An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.
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21 January 2017
Research Article|
January 18 2017
Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals
Dorothea Golze;
Dorothea Golze
a)
1Department of Chemistry,
University of Zürich
, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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Niels Benedikter
;
Niels Benedikter
2QMath, Department of Mathematical Sciences,
University of Copenhagen
, Universitetsparken 5, 2100 København, Denmark
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Marcella Iannuzzi;
Marcella Iannuzzi
1Department of Chemistry,
University of Zürich
, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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Jan Wilhelm;
Jan Wilhelm
1Department of Chemistry,
University of Zürich
, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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Jürg Hutter
Jürg Hutter
1Department of Chemistry,
University of Zürich
, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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J. Chem. Phys. 146, 034105 (2017)
Article history
Received:
November 01 2016
Accepted:
December 19 2016
Citation
Dorothea Golze, Niels Benedikter, Marcella Iannuzzi, Jan Wilhelm, Jürg Hutter; Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals. J. Chem. Phys. 21 January 2017; 146 (3): 034105. https://doi.org/10.1063/1.4973510
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