Analytical two-center integrals over Slater geminal functions

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 a 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 analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-γr12) term in the master integral.

28 pages, 0 figures, 7 tables

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• Accurate Born-Oppenheimer potentials for excited ${\Sigma }^{+}$ states of the hydrogen molecule
• Efficient approach to two-centre exponential integrals with applications to excited states of molecular hydrogen
• Calculation of Araki-Sucher correction for many-electron systems
• Potential energy curve for the $a^3{\Sigma }_u^{+}$ state of lithium dimer with Slater-type orbitals
• Atomic Bethe logarithm in the mean-field approximation
• Combining Slater-type orbitals and effective core potentials
• Calculation of STOs electron repulsion integrals by ellipsoidal expansion and large-order approximations