Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions

The exact Kohn-Sham iteration of generalized density-functional theory in finite dimensions with a Moreau-Yosida regularized universal Lieb functional and an adaptive damping step is shown to converge to the correct ground-state density.

Figure 1

Illustration of one iteration step.

Figure 2

Convergence of $\mathrm{\Delta }{E}_i=e_i-E_{ϵ}(v)$ for a ring-lattice system with external potential $v=\cos (2\theta )+0.2\cos (\theta )$ and different $ϵ$. The algorithm developed here is labeled “S” while the method “L” chooses the step length maximally [23, 27].