Two-Center Heteronuclear Hybrid Coulomb-Exchange Integrals

Abstract

The method introduced by Sklar and Lyddane, and used by Parr and Crawford, to evaluate two‐center hybrid Coulomb‐exchange integrals involving atoms with equal effective nuclear charges has been extended to include the case of unequal effective nuclear charges. Formulas for all thirty nonvanishing integrals of this type involving 2s and 2p Slater atomic orbitals (assuming that the 2s and 2p orbitals on the same atom have the same screening) are given in a form convenient for numerical calculations. These formulas are valid for both the homonuclear and the heteronuclear cases. The method here given has the advantage that all the integrals are expressed in terms of natural logarithms, exponentials, and exponential integrals, adequate tables of which are readily available. Exact numerical values obtained by this method for thirty hybrids involving carbon and oxygen atomic orbitals in CO₂ are given. These exact values have been used as a check on the validity of an approximation previously employed for these integrals.