ASA-LMTO

We have used the multisublattice generalization of the coherent potential approximation (CPA) in conjunction with the Linear-MufRn-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed for the local spin density approximation (LSDA) the Vosko-Wilk-Nusair parameterization". 

To summarize we have reproduced the intricate structural properties of the Fe-Co, Fe-Ni and the Fe-Cu alloys by means of LMTO-ASA-CPA theory. We conclude that the phase diagram of especially the Fe-Ni alloys is heavily influenced by short range order effects. The general trend of a bcc-fcc phase transition at lower Fe concentrations is in accordance with simple band Ailing effects from canonical band theory. Due to this the structural stability of the Fe-Co alloys may be understood from VGA and canonical band calculations, since the common band model is appropriate below the Fermi energy for this system. However, for the Fe-Ni and the Fe-Cu system this simple picture breaks down. 

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... 

IMPROVED LMTO-ASA METHODS PART II TOTAL ENERGY... 

To summarise, we have presented a way to improve an LMTO-ASA calculation of the electrostatic energy in a crystal. The method is stable and general in its formalism so that it should be applicable to a wide range of systems. In this talk we did not mention the exchange correlation energy. It is possible to make an expansion of the (xc(p(r)) in terms of the SSW s. Then the integral... 

While the structure of TIF is strongly influenced by the lone pair under ambient pressure, the thallous compounds of higher halogens are not. This can be quite well explained by theoretical calculations at the DFT-LMTO-ASA level [48]. 

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). 

The important point of (12) is, however, that it retains atomic information in the one electron wave functions of (11). In LMTO - ASA, e.g. the bandwidth W will depend essentially on the charge density (()ap evaluated at the surface of the atomic sphere, being large when ( ) p is high (the electron wave is hardly contained within the sphere), small when is low (the electron wave is mostly contained within the sphere). 

The results are conveniently and clearly expressed in a thermodynamic formalism this is why they find their place in this chapter. They depend however on parameters which are drawn from band-theory, especially from the LMTO-ASA (Linear Muffin-Tin Orbitals-Atomic Sphere Approximation) method. 

In order to apply Eq. (12) for the evaluation of equilibrium metallic volumes Vat, it is necessary to know the dependence on V of Wf in (12) and Ejpj in (4). The LMTO-ASA theory yields the R-dependence Wf However, Johansson and Skriver chose... 

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

Other full potential all-electron approaches have been developed. For instance, the FPLO (fiiU potential local orbital) code uses numerical orbitals constrained to be relatively short range. The use of linear muffin tin orbitals (LMTO) has led to the development of a series of approaches of different degrees of complexity and accuracy from LMTO-ASA (linear muffin tin orbital-atomic spheres approximation) to full potential LMTO. ... 

ZnS is obtained using the LMTO-ASA method and those for the nanocrystals are from the sp d model with nearest neighbor and anion-anion interactions. Adapted from [108]. 

Prior to the work of Ref [84], a series of LMTO calculations had studied UO2. A full-potential, non-spin-polarized LMTO treatment with a gradient-corrected XC model gave a lattice constant (fluorite structure) of 9.81 au, well below the experimental 10.34 au (see [84] for references to the other literature). An approximate LMTO (LMTO-ASA) non-spin-polarized treatment with LDA XC gave 9.92 au and a bulk modulus of 5 = 291 GPa versus the experimental value 207 GPa. Spin-polarized LDA calculations did give anti-ferromagnetic ordering (foimd experimentally) at the experimental lattice constant but the moment vanished at the LDA equilibrium value. All the results were metallic. 

Recently, Mackintosh and Andersen [1.86] reviewed the LMTO-ASA method and GdtzeVs et al. applications of it to the simple, transition, and noble metals [1.87]. Some other results may be found in unpublished notes by Andersen [1.88]. An elementary review by Andersen of the linear methods and their applications has recently appeared in [1.89]. 

There are two equally important aspects of the linear methods which I wish to emphasise here physical transparency and computational efficiency. The two aspects will be represented by the KKR-ASA and the LMTO-ASA equations, respectively, which within the LMTO method may be regarded as Siamese twins. They are mathematically equivalent, they share the same so-called structure constants, and they supplement each other in the sense that the KKR-ASA equations have a mathematical form which leads to physically simple concepts while the LMTO-ASA equations are very efficient on a computer. With this duality in mind the content of the book is organised as follows. 

In Chap.6 the atomic-sphere approximation is introduced and discussed, canonical structure constants are presented, and it is shown that the LMTO-ASA and KKR-ASA equations are mathematically equivalent in the sense that the KKR-ASA matrix is a factor of the LMTO-ASA secular matrix. In addition, we treat muffin-tin orbitals in the ASA, project out the i character of the eigenvectors, derive expressions for the spherically averaged electron density, and develop a correction to the ASA. 

In Chaps.7 and 8 it is shown how the LMTO method and the physically simple concepts contained in linear theory may be used in self-consistent calculations to estimate ground-state properties of metals and compounds. Here we treat the local-density approximation to the functional formalism of Hohenberg3 Kohn, and Sham, and the force relation derived by Andersen together with an accurate and a first-order pressure relation. In addition, the LMTO-ASA and KKR-ASA methods are generalised to the case of many atoms per cell. 

As shown in [6.6] the LMTO-ASA Hamiltonian matrix may be transformed into the two-centre form [6.7] where the hopping integrals are products of potential parameters and the canonical structure constants. This result was already stated in Sect.2.5. A less accurate two-centre approximation based upon the KKR-ASA equations will be presented in Sect.8.1.2. The canonical structure constants which, after multipiication by the appropriate potential parameters, form the two-centre hopping integrals are 1 isted in Table 6.1. The... 

In Chap.2 we introduced the concept of canonical bands based upon the KKR-ASA equations and used it to interpret energy bands calculated by the LMTO method. We did this because the KKR-ASA and LMTO-ASA methods are mathematically equivalent, as proven below. Specifically, we show that in a range around so narrow that the small parameter may be neglected the LMTO-ASA and KKR-ASA equations will lead to the same eigenvalues. 

Hence, the KKR-ASA matrix 4 is a factor of the LMTO-ASA matrix, and the LMTO and KKR methods are equivalent in the neighbourhood of E, as we wished to prove. 

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