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In most cases, STO integrals are evaluated assuming that the orbitals are directed towards each other, using spherical harmonics; however, in GTO-based software Cartesian GTOs are used, with the orbitals being aligned along the x, y or z axis.

Is there any way to evaluate STO integrals using Cartesian STOs, or convert between Cartesian and spherical STOs? For example, if I had a pz-type STO at (0,0,0) and another one at (1,1,1), is there any way to decompose the resultant expression in terms of spherical STO integrals?

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  • $\begingroup$ I would wager that the relevant recursion formulae are listed in L. Zülicke: Quantenchemie, unfortunately, it is hard to come by. $\endgroup$ – TAR86 Feb 21 '20 at 14:17
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    $\begingroup$ Have you considered to commit to the Materials Modeling Stack Exchange: area51.stackexchange.com/proposals/122958/… ? There's a higher concentration of computational researchers, including basis set expert Kirk Peterson. Several example questions were about basis sets. We will soon be in the private beta phase, where only a select group of users can participate. These users help to determine the style of questions for the future. $\endgroup$ – user1271772 Feb 22 '20 at 15:21
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    $\begingroup$ Are you able to be specific about which particular computer program for which you're interested in the STO implementation? I know at least 2 programs that use Slaters and the implementation is very different in each of them. $\endgroup$ – user1271772 Feb 23 '20 at 2:58

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