Approximate 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 identify 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.

近似动能密度泛函（KEDF）是无轨道密度泛函理论的核心。从微分维里定理中已经提出了对KEDF的空间导数依赖性的限制。我们在论证中发现了一个中心缺陷：对于任意密度，这种关系不是正确的，而仅对于最小密度和相应的化学势才成立。因此，与权利要求相反，这些关系不是约束，并且不提供关于近似KEDF的空间导数依赖性的独立信息。一个简单的论证也表明，对于任意v可表示密度的有效性不能通过吸引密度势双射来恢复。