Bond Lengths and Coordination Number

For AX molecules with no lone pairs in the valence shell of A, both the VSEPR model and the LCP model predict the same geometries, namely AX2 linear, AX3 equilateral triangular, AX4 tetrahedral, AX5 trigonal bipyramidal, and AX octahedral. Indeed Bent s tangent sphere model can be used equally as a model of the packing of spherical electron pair domains and as a model of the close packing of spherical ligands around the core of the central atom. 

An important consequence of the LCP model is that bond lengths are expected to increase with increasing coordination number from two to three to four to six. 

Bond lengths in AX molecules increase with increasing coordination number n. 

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Fig. 2. Correlation between bond lengths and coordination numbers (c.n.). A mean value for each c.n. has been calculated from Tables 8-11 single value (except for c.n. = 2) have been omitted...

Although the results obtained by comparison of bond lengths and coordination numbers are illustrative they should be used with care. Since this approach does not take into account the nature of the ligands it is only a very rough one. It is nevertheless remarkable, that solid and molecular tin(II) compounds (which differ also chemically) possess similar geometries and distances around the tin atom. 

Table 8.4 Bond Length and Coordination Number in the Chlorides, Fluorides, and Hydrides of Boron and Carbon...

The EXAFS, which occurs at higher energies above the edge, is due to the interference between the outgoing and the backscattered photoelectron waves (10-14). EXAFS provides information about the local structure of the x-ray absorbing atom. Typically, nearest neighbor bond lengths and coordination numbers can be determined to 0.02 A (1%) and one atom in four (25%) (4 ). The accuracy of these determinations is somewhat worse for outer-shell atoms, for disordered systems, or for systems with asymmetric distributions of atoms within a shell (15,16). 

Table II. Bond lengths and coordinations numbers obtained by fitting the Fourier filtered Mo EXAFS of the Co-Mo unsupported catalyst recorded in situ at room temperature. ...

Extended X-ray absorption fine structure (EXAFS) A technique for observing the local structure around a metal centre, using X-rays from a synchrotron source. The atom of interest absorbs photons at a characteristic wavelength and the emitted electrons, undergoing constructive or destructive interference as they are scattered by the surrounding atoms, modulate the absorption spectrum. The modulation frequency corresponds directly to the distance of the surrounding atoms while the amplitude is related to the type and number of atoms. In particular, bond lengths and coordination numbers may be derived. 

Full derivations of the theory were presented by Lee and Pendry and Ashley and Doniach in 1975. They showed that a complete quantitative description of th EXAFS process was possible and that accurate bond lengths and coordination numbers could be extracted from the analysis of EXAFS data. Lee and Pendry also showed that at high photoelectron energies, the curvature of the electron wave can be neglected and thus the theory can be greatly simplified into what has beeome known as the plane-wave approximation. This approximation results in an expression equivalent to that derived by Stem semi-empirically ... 

Why do we need to know bond lengths and coordination numbers with so high accuracy on interface systems ... 

As discussed early in this chapter, quantum confinement has little effect on the localized electronic levels of lanthanide ions doped in insulating nanocrystals. But when the particle size becomes very small and approaches to a few nanometers, some exceptions may be observed. The change of lanthanide energy level structure in very small nanocrystals (1-10 nm) is due to a different local environment around the lanthanide ion that leads to a drastic change in bond length and coordination number. Lanthanide luminescence from the new sites generated in nanoparticles can be found experimentally. The most typical case is that observed in nanofilms ofEu Y203 with a thickness of 1 nm, which exhibits a completely different emission behavior from that of thick films (100-500 nm) (Bar et al., 2003). 

The most detailed structures have been obtained from neutron diffraction data, when isotopic substitution methods have been possible to use. Neutrons are strongly scattered by hydrogen atoms, making it possible to determine not only bond lengths and coordination number of the metal ion, but also the orientation of the water molecules in its first coordination sphere. A summary of results is given in Table II (19-31). 

What emerges from this detailed EXAFS analysis is, first, that the tin is indeed substituted into the zeolitic framework. In many cases this kind of information is all that can be obtained from such an analysis—a first-shell fit in which the bond lengths and coordination numbers are consistent with a framework species versus a nonframework one. Flowever, in this example it was possible to analyze higher-shell data, up to a distance of 5 A, and thereby to determine the site in the zeolite framework where the tin is substituted. It is believed that the unique selectivity of this catalyst in Baeyer-Villiger oxidation reactions is a consequence of the occupation of specific crystallographically well-defined sites by tin in the framework of the zeolite in a spatially uniform manner. 

The structure of the species was well characterized particularly the NbO, NbNb, NbSi bonds lengths and coordination numbers. The catalytic data show clearly that dehydrogenation occurs majoritarily on monomeric species and dehydration on monolayer (bidimensional) structure for ethene (intra molecular reaction) and at last on dimeric species for both intra and inter molecular dehydration reaction. 

Hertz G (1920) Uber Absorptionslinien im Rdntgenspektmm. Physik Z 21 630-632 Holmes DJ, Batchelor DR, King DA (1988) Surface stracture determination by SEXAFS The reliability of bond lengths and coordination numbers from multi-shell analyses. Surface Sci 230 476-492 Huggins FE, Huffman GP (1996) Application of XAFS spectroscopy to coal geochemistry. In MD Dyar, C McCammon, MW Schaefer (eds) Mineral Spectroscopy A tribute to Roger G. Bums. Geochem Soc Spec PublNo. 5 11-23... 

X-ray diffraction metal carbonyl clusters ionic clusters metal clusters structure of duster Strudural information (bond lengths and coordination numbers around a given metal atom) based on radial eledron distribution from X-ray data RED gives only metal-metiil, not metal-support or metal-adsorbate contributions. 

As just mentioned, XAS can give information like oxidation state, neighboring atoms, bond lengths, and coordination numbers in metallomics and metalloproteomics with minimum sample preparation. Further, XAS can present its full advantages through combination with other techniques in metallomics and metalloproteomics. Therefore, in this part, we show the combined application of XAS with separation techniques like size-exclusion chromatography (SEC)... 

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