The local kinetic energy density revisited

Kinetic energy density (KED) plays a fundamental role in density functional theory, chemical bonding, etc. As a basic quantity, its definition is ambiguous, which will inevitably exert unpredictable adverse effects on application. We derive another form of local total energy density (ED) and KED based on the perturbation theory. Contrary to popular belief, our study reveals that energy is only distributed inside the potential well and exactly fills the entire potential well. It seems that the ambiguity of the quantum definition of total ED is eliminable by the stability of energy distribution, and there is a one-to-one correspondence between this form of KED and total ED. As a result, the ambiguity of the KED is also eliminable. Moreover, this new form of local KED 'selectively' agrees well with the key regions of other commonly used ones. However, it is much less localized than other forms. Its locality features imply that it may provide a native way to describe the strong correlation and the van der Waals interactions.