Exchange perturbation theory. I. General definitions and relations

We define a class of primitive functions which are least distorted from the unsymmetrized function F⁰, a product of atomic or other group functions, in the limit that the interactions between the groups have been turned off. These primitive functions have the property that at least one Schr\"odinger eigenfunction may be obtained from them by symmetry projection. It has been shown elsewhere that these functions satisfy a transformed Schr\"odinger equation in which the interactions between groups are screened. The screened potential is regarded as a perturbation and the corresponding Rayleigh-Schr\"odinger perturbation equations are derived. It is shown that a number of inequivalent, but equally valid energy expressions may be defined in terms of the primitive functions. Only when the primitive function is calculated exactly to infinite order will the different energy expressions all yield the same numerical value. It is suggested that this provides a check on the accuracy of approximate primitive functions.