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 a
llow a straightforward application of conjugate gradients by removing the e
xplicit 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.
(C) 1999 Academic Press.