Tight distance-dependent estimators for screening two-center and three-center short-range Coulomb integrals over Gaussian basis functions

Abstract

We derive distance-dependent estimators for two-center and three-center electron repulsion integrals over a short-range Coulomb potential, $\text{erfc}(\omega r_{12})/r_{12}$. These estimators are much tighter than one based on the Schwarz inequality and can be viewed as a complement to the distance-dependent estimators for four-center short-range Coulomb integrals and for two-center and three-center full Coulomb integrals previously reported. Because the short-range Coulomb potential is commonly used in solid-state calculations, including those with the HSE functional and with our recently introduced range-separated periodic Gaussian density fitting, we test our estimators on a diverse set of periodic systems using a wide range of the range-separation parameter $\omega$. These tests demonstrate the robust tightness of our estimators, which are then used with integral screening to calculate periodic three-center short-range Coulomb integrals with linear scaling in system size.

13 pages, 8 figures (main text)

References in corpus (5)

• Ideal regularization of the Coulomb singularity in exact exchange by Wigner-Seitz truncated interactions: towards chemical accuracy in non-trivial systems
• Hybrid-functional calculations with plane-wave basis sets: The effect of the singularity correction on total energies, energy eigenvalues, and defect energy levels
• Gaussian and plane-wave mixed density fitting for periodic systems
• Fast periodic Gaussian density fitting by range separation
• Fundamentals of Molecular Integrals Evaluation