Abstract
The multi-centre integrals of the orbital system Δn Y lm (∇) exp (−r 2) are evaluated using the Talmi transformation of nuclear shell theory. The integrals are simpler than those of the systems r 2n Y lm(r) exp (−r 2), x l y m z n exp (−r 2), (∂/∂x)l(∂/∂y)m(∂/∂z)n exp (−r 2) and the spherical oscillator functions. The integral types investigated are: overlap, electric dipole transition (momentum operator), kinetic energy, three-centre nuclear attraction, four-centre electronic repulsion, three-centre spin-orbit coupling, and magnetic dipole transition (three-centre integrals of the angular momentum operator).
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Fieck, G. The multi-centre integrals of derivative, spherical GTOs. Theoret. Chim. Acta 54, 323–332 (1980). https://doi.org/10.1007/BF00552466
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DOI: https://doi.org/10.1007/BF00552466