Correlated exponential functions in high precision calculations for diatomic molecules

Abstract

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 $r_{12}$ and the vanishing corresponding nonlinear parameter. Several methods of their evaluation are proposed.

26 pages, includes two tables with exemplary calculations

References in corpus (4)

• Born-Oppenheimer potential for H${}_2$
• ${\alpha }^4$ Ry corrections to singlet states of helium
• Accurate Born-Oppenheimer potential for HeH+
• Two-center two-electron integrals with exponential functions

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• Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer
• Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules
• 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
• Combining Slater-type orbitals and effective core potentials
• Analytically projected rotationally symmetric explicitly correlated Gaussian Functions with one-axis-shifted centers