A density matrix approach to the convergence of the self-consistent field iteration

<p style='text-indent:20px;'>In this paper, we present a local convergence analysis of the self-consistent field (SCF) iteration using density matrix as state fixed-point iteration. Conditions for are formulated in terms spectral radius Jacobian map. The relationship between and certain properties problem is explored by deriving upper bounds expressed higher gaps. This gives more information regarding how gaps eigenvalues affect convergence, hence these insightful on behaviour than standard results. We also provide detailed to describe difference exact factor an illustrative example. Finally numerical examples compare value with observed SCF, along our new characterization heuristic estimates situations where fail well capture convergence.</p>