Fast and Stable Algorithm for Analytical Evaluation of Two-Center Overlap Integrals Over Slater-Type Orbitals with Integer and Noninteger Principal Quantum Numbers

摘要

A unified algorithm is presented for analytical evaluation of two-center overlap integrals over Slater-type orbitals with integer and noninteger principal quantum numbers.Two-center overlap integrals are expressed as finite sum of Gaunt coefficients and auxiliary functions S_(n,n')~L(p,t).Special attention is paid to the efficient calculation of this auxiliary function by introducing analytic and recurrence relations.In order to test the accuracy of the formula for two-center overlap integrals,we performed an extensive study in which quantum numbers,orbital exponents,and internuclear distances were varied over wide ranges.We found that the method presented here for two-center overlap integrals is fully reliable for very high quantum numbers and the computation times are very low.