Distance-including rigorous upper bounds and tight estimates for two-electron integrals over long- and short-range operators

Thompson, Travis H. und Ochsenfeld, Christian (2017): Distance-including rigorous upper bounds and tight estimates for two-electron integrals over long- and short-range operators. In: Journal of Chemical Physics, Bd. 147, Nr. 14, 144101

Abstract

We introduce both rigorous and non-rigorous distance-dependent integral estimates for four-center two-electron integrals derived from a distance-including Schwarz-type inequality. The estimates are even easier to implement than our so far most efficient distance-dependent estimates [S. A. Maurer et al., J. Chem. Phys. 136, 144107 (2012)] and, in addition, do not require well-separated chargedistributions. They are also applicable to a wide range of two-electron operators such as those found in explicitly correlated theories and in short-range hybrid density functionals. For two such operators with exponential distance decay [e(-r12) and erfc(0.11 . r(12))/r(12)], the rigorous bound is shown to be much tighter than the standard Schwarz estimate with virtually no error penalty. The non-rigorous estimate gives results very close to an exact screening for these operators and for the long-range 1/r(12) operator, with errors that are completely controllable through the integral screening threshold. In addition, we present an alternative form of our non-rigorous bound that is particularly well-suited for improving the PreLinK method [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 138, 134114 (2013)] in the context of short-range exchange calculations. Published by AIP Publishing.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Chemie und Pharmazie > Department Chemie
• Themengebiete: 500 Naturwissenschaften und Mathematik > 540 Chemie
• ISSN: 0021-9606
• Sprache: Englisch