Computational strategies based on electron density fitting in relativistic density functional theory

We present an implementation of the density fitting approach for the Coulomb problem within the relativistic four-component Dirac-Kohn-Sham method employing G-spinor basis expansion. This is implemented in the Dirac-Kohn-Sham (DKS) module of the program BERTHA. The basic implementation, based on the Coulomb metric, is further extended to include the Poisson method, allowing the replacement of almost all Coulomb integrals with simple overlaps. A very accurate representation of the Coulomb energy may be obtained using a relatively modest number of scalar auxiliary basis functions. The method has been validated with a study of various gold clusters. For Au-2, it is shown that the relativistic density fitting approach preserves very high accuracy in the reproduction of the spectroscopic constants. The performance and scaling properties of the method have been assessed by calculations of the ground state of larger gold clusters. The scaling of the Coulomb matrix construction is reduced, as formally expected, from O(N-4) to O(N-3) with respect to the number of particles. The reduction in computation time both for the standard and Poisson fitting procedure is dramatic if compared with the conventional approach. These results appear to open new perspectives of applicability of the 4-component relativistic approach.