Electronic structure LMTO

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... 

A different approach is adopted here. Within the LMTO-ASA method, it is possible to vary the atomic radii in such a way that the net charges are non-random while preserving the total volume of the system . The basic assumption of a single-site theory of electronic structure of disordered alloys, namely that the potential at any site R depends only on the occupation of this site by atom A or B, and is completely independent of the occupation of other sites, is fulfilled, if the net charges... 

Table 8. A comparison of the electronic structures of CaFj and UO2, after LMTO-ASA band calculations (energies in Ryd) (from )...

Electronic structure determinations have been performed using the self-consistent LMTO method in the Atomic Sphere Approximation (ASA). 

To probe the electronic structures of the materials in the solid state, band structure calculations on the crystal structure of compound 22 were carried out. The results obtained by using the linear muffin-tin orbital (LMTO) self-consistent field (SCF) method support the interpretation that compounds 22 (R1 = Me, Et R2 = H) are small-band-gap semiconductors. 

Skriver, H. L. (1984). The LMTO Method Muffin-Tin Orbitals and Electronic Structure. Berlin Springer-Verlag. 

J. Kollar, L. Vitos, and H. L. Skriver, Electronic Structure and Physical Properties of Solids The Uses of the LMTO Method, edited by H. Dreysse, Lecture Notes in Physics, (Springer-Verlag, Berlin, 2000). 

Acknowledgements. The author wishes to thank his collaborators in the joint research referred to in this chapter. In particular he has benefit-ted from O.K. Andersen s expertise on his linear methods (LMTO, LAPW), from the extensive collaboration with M. Cardona on the electronic structures on semiconductors, not least the spin-splitting problems. R.C. Albers, M. Boring and G. Zwicknagl are thanked for their collaborations on the relativistic electronic structures of heavy-fermion materials, and A. Svane and L. Petit for several discussions and valuable information on their progress in the description of strongly correlated electron systems. 

This volume proposes to describe one particular method by which the self-consistent electronic-structure problem may be solved in a highly efficient manner. Although the technique under consideration, the Linear Muffin-Tin Orbital (LMTO) method, is quite general, we shall restrict ourselves to the case of crystalline solids. That is, it will be shown how one may perform self-consistent band-structure calculations for infinite crystals, and apply the results to estimate ground-state properties of real materials. 

The augmented spherical-wave method of Williams et al. [1.20] appeared in 1979 and is an efficient computational scheme to calculate self-consistent electronic structures and ground-state properties of crystalline solids. According to its inventors it is a "direct descendant of the LMTO technique", and a comparison will show that the two methods are indeed very similar. 

LMTO, DDNS, and SCFC, which are used to determine structure constants, eigenvalues, state densities, and ground-state properties, respectively. In addition, the package contains several utility programmes which allow the user to interpret and display in various fashions the electronic structure of the material considered. Table 9.1 contains the names and functions of all the programmes included. 

The entries in the two tables plus the programmes STR, (COR), and LMTO allow the reader to reproduce the self-consistent energy bands for 61 metals at the observed equilibrium radius. The tables may also be used to estimate the gross features of the electronic structure of these metals by means of (2.28,29) and (4.2,3,9,10,16). 

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. 

The question of alternative structure can be answered by electronic-structure theory, and it turns out that a quantitative answer is slightly more complicated because different magnetic properties are calculated for the [NaCl] and [ZnS] types. Nonetheless, non-spin-polarized band-structure calculations are quite sufficient to supply us with a correct qualitative picture. This has been derived using the TB-LMTO-ASA method and the LDA functional, and they give the correct lattice parameters with lowest energies for both structure types [267], just as for the case of CaO. 

The electronic structure of FeNis is easily calculated (TB-LMTO-ASA, LDA) for the nonmagnetic case, and we give the corresponding EKDS and the Fe-Ni and Ni-Ni COHP analyses in Figure 3.25(b). One might expect FeNis to be electronically similar to elemental Ni, and its EKDS is indeed almost superim-posable to the one of Ni, presented before in Figure 3.22. 

Fig. 3.35 LDA band structure and DOS (a) of nonmagnetic cubic MnAI according to TB-LMTO-ASA calculations with local projections of the Mn 3d contributions and COHP analyses (b) of the electronic structure.

We therefore switch to the spin-polarized case but still stay with the primitive cubic structure. It turns out that the total energies are lowered by 0.243 eV (LMTO-ASA, LDA) and 0.393 eV (FLAPW, GGA), simply due to the different occupations of the a. and jS spin sublattices. The number of unpaired electrons is 1.94 (LMTO-ASA, LDA) and 1.85 (FLAPW, GGA), respectively, and the charge transfer between A1 and Mn is almost unchanged. The new DOS plot on the basis of the LMTO electronic structure can be found in Figure 3.36(a). 

Electronic stmctures of some sesquioxides were calculated from the special interests on these materials properties. For example, Skorodumova et al. [5] calculated the electronic structure of Ce203 by FP-LMTO method for the purpose of clarifying the role of oxygen-poor Ce203 in catalytic property and its band gap and magnetic property were discussed on the basis of valence-band and core-state... 

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