Density of states calculations

Fig. 9.3 DFT (CASTER) band structure and densities of states calculated for the cFl 6-type compound Li2AIAg.

Fig. 9.8 Band structure and densities of states calculated for the compound Li2ZnGe in the non-centrosymmetric F43m cubic arrangement. Zn 3d inert orbitals (flat levels at -8 eV in the band structure) are not represented in the DOS.

Elastomers are solids, even if they are soft. Their atoms have distinct mean positions, which enables one to use the well-established theory of solids to make some statements about their properties in the linear portion of the stress-strain relation. For example, in the theory of solids the Debye or macroscopic theory is made compatible with lattice dynamics by equating the spectral density of states calculated from either theory in the long wavelength limit. The relation between the two macroscopic parameters, Young s modulus and Poisson s ratio, and the microscopic parameters, atomic mass and force constant, is established by this procedure. The only differences between this theory and the one which may be applied to elastomers is that (i) the elastomer does not have crystallographic symmetry, and (ii) dissipation terms must be included in the equations of motion. 

The fact that evaporated potassium arrives at the surface as a neutral atom, whereas in real life it is applied as KOH, is not a real drawback, because atomically dispersed potassium is almost a K+ ion. The reason is that alkali metals have a low ionization potential (see Table A.3). Consequently, they tend to charge positively on many metal surfaces, as explained in the Appendix. A density-of-state calculation of a potassium atom adsorbed on the model metal jellium (see Appendix) reveals that the 4s orbital of adsorbed K, occupied with one electron in the free atom, falls largely above the Fermi level of the metal, such that it is about 80% empty. Thus adsorbed potassium is present as K, with 8close to one [35]. Calculations with a more realistic substrate such as nickel show a similar result. The K 4s orbital shifts largely above the Fermi level of the substrate and potassium becomes positive [36], Table 9.2 shows the charge of K on several metals. 

However, in Ref. 59 also the first valence band spectrum of U has been measured by UPS, and shows a very sharp and, compared with Th, about 10 times more intense 5f peak at 0.3 eV below Ep. Thus the UPS peak at 0.75 eV and the XPS 0.6 eV peak for Th metal may be attributed to the same origin, namely 6d, as suggested by density of state calculations, the small shift between the two being induced by the different contribution of a possible 5 f tail in the UPS and XPS spectra. 

The XPS valence band as shown in Fig. 11, and especially the narrow and intense peak just below Ep (observed in all experiments) have been discussed following mainly hne I. Theoretical partial 5f density of states calculations agree in reproducing this feature, which can therefore be attributed to nearly pure 5 f states. But these density of states curves predict additional structmes which, although differing considerably in their position, are not observed experimentally. A maximum, observed only once at 1.8 eV might be qualitatively described by one calculation however, relatively poor statistics (only 100 c/s) may have artificially introduced this structure since it is difficult to understand why other XPS valence band spectra (of comparable or even higher resolutions) do not show it. 

Fig. 11. The valence band spectrum of a-U metal, as measured in XPS a), from Ref. 56 is compared with two one-electron density of states calculations (6) from Ref. 68, (c) from Ref. 69...

Fig. 16. Total and partial density of states calculated for YNi2B2C. using the local density approximation. The Fermi level Ef is at zero energy (Rosner et al. 2001).

The XPS valence band spectra picture directly the bonds between the atoms of the molecule, and are more characteristic of the compounds ( ) especially for polymers containing only carbon atoms could the technique (with the use of complementary reference spectra, and/or theoretical density of states calculations) be sensitive enough to allow an identification of isomers ... 

Fig. 3.1. Self-consistent energy bands and density of states calculated for GaAs (after Wang and Klein, 1981, reproduced with the publisher s permission).

Fig. 5.13. (a) X-ray photoelectron spectra of (Na20),(Si02)i, . The inset shows an enlargement of the valence region (after Ching et al. 1983). (b) X-ray photoelectron spectrum of Na2Si205 (i) compared with (ii) a density of states calculation (after Chingetal., 1983). 

Abstract It is demonstrated that the profile changes of x-ray emission spectra of various molecules and solids are successfully reproduced by the local and partial electron density of states calculated by the DV-Aa molecular orbital method. Some successful examples of the materials characterization by way of comparing the measured x-ray spectra and the DV-Afa calculations are also demonstrated. 

The existence of RUMs on complex surfaces in reciprocal space makes it hard to measure the actual flexibility of a structure when using calculations of RUMs only for a few representative wave vectors. We have developed the approach of using a density of states calculation to characterise the RUM flexibility (Hammonds et al. 1998b). In a material that has no RUMs, the density of states at low frequency a> has the usual form... 

Table 3. Comparison among the peaks in the density of states calculated using HF, BLYP, and MBPT(2) with basis sets 6-31G and 6-31G, respectively, and those measured by XPS and ARUPS [66] unit eV...

In random walk simulations with configurational temperature, the calculations are started with a convergence factor / = exp(O.l). When / > exp(10 ), the density of states calculated from the temperature is used as the initial density of states for the next stage, the convergence factor is reduced by and the temperature accumulators are reset to zero... 

Figure 8.03. (top) The density of states from rigorous band structure calculations (the zero of energy marks the Fermi level), (bottom) the density of states calculated using Weaire-Thorpe Hamiltonian (After Weaire et al., 1972). 

Figure 16. Top-. The absorption spectra of the special pair acceptor states P+ and P plotted over the fluorescence of the donor B. Although P+ has superior spectral overlap with B, it has a small intensity because it is dipole-forbidden. Bottom The density of states calculated for the donors and acceptors in B-to-P energy transfer. See Ref. 17.

The ionic bonding is reflected in the density of states of an alkali adsorbate. Figure 21 shows the change in density of states calculated by Lang and Williams (1978), for adsorbates on jellium with an electron density appropriate to Al, with the 2s state on the adsorbed Li broadened into a resonance centred above Ef. If the 2s state just broadened into a half-filled Lorentzian,... 

Figure B3.2.8. Comparison of the photoemission spectrum for the cetineite (Na Se) and the density of states calculated by the AFC ELAPW-A p method...

It is evident that the inner loop consisting of steps 2, 3, and 4 is just a convolution integral, f p(I) p(J — J)dl. Its repeated application folds in all of the vibrational normal modes in turn so that the complete density of states calculation is obtained after s iterations. 

Figure 9.4 Microcanonical rotational and vibrational prior distributions for the CgHg —> CgHg + C2H2 reaction. The structure in the C2H2 vibrational distribution is due to the sparse vibrational density of states and the use of exact density of states calculations. The rotational and C2H2 vibrational distributions are well described by canonical distributions.

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