Total electronic density of states

Fig. 8.9 Total electronic density of states along with the contribution of different atoms for the model systems SrgAl6Si4o (A1 occupies the 6c site), BagAl6Si3o (A1 occupies the 6c site) and SrgAli6Si3o (A1 fully occupies the 6c site and partially occupies the 16i site). Reprinted with permission from [17], Copyright (2012) American Chemical Society...

Fig. 9 Correlation between the Fermi level total electronic densities of states at transition metal (Pt and Pd) surfaces (in Ry atom ) and the corresponding C Knight shift of chemisorbed CO. (Partially reproduced with permission from Ref [25], Copyright by American Chemical Society.)...

Figure. 3 (a) Partial pair correlation function.s gij(B.) in liquid K-Sb alloys, (b) Total, partial, and local electronic densities of states in liquid Ko.soSbo.so- Cf. text. 

FIGURE 13 Total and partial (concerning the different types of electrons) electronic density of states calculated for YNi2B2C, using the local density approximation. The Fermi level Ep is defined as zero energy (from Rosner et al., 2001). 

As a result of a knowledge of the electronic density of states, it is then possible to assess the electronic contribution to the entropy. An example of these results is given in fig. 6.12 which shows not only the computed electronic entropies for Ti and Zr (the solid lines) but also the experimental values for these entropies as obtained by taking the measured total entropy and subtracting off the contributions due to vibrations. In addition to their ability to shed light on the entropies themselves, these results were also used to examine the relative importance of vibrations and electronic excitations to the hcp-bcc structural transformation in these metals. Unlike in the case of simple metals, it is found that the electronic contribution to the free energy difference is every bit as important as the vibrational terms. In particular, in the case of Ti, it is claimed that the measured entropy change... 

Measurement of the photoelectron intensity from single crystal samples as a function of both their kinetic energy and emission angle allows the total momentum of the photoelectrons to be determined, enabling band-maps of the electronic density of states of the material to be produced. See angle resolved ultraviolet photoelectron spectroscopy (ARUPS). 

Fig. 5. Electronic density of states (DOS) diagrams for (top) YbPdAl and (bottom) YbPdP. Solid lines total DOS daik gray shaded areas Pd contributions Eght gray shaded areas A] or P contributions. The energy zeros ate taken al the Fermi level.

Fig. 9. Electronic density of states of YbLiGe. Outline total DOS daik grey area Ge contribution light grey area Li contribution bold hne Yb-5d contribution.

Figure 8 Area under the Cr L2,3 levels in CrN films and elemental chromium. The minima were aligned and the areas under the peaks were evaluated in a fixed energy window after the background subtraction. The plot represents variation in the total unoccupied density of states in the films compared with elemental chromium. (Reproduced from Chourasia AR and Hood SJ (2001) Auger electron appearance potential spectroscopy. Surface and Interface Analysis 31 291-296.)...

However, if a true transition state is formed in which the electron essentially makes a multitude of transitions during the total lifetime of the state (which would be the assumption in the case of the BEBO or similar models), then it is hard to see how the reactions can be other than adiabatic. Basically, the rate equations predicted will be similar to the classical approach in Eqs. (82)-(87). The only modification introduced is the effect of the electronic density of states [cf. Eq. (99)], which is generally small. In the case of semiconductors, however, this may be different. 

FIG U RE 20.3 Total and partial electronic densities of states calculated for LijNH, LijCaNj, and LijCafNHlj. 

The electronic density of states (DOS) for the cluster models which mimic the adsorption of CO (a) on bcc-Fe(IOO) and (b) fcc-Cu(IOO) surfaces as a function of distances between CO and metal surfaces, calculated by the DV-Xa method. r(M-CO) denotes the distance between CO and metal (M) surfaces in A. The partial DOSs projected to 3d states of metal elements (left panels) and to total ones of CO molecule (right panels) are shown. The Fermi level in each configuration is defined as zero. 

One can detennine the total number of electrons in the system by integrating the density of states up to the highest occupied energy level. The energy of the highest occupied state is called the Eermi level or Eermi energy, E ... 

The total electron density contributed by all the electrons in any molecule is a property that can be visualized and it is possible to imagine an experiment in which it could be observed. It is when we try to break down this electron density into a contribution from each electron that problems arise. The methods employing hybrid orbitals or equivalent orbitals are useful in certain circumsfances such as in rationalizing properties of a localized part of fhe molecule. Flowever, fhe promotion of an electron from one orbifal fo anofher, in an electronic transition, or the complete removal of it, in an ionization process, both obey symmetry selection mles. For this reason the orbitals used to describe the difference befween eifher fwo electronic states of the molecule or an electronic state of the molecule and an electronic state of the positive ion must be MOs which belong to symmetry species of the point group to which the molecule belongs. Such orbitals are called symmetry orbitals and are the only type we shall consider here. 

For comparison, we applied also a simplified LCAO-DFT method to get the conductivity by means of the Kubo-Greenwood formula. This method is a hybrid between ab initio and empirical methods and is described in detail in Ref. [12]. It allows a faster computation of the electronic properties and the consideration of larger supercells than the Car-Parrinello method. Within this scheme it is also possible to split the total DOS into fractions referring to the sodium and tin atoms, respectively, i.e. to get the partial densities-of-states. 

Table 5.3 Contributions of -orbitals to the total electron density at the iron nucleus (in a.u. ) as a function of oxidation state and configuration. Calculations were done with the spin-averaged Hartree-Fock method and a large uncontracted Gaussian basis set. (17 1 Ip 5d If)... 

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