calculations on the GW100 set and silicon nanoclusters. We demonstrate the cost for constructing auxiliary basis and interpolation coefficients are negligible compared to the total cost. Compared to the conventional brute-force approach, the computation cost for evaluating all kernel matrix elements is reduced by nearly 3 orders of magnitude. The total cost for GW calculations can be reduced by four to eight times, depending on the system size.

The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules

“…This set came into existence first in a comparison between only three codes ( van Setten et al, 2015 ). In the meantime the developers of many other codes have used the set to test and benchmark their implementations, both for GW and other computational approaches aiming at the calculation of ionization energies and electron affinities ( Caruso et al, 2016 ; Vlček et al, 2017a ; Maggio et al, 2017 ; Wilhelm and Hutter, 2017 ; Govoni and Galli, 2018 ; Rodrigues Pela et al, 2018 ; Colonna et al, 2019 ; Gao and Chelikowsky, 2019 ; Brémond et al, 2020 ; Förster and Visscher, 2020 ; Gao and Chelikowsky, 2020 ; Bintrim and Berkelbach, 2021 ; Duchemin and Blase, 2021 ; Förster and Visscher, 2021 ; Wilhelm et al, 2021 ). At present over a hundred data sets have appeared for the GW100 set.…”

The Bethe-Salpeter Equation Formalism: From Physics to Chemistry

“…102 The separability of occupied and virtual states summations lying at the heart of these approaches are now spreading fast in quantum chemistry within the interpolative separable density fitting (ISDF) approach applied for calculating with cubic scaling the susceptibility needed in random-phase approximation (RPA) and GW calculations. [103][104][105] These ongoing developments pave the way to applying the GW@BSE formalism to systems containing several hundred atoms on standard laboratory clusters.…”

Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach

“…While such a moderate scaling already allows calculations on systems containing well over a hundred atoms on supercomputers, [64][65][66][67] attempts to deliver GW calculations with a lower scaling appeared with the seminal space-time approach by Rojas, Needs and Godby in 1995 68 and are now blooming. 24,42,[69][70][71][72][73][74][75][76] This space-time formalism 68 stands as the first cubic-scaling GW approach relying on the separability of the independent-electron susceptibility χ 0 as the product of two Green's functions when expressed over a real-space grid, adopting further a time representation. This factorisation allows decoupling the summation over occupied and virtual molecular orbital contributions, leading to a cubic scaling scheme instead of the traditional quartic scaling calculation of χ 0 .…”

“…[83][84][85] More recently, the interpolative separable density fitting (ISDF) approach 86,87 represents a versatile strategy to combine the standard quantum chemistry resolution-of-the-identity (RI) techniques with a separable representation of the coefficients of molecular orbital products over auxiliary basis sets. The ISDF approach is now developing in the pseudopotential planewave or real-space grid community, 72,[88][89][90][91] including a recent GW implementation. 72 Similarly, building on the expertise with resolution-of-the-identity (RI) techniques and/or real-space quadratures for Coulomb integrals, the ISDF scheme is also being explored by the quantum chemistry community working with localized (e.g.…”

“…The ISDF approach is now developing in the pseudopotential planewave or real-space grid community, 72,[88][89][90][91] including a recent GW implementation. 72 Similarly, building on the expertise with resolution-of-the-identity (RI) techniques and/or real-space quadratures for Coulomb integrals, the ISDF scheme is also being explored by the quantum chemistry community working with localized (e.g. Gaussian) basis sets for explicitly correlated all-electron calculations such as QMC or Möller-Plesset techniques.…”