Comment on: “Transforms for idempotency purification of density matrices in linear-scaling electronic-structure calculations” [Chem. Phys. Lett. 340 (2001) 552–558]

In a recent Letter, Holas introduced nth-order generalizations of the McWeeny canonical purification scheme, hoping that these might be useful in linear-scaling electronic structure theory methods that rely on purification of density matrices. In this comment we show that for theories that use purification to guide unconstrained optimizations, the generalizations offer no advantage.