Self-consistent band

Fig. 6. Self-consistent band structure (48 valence and 5 conduction bands) for the hexagonal II arrangement of nanotubes, calculated along different high-symmetry directions in the Brillouin zone. The Fermi level is positioned at the degeneracy point appearing between K-H, indicating metallic behavior for this tubule array[17. ...

We have carried out impurity calculations for a zinc atom embedded in a copper matrix. We first perform self consistent band theory calculations on pure Cu and Zn on fee lattices with the lattice constant of pure Cu, 6.76 Bohr radii. This yields Fermi energies, self consistent potentials, scattering matrices, and wave functions for both metals. The Green s function for a system with a Zn atom embedded in a Cu matrix... 

Van der Woude and Miedema [335] have proposed a model for the interpretation of the isomer shift of Ru, lr, Pt, and Au in transition metal alloys. The proposed isomer shift is that derived from a change in boundary conditions for the atomic (Wigner-Seitz) cell and is correlated with the cell boundary electron density and with the electronegativity of the alloying partner element. It was also suggested that the electron density mismatch at the cell boundaries shared by dissimilar atoms is primarily compensated by s —> electron conversion, in agreement with results of self-consistent band structure calculations. 

Saito, M. and A. Oshiyama. 1986. Self-consistent band structures of first-stage alkali-metal graphite intercalation compounds. J. Phys. Soc. Jpn. 55 4341-4348. 

Cu is no longer in evidence and the corrected AS values range from —3 to —7 eV. This energy arises from extraatomic relaxation, from charge renormalization and from any accumulated errors such as the omission of Self-consistent band calculations, made for all the metals except Zn, provide estimates of the renormalization shifts, — 3 eV for Ti and Cu and —4 to — 5 eV for the other metals (21). These values suggest quite modest contributions to AS from extraatomic relaxation. 

An important new development within solid-state theory is the combination of self-consistent band structure, structure determination, and molecular dynamics within the local-density approximation as developed by Car and Parrinello (1985). Our discussion follows that of Srivastava and Weaire (1987). 

Calculations of the self-consistent band structures predict relatively large band gaps for the optimized lattices. For example, in the case of AN, the band gaps at the T(0,0,0) point for phases V, IV, III, and II have values between 3.37-3.51 eV while for ADN the band gap is about 3 eV. These results indicate that both these two materials are electrical insulators at ambient conditions. 

Another scheme known as LDA-t-U has been developed [121-125] to add aspects of the Hubbard model [126,127] to self-consistent band structure calculations. It introduces additional interactions which depend on the occupation of the individual orbitals, and in that way an extra symmetry... 

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. 

In principle, the canonical number-of-states function n(P) contains all the structural information needed to perform self-consistent band calculations for a given crystal structure. No diagonalisations but only scalings... 

To avoid misunderstanding I mention that the above scaling cycle is used in the self-consistency procedure mainly to reduce the number of band-structure calculations needed. If one wants very accurate self-consistent bands one must include an energy-band calculation at the end of each self-consistent scaling cycle. However, the scaling procedure is so efficient that fully converged bands of most metals may be obtained with only one or two band calculations included in the complete self-consistency procedure. 

Krasovski E E, Starrost F and Schattke W1999 Augmented Fourier components method for constructing the crystal potential in self-consistent band-structure calculations Phys. Rev. B 59 10 504... 

Clearly, the treatment of a solid involving of the order of 10 3 electrons is even a more complicated matter than that of an isolated molecule or complex in spite of the simplifications introduced by symmetry, and the use of effective potentials, and thus of a band theoretical approach, is probably not adequate in the discussion of wave function sensitive parameters such as spin distributions. But many important properties of solids reflect the electronic energy levels, rather than the finer details of the electronic distributions, and in spite of the fact that band calculations are rarely carried through to self consistency, band structures and energies of simple compounds may be determined sufficiently well to provide a good comparison with experimental data. The main effort has been directed to metals, where the valence electrons are weakly bound, and to simple compounds of high symmetry with the sodium chloride or diamond-like structure. In the latter case this effort also reflects the importance of these compounds in solid state physics and electronics and the elucidation of the band structure was essential for an understanding of many of the important properties of these materials. 

J. Altieri and J. E. Kirzan, Self-Consistent Band Theoretic Models of DNA, J. Biol. Phys. 3, 103-110 (1975). 

Fig. 22. Results of self-consistent band-structure calculations for LaH (bottom) and LaHj (top). Depletion of conduction electrons at the Fermi level and large charge transfer toward t-site hydrogens is clearly seen in the LaHj curves. After Misemer and Harmon (1982).

Figure 3 Flow diagram of the self-consistent band calculation.

The one-electron band model which has been used so successfully to interpret the photoelectron spectra of the valence bands of many metals clearly will not be satisfactory by itself to interpret the 4f spectra of Ce. Indeed, self-consistent band calculations for both y- and a-Ce yield a 4f band about 1 eV wide which straddles the Fermi level (Glotzel 1978, Pickett et aL 1981, Podloucky and Glotzel, 1983). The filled portion extends only 0.1eV below the Fermi level and contains approximately one electron. It is hybridized with other states and is not a pure 4f band. The simple one-electron picture of photoemission based on these bands would predict a narrow 4f-derived peak at the Fermi level in both phases of Ce, and this is not observed. To describe adequately the photoemission spectra, we must then move beyond the one-electron picture. As discussed above, photoelectron spectra dxt final state spectra which reflect the initial states to a greater or lesser extent depending on the localization of the states themselves. 

We calculate the total RHF energy of the ionized metallic final state, the second term on the right side of eq. (25), by the methods described in section 2.1. RHF computations are performed for the 4f" Sd"" 6s free ions, renormalized atom crystal potentials are constructed, and self-consistent band calculations are carried out. Normalization of the wave functions to the WS sphere ensures that the final state cell has charge -l-lle. The q = 0 component of the full crystal potential, which arises from the charge of the other WS cells, is not included in the total energy since our intent is to compare to the completely screened limit where no such term appears (each cell in that case being neutral). Multiplet theory is again employed to place the 4f electrons into their Hund-rule states.. 

A number of lanthanide compounds with Pd, Sn, and In crystallize in the O13 Au structure. These compounds have been extensively studied because most of them are fairly easy to prepare by congruent solidification from the melt, sometimes even as single crystals. In addition the simple structure makes it possible to perform self-consistent band-structure calculations (Konig 1983). In fig. 8 XPS and BIS data are shown for YPdj (Hillebrecht et al. 1983b). Again the reduced intensity at p... 

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