Kinetic correlation energy

The first parenthesis in eq. (6.8) may be considered die kinetic correlation energy, while the second contains both exchange and potential correlation energy. 

A volcano plot correlates a kinetic parameter, such as the activation energy, with a thermodynamic parameter, such as the adsorption energy. The maximum in the volcano plot corresponds to the Sabatier principle maximum, where the rate of activation of reactant molecules and the desorption of product molecules balance. 

Zhao, Q., R. C. Morrison, and R. G. Parr. 1994. From electron density to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies. Phys. Rev. A 50, 2138. 

M2-CO the first adduct bond energies are greater for Co, Ru, Pd, W, Ir, and Pt than V, Fe, Ni, Nb, and Mo. For the trimers, iron has a weaker bond than the other metals studied. For the tetramer and larger clusters the reactivity is controlled by the value of kn and no longer by the competition between uni molecular decomposition and collisional stabilization. The large cluster regime is not covered by this model used to make the correlation between kinetics and energeti cs. 

Fig. 2-10. Profile of electron density and electronic potential energy across a metal/vacuum interface calculated by using the jellium model of metals MS = jellium surface of metals Xf = Fermi wave length p. - average positive charge density P- s negative charge density V = electron exchange and correlation energy V, - kinetic energy of electrons. [From Lange-Kohn, 1970.]...

The major advantage of a 1-RDM formulation is that the kinetic energy is explicitly defined and does not require the construction of a functional. The unknown functional in a D-based theory only needs to incorporate electron correlation. It does not rely on the concept of a fictitious noninteracting system. Consequently, the scheme is not expected to suffer from the above mentioned limitations of KS methods. In fact, the correlation energy in 1-RDM theory scales homogeneously in contrast to the scaling properties of the correlation term in DPT [14]. Moreover, the 1-RDM completely determines the natural orbitals (NOs) and their occupation numbers (ONs). Accordingly, the functional incorporates fractional ONs in a natural way, which should provide a correct description of both dynamical and nondynamical correlation. 

G. K. E. Chan and N. C. Handy, An extensive study of gradient approximations to the exchange-correlation and kinetic energy functionals. J. Chem. Phys. 112, 5639—5653 (2000). 

---