Computation of two-electron Gaussian integrals for wave functions including the correlation factor r12exp(−γr122) Original Research Article

Explicitly correlated molecular electronic-structure calculations with the damped correlation factor r12exp(−γr122) require two-electron integrals that are different from the already implemented R12 integrals. The aim of such a correlation factor, which combines the interelectronic distance with a Gaussian-type function, is to avoid integrals with large interelectronic distances, thus making it possible to use R12 methods for large molecular systems. In particular, an important perspective of the new correlation factor is to be able to utilize local-correlation techniques for explicitly correlated wave functions, such that computation times will asymptotically scale linearly with the size of the molecule. For the development of such techniques, the correlation factor must be restricted to the (physically meaningful) short range of the correlation cusp of the Coulomb hole. In the present paper, the evaluation of all two-electron integrals needed for damped-R12 theory is described, as implemented in a local version of the Dalton program.