CPA coherent potential

It would be interesting to compare these results with those of a CPA (coherent potential approximation) calculation. For a real test of both methods a system should be found which shows a more pronounced change when going from one phase to the other, than found for the system presented in this paper. 

CPA coherent-potential approximation EXAFS extended X-ray absorption fine structure... 

The present paper is devoted to the theoretical formulation and numerical implementation of the NDCPA. The dynamical CPA is a one-site approximation in which variation of a site local environment (due to the presence, for example, of phonons with dispersion) is ignored. It is known from the coherent potential theory for disordered solids [21], that one can account in some extension the variation of a site local environment through an introduction of a nonlocal cohcn-cnt potential which depends on the difference between site... 

We have used the multisublattice generalization of the coherent potential approximation (CPA) in conjunction with the Linear-MufRn-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed for the local spin density approximation (LSDA) the Vosko-Wilk-Nusair parameterization". 

Application of the Coherent Potential Approximation (CPA) alloy theory in connec-... 

Ffom a theoretical point of view, stacking fault energies in metals have been reliably calculated from first-principles with different electronic structure methods [4, 5, 6]. For random alloys, the Layer Korringa Kohn Rostoker method in combination with the coherent potential approximation [7] (LKKR-CPA), was shown to be reliable in the prediction of SFE in fcc-based solid solution [8, 9]. 

The improvement came in the form of the coherent-potential approximation (CPA) (Soven 1967, Taylor 1967, Velicky et al 1968), which remedied the lack of self-consistency exhibited by the ATA. The crux of this approach is that each lattice site has associated with it a complex self-consistent potential, called a coherent potential (CP). The CP gives rise to an effective medium with the important property that removing that part of the medium belonging to a particular site, and replacing it by the true potential, produces, on average, no further scattering. Because the CPA is used for our discussion of chemisorption on DBA s, its mathematical formulation is given below. 

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... 

The most essential progress from the point of view of application of this theory in catalysis and chemisorption has actually been achieved by the very first papers (48-50), where the so-called coherent potential approximation (CPA) was developed and applied. By means of this, photoemission data were explained in a quite satisfying way and the catalytic research got full theoretical support for some of the ideas introduced in catalysis earlier on only semiempirical grounds (5) namely, individual components are distinguishable for molecules from the gas phase and the alloy atoms preserve very much of their metallic individuality also in alloys—something that was impossible according to the RBT and the early electronic theory of catalysis. 

We summarize below the main theoretical approaches to the binary alloy, i.e. those based on the coherent-potential approximation (CPA).156... 

Impurity and Aperiodicity Effects in Polymers.—The presence of various impurity centres (cations and water in DNA, halogens in polyacetylenes, etc.) contributes basically to the physics of polymeric materials. Many polymers (like proteins or DNA) are, however, by their very nature aperiodic. The inclusion of these effects considerably complicates the electronic structure investigations both from the conceptual and computational points of view. We briefly mentioned earlier the theoretical possibilities of accounting for such effects. Apart from the simplest ones, periodic cluster calculations, virtual crystal approximation, and Dean s method in its simplest form, the application of these theoretical methods [the coherent potential approximation (CPA),103 Dean s method in its SCF form,51 the Hartree-Fock Green s matrix (resolvent) method, etc.] is a tedious work, usually necessitating more computational effort than the periodic calculations... 

In the last years 4-8 mol percent hydrogen impurities have been found in (SN) at IBM, San Jose ( ). One of the most probable site of H bonding is the N atom in the (SN) units. To investigate the effect of randomly distributed H atoms on the band structure of (SN) we have performed a single site one-band coherent potential approximation (CPA) calculation for the (SN)... 

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