On the fast evaluation of three-center nuclear attraction integrals using one-range addition theorems for Slater functions

Abstract

Using one-range addition theorems, the three-center nuclear attraction integrals are expressed through the overlap integrals containing χand χ α -Slater-type orbitals (χ -STOs andFor the fast calculation, the partial summation is utilized for some indices of series expansion relations which correspond to progressively increasing upper limits. The binomial coefficients are stored in the memory of the computer. The convergence and accuracy of series are tested by calculating concrete cases. The best values are obtained for α = 0.

Israfil I. Guseinov: A pioneer of the quantum theory of atomic, molecular, and nuclear systems*

“…In Refs. , by the use of Guseinov's symmetrical and unsymmetrical one‐range addition theorems for integer and noninteger n STOs and complete sets of ‐METOs, one‐ and two‐electron multicenter electron‐repulsion integrals with the arbitrary location of STOs are expressed in terms of overlap integrals. The final results are of a simple structure and are, therefore, especially useful for machine computations.…”

“…, the prepared computer program for Guseinov's CHFR equations can be successfully applied to the study of various properties of atomic, molecular, and nuclear systems. Note that all of the one‐ and two‐electron multicenter integrals over STOs arising in the solution of CHFR equations have been evaluated using Guseinov's symmetrical and unsymmetrical one‐range addition theorems …”