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Third-Generation TB-LMTO

  • O. K. Andersen (a1), C. Arcangeli (a1), R. W. Tank (a1), T. Saha-Dasgupta (a1), G. Krier (a1), O. Jepsen (a1) and I. Dasgupta (a1)...

Abstract

We describe the screened Korringa-Kohn-Rostoker (KKR) method and the third-generation linear muffin-tin orbital (LMTO) method for solving the single-particle Schrödinger equation for a MT potential. In the screened KKR method, the eigenvectors CRL,i are given as the non-zero solutions, and the energies ε i as those for which such solutions can be found, of the linear homogeneous equations: , where Ka (ε) is the screened KKR matrix. The screening is specified by the boundary condition that, when a screened spherical wave is expanded in spherical harmonics Y R′L′ (ȓR′) about its neighboring sites R′, then each component either vanishes at a radius, rR′=aR′L′, or is a regular solution at that site. When the corresponding “hard” spheres are chosen to be nearly touching, then the KKR matrix is usually short ranged and its energy dependence smooth over a range of order 1 Ry around the centre of the valence band. The KKR matrix, Kν), at a fixed, arbitrary energy turns out to be the negative of the Hamiltonian, and its first energy derivative, Kν), to be the overlap matrix in a basis of kinked partial waves, φ RL ν, r R ), each of which is a partial wave inside the MT-sphere, tailed with a screened spherical wave in the interstitial, or taking the other point of view, a screened spherical wave in the interstitial, augmented by a partial wave inside the sphere. When of short range, K (ε) has the two-centre tight-binding (TB) form and can be generated in real space, simply by inversion of a positive definite matrix for a cluster. The LMTOs, χ RL ν), are smooth orbitals constructed from φ RL ν, r R ) and φ RL ν, r R ), and the Hamiltonian and overlap matrices in the basis of LMTOs are expressed solely in terms of Kν) and its first three energy derivatives. The errors of the single-particle energies ε i obtained from the Hamiltonian and overlap matrices in the φ(εν)- and χ(εν) bases are respectively of second and fourth order in ε i – ε i . Third-generation LMTO sets give wave functions which are correct to order ε i – εν, not only inside the MT spheres, but also in the interstitial region. As a consequence, the simple and popular formalism which previously resulted from the atomic-spheres approximation (ASA) now holds in general, that is, it includes downfolding and the combined correction. Downfolding to few-orbital, possibly short-ranged, low-energy, and possibly orthonormal Hamiltonians now works exceedingly well, as is demonstrated for a high-temperature superconductor. First-principles sp 3 and sp 3 d 5 TB Hamiltonians for the valence and lowest conduction bands of silicon are derived. Finally, we prove that the new method treats overlap of the potential wells correctly to leading order and we demonstrate how this can be exploited to get rid of the empty spheres in the diamond structure.

