Efficient Evaluation of Exact Exchange for Periodic Systems via Concentric Atomic Density Fitting

Abstract

The evaluation of exact (Hartree--Fock, HF) exchange operator is a crucial ingredient for the accurate description of electronic structure in periodic systems through ab initio and hybrid density functional approaches. An efficient formulation of periodic HF exchange in LCAO representation presented here is based on the concentric atomic density fitting (CADF) approximation, a domain-free local density fitting approach in which the product of two atomic orbitals (AOs) is approximated using a linear combination of fitting basis functions centered at the same nuclei as the AOs in that product. Significant reduction in the computational cost of exact exchange is demonstrated relative to the conventional approach due to avoiding the need to evaluate four-center two-electron integrals, with sub-millihartree/atom errors in absolute Hartree-Fock energies and good cancellation of fitting errors in relative energies. Novel aspects of the evaluation of the Coulomb contribution to the Fock operator, such as the use of real two-center multipole expansions and spheropole-compensated unit cell densities are also described.

arXiv comment33 pages, 3 figures

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• Robust Pipek-Mezey Orbital Localization in Periodic Solids
• Density fitting in periodic systems: application to TDHF in diamond and oxides
• Economical Quasi-Newton Self Consistent Field Solver
• Exact Exchange with Range-separated Algorithm for Thermodynamic Limit of Periodic Hartree-Fock Theory
• Efficient Computation of the Long-Range Exact Exchange using an Extended Screening Function
• Low-scaling \textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework