Exchange energy functionals based on the density matrix expansion of the Hartree-Fock exchange term

In a recent paper (Koehl, R. M., Odom, G. K., and Scuseria, G. E., 1996, Molec. Phys. 87, 835), we proposed a generalized version of the density matrix expansion of Negele and Vautherin. In the present paper, we have further modified this expansion by augmenting the second order term to explicitly include gradient corrections and correcting the Fermi momentum to account for the non-uniformity of the electron density. The resulting functional gives better results than the original exchange functional according to some preliminary hybrid calculations using Hartree–Fock densities for the G2 set of Pople and co-workers. While most of our investigations only concern closed shell molecules, we show that the results are easily generalized to the open shell case. The functionals thus obtained offer the possibility of improving the accuracy of existing exchange-correlation functionals.