International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 2.2, p. 302
Section 2.2.11.6. LMTO (linear combination of muffin-tin orbitals) method
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Institut für Materialchemie, Technische Universität Wien, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria |
The LMTO method (Andersen, 1975; Skriver, 1984) is the linearized counterpart to the KKR method, in the same way as the LAPW method is the linearized counterpart to the APW method. This widely used method originally adopted the atomic sphere approximation (ASA) with overlapping atomic spheres in which the potential was assumed to be spherically symmetric. Although the ASA simplified the computation so that systems with many atoms could be studied, the accuracy was not high enough for application to certain questions in solid-state physics.
Following the ideas of Andersen, the augmented spherical wave (ASW) method was developed by Williams et al. (1979). The ASW method is quite similar to the LMTO scheme.
It should be noted that the MTA and the ASA are not really a restriction on the method. In particular, when employing the MTA only for the construction of the basis functions but including a generally shaped potential in the construction of the matrix elements, one arrives at a scheme of very high accuracy which allows, for instance, the evaluation of elastic properties. Methods using the unrestricted potential together with basis functions developed from the muffin-tin potential are called full-potential methods. Now for almost every method based on the MTA (or ASA) there exists a counterpart employing the full potential.
References
Andersen, O. K. (1975). Linear methods in band theory. Phys. Rev. B, 12, 3060–3083.Google ScholarSkriver, H. L. (1984). The LMTO method. Springer series in solid-state sciences, Vol. 41. Berlin, Heidelberg, New York, Tokyo: Springer.Google Scholar
Williams, A. R., Kübler, J. & Gelatt, C. D. Jr (1979). Cohesive properties of metallic compounds: Augmented-spherical-wave calculations. Phys. Rev. B, 19, 6094–6118.Google Scholar