Variational Principle and Slater's Generalized Hartree-Fock Theory for Nuclei

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Abstract
The Hartree-Fock (HF) equations are generalized to take correlation into account, without replacing the exchange potential by a local approximation as Slater originally did. The nonlocal generalized HF equations are then obtained from a variational principle, that an energy functional be stationary at the true ground-state energy with respect to variations of the orbitals from orthogonality. The single-particle Hamiltonian is Hermitian, and there are no off-diagonal Lagrangian multipliers, in contrast to the multi-configuration variational approaches. The best local approximation to the nonlocal equation gives essentially Slater's original equation, in which the average potential due to the other particles is given in terms of an integral over the product of the two-body potential and the true pair correlation function divided by the local density.