The exchange-energy density functional based on the modified becke-roussel model

In this paper, we present a simple numerical approach to implement the modified Becke-Roussel (mBR) model for the purpose of developing an exchange density functional suitable for applications to atoms or molecules. Three steps constitute our approach. The first step is to model the exchange hole with the mBR distribution with the form of ρX^mBRσ) (α/π)^3/2 exp (-αr²) at each reference point, where R and r represent, respectively, the diffuseness and the distance of the model exchange hole from the reference point. We propose an iterative procedure to determine the values (α, r) during the Kohn-Sham DFT calculation. Second, we make a GGA correction to the functional obtained in the first step by adopting the conventional GGA formula to the gradients of the spin density as well as the mBR exchange hole (mBRGGA). In the third step, mBR-GGA is combined with Diracs exchange functional to restore the exchange energy at the homogeneous electron gas limit (mBR-hyb). We demonstrate that the exchange energy densities of the mBR-based methods obey the -1/r asymptotic behaviors by virtue of the fact that the electron density in a hydrogenic atom is used as a prototypical exchange hole. Furthermore, we perform several test calculations for the properties of small molecules. For atomization energies for 35 molecules in the G2 set, the mean absolute deviation (MAD) with respect to the experiment is estimated to be 4.9 kcal/mol by the mBR-hyb functional, which is much smaller than the value of PBE functional (7.7 kcal/mol). The MAD for the enthalpies of formation of 68 molecules in the G3 set is evaluated as 9.4 kcal/mol by the present method, while that is given as 18.7 kcal/mol by the PBE functional. These results suggest the possibility of the present functional based on the mBR model for the applications to atoms or molecules.