Formulas and Numerical Tables for Overlap Integrals

Abstract

Explicit formulas and numerical tables for the overlap integral S between AO's (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npσ, and npπ AO's. They are based on approximate AO's of the Slater type, each containing two parameters μ [equal to Z/(n—δ)], and n—δ, where n—δ is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p=½(μ a +μ b )R/a H , R being the interatomic distance, and t=(μ a —μ b )/(μ a +μ b ). Master tables of computed values of S are given over wide ranges of p and t values corresponding to actual molecules, and also including the case p=0 (intra‐atomic overlap integrals). In addition, tables of computed S values are given for several cases involving 2‐quantum s, p hybrid AO's. Hybrid S values for any desired type of hybrid can be obtained very easily from the tables as simple linear combinations of non‐hybrid S values. It is shown how S values corresponding to orthogonalized Slater AO's and approximate S values for SCF (self‐consistent‐field) AO's can also be obtained as linear combinations of the Slater‐AO S values. S values for carbon‐carbon 2pσ‐ and 2pπ‐bonds using SCF carbon AO's have been computed (see Table in Section Vb); they correspond to stronger overlap than for Slater AO's. Non‐localized MO group‐orbital S values are also discussed, and are illustrated by an application to H2O. The use of the tables to obtain dipole moments for electronic transitions in certain cases is also mentioned. The use of the tables to obtain S values for various specific atom‐pairs and bond‐types, and resulting conclusions, will be discussed in another paper.