A constrained optimization algorithm for total energy minimization in electronic structure calculations

A new direct constrained optimization algorithm for minimizing the Kohn–Sham (KS) total energy functional is presented in this paper. The key ingredients of this algorithm involve projecting the total energy functional into a sequence of subspaces of small dimensions and seeking the minimizer of total energy functional within each subspace. The minimizer of a subspace energy functional not only provides a search direction along which the KS total energy functional decreases but also gives an optimal “step-length” to move along this search direction. Numerical examples are provided to demonstrate that this new direct constrained optimization algorithm can be more efficient than the self-consistent field (SCF) iteration.