Reply to comment on calculation of two-center nuclear attraction integrals over integer and noninteger n-Slater-type orbitals in nonlined-up coordinate systems

TL;DR

This paper defends the originality and stability of a computational method for two-center nuclear attraction integrals over n-Slater-type orbitals, emphasizing its independence from prior expansion formulas and its suitability for large-scale calculations.

Contribution

It presents an original algorithm for calculating two-center nuclear attraction integrals that is mathematically independent and stable, countering previous claims of derivation from existing formulas.

Findings

The algorithm is independent of Guseinov's expansion formulas.

It is stable and suitable for large-scale computations.

The method's correctness is validated through its independence and stability.

Abstract

The comments of Guseinov on our paper (T. Ozdogan, S. Gumus and M. Kara, J. Math. Chem., 33 (2003) 181) are critically analyzed. Contrary to his comments, it is proved that the expansion formula for the product of two normalized associated Legendre functions in ellipsoidal coordinates and the expressions for two-center nuclear attraction integrals have been obtained independently, by the use of basic mathematical rules, not by changing the summation indices of expansion relationships contained in his articles. Therefore, our algorithm is original, is not affected from possible instability problems and can be used in large-scale calculations without loss of significant figures. Meanwhile, it should be mentioned that his comment on the transformation of our formulae into his formulae proves the correctness of our algorithm and therefore can be regarded as a nice sound of science.