1109.5473 (Antoine Levitt)

Convergence of gradient-based algorithms for the Hartree-Fock equations    [PDF]

Antoine Levitt

The numerical solution of the Hartree-Fock equations is a central problem in
quantum chemistry for which numerous algorithms exist. Attempts to justify
these algorithms mathematically have been made, notably in by Cances and Le
Bris in 2000, but, to our knowledge, no complete convergence proof has been
published. In this paper, we prove the convergence of a natural gradient
algorithm, using a gradient inequality for analytic functionals due to
Lojasiewicz. Then, expanding upon the analysis of Cances and Le Bris, we prove
convergence results for the Roothaan and Level-Shifting algorithms. In each
case, our method of proof provides estimates on the convergence rate. We
compare these with numerical results for the algorithms studied.

View original: http://arxiv.org/abs/1109.5473