LMTO: Linear Muffin-Tin Orbitals
Definition:A special basis set for ab initio electronic structure calculations.
Explanation:The delocalized wave function of a metal or any other crystalline material always exhibits two completely different regions. While it oscillates rapidly in the region of the atomic cores, thereby reflecting the high kinetic energy of the electrons, it is a relatively smooth function between the atoms. Therefore, most ab initio methods partition the space of a crystal into spheres around the cores and the interstitial space (Figure 1). When viewed in two dimensions, such a partitioning scheme strongly resembles the muffin-tin pan; hence, it is given the name as muffin-tin approximation and muffin-tin orbitals. In fact, the a number of strategies to partition the aforementioned two regions led to a large variety of ab initio methods available today.

The extremely efficient LMTO method which is applied in several Steel ab initio projects simply discards the interstitial space by blowing up the atomic spheres until they overlap (atomic sphere approximation) and fill up the entire space. For the region inside the spheres, a minimal basis is used consisting of one s, three p and five d orbitals at each atomic site; for that outside of the spheres, rapidly decaying Hankel functions are used. Employing an atom-like basis set results an ab initio method, which is not only quite fast but also gets quite close to the chemist’s idea of atoms and bonds. Indeed, LMTO theory allows more solid state quantum chemical insight than the plane-wave codes, which is more flexible in computation.
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Fig. 1: (a) Schematic drawing of a muffin-tin potential, (b) the atomic sphere approximation (ASA), and (c) a muffin-tin pan that gave the partitioning scheme its name.
SFB-Link:The TB-LMTO-ASA program code from Stuttgart is used in the Steel ab initio project in order to analyze the bonding situation in selected structural motifs which appear in metals, steels, or carbides. The applied density functional theory (→DFT) code and the implemented Crystal Orbital Hamilton Population (→COHP) technique ideally complement each other.
References:[1] G. Krier, O. Jepsen, A. Burkhardt, O. K. Andersen, The TB-LMTO-ASA program, version 4.7, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.
[2] O. K. Andersen, Phys. Rev. B 1975, 12, 3060.
[3] H. Skriver, The LMTO Method, Springer, Berlin 1984.
[4] O. K. Andersen, in The Electronic Structure of Complex Systems (Eds: P. Phariseau, W. M. Temmerman), Plenum, New York 1984.
[5] O. K. Andersen, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571.