Local Bond Distances

A discussion on the main spectroscopic techniques used in mineralogy and materials science is beyond the scope of this chapter. Several treatises and scientific papers dealing with this topic are already available. On the other hand, a thorough understanding of the local phenomena occurring when chromium is incorporated into the octahedral site of a perovskite structure, and, consequently, the know-how of deriving chromium-oxygen local distances is an essential requirement For this reason, in this section, it will be briefly explained how to obtain local bond distances by means of the electronic absorption spectroscopy (EAS), which is one of the most common and well-documented spectroscopic techniques in mineral sciences. 

Strength Dq of the sixfold coordinated Cr ion (i.e., the energy of its band) corresponds to the inverse fifth power of the mean metal-oxygen bond distances  

The local chromium-oxygen bond distance for each composition of the perov- 

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Rodriguez-Monge, L., and S. Larsson. 1995. Conductivity in polyacetylene, 1. Ab-initio calculation of charge localization, bond distances, and reorganization energy in model molecules. / Chem Phys 102 7106. 

The extent of the mismatch between average and local bond distances at the perovskite octahedral site can be parameterized by means of the structural relaxation coefficient (e) ... 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

The consequence of the presence of scroll helicity in a tubule is expected to be that any increase (decrease) of the intralayer C—C distance G will increase (decrease) the local length of the spiral, but not necessarily the mean interlayer distance, since the scroll can easily adapt its radius of curvature to minimize, if necessary, any energetic strain due to a stress in the local bond lengths. 

CC bond distances in localized allylic systems have been held at 1. 5A and 1.3A (typical of CC single and double bond lengths, respectively), and at 1.4A for delocalized systems. 

Examine the geometry of methylbenzyne. Measure carbon-earbon distances. Which 7C bonds are deloealized and whieh are localized Is there really a triple bond (Compare bond distance to triple bond in hexa-l,5-dien-3-yne and to partial double bonds in benzene). Are you able to draw a single Lewis structure whieh adequately represents the geometry of the molecule ... 

These limitations, most urgently felt in solid state theory, have stimulated the search for alternative approaches to the many-body problem of an interacting electron system as found in solids, surfaces, interfaces, and molecular systems. Today, local density functional (LDF) theory (3-4) and its generalization to spin polarized systems (5-6) are known to provide accurate descriptions of the electronic and magnetic structures as well as other ground state properties such as bond distances and force constants in bulk solids and surfaces. 

Local surface structure and coordination numbers of neighbouring atoms can be extracted from the analysis of extended X-ray absorption fine structures (EXAFS). The essential feature of the method22 is the excitation of a core-hole by monoenergetic photons modulation of the absorption cross-section with energy above the excitation threshold provides information on the distances between neighbouring atoms. A more surface-sensitive version (SEXAFS) monitors the photoemitted or Auger electrons, where the electron escape depth is small ( 1 nm) and discriminates in favour of surface atoms over those within the bulk solid. Model compounds, where bond distances and atomic environments are known, are required as standards. 

By Fourier transforming the EXAFS oscillations, a radial structure function is obtained (2U). The peaks in the Fourier transform correspond to the different coordination shells and the position of these peaks gives the absorber-scatterer distances, but shifted to lower values due to the effect of the phase shift. The height of the peaks is related to the coordination number and to thermal (Debye-Waller smearing), as well as static disorder, and for systems, which contain only one kind of atoms at a given distance, the Fourier transform method may give reliable information on the local environment. However, for more accurate determinations of the coordination number N and the bond distance R, a more sophisticated curve-fitting analysis is required. 

It is interesting to note that these complexes are mixed-valent MnmMnIV complexes. Based on the relative structural data [the bond distances of the MnA atom are shorter than those of MnB], it has been concluded that in [Mn202(bipy)4]3+ one of the manganese ions is in the oxidation state IV [Mn(B)] and the other in the oxidation state III [Mn(A)]. Hence, the complex would have to be classified as a mixed-valent derivative with localized charge (Robin-Day Class I). Conversely, the two manganese sites are identical in [Mn202(phen)4]" +, from which one can infer that the charge is delocalized over the two centres (Robin-Day Class III). 

The Osl-Nl-N2-Os2 axis is not perfectly linear. The inequality of the bond distances (which would assign the oxidation states III to the Osl atom and II to the Os2 atom, respectively) should classify the monocation as a charge localized (Class I) mixed-valent species. Nevertheless, this result is in contrast with the electrochemical separation of the two... 

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