Coarse-grained density functional theories for metallic alloys: Generalized coherent-potential approximations and charge-excess functional theory

Abstract

The class of the generalized coherent-potential approximations ͑GCPAs͒ to the density functional theory ͑DFT͒ is introduced within the multiple scattering theory formalism with the aim of dealing with ordered or disordered metallic alloys. All GCPA theories are based on a common ansatz for the kinetic part of the Hohenberg-Kohn functional and each theory of the class is specified by an external model concerning the potential reconstruction. Most existing DFT implementations of CPA-based theories belong to the GCPA class. The analysis of the formal properties of the density functional defined by GCPA theories shows that it consists of marginally coupled local contributions. Furthermore, it is shown that the GCPA functional does not depend on the details of the charge density and that it can be exactly rewritten as a function of the appropriate charge multipole moments to be associated with each lattice site. A general procedure based on the integration of the qV laws is described that allows for the explicit construction of the same function. The coarse-grained nature of the GCPA density functional implies a great deal of computational advantages and is connected with the O͑N͒ scalability of GCPA algorithms. Moreover, it is shown that a convenient truncated series expansion of the GCPA functional leads to the charge-excess functional ͑CEF͒ theory ͓E. Bruno et al., Phys. Rev. Lett. 91, 166401 ͑2003͔͒, which here is offered in a generalized version that includes multipolar interactions. CEF and the GCPA numerical results are compared with status of art linearized augmented plane wave ͑LAPW͒ fullpotential density functional calculations for 62 bcc-and fcc-based ordered CuZn alloys, in all the range of concentrations. Two facts clearly emerge from these extensive tests. In the first place, the discrepancies between GCPA and CEF results are always within the numerical accuracy of the calculations, both for the site charges and the total energies. In the second place, the GCPA ͑or the CEF͒ is able to very carefully reproduce the LAPW site charges and a good agreement is obtained also about the total energies.

Probing atomic environments in alloys by electron spectroscopy

“…A generalization of the CEFM has been described in Ref. 37 which does not rely upon the spherical approximation. While the NRA-CEFM could be generalized in an analogous manner, it is not clear whether this would be fruitful.…”

“…Conventional CPA calculations do not take into account Madelung interactions, and hence for GCPA theories based upon CPA effective media b X is simply the charge of an X site obtained from a conventional CPA calculation, and E X is the corresponding X energy. Calculations reveal that GCPA effective media are numerically indistinguishable 37 for all alloys with the same composition. Hence the same applies for the quantities b X , a X and E 0 : these quantities are transferable between such systems.…”

“…(2) can be derived within the class of generalized coherent potential approximations (GCPAs) described by Bruno et al 37 , with the additional -essentially exact 37 -assumption that charge transfer due to Madelung interactions 48 is small. Here we consider the CEFM within this framework, in which case b X is equivalent to the charge of an X site embedded in the GCPA effective medium for the system under consideration, given the constraint that the site's Madelung potential is 0.…”

Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

“…Найбільш плідними виявилися комбінації метод, яких розвину-то для ідеальних кристалів, зокрема, методи функціоналу густини з кластерними підходами [49][50][51] та методами теорії невпорядкова-них систем [49,[52][53][54][55][56]. Суттєву роль у здійсненні нових підходів відіграв проґрес в області обчислювальної техніки.…”

Electronic Structure and Interplay of Atomic and Magnetic Orders of Alloys with Narrow $d$-Bands

“…Найбільш продуктивними виявилися комбінації ме-тод, що розвинуті для ідеальних кристалів, зокрема, метода функ-ціоналу густини з кластерними підходами [8][9][10] та методами теорії невпорядкованих систем [8,[11][12][13][14][15]. Відповідне узагальнення під-ходів, які були розвинуті для цілком впорядкованих кристалів, стримувалося складністю проведення усереднення по ріжних кон-фіґураціях, що характеризують невпорядковану систему.…”