Development of Kinetic Energy Density Functional Using Response Function Defined on the Energy Coordinate (Jul, 10.1002/qua.26969, 2022)

A kinetic energy functional Ekine$$ {E}_{\mathrm{kin}}<^>e $$ was developed within the framework of the density-functional theory (DFT) based on the energy electron density for the purpose of realizing the orbital-free DFT. The functional includes the nonlocal term described with the linear-response function (LRF) of a reference system. As a notable feature of the present approach, the LRF is represented on the energy coordinate epsilon defined for each system of interest. In addition, an atomic system is taken as a reference system for the construction of the LRF, which shows a clear difference from the conventional approach based on the homogeneous electron gas. The explicit form of the functional Ekine$$ {E}_{\mathrm{kin}}<^>e $$ was formulated by means of the Taylor series expansion of the kinetic energy. The functional Ekine$$ {E}_{\mathrm{kin}}<^>e $$ was applied to the calculations of the kinetic energies of the pseudo atoms that mimics H, He, Ne, and Ar. Explicitly, the kinetic energy of each atom was computed using the functional Ekine$$ {E}_{\mathrm{kin}}<^>e $$ with respect to the variation of the valence charge Z(v) of each atom. In these calculations, the electron density n optimized by the Kohn-Sham DFT was adopted as an argument of the functional. It was found that the results are in excellent agreements with those given by the Kohn-Sham DFT. We also devised a method to perform the self-consistent field calculation utilizing the functional Ekine$$ {E}_{\mathrm{kin}}<^>e $$. The method was applied to the computation of the radial distribution functions of the electrons in the pseudo Ne and Ar atoms. It was demonstrated that the results reasonably agree with those yielded by the Kohn-Sham DFT.