Atoms in molecules and crystals

Abstract A new approach to the problems of the electronic structure of molecules is proposed. The basis for this treatment is the observation that the energies of atomization of molecules are small relative to their total energies. Accordingly, a perturbation theory is developed in which the unperturbed states consist of isolated atoms and ions, and the mutual approach of these atomic species is treated as the result of a perturbation. In common with other theories, the total molecular eigenfunction is expressed linearly in terms of more simple functions. It is argued that when these more simple functions are of the orbital type, this expansion converges only slowly. On the other hand, if the orbital approach is abandoned, an expansion in terms of so-called composite functions will converge much more rapidly. This representation has the advantage that, at infinite internuclear separations, the composite functions are eigenfunctions. A new use is found for atomic orbitals. They are used in order to construct approximate atomic functions, for which purpose they were originally intended. These approximate atomic functions are then employed to estimate only the perturbation or interaction terms. The energies of the unperturbed states (isolated atoms and ions) must either be determined by the use of more complex atomic functions, or by an appeal to experimentally determined atomic term values.