Failure of density-matrix minimization methods for linear-scaling density-functional theory using the Kohn penalty-functional

Abstract

We examine the recently-proposed scheme [Kohn W., Phys. Rev. Lett. 76, 3168 (1996)] for performing linear-scaling calculations within density-functional theory by direct minimization with respect to the single-particle density-matrix using a penalty-functional to exactly enforce the idempotency constraint. We show that such methods are incompatible with standard minimization algorithms (using conjugate gradients as an example) and demonstrate that this is a direct result of the non-analytic form of penalty-functional which must be chosen to obtain a variational principle for the total energy.