Unconstrained Energy Functionals for Electronic Structure Calculations

Abstract

The performance of conjugate gradient schemes for minimizing unconstrained energy functionals in the context of condensed matter electronic structure density functional calculations is studied. The unconstrained functionals allow a straightforward application of conjugate gradients by removing the explicit orthonormality constraints on the quantum-mechanical wave functions. However, the removal of the constraints can lead to slow convergence, in particular when preconditioning is used. The convergence properties of two previously suggested energy functionals are analyzed, and a new functional is proposed, which unifies some of the advantages of the other functionals. A numerical example derived from a diamond crystal confirms the analysis.