Combined Extended Rejoinder to "Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives" by I. I. Guseinov (Chem. Phys., Vol. 309 (2005), pp. 209-213)"

TL;DR

This paper defends Guseinov's earlier work on addition theorems for Coulomb potentials against Weniger's critique, demonstrating the validity and computational testing of their formulas and dismissing the critique as minor and unfounded.

Contribution

The paper provides a detailed rebuttal to Weniger's critique, reaffirming the correctness and computational validation of Guseinov's addition theorems for Coulomb potentials.

Findings

Weniger's critique is based on minor, irrelevant aspects.

Guseinov's formulas were tested and validated through computer calculations.

Claims of flaws in the theoretical framework are unfounded.

Abstract

This article is a thorough critique to the Weniger's comments made to our papers published in prestigious journals in the recent years. A detailed and critical examination of the arguments that led to the suggested comment by Weniger reveals some serious flaws. In our published papers we have shown that the unsymmetrical and symmetrical one-range addition theorems for Slater type orbitals, Coulomb-Yukawa like correlated interaction potentials (CIPs) and their derivatives are derived from the expansions in terms of -ETOs that are complete and orthonormal sets of exponential type orbitals in corresponding Hilbert spaces, where The concrete criticism raised in Weniger's comment against our papers actually touches a very minor aspect of the works that are not relevant at all for the conclusions, which are made. As can be seen from our papers, all of the formulas for different kinds of multicenter integrals over Slater type orbitals with integer and noninteger principal quantum numbers obtained by the use of unsymmetrical and symmetrical one-range addition theorems were tested by computer calculations. We reject the Weniger's personal views about papers published by Guseinov and his coworkers from 1978 to 2006 and respectable referees on one-range addition theorems and multicenter integrals. All claims of inconsistencies and flaws in the theoretical framework are rejected as unfounded. This rejoinder paper contains all of the answers to Weniger's comments.