Rapid filtration algorithm to construct a minimal basis on the fly from a primitive Gaussian basis

In a recent work [M.J. Rayson, P.R. Briddon, Phys. Rev. B 80 (2009) 205104] an implementation of filter diagonalisation with localisation constraints was shown to provide an accurate and highly efficient method to solve the Kohn–Sham equations using a primitive Gaussian basis for systems containing several thousand electrons. In this work, an alternative filtration algorithm is proposed, based on a rational approximation to the filtration function, to replace the kernel of this algorithm. This approach is considerably faster than the diagonalisation approach used previously and also its performance is largely independent of the filtration temperature, aiding a more flexible approach to the construction of filtered basis sets.