Modification of the Vector Model to Include a First-Order Nonorthogonality Correction

Abstract

When the vector model is used to describe chemical bonding it appears that the orbitals participating in bond formation are required to be orthogonal. The success of the model on an empirical basis is puzzling because chemical bonding will not occur without overlap. In the present work the many-electron functions, consisting of products of appropriately overlapping ordinary atomic orbitals, are orthogonalized. The characteristic simple form of the model is then retained provided that the exchange integral is replaced by a corrected exchange integral called a bond integral. The success of the model becomes less puzzling because this integral is usually evaluated empirically. The nature of the bond integral is examined in the framework of the Heitler-London treatment of the hydrogen molecule.