Delocalized valence states

To determine the BEs (Eq. 1) of different electrons in the atom by XPS, one measures the KE of the ejected electrons, knowing the excitation energy, hv, and the work function, electronic structure of the solid, consisting of both localized core states (core line spectra) and delocalized valence states (valence band spectra) can be mapped. The information is element-specific, quantitative, and chemically sensitive. Core line spectra consist of discrete peaks representing orbital BE values, which depend on the chemical environment of a particular element, and whose intensity depends on the concentration of the element. Valence band spectra consist of electronic states associated with bonding interactions between the... 

In the pseudopotential method, core states are omitted from explicit consideration, a plane-wave basis is used, and no shape approximations are made to the potentials. This method works well for complex solids of arbitrary structure (i.e., not necessarily close-packed) so long as an adequate division exists between localized core states and delocalized valence states and the properties to be studied do not depend upon the details of the core electron densities. For materials such as ZnO, and presumably other transition-metal oxides, the 3d orbitals are difficult to accommodate since they are neither completely localized nor delocalized. For example, Chelikowsky (1977) obtained accurate results for the O 2s and O 2p part of the ZnO band structure but treated the Zn 3d orbitals as a core, thus ignoring the Zn 3d participation at the top of the valence region found in MS-SCF-Aa cluster calculations (Tossell, 1977) and, subsequently, in energy-dependent photoemission experiments (Disziulis et al., 1988). 

Mixed-valency and thermally induced transition between localized and delocalized valence states was observed with Eu Mossbauer spectroscopy of the interme-tallic compound EuNiP [70] (Fig. 2.39). 

Lindenberg and Ratner have discussed the question of localized versus delocalized valency states by using a four-site model. In the simplest case, this is the system H2 H2, in which the two H-H distances can be varied to provide different values of the coupling parameter. The criteria for valence trapping, and rates of intramolecular electron transfer are discussed in terms of the model. ... 

In this way we come to class III complexes, i.e. complexes in which the two sites are indistinguishable and the element has a non-integral oxidation state (delocalized valence). Usually one divides this class in two subclasses. In class IIIA the delocalization of the valence electrons takes place within a cluster of equivalent metal ions only. An example is the [NbgCli2] ion in which there are six equivalent metal ions with oxidation state + 2.33. In class IIIB the delocalization is over the whole lattice. Examples are the linear chain compound K2Pt(CN)4.Bro.3o. 3H2O with a final oxidation state for platinum of 2.30, and three-dimensional bronzes like Na WOg. 

The position of the 4-derived t2g band in the mixed oxides shifts from 0.8 eV for Ru02 to 1.5 eV for Ir02 proportional to the composition of the oxide. As a consequence of common 4-band formation the delocalized electrons are shared between Ir and Ru sites. In chemical terms, Ir sites are oxidized and Ru sites are reduced and electrochemical oxidation potentials are shifted. Oxidation of Ru sites to the VIII valence state is now prohibited. Thus corrosion as well as 02 evolution on Ru sites is reduced which explains the Tafel slope and overpotential behaviour. Most probably Ru sites function as Ir activators [83]. 

The low BE region of XPS spectra (<20 — 30 eV) represents delocalized electronic states involved in bonding interactions [7]. Although UV radiation interacts more strongly (greater cross-section because of the similarity of its energy with the ionization threshold) with these states to produce photoelectrons, the valence band spectra measured by ultraviolet photoelectron spectroscopy (UPS) can be complicated to interpret [1], Moreover, there has always been the concern that valence band spectra obtained from UPS are not representative of the bulk solid because it is believed that low KE photoelectrons have a short IMFP compared to high KE photoelectrons and are therefore more surface-sensitive [1], Despite their weaker intensities, valence band spectra are often obtained by XPS instead of UPS because they provide... 

Only for a special class of compound with appropriate planar symmetry is it possible to distinguish between (a) electrons, associated with atomic cores and (7r) electrons delocalized over the molecular surface. The Hiickel approximation is allowed for this limited class only. Since a — 7r separation is nowhere perfect and always somewhat artificial, there is the temptation to extend the Hiickel method also to situations where more pronounced a — ix interaction is expected. It is immediately obvious that a different partitioning would be required for such an extension. The standard HMO partitioning that operates on symmetry grounds, treats only the 7r-electrons quantum mechanically and all a-electrons as part of the classical molecular frame. The alternative is an arbitrary distinction between valence electrons and atomic cores. Schemes have been devised [98, 99] to handle situations where the molecular valence shell consists of either a + n or only a electrons. In either case, the partitioning introduces extra complications. The mathematics of the situation [100] dictates that any abstraction produce disjoint sectors, of which no more than one may be non-classical. In view if the BO approximation already invoked, only the valence sector could be quantum mechanical9. In this case the classical remainder is a set of atomic cores in some unspecified excited state, called the valence state. One complication that arises is that wave functions of the valence electrons depend parametrically on the valence state. 

The first transition would be expected to be of higher energy than the second from simple atomic charge considerations. Because the two atoms are of equal abundance, the two peaks have essentially equal intensities. Unfortunately, the observation of two XPS peaks does not rule out the possibility of delocalized valence electrons in the ground state. Two transitions are expected even in that case because of polarization of the excited state by the core ionization 123 The ground state of a delocalized mixed valence compound can be crudely represented by the formula M-M, where the intermediate position of the dot indicates that the odd valence electron is equally shared by the two metal atoms. The two XPS transitions can then be represented as follows,... 

The appearance of only one XPS peak for a mixed valence compound is consistent with a delocalized ground state (and excited state). Bifeirocenylene (II, III) picrate, whose structure is shown in Fig. 8, probably fits in this category. The Mossbauer spectrum of the complex indicates only one kind of iron atom, and the Fe 2p3,2 spectrum consists of only one peak with a weak shoulder at higher binding energy 29). It should be recognized, however, that even in the case of a localized system in which two XPS peaks are expected, if the chemical shift between the two peaks is less than the resolution of the spectrometer, only one peak will be observed. 

Over the past 10-15 years, several model systems that maintain the copper ion mixed-valence, delocalized electronic state with short Cu-Cu bond distances as in the CcO enzyme—Cu -Cu Cu -Cu =Cu Cu - —have been... 

The term mixed valence state has been used in two connotations (1) to mean two coupled irons with different formal charge (e.g., Fe Fe ) and (2) to mean two (or more) irons coupled and electronically delocalized to have fractional formal charge (e.g., 2Fe from delocalized Fe -t- Fe " "). We use mixed valence only in the former meaning. 

In a) and P) the non bonding-hypothesis for 5 f electrons is retained, differences in cohesive energy being only due to promotion of outer electrons from one to another orbital state and ionization energies (or electron affinities) due to the different valence states attained. Therefore, any further discrepancy found with experimental values, is indicative of the metallic bonding introduced by delocalization of the 5f electrons (point y). 

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