Model density approach to the Kohn-Sham problem: Efficient extension of the density fitting technique

We present a novel procedure for treating the exchange-correlation contributions in the Kohn-Sham procedure. The approach proposed is fully variational and closely related to the so-called "fitting functions" method for the Coulomb Hartree problem; in fact, the method consistently uses this auxiliary representation of the electron density to determine the exchange-correlation contributions. The exchange-correlation potential and its matrix elements in a basis set of localized (atomic) orbitals can be evaluated by reusing the three-center Coulomb integrals involving fitting functions, while the computational cost of the remaining numerical integration is significantly reduced and scales only linearly with the size of the auxiliary basis. We tested the approach extensively for a large set of atoms and small molecules as well as for transition-metal carbonyls and clusters, by comparing total energies, atomization energies, structure parameters, and vibrational frequencies at the local density approximation and generalized gradient approximation levels of theory. The method requires a sufficiently flexible auxiliary basis set. We propose a minimal extension of the conventional auxiliary basis set, which yields essentially the same accuracy for the quantities just mentioned as the standard approach. The new method allows one to achieve substantial savings compared with a fully numerical integration of the exchange-correlation contributions.