Linear-muffin-tin orbital method

B. Wenzien J. Kudrnovsky, V. Drchal and M. Sob, On the calculation of the surface Green s function by the tight-binding linear-muffin tin orbital method, J. Phys. Condens. Matter 1, 9893 (1989). 

Weyrich, K.H. (1988) Full-potential linear muffin-tin-orbital method, Phys. Rev., B37, 10269-10282. 

Bulk modulus has been calculated from first principles by a local-density approximation [19] and by a linear muffin-tin orbital method [10], suggesting a value B = 165 GPa. Measurements of bulk modulus in high-pressure induced rock salt phase yielded 170 GPa [20]. 

Note A/B implies A grown or strained to B and vice versa. A B implies no growth direction or explicit strain dependence, i.e. natural. ) T = theoretical E = experimental AVL = average lattice XPS = X-ray photoelectron spectroscopy PL = photoluminescence CL = cathodoluminescence UPS = ultraviolet photoelectron spectroscopy LMTO = linear muffin tin orbital method LAPW = linearised augmented plane wave method PWP = plane wave pseudopotential method VCA = virtual crystal approximation. 

T = theoretical LMTO = linear muffin tin orbital method. 

Electronic Structure Calculations. We have used first-principles electronic structure calculations as manifest in the (spin) density functional linearized muffin-tin orbital method to examine whether the asymmetry in properties is reflected in a corresponding asymmetry in the one-electron band structure. While in a more complete analysis explicit electron correlation of the Hubbard U type would be intrinsic to the calculation,17 we have taken the view that one-electron bandwidths point to the possible role that correlation might play and that correlation could be a consequence of the one-electron band structure rather than an integral part of the electronic structure. We have chosen the Lai- Ca,Mn03 system for our calculations to avoid complications due to 4f electrons in the corresponding Pr system. 

There are a number of band-structure methods that make varying approximations in the solution of the Kohn-Sham equations. They are described in detail by Godwal et al. (1983) and Srivastava and Weaire (1987), and we shall discuss them only briefly. For each method, one must eon-struct Bloch functions delocalized by symmetry over all the unit cells of the solid. The methods may be conveniently divided into (1) pesudopo-tential methods, (2) linear combination of atomic orbital (LCAO) methods (3) muffin-tin methods, and (4) linear band-structure methods. The pseudopotential method is described in detail by Yin and Cohen (1982) the linear muffin-tin orbital method (LMTO) is described by Skriver (1984) the most advanced of the linear methods, the full-potential linearized augmented-plane-wave (FLAPW) method, is described by Jansen... 

More recently, Boness et al. (1986) calculated the band structure of both e-Fe and 7-Fe using the linear muffin-tin-orbital method under conditions corresponding to pressures ranging from 4 to 980 GPa. The results were used to, in turn, calculate electronic thermodynamic quantities such as the electronic specific heat and the electronic Gruneisen parameter, useful quantities with which to constrain models of the Earth s core. 

The work functions for low-index surfaces of the 4d transition metals have been calculated by a full-potential linear-muffin-tin-orbital method using a slab geometry (a periodic arrangement of 7-layer metal slabs and 10-layer vacuum slabs) (29), and the results (Fig. 8) agree well with experimental results. This is a considerable improvement with respect to extended Hiickel calculations for slab [30 (see footnote 21) ] or cluster [i0 (see Chapter 3)] geometries, which usually yield values closer to the atomic ionization energies. However, the shape of the DOS curves and the relative position of the Fermi level as found by the extended Hiickel calculations are reasonably similar to those obtained by the more sophisticated methods. Therefore, it seems that the major error is in the determination of the dipole layer potential. (Further analysis of this topic would lead us beyond the scope of this chapter.)... 

Figure 5 Total (per unit cell) and local (per space-filling atomic spheres of equal size at both Pt and Sn sites) densities of states of PtsSn, calculated by the tight-binding linear muffin-tin orbitals method. At positive (sample-) bias voltages the unoccupied states above E are imaged in the STM. From Ref. [27].

Early theoretical studies based on a semi-empirical self-consistent tight-binding scheme indicate that the core-level shifts in the Pd/W(l 10) and PtAV(l 10) systems come from initial state effects (d-s,p rehybridisation, for example) [37]. The calculated shift for the Pd core level was 0.7 eV versus the value of 0.8 eV measured experimentally [53]. More sophisticated calculations (fiill-potential linear muffin-tin orbital method with LDF) for the Pd/Mo(110) system also indicate that the Pd 3d core-level shifts reflect initial state effects (substantial polarization of electrons around Pd) [40]. In this case, the calculated Pd 3ds/2 core level (0.9 eV) is identical to the experimental value and most of it (0.77 eV) comes from initial state effects while the rest (0.13 eV) originates in changes in the screening of the core hole [40]. 

Figure 10. Lowest conduction band along V-K for GaAs as calculated by means of the relativistic linear muffin-tin-orbital method. The spin splitting was exaggerated for clarity by a factor of 5. The dashed line shows the band without spin splitting. The part K-X of the [110] line is not included in the figure. The splitting is zero at the X-point, (l,l,0)27r/a (equivalent to (2,0,0)27r/a).

In Chap.5 we derive the LCMTO equations in a form not restricted to the atomic-sphere approximation, and use the , technique introduced in Chap.3 to turn these equations into the linear muffin-tin orbital method. Here we also give a description of the partial waves and the muffin-tin orbitals for a single muffin-tin sphere, define the energy-independent muffin-tin orbitals and present the LMTO secular matrix in the form used in the actual programming, Sect.9.3. 

At this stage it should be clear that the linear theory outlined in the preceding chapters may be applied at many levels of approximation. In the most favourable cases one may obtain energy levels simply by means of a pocket calculator, and this will often suffice for an overall picture of the band structure one wants to study. On the other hand, for most applications one must resort to calculations on a large-scale electronic computer, and to that end we now present a package of computer programmes, LMTOPACK, based on the linear muffin-tin orbital method. 

Lambrecht, W.R.L. and Andersen, O.K. (1986) Minimal basis sets in the linear muffin-tin orbital method applications to the diamond-structure crystals C, Si, and Ge, Phys. Rev, B34, 2439-2449. 

AE-LMTO All-electron tight-binding linear muffin-tin orbitals method AF Antiferromagnetic... 

AEI Atomic exchange interaction (model) LMTO Linear muffin-tin orbital (method)... 

The present electronic-structure calculation is based on a linearized muffin-tin orbital method (Zhukov et al. 1990). As the structural model was taken the idealized structure of a-La82 where a small distortion from the square form of the Flahaut pyramid foundations and the non-equivalent positions of the (82) "pairs were ignored. This simplification was assumed to have no noticeable effect on the energy-band structure calculated. Figure 8... 

Using a linear muffin-tin orbital method, [2002Boz] calculated the formation energies of (Co,Cr)o.5Feo and Coo.5(Fe,Cr)o,5 alloys with B2 structure. They predicted that in both cases Cr atoms prefer to occupy tire Fe sublattice. Also, the calculated formation energies are predicted to be more positive compared to binary Coo.sFco.s. 

By using the tight-binding linearized muffin-tin orbital method combined with die coherent-potential approximation (TB-LMTO-CPA) the total energies, bulk moduli, equilibrium lattice parameters, magnetie moments, and hyperfine fields of bcc solid solution were ealeulated by [2000San], and are in qualitative agreement with experimental trends. 

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