Two-center two-electron integrals with exponential functions

Details Two-center two-electron integrals with exponential functions Two-center two-electron integrals with exponential functions

2009-05-11

arxiv.org/abs/0905.1635v3

Phys. Rev. A 80, 032520 (2009)

Physics

Chemical Physics

14 pages, 1 figure, corrected notation

Scientific paper

10.1103/PhysRevA.80.032520

We present an efficient approach to evaluate two-center two-electron integrals with exponential functions and with an arbitrary polynomial in electron-nucleus and electron-electron distances. We show that the master integral with the single negative power of all distances can be obtained from the second order differential equation in $r$, the distance between nuclei. For particular values of nonlinear parameters corresponding to the James-Coolidge basis, we find a fully analytic expression. For integrals with arbitrary powers of all distances, we construct recursion relations which starts from the master integral. The presented approach opens a window for the high precision calculations of relativistic effects in diatomic molecules.

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