Coherent-potential approximation, CPA

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-... 

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. 

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)... 

The coherent potential approximation (CPA) was originally developed by Soven for the electronic problem and by Taylor for the phonon problem. The basic assumption of CPA is that a random medium with diagonal disorder can be described by an efiiective periodic Hamiltonian of the type... 

Contents H.Matsuda Atoms as Constituents of Matter. - T. Tsuneto System of Protons and Electrons. - T. Tsuneto Helium. - T. Tsuneto Superfluid Helium 3. - T.Matsubara Metals. - T.Matsubara Non-metals. - T.Matsubara Localized Electron Approximation. - T.Murao Magnetism. - T.Murao Magnetic Properties of Dilute Alloys - the Kondo Effect. - H.Matsuda Random Systems. - F. Yonezawa Coherent Potential Approximation (CPA).- References.- Subject Index. 

Finally we mention some of our recent work using the coherent potential approximation (CPA) to study the effects of cation alloying on In the 2-1-4 material. In particular Ba and Sr... 

We have obtained a broad range of detailed quantitative results relating to universality in the absence of the electron-phonon interaction by various theoretical techniques. The methods include perturbation theory, the coherent potential approximation (CPA), field theory, path integral methods, numerical calculations and the potential well analogy. The results include the density of states, the nature of the wave functions, the mean free path, the energy dependent... 

Abe and Toyozawal have shown numerically that this non-universal form can be approximated by a simple exponential for the particular case of Gaussian single site disorder perturbing a semicircular density of states in the Coherent Potential Approximation (CPA). 

The coherent potential approximation (CPA) within the tight binding Slater-Koster scheme is briefly reviewed as a theoretical tool for the study of the electronic properties of amorphous semiconductor hydrides. 

The Coherent Potential Approximation (CPA) of the electronic structure of a disordered system is based on the idea that the disordered system should be replaced by an effective medium. This medium has the property that the statistical average of the fluctuation from its potential (the so-called coherent potential) should be equal to zero. In other words, each site but one is replaced by an unknown coherent potential. One then puts at the reference site (see Figure 4.13) an A or a B component (in the simplest case of a binary disordered system) with respective probabilities 1 — /and /. After that one solves the problem of this single impurity imbedded in the effective medium characterized by the coherent potential, which is determined by the requirement that the average scattering (fluctuation) from the reference site is also zero. 

In the second method, going beyond Bom, we examined the density of states within the coherent potential approximation (CPA) which takes into account multiple scattering processes. One might think that on this level impurity states are introduced in the gap. However, we find [16] that the existence of such localized impurity states strongly depends on the relative strength of site vs. bond impurity. Only states in the gap due to disorder can be found if the site amplitude f/s is stronger than the bond amplitude Ufc. Since CPA is an effective medium theory this result might be questionable in one dimension. 

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