Theory of Condensed Matter, Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, U.K.
We examine the recently-proposed scheme [W. Kohn, 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.
PACS numbers: 71.15.Mb