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The numerical solution of the Hartree-Fock equations is a central problem inquantum chemistry for which numerous algorithms exist. Attempts to justifythese algorithms mathematically have been made, notably in by Cances and LeBris in 2000, but, to our knowledge, no complete convergence proof has beenpublished. In this paper, we prove the convergence of a natural gradientalgorithm, using a gradient inequality for analytic functionals due toLojasiewicz. Then, expanding upon the analysis of Cances and Le Bris, we proveconvergence results for the Roothaan and Level-Shifting algorithms. In eachcase, our method of proof provides estimates on the convergence rate. Wecompare these with numerical results for the algorithms studied.

Convergence of gradient-based algorithms for the Hartree-Fock equations