Partial /-like density of state

D. Densities of States and Partial /-like Densities of States for the Stoichiometric Monocarbides and Mononitrides of Ti, V, Zr, and Nb... 

Figure 7 LCAO partial /-like densities of states, g ,(E), in units of states of both spin directions per Ryd and unit cell for TiC (top) and TiN (bottom). The energy (Ryd) refers to the muffin-tin zero To of the APW calculation. Dotted curves, gf Ey, broken curves, g E) (with X = C, N) full curves, gJ E). (From Refs. 17 and 18. Reproduced with the permission of the Institute of Physics Publ., Institute of Physics Publ.)...

Figure 12 LAPW total, g E), and local partial /-like densities of states, g (E), for TiC in units of states of both spin directions per Ryd and unit cell, calculated by means of the full-potential LAPW method...

D. Total Densities of States and Local Partial /-like Densities of States of Substoichiometric Transition Metal Carbides and Nitrides MX (x< 1)... 

Figure 1 2 5. Panel (a) The total density of states (DOS) of a superlattice of nanotubes. The partial DOS of each subband n=l,2,3 gives a peak near the bottom of each subband. Panel (b) shows the details of the DOS near the bottom of the third subband as function of the reduced Liftshitz parameter "z" = (EF — Ec)/W where W=36.6 meV is the dispersion of the third subband in the y direction of the superlattice, transversal to the nanotube direction. The type (I) ETT occurs at the subband edge ( z =-l) where the partial DOS of the third subband gives the step-like increase of the DOS. The type (III) ETT occurs at z =0 where the DOS shows the main peak...

Fig. 21. Palladium L,-XANES and K-XANES are compared with the calculated theoretical p(E) from the p-like partial density of states taking account of the matrix element of the Pd crystal before and after it has been smeared to account for lifetime effects. The difference between the L, and the K-edge is due to the better instrumental energy resolution in the energy range of the Lj edge and shorter core hole lifetime at the K-edge...

The d eigenfunction is of significance in the transition metal formation. Figure 13.10 shows the partial density of states for ruthenium. There are several features of the partial densities of states for this metal, which are typical for the transition metals in general. First, the density of states is dominated by the d component. The onset of the conduction bands has s-like character below the d band, followed by significant d-non-d hybridization at the bottom of the d band. 

Figure 32. Calculated occupied densities of states for the bulk and the (100) surface of pyrite projected onto the Fe 3d orbitals, from Rosso et al. (1999a). The z axis is arbitrarily chosen to be parallel to the surface normal direction. dz2-like states are shifted to higher energy and partially depopulated at the surface. Other states with a z-component show similar trends but to lesser degrees. Nonbonding dxy states are changed very little because overlap with S 3p orbitals is unchanged in the lateral directions at the surface. The density of dx2.y2 states increases at the surface, likely indicating a shift of electron density from dangling bond dz2 states into remaining Fe-S bonds at the surface.

Nc is the carrier concentration at 7 = 0 in the partially filled quasiparticle conduction bands including the d electrons, and AE is the gap or pseudo gap. poiE) is the density of states (DOS) per cell and per eV In some theories it is assumed that the heavy mass quasiparticles hardly contribute to the conductivity process. However, a simple estimate shows that there are about 10 times more heavy-f-like quasiparticles within k T of Ep than d electrons, so if their effective mass would be lOOOw they would contribute about the same to the conductivity than the light weight d electrons. By imposing in order to keep the total number of heavy quasiparticles unchanged,... 

Computational studies suggest that the mechanism of the proline catalyzed aldol cyclization is best described by the nucleophilic addition of the neutral enamine to the carbonyl group together with hydrogen transfer from the proline carboxylic acid moiety to the developing alkoxide. A metal-free partial Zimmerman-Traxler-type transition state involving a chair-like arrangement of enamine and carbonyl atoms and the participation of only one proline molecule has been established [118,119]. On the basis of density functional theory (DFT) calculations Cordova and co-workers [120,121] have studied the primary amino acid intermolecular aldol reaction mechanism. They demonstrated that only one amino acid molecule is involved in the... 

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