Trivial Constraints on Orbital-free Kinetic Energy Density Functionals

Abstract

Kinetic energy density functionals (KEDFs) are central to orbital-free density functional theory. Limitations on the spatial derivative dependencies of KEDFs have been claimed from differential virial theorems. We point out a central defect in the argument: the relationships are not true for an arbitrary density but hold only for the minimizing density and corresponding chemical potential. Contrary to the claims therefore, the relationships are not constraints and provide no independent information about the spatial derivative dependencies of approximate KEDFs. A simple argument also shows that validity for arbitrary $v$-representable densities is not restored by appeal to the density-potential bijection.

5 pages

References in corpus (4)

• Laplacian-level kinetic energy approximations based on the fourth-order gradient expansion: Global assessment and application to the subsystem formulation of density functional theory
• Visualization and analysis of the Kohn-Sham kinetic energy density and its orbital-free description in molecules
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Cited by in corpus (4)

• Towards accurate orbital-free simulations: a generalized gradient approximation for the non-interacting free energy density functional
• Methods to generate the reference total and Pauli kinetic potentials
• Some Problems in Density Functional Theory
• On the Kinetic Energy Density Functional: The Limit of the Density Derivative Order