TB-LMTO

The LMTO method [58, 79] can be considered to be the linear version of the KKR teclmique. According to official LMTO historians, the method has now reached its third generation [79] the first starting with Andersen in 1975 [58], the second connnonly known as TB-LMTO. In the LMTO approach, the wavefimction is expanded in a basis of so-called muffin-tin orbitals. These orbitals are adapted to the potential by constmcting them from solutions of the radial Scln-ddinger equation so as to fomi a minimal basis set. Interstitial properties are represented by Hankel fiinctions, which means that, in contrast to the LAPW teclmique, the orbitals are localized in real space. The small basis set makes the method fast computationally, yet at the same time it restricts the accuracy. The localization of the basis fiinctions diminishes the quality of the description of the wavefimction in die interstitial region. 

Second, using the fully relativistic version of the TB-LMTO-CPA method within the atomic sphere approximation (ASA) we have calculated the total energies for random alloys AiBi i at five concentrations, x — 0,0.25,0.5,0.75 and 1, and using the CW method modified for disordered alloys we have determined five interaction parameters Eq, D,V,T, and Q as before (superscript RA). Finally, the electronic structure of random alloys calculated by the TB-LMTO-CPA method served as an input of the GPM from which the pair interactions v(c) (superscript GPM) were determined. In order to eliminate the charge transfer effects in these calculations, the atomic radii were adjusted in such a way that atoms were charge neutral while preserving the total volume of the alloy. The quantity (c) used for comparisons is a sum of properly... 

Figure 1. The effective pair interactions as functions of alloy composition for the alloy system Al-Ni. The results of the CWIS based on the FP-LAPW calculations for 5 ordered structures (full line) and on the TB-LMTO-CPA for 5 disordered alloys (dash line) are compared with the the results of the GPM (dotted line).

We conclude that more work is need<. In particular it would be useful to repeat the TB-LMTO-CPA calculations using also other methods for description of charge transfer effects, e.g., the so-called correlated CPA, or the screened-impurity modeP. One may also cisk if a full treatment of relativistic effects is necessary. The answer is positive , at least for some alloys (Ni-Pt) that contain heavy elements. 

For the description of the random Hamiltonian we employ TB-LMTO formalism in the most tight binding representation . The Hamiltonian for the binary random alloy takes the form ... 

Fig. 12.3 DOSs (states/eV cell) for the MnuAlseGea compound from TB-LMTO-ASA calculations. The Fermi energy (Ef)=0 eV. The pseudogap region near the Ep is enlarged in the inset. The vertical dashed...

Jepsen, O., Burkhardt, A. and Andersen, O.K. (1999) The program TB-LMTO-ASA Version 4.7 (Max-Planck Institute fur Festkorperforschung, Stuttgart). 

TB-LMTO tight binding-linear muffin tin orbitals ... 

We employ the ASR coupled with TB-LMTO for a first-principle determination of the configuration averaged peeled off Green function Gu,k) = zl — H, ... 

Andersen, O. K. Jepsen, O. et al. The Stuttgart TB-LMTO-ASA-47 Program, MPI fiir Feukorperforschung Stuttgart, 1998. (b) Skriver. H. L. The LMTO Method. Springer Berlin. 1984. 

Within density-functional theory, a linear combination of overlapping non-orthogonal orbitals from first principles may be utilized to arrive at at full-potential local orbital (FPLO) method [213], and this k-dependent LCAO approach comes close to full-potential APW-based methods (see Sections 2.15.3 and 2.15.4) in terms of numerical accuracy, although FPLO is much faster simply because of the locality of the basis set. Even faster, due to a strongly simplified potential, is a parameter-free (density-functional) tight-binding method called TB-LMTO-ASA, derived through localization of a delocalized basis set (see Section 2.15.4). 

Given the self-consistent density-functional calculation, let us now visualize the electronic structure of CaO in real space. Because the rock-salt structure is very regular, even a simpler DFT calculation (in terms of atomic potentials) will now suffice, and we therefore recalculate the electronic structure by means of the, much faster, TB-LMTO-ASA method. Since we also know the experimental lattice parameter a with absolute certainty, the less accurate LDA functional will perform nicely for that a. Figure 3.2 shows the theoretical electron density p(r) in the (100) plane, with the Ca atoms in the corners/center and the O atoms lying inbetween. 

In addition, let us quantum-chemically analyze the electronic structure of this simple material in terms of chemical bonding. This is very easy to do because the above-mentioned TB-LMTO-ASA method operates with an extremely short-ranged basis set, such that electron and energy-partitionings are straightforward. Figure 3.3 shows the results, namely the band structure, the density-of-states, and the crystal orbital Hamilton population analysis. 

Fig. 3.3 Band structure (a), density-of-states (b) with Ca contributions in biack, and Ca-0 crystai orbitai Hamiiton popuiation (c) of CaO in the [NaCi] structure type, according to a TB-LMTO-ASA caicuiation and the LDA.

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