Coarse Grained Density Functional Theories for Metallic Alloys: Generalized Coherent Potential Approximations and Charge Excess Functional Theory

摘要

The class of the Generalized Coherent Potential Approximations (GCPA) to theDensity Functional Theory (DFT) is introduced within the Multiple ScatteringTheory formalism for dealing with, ordered or disordered, metallic alloys. AllGCPA theories are based on a common ansatz for the kinetic part of theHohenberg-Kohn functional and each theory of the class is specified by anexternal model concerning the potential reconstruction. The GCPA densityfunctional consists of marginally coupled local contributions, does not dependon the details of the charge density and can be exactly rewritten as a functionof the appropriate charge multipole moments associated with each lattice site.A general procedure based on the integration of the 'qV' laws is described thatallows for the explicit construction the same function. The coarse grainednature of the GCPA density functional implies great computational advantagesand is connected with the O(N) scalability of GCPA algorithms. Moreover, it isshown that a convenient truncated series expansion of the GCPA functional leadsto the Charge Excess Functional (CEF) theory [E. Bruno, L. Zingales and Y.Wang, Phys. Rev. Lett. {\bf 91}, 166401 (2003)] which here is offered in ageneralized version that includes multipolar interactions. CEF and the GCPAnumerical results are compared with status of art LAPW full-potential densityfunctional calculations for 62, bcc- and fcc-based, ordered CuZn alloys, in allthe range of concentrations. These extensive tests show that the discrepanciesbetween GCPA and CEF are always within the numerical accuracy of thecalculations, both for the site charges and the total energies. Furthermore,GCPA and CEF very carefully reproduce the LAPW site charges and the totalenergy trends.