Bonding band structure calculations

The simplest approximation to the complete problem is one based only on the electron density, called a local density approximation (LDA). For high-spin systems, this is called the local spin density approximation (LSDA). LDA calculations have been widely used for band structure calculations. Their performance is less impressive for molecular calculations, where both qualitative and quantitative errors are encountered. For example, bonds tend to be too short and too strong. In recent years, LDA, LSDA, and VWN (the Vosko, Wilks, and Nusair functional) have become synonymous in the literature. 

In solid state physics, the sensitivity of the EELS spectrum to the density of unoccupied states, reflected in the near-edge fine structure, makes it possible to study bonding, local coordination and local electronic properties of materials. One recent trend in ATEM is to compare ELNES data quantitatively with the results of band structure calculations. Furthermore, the ELNES data can directly be compared to X-ray absorption near edge structures (XANES) or to data obtained with other spectroscopic techniques. However, TEM offers by far the highest spatial resolution in the study of the densities of states (DOS). 

Density functional calculations of molecules, using a Hamiltonian including density functionals, frequently reproduce observed properties, such as bond and excitation energies, reaction profiles, and ionization energies (Ziegler 1991). For tetrafluoroterephthalonitrile (l,4-dicyano-2,3,5,6 tetrafluorobenzene), there is excellent agreement between the electron density from a density functional calculation (Delley 1986) and the X-ray diffraction results (Hirshfeld 1992) (see chapter 5). Avery et al. (1984) have proposed the use of experimental densities in crystals as a basis for band structure calculations. 

For atomic H adsorption on surfaces the electronic structure as obtained by UPS studies and DFT calculations on Ni, Pd, and Pt shows a similar picture. There is a strong bonding H-induced feature around 7-9 eV below the Fermi level observed both in UPS and band structure calculations [43]. This has been related to that the H Is level interacts with both the metal -and 7-bands. Since the H Is level is much lower in energy in comparison with the previously discussed adsorbates, for which the outer level was of p character, it is anticipated that the metal s-electrons will be more strongly mixed into the adsorbate bonding resonance. Since no X-ray spectroscopy measurements can be conducted on H it is difficult to derive how much H Is character there is in the 7-band region, respectively, above the Fermi... 

Figure 11 2 3. Band structure of MgB2 calculated for the distorted geometry. The displacement of B atoms is f = 0.005/atom (fraction unit) that correspond to 0.032 A0 of B1-B2 bond length elongation for stretching vibration (E2g(a) phonon mode amplitude). At this displacement, the lower splitoff c band has just sank below EF. The Fermi level - EF is indicated by the dashed line. The band structure calculations indicate that dominant is Oi-G2 and Gi-71 bands coupling over the E2g phonon mode...

In extreme cases a multiple-scattering, sharp resonant structure can result in which the electron is in a quasi-bound state (155). One example is the white line, which is among the most spectacular features in X-ray absorption and is seen in spectra of covalently bonded materials as sharp ( 2eV wide) peaks in absorption immediately above threshold (i.e., the near continuum). The cause of white lines has qualitatively been understood as being due to a high density of final states or due to exciton effects (56, 203). Their description depends upon the physical approach to the problem for example, the LiUii white lines of the transition metals are interpreted as a density-of-states effect in band-structure calculations but as a matrix-element effect in scattering language. 

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