  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, that
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.
