Coherent potential approximation theory

LOCAL CHARGE DISTRIBUTIONS IN METALLIC ALLOYS A LOCAL FIELD COHERENT POTENTIAL APPROXIMATION THEORY... 

In this paper we shall develop a new version of Coherent Potential Approximation theory (CPA). We apply a local external field and study the response of the mean field CPA alloy. Because of the fluctuation-dissipation theorem, the response to the external field must be equal to the internal field caused by electrostatic interactions. This new theoretical scheme, avoiding the consideration of specific supercells, will enable us to explore a broad range of fields and clarify certain aspects of the mentioned qV relations. 

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

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. 

Nesbet, R.K. (1992). Full-potential revision of coherent-potential-approximation alloy theory, Phys. Rev. B 45, 13234-13238. 

In the realm of theory also, greater demands will be made. As such studies (37—39) as those of Cu—Ni (Fig. 13) and Ag—Pd (Fig. 14) have shown, the d levels of the two species in transition metal alloys tend to maintain their atomic identities, at least when the levels in the pure components are sufficiently well separated in energy. However, neither calculation nor experiment has been done with refinement sufficient for quantitative testing of a theory, such as the coherent potential approximation, designed to describe the d band behavior. In pure metals and intermetallic compounds, band calculations can be compared directly with experiment if transition probabilities and relaxation effects are understood. With care they can be used also in evaluation of the effective interelectronic terms which enter equations such as (18a). Unfortunately, one cannot, by definition, produce a set of selfconsistent band calculation results for a matrix of specific valence electron snpmdl.. . configurations thus, direct estimates for I of Eq. (18a) or F of Eq. (18b) cannot be made. However, band calculations for a set of systems can indicate whether or not it is reasonable to factor level shifts into volume and electron count terms, in the manner of Eqs. (18a) and (23). When this cannot be done, one must revert to a more general expression for a level shift, such as Eq. (1). 

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... 

In spite of the apparent consistency of the experimental results with calculations based on the t-matrix theory, the question of the validity of the application of this theory to strong-scattering liquid metals and alloys remains. Harris et al. (1978) have approached this question theoretically by means of a coherent-potential approximation displaying a Debye-Waller factor type of temperature dependence. They succeed by means of this strong-scattering model to reproduce, in semiquantitative fashion, the negative dp, /dr for liquid SnCe. 

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. 

COHERENT POTENTIAL APPROXIMATION WITHIN THE EXACT MUFFIN-TIN ORBITALS THEORY... 

One of the most successful approximations for calculations of the electronic structure and total energy of random substitutional alloys is the coherent potential approximation (CPA). It is based on the assumption that the alloy may be replaced by an ordered effective medium, the parameters of which must be determined self-consistently. The CPA was originally introduced by Soven for the electronic structure problem and by Taylor for phonons in random alloys. Combined with the multiple scattering theory, the CPA... 

Possibly the best known and most widely used self-consistent alloy theory is based on the coherent-potential approximation (CPA) [4,5] developed for the study of disordered (random) alloys. The properties of the CPA are by now well understood, and have been discussed in a number of publications [6] and books [7]. 

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... 

Each of the semi-classical trajectory surface hopping and quantum wave packet dynamics simulations has its pros and cons. For the semi-classical trajectory surface hopping, the lack of coherence and phase of the nuclei, and total time per trajectory are cons whereas inclusion of all nuclear degrees of freedom, the use of potentials direct from electronic structure theory, the ease of increasing accuracy by running more trajectories, and the ease of visualization of results are pros. For the quantum wave packet dynamics, the complexity of setting up an appropriate model Hamiltonian, use of approximate fitted potentials, and the... 

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