On the Short-Range Behavior of Correlated Pair Functions from the Adiabatic-Connection Fluctuation-Dissipation Theorem of Density-Functional Theory.

Abstract

The short-range behavior of correlated pair functions from the adiabatic-connection fluctuation-dissipation theorem (ACFD) of density functional theory (DFT) employing local exchange-correlation kernels has been analyzed. It has been found that for large basis sets the pair function exhibits unphysical humps for small interelectronic distances if the adiabatic local density approximation kernel is used in the ACFD scheme (this method is termed ACFD/ALDA in this work). However, up to basis set sizes of quadruple-ζ type quality, the correlated pair function of ACFD/ALDA behaves physically correct and the method yields reasonable results for atomization energies, ionization potentials, and intermolecular interaction energies. In order to correct the deficiencies of the pair function of ACFD/ALDA for large basis sets, a short-range correction scheme has been devised on the basis of a combination of the ACFD/ALDA pair function for the large distance regime with a proper physically correctly behaving pair function at smaller distances. While this approach, termed as ACFD/ALDAcorr, practically yields results close to those of the ACFD/ALDA method for finite basis sets, it enables basis set extrapolation techniques and thus can take dynamic correlation effects fully into account in contrast to the ACFD/ALDA approach. This work also presents an efficient density-fitting algorithm to compute the ACFD correlation energies that enables the calculation of correlation energies of extended molecular systems.