Kohn-Sham inversion and iterative energy minimization

A scheme is presented for inverting the Kohn-Sham procedure so that the local potential is obtained that has a given electron density as its ground state. The central idea is to constrain the electron density using a position-dependent Lagrange multiplier and perform iterative minimization with respect to the orbitals. The required potential is obtained from the Lagrange multiplier. The method is then applied to the iterative minimization of the Kohn-Sham energy functional. In contrast to conventional mixing schemes presently employed, at each stage of the minimization orbitals and an electron density are consistent and a variational upper bound of the energy is obtained. The convergence of the iterations onto the ground state can be very rapid. Real-space implementation with applications to Li clusters, and CH4 and CO2 molecules is presented.