Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals

摘要

An integral scheme for the efficient evaluation of two-center integrals overcontracted solid harmonic Gaussian functions is presented. Integral expressionsare derived for local operators that depend on the position vector of one ofthe two Gaussian centers. These expressions are then used to derive the formulafor three-index overlap integrals where two of the three Gaussians are locatedat the same center. The efficient evaluation of the latter is essential forlocal resolution-of-the-identity techniques that employ an overlap metric. Wecompare the performance of our integral scheme to the widely used CartesianGaussian-based method of Obara and Saika (OS). Non-local interaction potentialssuch as standard Coulomb, modified Coulomb and Gaussian-type operators, thatoccur in range-separated hybrid functionals, are also included in theperformance tests. The speed-up with respect to the OS scheme is up to threeorders of magnitude for both, integrals and their derivatives. In particular,our method is increasingly efficient for large angular momenta and highlycontracted basis sets.