Gaussian-based first-principles calculations on large systems using the Fourier Transform Coulomb method

Abstract

The Fourier Transform Coulomb method is described and discussed. The method reduces the quadratic scaling of the calculation of the Coulomb energy and operator matrix elements with the molecular size to an essentially linear scaling. It also reduces the quartic scaling with respect to basis set quality with constant molecular size to quadratic or lower. A major computational expense in our initial implementation, the calculation of contributions from integrals with one core-type basis function is greatly improved in the current program. This is particularly advantageous in analytical derivative calculations. The method is illustrated with large calculations on alpha helical polyalanines. The largest calculations involve over 3600 basis functions for Ala 15. Current work on further improvements of the efficiency of the method is discussed.