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1 Korringa, M., Physica 13, 392 (1947);
Kohn, W. and Rostoker, J., Phys. Rev. 94, 1111 (1954).
2 Andersen, O.K., Postnikov, A.V., and Savrasov, S. Yu., in Applications of Multiple Scattering Theory to Materials Science, eds. Butler, W.H., Dederichs, P.H., Gonis, A., and Weaver, R.L., MRS Symposia Proceedings No. 253 (Materials Research Society, Pittsburgh, 1992) p 37.
3 Andersen, O.K., Jepsen, O., and Krier, G. in Lectures on Methods of Electronic Structure Calculations, edited by Kumar, V., Andersen, O.K., and Mookerjee, A. (World Scientific Publishing Co., Singapore, 1994), pp. 63124.
4 Zeller, R., Dederichs, P.H., Ujfalussy, B., Szunyogh, L., and Weinberger, P., Phys. Rev. B 52, 8807 (1995).
5 Andersen, O.K., Solid State Commun. 13, 133 (1973);
Andersen, O.K., Phys. Rev. B 12, 3060 (1975);
Jepsen, O., Andersen, O.K., and Mackintosh, A.R., Phys. Rev. 12, 3084 (1975).
6 Andersen, O.K. and Jepsen, O., Phys. Rev. Lett. 53, 2571 (1984).
7 Skriver, H.L., The LMTO Method (Springer-Verlag, Berlin, 1984).
8 Skriver, H.L. and Rosengaard, N.M., Phys. Rev. B 43, 9538 (1991);
Turek, I., Drchal, V., Kudrnovsky, J., Sob, M., and Weinberger, P., Electronic Structure of Disordered Alloys, Surfaces, and Interfaces (Kluwer Academic Publishers, Boston/London/Dordrecht, 1997).
9 Andersen, O.K., Jepsen, O. and Sob, M., in Lecture Notes in Physics: Electronic Band Structure and Its Applications, eds. Yussouff, M. (Springer-Verlag, Berlin, 1987).
10 Lambrecht, W.R.L. and Andersen, O.K., Phys. Rev. B 34, 2439 (1986).
11 Andersen, O.K., Pawlowska, Z. and Jepsen, O., Phys. Rev. B 34, 5253 (1986).
12 Pettifor, D.G., J. Phys. F 7, 613 (1977);
Pettifor, D.G., J. Phys. F 7, 1009 (1977);
Pettifor, D.G., J. Phys. F 8, 219 (1978).
13 Andersen, O.K. and Woolley, R.G., Mol. Phys. 26, 905 (1973).
14 Haydock, R. in Solid State Physics 35 edited by Ehrenreich, H., Seitz, F., and Turnbull, D. (Springer Verlag, Berlin, 1980) p. 129.
15 Nowak, H.J., Andersen, O.K., Fujiwara, T., Jepsen, O. and Vargas, P., Phys. Rev. B 44, 3577 (1991);
Vargas, P., C., in Lectures on Methods of Electronic Structure Calculations, edited by Kumar, V., Andersen, O.K., and Mookerjee, A. (World Scientific Publishing Co., Singapore, 1994), pp. 147191;
Frota-Pessoa, S., Phys. Rev. B 36, 904 (1987);
Bose, S.K., Jepsen, O., and Andersen, O.K., Phys. Rev. B 48, 4265 (1993).
16 The Stuttgart TB-LMTO program, http://www.mpi-stuttgart.mpg.de
17 Jepsen, O. and Andersen, O.K., Z. Phys. B 97, 35 (1995).
18 Gunnarsson, O., Harris, J., and Jones, R.O., Phys. Rev. B 15, 3027 (1977);
Weyrich, K.H., Solid State Commun. 54, 975 (1985);
Springborg, M. and Andersen, O.K., J. Chem. Phys. 87, 7125 (1986);
Methfessel, M., Phys. Rev. 38, 1537 (1988);
Methfessel, M., Rodriguez, C.O., and Andersen, O.K., Phys. Rev. B 40, 2009 (1989); J. Wills (unpublished);
Savrasov, S.Y., Phys. Rev. B 54, 16470 (1996).
19 An exception is: Vitos, L., Kollar, J., and Skriver, H.L., Phys. Rev. B 49, 16694 (1994).
20 Tank, R.W., Andersen, O. K., Krier, G., Arcangeli, C., and Jepsen, O. (unpublished).
21 In order to make K positive-, rather than negative definite, we have defined K with the opposite sign as in Ref. 3.
22 This neglects the high-order term
23 Andersen, O. K., Jepsen, O., Liechtenstein, A. I., and Mazin, I. I.; Phys. Rev. B 49, 4145 (1994);
Andersen, O. K., Liechtenstein, A. I., Jepsen, O., and Paulsen, F.; J. Phys. Chem. Solids 56, 1573 (1995).
24 Saha-Dasgupta, T., Andersen, O. K., Krier, G., Arcangeli, C., Tank, R.W., Jepsen, O., and Dasgupta, I. (unpublished).
25 Müller, T. F. A., Anisimov, V., Rice, T. M., Dasgupta, I., and Saha-Dasgupta, T. (unpublished) cond-mat/9802029.
26 Savrasov, S. Y. and Andersen, O. K., Phys. Rev. Lett. 77, 4430 (1996).
27 Chadi, D. J. and Cohen, M. L., phys. status solidi 68, 405 (1975).
28 Cohen, R. E., Stixrude, L., and Wasserman, E., Phys. Rev. B 56, 8575 (1997).
29 McMahan, A. K. and Klepeis, J. E., Phys. Rev. B 56, 12 250 (1997).
30 Arcangeli, C., Andersen, O.K., and Tank, R.W. (unpublished).

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