A bivariate view of Kohn-Sham iteration and the case for potential mixing

A bivariate perspective on Kohn-Sham density functional theory is proposed, treating potential and density as simultaneous independent variables, and used to make fruitful connection between Lieb’s rigorous foundational framework and practical Kohn-Sham computation. Support is found for potential-mixing schemes, but not for more standard density-mixing. Under presumably-generic conditions, total energy can be lowered from one iteration to the next. Density, intrinsic and total energy are analytic functions of the noninteracting potential on the open set of potentials having a single isolated ground spin-multiplet.