New developments in the Fourier transform Coulomb method: Efficient and accurate localization of the filtered core functions and implementation of the Coulomb energy forces

Abstract

A new linear scaling approach for the solution of Coulomb problem called the Fourier transform Coulomb (FTC) method has been published recently. Two further developments will be presented in this article. First, an efficient and accurate technique to localize the so-called filtered core functions is introduced, which considerably improves the scaling property of the method and speeds up the most time consuming computational steps by one and two orders of magnitude. An efficient scheme to implement the Coulomb forces is also presented using the localization technique. Besides these methodological developments, detailed results are shown for the scaling property of the computational cost, which is linear in both system and in basis set size. Huge speed ups are achieved compared to the analytical integral evaluation based technique in line with traditional ab initio accuracy requirements. Additionally, ongoing and further possible improvements for every main computational step are also discussed in detail.