Functional kinetic energy

Wang L-W and Teter M P 1992 Kinetic-energy functional of the electron density Phys. Rev. B 45 13 196-220... 

SmarglassI E and Madden P A 1994 Orbital-free kinetic-energy functionals for first-principles molecular dynamics Phys. Rev. B 49 5220-6... 

Wang Y A, Govind N and Carter E A 1998 Orbital-free kinetic energy functionals for the nearly-free electron gas Phys. Rev. B 58 13 465... 

The foundation for the use of DFT methods in computational chemistry was the introduction of orbitals by Kohn and Sham. 5 The main problem in Thomas-Fermi models is that the kinetic energy is represented poorly. The basic idea in the Kohn and Sham (KS) formalism is splitting the kinetic energy functional into two parts, one of which can be calculated exactly, and a small correction term. 

Kinetic energy functional, calculated from a Slater determinant Internal energy Unitary matrix... 

By Harriman s theorem already cited there is always at least one such FORDO for each legitimate p. We now define the KS kinetic energy functional, which for a fixed number of particles is system independent, as... 

Wesolowski, T. A., H. Chermette, and J. Weber. Accuracy of Approximate Kinetic Energy Functionals in the Model of Kohn-Sham Equations with Constrained Electron Density the FH-NCH complex as a Test Case. J. Chem. Phys. In press. 

T p represents the electronic kinetic energy functional Vec[p the electron-electron interaction energy functional... 

The hardness kernels in Equation 24.110 depend on the kinetic energy functional as well as on the electron-electron interactions. Thomas-Fermi models can be used to evaluate the kinetic part of these hardness kernels and can be combined with a band structure calculation of the linear response X -... 

Nalewajski, R. F. 2002b. Studies of the nonadditive kinetic energy functional and the coupling between electronic and geometrical structures. In Recent Advances in Density Functional Methods, Part III., (Eds.) V. Barone, A. Bencini, and P. Fantucci, pp. 257-277. Singapore World Scientific. 

Fig. 6. Potential distribution and electron kinetic energy functions in a simple ion source using the R.P.D. method (see text) the effect of a variable retarding potential is shown schematically.

Table 1 Energies (in KeV) of single positive ions evaluated with (AH) a full relativistic kinetic energy functional without exchange [15] the c -order semi-relativistic functional (Eq. 46) without (1) and with (2) the relativistic exchange correction ((f-term), all using near-nuclear corrections, compared to Dirac-Fock (DF) values.

The reason for calling I [n] the noninteracting kinetic energy functional is recognized immediately when the GS problem of a system of N noninteracting electrons, moving in an external potential rs(r), is considered. In analogy with Eq. (9) we write... 

The exchange-correlation (xc) energy functional defined above is shown to consist of two contributions a difference between the interacting and noninteracting kinetic energy functionals and the nonclassical part of the electron-electron interaction energy functional. Using Eq. (44) we rewrite Eq. (14) as... 

The HF GS density nGs(f), occurring in Eq. (64), coincides with the density calculated according to Eq. (29) from [the solutions of the HF equations (33)], because the two ways of calculation of s at equivalent. By adding and subtracting the noninteracting kinetic energy functional to HF functional in... 

Thus, in a very natural way, a universal factor arises in the kinetic energy functional which is modulated by the function t (/), where the latter contains specific information pertaining to the JV-electron system at hand. 

The way in which local-scaling transformations have been used for the minimization of the kinetic energy functional is as follows [108-111], An arbitrary Slater determinant is selected to be the orbit-generating... 

Note that for g > 2, only the kinetic energy functional needs to be approximated. Equation (1) is equally valid whether pg corresponds to a pure state or to an ensemble with a fixed number of electrons, N. In the rest of this chapter we wiU assume an ensemble average. 

Compared to computational approaches based on the g-electron density, approaches based on the g-electron reduced density matrix have the advantage that the kinetic energy functional can be written in an explicit form ... 

The orbital representation is not used in most of the recent work on computational methods based on diagonal elements of density matrices. This is partly for historical reasons—most of the work has been done by people trained in density functional theory—and partly this is because most of the available kinetic energy functionals are known only in first-quantized form. For example, the popular generalized Weisacker functional [2, 7-11],... 

The kinetic energy functional in this case is the Weisacker kinetic energy [56],... 

P. W. Ayers, Generalized density functional theories using the l -electron densities development of kinetic energy functionals. J. Math. Phys. 46, 062107 (2005). 

P. K. Acharya, L. J. Bartolotti, S. B. Sears, and R. G. Parr, An atomic kinetic energy functional with full Weizsacker correction. Proc. Natl. Acad. Sci. USA 77, 6978-6982 (1980). 

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). 

The classical mechanical equations of motion for the 3N qk coordinates can be written in tenns of the above potential energy and the following kinetic energy function ... 

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