Accurate Reference Data for the Non-Additive Non-Interacting Kinetic Energy in Covalent Bonds

Abstract

The non-additive non-interacting kinetic energy is calculated exactly for fragments of H$_2$, Li$_2$, Be$_2$, C$_2$, N$_2$, F$_2$, and Na$_2$ within partition density-functional theory. The resulting fragments are uniquely determined and their sum reproduces the Kohn-Sham molecular density of the corresponding XC functional. We compare the use of fractional orbital occupation to the usual PDFT ensemble method for treating the fragment energies and densities. We also compare Thomas-Fermi and von Weiz{\"a}cker approximate kinetic energy functionals to the numerically exact solution and find significant regions where the von Weiz{\"a}cker solution is nearly exact.