GRADIENT FLOW BASED KOHN--SHAM DENSITY FUNCTIONAL THEORY MODEL.

In this paper, we propose and analyze a gradient flow based model for electronic structure calculations. First, based on an extended gradient flow proposed in this paper, we propose a Kohn--Sham gradient flow based model. We prove that our gradient flow based model is orthogonality preserving, the extended gradient has an exponential decay over time t, and the equilibrium point is a local minimizer of the Kohn--Sham energy functional. Then we propose a midpoint scheme to carry out the temporal discretization, which is proven to be orthogonality preserving, too. Based on the midpoint scheme, we design a practical orthogonality preserving iteration scheme which can deal with the propagation of the gradient flow based model and prove that the scheme produces approximations that converge to a local minimizer with some convergence rate under some reasonable assumptions. Finally, we report a number of numerical experiments that validate our theoretical results. [ABSTRACT FROM AUTHOR]