*From*: Thomas Manz <tmanz(!)nmsu.edu>*Subject*: CCL:G: two-electron range-separated Coulomb and exchange integrals*Date*: Mon, 28 Sep 2015 14:39:47 -0600

Hi,

The range-separated Coulomb
integral

1/r = erf(k*r)/r +
(1-erf(k*r))/r

arises in range-separated hybrid
functionals.

There are many papers about functionals that use this
kind of range-separation.

My question is regarding the 2-electron
integral terms (i.e., exchange and Coulomb integrals)

using this type
of range separation. Does anyone know where the analytic forms for this have
been published?

They should be of the
form

<g1(r1)*g2(r1)*(erf(k*r)/r)*g3(r2)*g4(r1)>

where
<> means integrate over positions r1 and r2 and g1, g2, g3, g4 are
Gaussian basis sets.

We are actually trying to do the
analogous Coulomb/exchange integrals for electrons confined to a plane (i.e.,
two-dimensional Gaussians), but we maybe could figure out how to do this by
looking at the three-dimensional case.

I would be
grateful if anyone could provide references on the mathematical derivations of
the analytic integrals for the three-dimensional
case.

Sincerely,

Tom Manz