Analytical two-center integrals over Slater geminal functions

Michał Lesiuk and Robert Moszynski
Phys. Rev. A 86, 052513 – Published 26 November 2012

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 exp(γr12) term.

  • Received 4 September 2012

DOI:https://doi.org/10.1103/PhysRevA.86.052513

©2012 American Physical Society

Authors & Affiliations

Michał Lesiuk* and Robert Moszynski

  • Faculty of Chemistry, University of Warsaw and Pasteura 1, 02-093 Warsaw, Poland

  • *lesiuk@tiger.chem.uw.edu.pl

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 86, Iss. 5 — November 2012

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×