Abstract
We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing an inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analyzed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the correctness and usefulness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the term.
- Received 4 September 2012
DOI:https://doi.org/10.1103/PhysRevA.86.052513
©2012 American Physical Society