Stochastic algorithms for self-consistent calculations of electronic structures

The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations electron structures is studied. formulated by rewriting electronic charges as trace/diagonal matrix function, which subsequently expressed statistical average. function further approximated using Krylov subspace approximation. As result, each SCF iteration only samples one random vector without having to compute all orbitals. We consider common practice iterations with damping and mixing. prove that iterates from general linear mixing scheme converge in probabilistic sense when error has second finite moment.