Transforms for idempotency purification of density matrices in linear-scaling electronic-structure calculations

A family of purification transforms (of the nth-order convergence, n>2) is proposed, which is a generalization of the McWeeny transform (of the second-order convergence). These transforms can be applied in calculational schemes where the number of basis functions exceeds the number of occupied orbitals in the density matrix. Another family of purification transforms, proposed recently by Kryachko Chem. Phys. Lett. 318 (2000) 210], is shown to be applicable in such schemes only where these numbers are equal. Various properties of these two families are discussed.