Local-density state approximation

There are a number of model exchange-correlation functionals for the ground-state. How do they perform for ensemble states Recently, several local density functional approximations have been tested [24]. The Gunnarsson-Lundqvist-Wilkins (GLW) [26], the von Barth-Hedin (VBH)[25] and Ceperley-Alder [27] local density approximations parametrized by Perdew and Zunger [28] and Vosko, Wilk and Nusair (VWN) [29] are applied to calculate the first excitation energies of atoms. 

Plutonium has physical properties which cannot be accounted for within the local density-functional approximations. It undergoes a very large lattice expansion (a -> 5) at 600 K, but the L(S)DA cannot predict this. The reason is that this scheme cannot describe correlations sufficiently accurately. The / states are itinerant in the light actinides but localized in the... 

The stress theorem determines the stress from the electronic ground state of any quantum system with arbitrary strains and atomic displacements. We derive this theorem in reciprocal space, within the local-density-functional approximation. The evaluation of stress, force and total energy permits, among other things, the determination of complete stress-strain relations including all microscopic internal strains. We describe results of ab-initio calculations for Si, Ge, and GaAs, giving the equilibrium lattice constant, all linear elastic constants Cy and the internal strain parameter t,. 

The electronic polaron model is based on the assumption that the band calculation using the local-density functional approximation gives the correct ground state of the system. The agreement between the calculated Fermi surface geometry and the... 

Local Density Approximation in Quantum Chemistry and Solid State Physics J. P. Dahl,... 

Theoretical calculations were performed with the linear muffin tin orbital (LMTO) method and the local density approximation for exchange and correlation. This method was used in combination with supercell models containing up to 16 atoms to calculate the DOS. The LMTO calculations are run self consistently and the DOS obtained are combined with the matrix elements for the transitions from initial to final states as described in detail elsewhere (Botton et al., 1996a) according to the method described by Vvedensky (1992). A comparison is also made between spectra calculated for some of the B2 compounds using the Korringa-Kohn-Rostoker (KKR) method. 

Parr, R.G. Aspects of Density Functional Theory . In Local Density Approximations in Quantum Chemistry and Solid State Physics , Dahl, J.P. and Avery, J., Eds. Plenum Press New York, 1984, pp. 21-31. 

Casida, M. E., Jamorski, C., Casida, K. C., Salahub, D. R., 1998, Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory Characterization and Correction of the Time-Dependent Local Density Approximation Ionization Threshold , J. Chem. Phys., 108, 4439. 

Here, we pointed to the problem of theoretical representation, in particular, in two aspects of theory (i) the existence of highly mobile atoms at the surface such as hydrogen, which are usually not considered in the atomistic models and (ii) the importance of bandgaps and relative energy levels of electronic states, which is often distorted in local density approximations. In both respects, a quick fix to the problem is not very likely. However, as both theory and experiment continue to be developed and applied in common research projects, it can be expected that the actual understanding of the processes involved in reaction on model catalysts will substantially improve over the next 10 years. After all, the ability to trace reactions and to account for the position and charge state of each reactant is already a realization of what seemed 20 years ago a fiction rather than fact. 

Density-functional theory, developed 25 years ago (Hohenberg and Kohn, 1964 Kohn and Sham, 1965) has proven very successful for the study of a wide variety of problems in solid state physics (for a review, see Martin, 1985). Interactions (beyond the Hartree potential) between electrons are described with an exchange and correlation potential, which is expressed as a functional of the charge density. For practical purposes, this functional needs to be approximated. The local-density approximation (LDA), in which the exchange and correlation potential at a particular point is only a function of the charge density at that same point, has been extensively tested and found to provide a reliable description of a wide variety of solid-state properties. Choices of numerical cutoff parameters or integration schemes that have to be made at various points in the density-functional calculations are all amenable to explicit covergence tests. 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

Some of the major areas of activity in this field have been the application of the method to more complex materials, molecular dynamics, [28] and the treatment of excited states. [29] We will deal with some of the new materials in the next section. Two major goals of the molecular dynamics calculations are to determine crystal structures from first principles and to include finite temperature effects. By combining molecular dynamics techniques and ah initio pseudopotentials within the local density approximation, it becomes possible to consider complex, large, and disordered solids. 

The scanning tunneling microscope uses an atomically sharp probe tip to map contours of the local density of electronic states on the surface. This is accomplished by monitoring quantum transmission of electrons between the tip and substrate while piezoelectric devices raster the tip relative to the substrate, as shown schematically in Fig. 1 [38]. The remarkable vertical resolution of the device arises from the exponential dependence of the electron tunneling process on the tip-substrate separation, d. In the simplest approximation, the tunneling current, 1, can be simply written in terms of the local density of states (LDOS), ps(z,E), at the Fermi level (E = Ep) of the sample, where V is the bias voltage between the tip and substrate... 

Werden SH, Davidson ER (1984) In Dahl JP, Avery J (eds) Local density approximations in quantum chemistry and solid state physics. Plenum, New York, p 33... 

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