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

TL;DR

This paper computes the non-additive non-interacting kinetic energy exactly for various diatomic molecules within partition density-functional theory, comparing different methods and approximations to improve understanding of molecular fragment energies.

Contribution

It provides exact calculations of the non-additive kinetic energy for molecular fragments and compares fractional orbital occupation with ensemble methods, highlighting the accuracy of von Weizsäcker functional.

Findings

Von Weizsäcker approximation closely matches exact solutions in key regions.

Fractional orbital occupation offers advantages over ensemble methods.

Exact fragment energies reproduce molecular densities accurately.

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.