On the extremum problem of the energy functional on the set of Slater determinants

Abstract

Differential properties of the energy functional on the set of Slater determinants are defined according to a new differential calculus on complex Banach spaces previously considered. Such properties permit us to derive, with a new and rigorous procedure, the Hartree–Fock equations and to define an iterative method of the gradient type to minimize this functional on the above set. For a large class of one-body and two-body potentials, including Coulombic potentials, we show that our gradient method yields a decreasing sequence of values of the energy functional and a sequence of approximate solutions of the Hartree–Fock equations. The convergence of the latter sequence to a solution of these equations is proved in any finite-dimensional subspace.