Poisson-transformed density fitting in relativistic four-component Dirac–Kohn–Sham theory

Abstract

We present recent developments in the implementation of the density fitting approach for the Coulomb interaction within the four-component formulation of relativistic density functional theory [Belpassi et al., J. Chem. Phys. 124, 124104 (2006)]. In particular, we make use of the Poisson equation to generate suitable auxiliary basis sets and simplify the electron repulsion integrals [Manby and Knowles, Phys. Rev. Lett. 87, 163001 (2001)]. We propose a particularly simple and efficient method for the generation of accurate Poisson auxiliary basis sets, based on already available standard Coulomb fitting sets. Just as is found in the nonrelativistic case, we show that the number of standard auxiliary fitting functions that need to be added to the Poisson-generated functions in order to achieve a fitting accuracy equal or, in some cases, better than that of the standard procedure is remarkably small. The efficiency of the present implementation is demonstrated in a detailed study of the spectroscopic properties and energetics of several gold containing systems, including the Au dimer and the CsAu molecule. The extraction reaction of a H(2)O molecule from a Au(H(2)O)(9) (+) cluster is also calculated as an example of mixed heavy-light-atom molecular systems. The scaling behavior of the algorithm implemented is illustrated for some closed shell gold clusters up to Au(5) (+). The increased sparsity of the Coulomb matrices involved in the Poisson fitting is identified, as are potential computational applications and the use of the Poisson fitting for the relativistic exchange-correlation problem.