CCL:G: two-electron range-separated Coulomb and exchange integrals


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 
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.


Tom Manz