Abstract
An approximation to the exchange-hole density is proposed for the evaluation of the exact exchange energy in electronic structure calculations within the density-functional theory and the Kohn-Sham scheme. Based on the localized nature of density matrix, the exchange hole is divided into the short-range (SR) and long-range (LR) parts by using an adequate filter function, where the LR part is deduced by matching of moments with the exactly calculated SR counterpart, ensuring the correct asymptotic $\ensuremath{-}1/r$ behavior of the exchange potential. With this division, the time-consuming integration is truncated at a certain interaction range, largely reducing the computation cost. The total energies, exchange energies, exchange potentials, and eigenvalues of the highest-occupied orbitals are calculated for the noble-gas atoms. The close agreement of the results with the exact values suggests the validity of the approximation.
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