Accurate Atomic and Molecular Wave Functions Without Exchange

A perturbation-theoretic procedure is developed for obtaining the spatial function ${\Phi }_0$ for the many-electron problem, from which the total wave function can be projected by the relation $\Psi =\Sigma i^{}{\tilde{D}}_{i0\mathrm{}}\left(\mathcal{r}\right)D_{i0\mathrm{}}\left(\sigma \right){\Phi }_0\left(\mathcal{r}\right){\chi }_0\left(\sigma \right)$. This function is expanded in a perturbation series in which the ${{\Phi }_0}^0$ contains a sufficient set of pair symmetries of ${\Phi }_0$ itself, such as in the Hartree nonantisymmetrized wave function for closed-shell atoms. When the expansion converges, the remaining symmetries are introduced exactly. The energy eigenvalue does not contain the usual "exchange" terms, since the zeroth-order Hamiltonian, unlike the Hartree-Fock ${\mathrm{H}}_0$, has no degeneracies. Applications to interaction energies in molecular crystals and asymmetric wave functions are discussed briefly.