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Density functional theory (DFT) is a widely used and
accurate approach to the
modeling of complex electronic systems with many electrons and light
atoms. In recent years, a number of methodological improvements has dramatically increased the size and complexity of the molecular systems that can be studied. In order to model systems containing heavy nuclei the methods of relativistic quantum mechanics must be adopted, to capture scalar and spin-dependent interactions that are neglected in the conventional non-relativistic formulation of quantum chemistry. The extension of DFT within the four-component generalization of the Kohn-Sham method, which we will refer to as the Dirac-Kohn-Sham (DKS) scheme, was formulated by Rajagopal and Macdonald and Vosko. The DKS calculations possess an intrinsically greater computational cost than analogous non-relativistic approaches, mainly because of the four-component structure in the matrix representation of the DKS equations. Contrary to what may be commonly thought, the relativistic four-component formulation does not introduce any unfavorable scaling factor with respect to theIn this work we present an implementation of the density fitting approach to the solution of the Coulomb problem within the relativistic four-component Dirac-Kohn-Sham method employing G-spinor basis expansion, as implemented in the DKSof the relativistic program BERTHA. We have shown that there is no need to introduce distinct basis sets in which to expand separately the large- and small-component densities. A very accurate representation of the DKS matrix may be obtained using a relatively modest number of scalar auxiliary basis functions. The implementation of the DKS density fitting in the DKS formalism truly opens new perspectives of applicability of the 4-component relativistic approach. number of particles. |
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