Energy density functionals

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 stiffness matrix, Cy, has 36 constants in Equation (2.1). However, less than 36 of the constants can be shown to actually be independent for elastic materials when important characteristics of the strain energy are considered. Elastic materials for which an elastic potential or strain energy density function exists have incremental work per unit volume of... 

Kawabata, S. and Kawai, H. Strain Energy Density Functions of Rubber Vulcanizates from Biaxial Extension. Vol. 24, pp. 89 — 124. 

Kryachko E. S., Ludena E. V., "Energy Density Functional Theory of Many-Electron Systems" Kluwer, Dordrecht, 1990. 

This will be the form of the profile if we used a fully local free energy density functional in our calculation. In the case of the HS-B2-approximation the fully local functional would... 

The results of the simple DHH theory outlined here are shown compared with DH results and corresponding Monte Carlo results in Figs. 10-12. Clearly, the major error of the DH theory has been accounted for. The OCP model is greatly idealized but the same hole correction method can be applied to more realistic electrolyte models. In a series of articles the DHH theory has been applied to a one-component plasma composed of charged hard spheres [23], to local correlation correction of the screening of macroions by counterions [24], and to the generation of correlated free energy density functionals for electrolyte solutions [25,26]. The extensive results obtained bear out the hopeful view of the DHH approximation provided by the OCP results shown here. It is noteworthy that in... 

Lacks, D. J., Gordon, R. G., 1993, Pair Interactions of Rare-Gas Atoms as a Test of Exchange-Energy-Density Functionals in Regions of Large Density Gradients , Phys. Rev. A, 47, 4681. 

Mebel, A. M., Morokuma, K., lin, M. C., 1995, Modification of the GAUSSIAN-2 Theoretical Model The Use of Coupled-Cluster Energies, Density Functional Geometries, and Frequencies , J. Chem. Phys., 103, 7414. 

Theophilou, A., 1979, The Energy Density Functional Formalism for Excited States , J. Phys. C, 12, 5419. 

E.S. Kryachko and E.V. Ludena Energy Density Functional Theory of... 

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. 

See for example, Jones, R., and Gunnarsson, O. Rev. Mod. Phys. 61, 689 (1990) Parr, R.G., and Yang, W. (1990), Density Functional Theory of Atoms and Molecules, Oxford University Press, New York Kryachko, E.S., and Ludena, E.V. Energy Density Functional Theory of Many Electron Systems Kluwer Academic Publishers, 1990 Callaway, J., and March, N.H. Solid State Phys. 38, 135 (1984). 

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... 

The derivation of these expressions involves lengthy algebra details which can be found in Ghosh and Dhara [14]. Here, the internal energy C/int[pJ] is basically the classical Coulomb energy, while the term xc[p,j] denotes the well-known XC energy density functional. With a suitable chosen form for xc[p,jL Equations 6.19 through 6.21 have to be solved self-consistently for the density and the current density. 

Thus, the response kernel for the interacting system can be obtained from that of the noninteracting system if one has a suitable functional form for the XC energy density functional for TD systems. The standard form for the kernel yo(r, r" Kohn Sham orbitals (/ (r), their energy eigenvalues sk, and the occupation numbers nk, is given [17,19] by... 

Relativistic mean field (RMF) models have been applied successfully to describe properties of rinite nuclei. In general ground state energies, spin-orbit splittings, etc. can be described well in terms of a few parameters ref. [18]. Recently it has lead to the suggestion that the bulk SE is strongly correlated with the neutron skin [19, 20] (see below). In essence the method is based upon the use of energy-density functional (EDF) theory. 

The energy density function p v) is defined so that dE—p v)dv is the amount of available radiation energy per unit volume originating in radiation with frequency in the infinitesimal interval [v,v + dv]. Thus, p v) is expressed in the SI units J/(m Hz) = J s/m, so that Bg and Bg have the SI units m /(J s ). Ag is expressed in s The Einstein coefficients defined in this manner are related to the line strength by... 

Let us assume a many-electron atom enclosed within an infinitely hard spherical cavity of radius R and develop the method and calculations so that we may recover the free-atom case when . This procedure also allows to look at the evolution of its ground state energy as the cage volume shrinks as has been done elsewhere [25,53]. The TFDW energy-density functional for an atom enclosed within a spherical cavity of radius R is written as... 

Table 1. Best orbital parameters and total energies tfd(i/s)w for the ground state of selected free atoms obtained through the TFD(1/8)W energy density functional... 

Intra-Orbit Optimization of Energy Density Functionals. 205... 

Results of Explicit Analytic Energy Density Functionals... 

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