Kinetic energy density definite positive

The interaction between bonded atoms is characterized by the values of p(r), V-p(r), G r) and V(r) at the bond critical point. G(r) is the positive definite kinetic energy density and V(r) is the potential energy density. At a bond critical point, the kinetic and potential energy densities are related to the Laplacian by the local form of the virial relation ... 

G(r) is the positive definite form of the kinetic energy density [11] and the virial field v(r) may be expressed as... 

K y) appears to be the sum of two contributions the first one Tfr) = yields the expectation value of the kinetie energy when integrated over all space. This contribution is always positive, it is called the definite positive kinetic energy density. The integral over space of the remaining contribution vanishes. For either a real wavefunetion or a stationary state the quantum mechanical current is zero and therefore this remaining term... 

Moreover, this term is the difference of the kinetic energy density of the actual system and of that of a system of spin-free independent particles both with identical one-particle densities />(r).For real wavefunctions or for stationary states, it is simply the difference of the definite positive kinetic energies since the (unwanted) remaining contributions cancel one another. Another attractive property of the non-von Weizsacker contribution is that it appears to be the trace of the Fisher s Information matrix[28]. 

For practical applications, we will not consider T(r) itself but rather the definite positive kinetic energy density of independent particles r (r) which appears in the exact density functional theory[31j. Within this framework, the non-von Weizsacker term accounts only for the Fermi correlation and is usually referred to as Pauli kinetic energy density[32]. Another propery of r ff(r) is its relationship to the conditional probability rO for... 

The definite positive kinetic energy density has received a considerable attention in order to build approximate kinetic energy functionals to be used in a density functional theory not based on orbitals (for a review of such functionals see Lacks and Gordon[33]). Among the most promising routes to this goal, we can mention the approximation proposed by Lee, Lee and Parr[34] ... 

Because electron densities are positive-definite, the contribution of the electron gas to interaction energy takes the same sign as the electron gas functional (see Clugston, 1978). Hence, the kinetic energy term is repulsive (cf eq. 1.148 and 1.154), exchange energy is attractive (cf eq. 1.148 and 1.154), and the correlation term is also attractive (cf eq. 1.149, 1.150, and 1.152). 

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