Kinetic energy densities

Cortona embedded a DFT calculation in an orbital-free DFT background for ionic crystals [183], which necessitates evaluation of kinetic energy density fiinctionals (KEDFs). Wesolowski and Warshel [184] had similar ideas to Cortona, except they used a frozen density background to examine a solute in solution and examined the effect of varying the KEDF. Stefanovich and Truong also implemented Cortona s method with a frozen density background and applied it to, for example, water adsorption on NaCl(OOl) [185]. 

Wang Y A and Carter E A 2000 Orbital-free kinetic-energy density functional theory Theoretical Methods in Condensed Phase Chemistry (Progress in Theoretical Chemistry and Physics Series) ed S D Schwartz (Boston Kluwer) pp 117-84... 

Wang Y A, Govind N and Carter E A 1999 Orbital-free kinetic-energy density functionals with a density-dependent kernel Phys. Rev. B 60 16 350... 

The penetrability of a fragment depends on its kinetic energy density (KED), given by... 

A j, = Model constant for reaction n C = Concentration of species i (mole m ) k = Turbulent kinetic energy density (m s )... 

Adamo, C., Ernzerhof, M., Scuseria, G. E., 2000, The meta-GGA Functional Thermochemistry with a Kinetic Energy Density Dependent Exchange-Correlation Functional , J. Chem. Phys., 112, 2643. 

Robinson, E.A., Johnson, S.A., Tang, T.-H., Gillespie, R.J. (1997). Reinterpretation of the lengths of bonds to fluorine in terms of an almost ionic model. Inorganic Chemistry, 36, 3022-3030. Schinder, H.L. Becke, A.D. (2000). Chemical contents of the kinetic energy density. Journal of Molecular Structure (THEOCHEM), 527, 51-61. 

In the Thomas-Fermi model,49 the kinetic energy density of the electron gas is written as... 

Glossman, M. D., L. C. Baibas, A. Rubio, and I. A. Alonso. 1994. Nonlocal Exchange and Kinetic Energy Density Functionals with Correct Asymptotic Behavior for Electronic Systems. Int. I. Q. Chem. 49, 171. 

Calculate the total number density and (kinetic) energy density (in eV cm-3) of cosmic-ray protons from Eq. (9.5) and deduce their average energy. 

Glossman, M. D., Baibas, L. C., Rubio, A. and Alonso, J. A. Nonlocal exchange and kinetic energy density functionals with correct asymptotic behavior for electronic systems, Int.J. Quantum ( hem., 49 (1994), 171-184... 

In a pericyclic reaction, the electron density is spread among the bonds involved in the rearrangement (the reason for aromatic TSs). On the other hand, pseudopericyclic reactions are characterized by electron accumulations and depletions on different atoms. Hence, the electron distributions in the TSs are not uniform for the bonds involved in the rearrangement. Recently some of us [121,122] showed that since the electron localization function (ELF), which measures the excess of kinetic energy density due to the Pauli repulsion, accounts for the electron distribution, we could expect connected (delocalized) pictures of bonds in pericyclic reactions, while pseudopericyclic reactions would give rise to disconnected (localized) pictures. Thus, ELF proves to be a valuable tool to differentiate between both reaction mechanisms. 

Aside from the well-known LDA (local density approximation (26, 27) BLYP (Becke-Lee-Yang-Parr (28, 29)) and B3LYP (29, 30) functionals, we considered the more recent B97-1 functional (which is a reparametrization (31) of Becke s 1997 hybrid functional), the B97-2 functional (32) (a variation of B97-1 which includes a kinetic energy density term), and the HCTH-407 (33) functional of Boese and Handy (arguably the best GGA functional in existence at the time of writing). The rationale behind the Wlc (Weizmann-1 cheap) approach is extensively discussed elsewhere. (34,35) For the sake of self-containedness of the paper, we briefly summarize the steps involved for the specific system discussed here ... 

R. Modeling antimalarial activity application of kinetic energy density quantum similarity measures as descriptors in QSAR./. Chem. Inf. Comput. Sci. 2000, 40, 1400—1407. 

The energy of the electron gas is composed of two terms, one Hartree-Fock term (T)hp) and one correlation term (Hartree-Fock term comprises the zero-point kinetic energy density and the exchange contribution (first and second terms on the right in equation 1.148, respectively) ... 

With the purpose of evaluate not only the energy but also the electron density itself, Ashby and Holzman [15] performed calculations in which the relativistic TF density was replaced at short distancies from the nucleus from the one obtained for the 1 s Dirac orbital for an hydrogenic atom, matched continuously to the semiclassical density at a switching radius rg where the kinetic energy density of both descriptions also match. 

The different techniques utilized in the non-relativistic case were applied to this problem, becoming more involved (the presence of negative energy states is one of the reasons). The most popular procedures employed are the Kirznits operator conmutator expansion [16,17], or the h expansion of the Wigner-Kirkwood density matrix [18], which is performed starting from the Dirac hamiltonian for a mean field and does not include exchange. By means of these procedures the relativistic kinetic energy density results ... 

A differential virial theorem represents an exact, local (at space point r) relation involving the external potential u(r), the (ee) interaction potential u r,r ), the diagonal elements of the 1st and 2nd order DMs, n(r) and n2(r,r ), and the 1st order DM p(ri r2) close to diagonal , for a particular system. As it will be shown, it is a very useful tool for establishing various exact relations for a many electron systems. The mentioned dependence on p may be written in terms of the kinetic energy density tensor, defined as... 

This is a real, symmetric tensor, the trace of which is the non-negative kinetic energy density (scalar)... 

---