Summary
Some types of recurrence relations are modified to overcome the cases in which their conventional application is unstable in both the forward and backward directions. The original recurrence relations — connecting adjacent elements — are replaced by more general ones, where the non-adjacent elements are connected by coefficients obtained by new sets of relations derived from the original ones. This modification can be helpful for the calculation of the complicated molecular integrals with Slater Type Orbitals (STOs).
As a simple test we prove that some auxiliary functions — previously evaluated by expensive expansions — appearing in two-center two-electron integrals can be thus calculated with very low computer cost and high accuracy.
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Fernández Rico, J., López, R., Ramírez, G. et al. Auxiliary functions for Slater molecular integrals. Theoret. Chim. Acta 85, 101–107 (1993). https://doi.org/10.1007/BF01374580
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DOI: https://doi.org/10.1007/BF01374580