**P. D. Haynes and M. C. Payne**

**Theory of Condensed Matter, Cavendish Laboratory,
Madingley Road, Cambridge CB3 0HE, United Kingdom**

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

Peter Haynes