Direct analytical calculation of first-order density matrix elements through third order

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Abstract
A theory which permits the analytical calculation of atomic and molecular first‐order density matrices in a computationally tractable manner is developed. Contour integral techniques are used to derive an equation relating the first‐order density matrix γ to certain eigenvectors which arise in our earlier theory of molecular ionization potentials and electron affinities. By analytically evaluating the resulting contour integral, we obtain a closed expression giving γ in terms of Hartree‐Fock orbital energies and two‐electron integrals.