Perturbation theory with operator techniques is applied to a nondegenerate many-electron system taking the entire electron-electron repulsions, $\Sigma {i>j}^{}{r_{\mathrm{ij}}}^{-1\mathrm{}}$, as the perturbation. The first order wave function ${\mathbf{X}}_1$, is obtained rigorously in terms of the first order wave functions of independent two-electron systems. The wave functions of these electron pairs contain nuclear parameters and can be obtained individually by variational or other methods, then used in various atoms or molecules. For example Li atom is built up completely from the ${\mathrm{}\left(1s\right)\mathrm{}}^2{}_{}{}^1{}_{}{}^{}S$, $\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^3{}_{}{}^{}S$ states of ${\mathrm{Li}}^{+}$. The ${\mathrm{X}}_1$ gives the energy to third order and as an upper limit to the exact $E$. The $E_2$ is equal to the sum of complete pair interactions plus many-body terms of two types: (a) "cross polarization," which exists even in no-exchange intermolecular forces, and (b) Fermi correlations.

• Received 25 July 1960

DOI:https://doi.org/10.1103/PhysRev.122.493