2012/09/30 by Krzysztof Pachucki · 1 citation
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Mathematical functions and polynomials #physics.chem-ph #quant-ph
paper · pdf · doi:10.1103/physreva.86.052514
published as Phys. Rev. A 86, 052514 (2012) · 26 pages, includes two tables with exemplary calculations
openalex publication_date 2012/11/26 · arxiv created 2012/11/29 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional integral representation is found, which is suited for the numerical evaluation. Together with recurrence relations, it makes possible the calculation of the two-center two-electron integral with arbitrary powers of electron distances. Alternative approach via the Taylor series in the internuclear distance is also investigated. Although numerically slower, it can be used in cases when recurrences lose stability. Separate analysis is devoted to molecular integrals with integer powers of interelectronic distances r12 and the vanishing corresponding nonlinear parameter. Several methods of their evaluation are proposed.