Experimental band structures

In principle, valence band XPS spectra reveal all the electronic states involved in bonding, and are one of the few ways of extracting an experimental band structure. In practice, however, their analysis has been limited to a qualitative comparison with the calculated density of states. When appropriate correction factors are applied, it is possible to fit these valence band spectra to component peaks that represent the atomic orbital contributions, in analogy to the projected density of states. This type of fitting procedure requires an appreciation of the restraints that must be applied to limit the number of component peaks, their breadth and splitting, and their line-shapes. 

Finally, we show in Figure 12 the experimental band structures together with the calculated ones for polyethylene.62 These density-functional results (with a local-density approximation) demonstrate a very good agreement between theory and experiment, but it should be stressed that the experimental data have been shifted rigidly about 2 eV upwards in energy, which is consistent with the results above. We add that band structures from Hartree-Fock calculations were in general too wide,63 which is a common deficiency of Hartree-Fock calculations. 

Fig. 6 Experimental band structure of LB NADPO-11 along the direction perpendicular to the surface. The straight line is a guide for the eyes.

It should be noted that a comprehensive ELNES study is possible only by comparing experimentally observed structures with those calculated [2.210-2.212]. This is an extra field of investigation and different procedures based on molecular orbital approaches [2.214—2.216], multiple-scattering theory [2.217, 2.218], or band structure calculations [2.219, 2.220] can be used to compute the densities of electronic states in the valence and conduction bands. 

As an example of a nanotube representative of the diameters experimentally found in abundance, we have calculated the electronic structure of the [9,2] nanotube, which has a diameter of 0.8 nm. Figure 8 depicts the valance band structure for the [9,2] nanotube. This band structure was calculated using an unoptimized nanotube structure generated from a conformal mapping of the graphite sheet with a 0.144 nm bond distance. We used 72 evenly-spaced points in the one-... 

Valence band spectra provide information about the electronic and chemical structure of the system, since many of the valence electrons participate directly in chemical bonding. One way to evaluate experimental UPS spectra is by using a fingerprint method, i.e., a comparison with known standards. Another important approach is to utilize comparison with the results of appropriate model quantum-chemical calculations 4. The combination with quantum-chcmica) calculations allow for an assignment of the different features in the electronic structure in terms of atomic or molecular orbitals or in terms of band structure. The experimental valence band spectra in some of the examples included in this chapter arc inteqneted with the help of quantum-chemical calculations. A brief outline and some basic considerations on theoretical approaches are outlined in the next section. 

The experimental UPS spectra of the emeraldine base form of polyaniline is compared with VEH-derived DOVS in Figure 5-18 97. The DOVS were derived from the VEH band structure calculations shown at the bottom of Figure 5-18. 

Although residue compounds are difficult to characterize experimentally, they should constitute only a minor perturbation on the band structure of pure graphite. Efforts to model the electronic properties in the dilute-concentration limit by perturbing the Slonczewski-Weiss-McClure model for graphite have been made (D5). 

The optical properties of solid Sg have been studied by ab initio MO calculations of the energy band structure [70] but no experimental data for solid Sg are known. 

A comparison of the band structure diagram and these two measurements shows that experimentally the main measured intensity is constrained to a few of the bands present. In the first Brillouin zone the ct, band is found to be occupied, in the second zone 02. No sign of o, or the % band is found for the T M measurement. For the A-L measurement the same bands as for the T-M measurement contribute but in addition the n band is observed, mainly in the first Brillouin zone. These experiments are a beautiful, direct observation of the nodal plane of the % electrons in momentum space. 

Figure 14 The left hand side shows the band structures of poly(pyridine) calculated using a DFT-LMTO method for helical polymers. The right hand side shows its calculated density of states spectrum (solid line) and the experimental UPS spectrum (dashed line). The UPS spectrum was taken from Miyamae et al. [104]. Reproduced with permission from Vaschetto et al. [103], Figure 6. Copyright 1997 the American Chemical Society.

Surprisingly little has been done to take advantage of these valence band spectra, perhaps because of some of the challenges in interpretation. In principle, it should be possible to fit these spectra with component peaks that correspond to contributions from individual atomic valence orbitals. However, a proper comparison of the experimental and calculated band structures must take into account various correction factors, the most important being the different photoelectron cross-sections for the orbital components. 

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