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The Muffin-Tin-Orbital Point of View

  • O. K. Andersen (a1), A. V. Postnikov (a1) and S. Yu. Savrasov (a1)

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.

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1. , Korringa, Physica 13, 392 (1947).
2. Kohn, W. and Rostoker, N., Phys. Rev. 94, 1111 (1954).
3. Andersen, O. K. in: Computational Methods in Band Theory, eds. Marcus, P.M., Janak, J.F., and Williams, A.R. (Plenum, 1971) p. 178.
4. Andersen, O.K., Europhysics News 12, 5, 1 (1981) and in, The Elec
5. Skriver, H. L., The LMTO Method (Springer, New York, 1984)
6. An LMTO impurity Green's-function method is described in, Gunnarsson, O., Jepsen, O., and Andersen, O. K., Phys. Rev. B 27, 7144 (1983).
7. For an LMTO-CPA method, see: Kudrnovsky, J., Drchal, V., and Masek, J., Phys. Rev. B 35, 2487 (1987). J. Kudrnovsky, S.K. Bose, and O.K. Andersen, Phys. Rev. B 43, 4613 (1991) is a recent application.
8. The LMTO surface Green's-function method is described in, Skriver, H.L. and Rosengaard, N.M., Phys. Rev. B 43, 9538 (1991)
9. For a recent, typical LMTO application, see: Rodriguez, C.O., Liechtenstein, A.I., Mazin, I.I., Jepsen, O., Andersen, O.K., and Methfessel, M., Phys.Rev. B 42, 2692 (1990)
10. Andersen, O.K., Jepsen, O., and Gltzel, D., in Highlights of Condensed-Matter Theory, edited by Bassani, F., Fumi, F., and Tosi, M.P (North Holland, N.Y. 1985).
11. Andersen, K. and Jepsen, O., Phys. Rev. Lett. 53, 2571 (1984).
12. For the LMTO recursion method, see: Nowak, H.J., Andersen, O.K., Fujiwara, T., and Jepsen, O., Phys. Rev. B 44, 3577 (1991). Typical, recent applications are: S.K. Bose, J. Kudrnovsky, I.I. Mazin, and O.K. Andersen, Phys. Rev. B 41, 7988 (1990); and, P.R. Peduto, S. Frota-Pessoa, and M. Methfessel, Phys. Rev. 44, 13 2893 (1991)
13. Lambrecht, W.R.L. and Andersen, O.K., Phys. Rev. B 34, 2439 (1986); O.K. Andersen, T. Paxton, M. Schilfgaarde, and 0. Jepsen (unpublished).
14. Fernando, G.W., Cooper, B.R., Ramana, M.V., Krakauer, H., and Ma, C.Q., Phys. Rev. Lett. 56, 2299 (1986).
15. Weyrich, K.H., Phys. Rev. B 37, 10269 (1988)
16. Blöchl, P., Thesis, University of Stuttgart (1989)
17. Springborg, M. and Andersen, O.K., J. Chem. Phys. 87, 7125 (1987)
18. Methfessel, M., Phys. Rev. B 38, 1537 (1988); M. Metfessel, C.O. Rodriguez, O.K. Andersen, Phys.Rev. B 40, 2009 (1989)
19. Savrasov, S. and Savrasov, D., Phys. Rev. (to be published). In this full-potential LMTO method the integrals over all space are performed as sums of integrals over cells. Each cell integral is performed as a surface integral and thus avoids the slowly converging spherical-harmonics expansion of the cellular step-function ØR(r).
20. Andersen, O.K.: Mont Tremblant Lecture Notes 1973 (unpublished). Much of this material was published in Ref. 5.
21. For details, see Chapter 3 and Appendix 2 of Ref. 20.
22. When defining the MTO for K2>0 we could have added any constant times the Bessel function, i.e. ijim(k,r), to the partial wave. This would have made no difference for a crystal because a Bloch sum of Bessel functions Dr ΔT exp(ik.T)δ(K,r-R-T) vanishes everywhere, except when k is on the free-electron Fermi surface with energy ic 2 in which case the function diverges everywhere. In the formalism, n would then be substituted by n+ij, and cotn by cotn+i. In the addition theorem (2.7) (and (6.2)) the substitution of n by n+ij would according to what was said above, modify the structure constants to BR,m,Rim (k,k)-iσR,Rσ,π, m and the KKR equations (2.8) would thus be unchanged.
23. Andersen, O.K., Phys. Rev. Lett. 27, 1211 (1971).
24. Andersen, O.K., Solid St. Commun. 13, 133 (1973).
25. Williams, A.R. and Morgan, J.W., J. Phys. C 7, 37 (1974).
28. See papers in these proceedings by Brown, R.G., Butler, W.H., Gonis, A., and Nesbet, R.K.; as well as references therein.
27. Appendix 13 of Ref. 20.
28. Andersen, O.K. and Kasowski, R.V., Phys. Rev. B 4, 1064 (1971); R.V. Kasowski and O.K. Andersen, Solid St. Commun. 11, 799 (1972)
29. Andersen, O.K. and Woolley, R.G., Molecular Physics 26, 905 (1973)
30. Andersen, O.K., Phys. Rev. B 12, 3060 (1975)
31. Harris, J., in Electronic Structure of Complex Systems, eds. Phariseaux, P. and Temmerman, W.M (Plenum, 1984) and refs. therein
32. Andersen, O.K., Methfessel, M., Rodriguez, C.O., Blöchl, P., Polatoglou, H.M., in Atomistic Simulation of Materials, Eds. Vitek, V. and Srolovitz, J. (Plenum, 1989), p. 1.
33. Andersen, O. K., Pawlowska, Z., and Jepsen, O., Phys. Rev. B34, 5253 (1986).
34. Andersen, O. K., Jepsen, O., and Sob, M., in Electronic Band Structure and its Applications, ed. Yussouff, M. (Springer Lecture Notes, 1987).
35. See, for instance, Hubbard, J., Proc. Phys. Soc. Lond. 92, 921 (1967)
36. Kollar, J. and Ujfalussy, B., J. Phys.: Condens. Matter (in print)

The Muffin-Tin-Orbital Point of View

  • O. K. Andersen (a1), A. V. Postnikov (a1) and S. Yu. Savrasov (a1)

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