A generalization of the hartree‐fock one‐particle potential

By making the assumption that the addition (subtraction) of an electron from a many-body wave function may be represented by a single spin orbital, variationally determined, two distinct one-particle potentials are derived. They represent, respectively, the effective interaction of the (N - 1)-electron system with the Nth electron, and the effective interaction of the N-electron system with the (N + 1)th electron. Nonlocal exchange arises because of the indistinguishability of electrons. The “core” electrons are allowed to be correlated with each other and to be polarized by the electron in question. Eigenvalues to these potentials represent, respectively, ionization potentials and electron affinities, and the eigenfunctions are variationally determined spin orbitals (“standing-wave solutions”), termed the “natural transition orbitals.” The two-body density matrix of a reference state approximating an eigenfunction of the many-body Hamiltonian is required as input to the theory. Given this input, the method is linear, requiring no interations. In the limit of no correlation in the reference N-body state (provided the occupied orbitals span the Hartree-Fock space), the two potentials reduce to the unrestricted Hartree-Fock potential for occupied and virtual orbitals.