Guseinov Israfil, Mamedov Bahtiyar
Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey.
J Mol Model. 2002 Sep;8(9):272-6. doi: 10.1007/s00894-002-0098-5. Epub 2002 Sep 6.
The series expansion formulae are derived for the overlap integrals with arbitrary integer n and noninteger n* Slater-type orbitals (ISTOs and NISTOs) in terms of a product of well-known auxiliary functions A(sigma) and B (k). The series becomes an ordinary closed expression when both principal quantum numbers n* and n'* of orbitals are integer n*= n and n'= n'. These formulae are especially useful for the calculation of overlap integrals for large quantum numbers. Accuracy of the results is satisfactory for values of integer and noninteger quantum numbers up to n= n'=60, n= n'*<33 and for arbitrary values of screening constants of orbitals and internuclear distances.
根据著名的辅助函数A(σ)和B(k)的乘积，推导出了任意整数n和非整数n的斯莱特型轨道（ISTO和NISTO）重叠积分的级数展开公式。当轨道的主量子数n和n'均为整数n = n且n'* = n'时，该级数变为普通的封闭表达式。这些公式对于大量子数重叠积分的计算特别有用。对于整数和非整数量子数，当n = n' = 60、n* = n'* < 33以及轨道屏蔽常数和核间距的任意值时，结果的精度令人满意。
