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 charge-distributions. 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 [ and ], 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/r12 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.
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14 October 2017
Research Article|
October 09 2017
Distance-including rigorous upper bounds and tight estimates for two-electron integrals over long- and short-range operators
Travis H. Thompson;
Travis H. Thompson
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU)
, Butenandtstr. 7, D-81377 Munich, Germany
and Center for Integrated Protein Science Munich (CIPSM) at the Department of Chemistry, University of Munich (LMU)
, Butenandtstr. 5-13, D-81377 Munich, Germany
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Christian Ochsenfeld
Christian Ochsenfeld
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU)
, Butenandtstr. 7, D-81377 Munich, Germany
and Center for Integrated Protein Science Munich (CIPSM) at the Department of Chemistry, University of Munich (LMU)
, Butenandtstr. 5-13, D-81377 Munich, Germany
Search for other works by this author on:
J. Chem. Phys. 147, 144101 (2017)
Article history
Received:
July 04 2017
Accepted:
September 05 2017
Citation
Travis H. Thompson, Christian Ochsenfeld; Distance-including rigorous upper bounds and tight estimates for two-electron integrals over long- and short-range operators. J. Chem. Phys. 14 October 2017; 147 (14): 144101. https://doi.org/10.1063/1.4994190
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