Valence coordinate

While it is possible to solve the vibrational problem using any one of a number of coordinate systems (Cartesian coordinates, spherical polar coordinates, valence coordinates, etc.), it is often most convenient to employ some type of valence... 

The well-known GF matrix technique of E. B. Wilson and his colleagues for calculating the harmonic frequencies of polyatomic molecules is based on the use of valence coordinates, also referred to as internal coordinates. What is presented here is merely a sketch of the method a fuller discussion would require extensive use of matrix algebra, which is beyond the scope of this book. The appendix on matrices in this chapter serves only as a very short introduction to such methods. For details reference should be made to the classical work of E. B. Wilson, J. C. Decius and P. C. Cross (WDC) in the reading list. 

In Equation 3.43 F now is the matrix of the force constants in valence coordinates. Again one finds normal mode coordinates, Qi, corresponding to the normal mode... 

The Cl shift of Mossbauer spectra provides a measure of the total electron density in the nucleus of an atom, i/r(o), relative to some reference standard. For Fe, 8 is quite sensitive to valence, coordination number, or number and type of bonds to its ligands. Unlike chemical shifts in NMR spectra which are frequently dominated by the spin... 

CoNiMn408, Ni2Mn40s and NisMnsOj. In the spectra of the noncubic Mn40 and the noncubic CoMn204, the extended fine structure is missing. It is apparent that the extended fine structure does pertain solely to the crystal lattice and is not dependent on the valence, coordination, or nature of the atom giving rise to the absorption spectrum. 

In the liquid-phase oxidation of acrolein, the metal ion with higher valence coordinates acrolein to produce an acyl radical by hydrogen abstraction. 

VLNW VNCR voc VS1 Very low-activity nuclear waste Valence coordination number ratio Volatile organic compound Vertical scanning interferometry... 

Within the harmonic approximation the choice of a system of internal coordinates is irrelevant provided they are independent and that a complete potential function is considered ). For example, the vibrations of HjO can be analysed in terms of valence coordinates (r, >2, or interatomic coordinates (r, r, 3) and any difference in the accuracy to which observed energy levels are fitted (considering all the isotopic species H2O, HDO and D2O) will be due to the neglect of anharmonic terms. If one makes the approximation of a diagonal force field so that one is comparing the two potentials... 

In most instances, the magnetic structure of a compound can be understood to be based on interacting localized spin centers, such as classical 3d/4d/5d transition metal ions and 4f lanthanide or 5f actinide cations with unpaired electrons. Note that while the assumption of localized moments is valid for many compounds comprising such spin centers, even partial electron delocalization in mixed-valence coordination compounds renders many localized spin models inapplicable. 

The separation into a vibrational and an electronic part is implied by the Placzek polarizability theory. The further analysis of vibrational motions has in the past typically been accomplished by calculating the vibrational energy distribution in valence coordinates. For the large-scale skeletal motions often important in ROA, and for relating Raman and ROA scattering cross-sections to the vibrational motions of structural parts of an entity, a different approach is needed. 

Although the active species containing a Cr C bond is difficult to determine, an oxidative addition of ethylene to low-valence coordinatively unsaturated chromium ions is proposed to produce such species [219] ... 

An interesting alternative to the conventional one-electron photocatalysts was the discovery of two-electron photocatalysts in the form of mixed-valence coordination compounds [118]. The two-electron photocatalysis can be useful in activation of small molecules of energy consequence, especially hydrogen and oxygen (more details can be found in Chapter 21). 

Rosenthal J, Bachman J, Dempsey JL, et al. Oxygen and hydrogen photocatalysis by two-electron mixed-valence coordination compounds. Coord Chem Rev 2005 249 1316-26. 

The essential difference between the S.V F.F. and the complete haimonic oscillator treatment does not of course lie in the choice of aience coordinates it lies in the fact that the former represents the potential energy as the sum of a set ol squared terms only that is, no interactions in the form of cross-products are allowed. It is possible to obtain a complete description of the force field to the harmonic oscillator approximation using valence coordinates if all the cross terms of the form /crA,B G c inserted. (It should... 

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