The Muffin-Tin-Orbital Point of View
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THE MUFFIN-TIN-ORBITAL POINT OF VIEW. 0. K. ANDERSEN, A. V. POSTNIKOV*, and S. Yu. SAVRASOVt. Max-Planck-Institut fuir Festk6rperforschung, D-7000 Stuttgart 80, FRG.
Abstract. We review the interpretation of multiple-scattering theory in terms of muffin-tin orbitals. The use of slightly overlapping muffin-tin wells is justified rigorously. It is shown that the structure constants may be screened for a useful range of positive and negative energies, and that the screening may be chosen to yield desirable properties of the KKR matrix. Energy linearization and the linear muffin-tin-orbital method are discussed. I. Introduction. The formulation by Korringa,' Kohn and Rostoker 2 (KKR) of the electronic bandstructure problem as one of self-consistent multiple scattering between muffin-tin (MT) wells, is most elegant and, as regards the number of algebraic equations to be solved, also economic. Still, the KKR method is subtle, and in order to understand it, a muffin-tinorbital (MTO) point of view was introduced many years ago. 3 The insights it provided, suggested a number of simplifying approximations and lead to the development of methods which used linear-combinations of MTO's to solve the electronic-structure problem in a practical way and to circumvent the KKR restriction to MT-potentials. At the time, these approximations were not generally accepted, and certain aspects of the MTO formalism were found involved. As a consequence, the developments of the KKR and MTO methods departed, and although both methods were used for the same kind of applications, such as the electronic structure of complex systems, 4 5 impurities,8 substitutionally disordered alloys, 7 surfaces, 8 and total-energy calculations in situations of low symmetry, 9 there was little fruitful cross fertilization. The language barrier grew with each new development. Now, after twenty years of applications and developments in both camps, it may be time to exchange ideas. In this paper we shall try to explain the MTO point of view using the normal KKR notation as far as possible, that is, until the end of Sect. VI. In Sect. II we the define the MTO's and derive the KKR equations. Then, in the following section, we give the historical reason for the seemingly drastic approximation of fixing the kinetic energy outside the MT-wells (K2--•2=0) and letting the MT-spheres inflate to space-filling Wigner-Seitz (WS) spheres. In Sect. IV we reflect on the vividly discussed problem of multiple scattering between cellular wells. Then, in Sect. V we show that the use of phase shifts calculated for slightly overlapping potential wells, corresponds to superposing the potential wells. The error term is calculated and found to be of second order in the overlap volume times the potential-discontinuity. For close-packed WS-spheres, this error is found to be numerically small. In Sect. VI we show, that in KKR theory it is possible Mat. Res. Soc. Symp. Proc. Vol. 253. ©1992 Materials Research Society
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to use wave-equation solutions which are localized in r-space and an
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