Density-Functional Theory for Random Alloys: Total Energy within the Coherent-Potential Approximation

Theory of electronic transport in random alloys with short-range order: Korringa-Kohn-Rostoker nonlocal coherent potential approximation

“…37 and 38 In Ref. 38, in a generalization of the work of Johnson et al, 4,5 it is described how to specify a configurationally averaged electronic Grand potential ⍀ in terms of KKR-NLCPA quantities and charge densities ␥ C ͑r I ͒ and one-electron potentials v ␥ C ͑r I ͒ different for each cluster configuration. The functional minimization of ⍀ with respect to the charge densities, ␥ C ͑r I ͒'s, determines the total energy of the system and requires ␥ C ͑r I ͒'s and v ␥ C ͑r I ͒'s to be found self-consistently.…”

“…Omission of the effect of the latter can lead to an underestimate of the conductivity. 21,22 Although in principle the recently developed SCF-KKR-NLCPA method 38 can provide the appropriate self-consistent one-electron charge densities and potentials, ␥ C ͑r I ͒'s and v ␥ C ͑r I ͒, for our transport calculations, in these first applications, we use those generated by the faster, simpler SCF-KKR-CPA method 4,5 in order to explore the new aspects of our theory.…”

“…In particular, in combination with density functional theory [2][3][4][5] ͑DFT͒ and the Korringa-Kohn-Rostoker method of band theory, [6][7][8] it provides a fully first-principles description of such systems. A long history of successful applications [9][10][11][12][13][14] attests to the utility and accuracy to which the method is capable.…”

Temperature and composition dependence of short-range order and entropy, and statistics of bond length: the semiconductor alloy (GaN)1−x(ZnO)x

“…Understanding the role of order and disorder in determining physical properties such as bond length, is complicated by the difficulty in modelling the numerous local chemical environments of the alloy. Theoretical approaches assuming effective medium (coherent potential approximation, CPA) [5][6] [7], periodic virtual crystal with the actual configuration treated as perturbations (virtual crystal approximation, VCA), and random alloy with special quasirandom structure (SQS) [8] mimicking the correlation function, may not be sufficient, especially because of large deviations from complete disorder. Increased computational power now allows accurate computational prediction of short-range order (SRO) using density-functional theory (DFT).…”

Generalized inclusion of short-range ordering effects in the coherent potential approximation for complex-unit-cell materials

“…Such separation is used to efficiently determine the electronic propagator G(k, ), and from it the electronic charge density. This provides the necessary input for a further iteration of the Kohn-Sham scheme, until convergence is achieved and additional observables may be determined 32 .…”