Valence force coordinates

From calculations made for a number of simple molecules, it has become clear that in the cubic and quartic part of the potential written in curvilinear valence-force coordinates, the diagonal bond-stretching force constants (fm and fmr) are much larger than the bending and interaction constants. On this observation is based the simplest model potential, the anharmonic simple valence-force (SVF) model that consists of a complete harmonic potentialf with only the diagonal cubic and quartic stretching constants) and fmr added,... 

N02,239,247,248,256 and C102256 should be regarded as tentative since they are based on various model potentials (as indicated in the footnotes) and on much less extensive sets of data. Table 3 lists the values of the cubic constants in the valence-force coordinate space (fyt) and in the dimensionless normal coordinate space (kg/s") as obtained for... 

The primary characteristic of d-transition metals is their ability to assume several oxidation states with different stabilities. Of special interest is the stabilization of unstable oxidation states of transition metals, which is of great significance in explaining the essence of "strengthening of the main valence by means of saturation of secondary valence forces" (coordination number) (7). 

Ur<-)y-Bradley form, 179 in valence force coordinates, 174 Potential function (nee Potential energy) Potential minima, molecules with sevci al, 200. ... 

After the first unsuccessful attempts to record a matrix IR spectrum of the methyl radical, reliable data were obtained by the use of the vacuum pyrolysis method. IR spectra of the radicals CH3 and CD3 frozen in neon matrices were measured among the products of dissociation of CH3I, (CH3)2Hg and CD3I (Snelson, 1970a). The spectra contained three absorptions at 3162 (1 3), 1396 V2) and 617 cm (I l) belonging to the radical CH3 and three bands 2381, 1026 and 463 cm assigned to the radical CD3. Normal coordinate analysis of these intermediates was performed and a valence force field calculated. In accordance with the calculations, methyl radical is a planar species having symmetry >31,. 

IR absorptions of these species were assigned to fundamental modes by comparison with the spectra of stable perfluoroorganic compounds. Normal coordinate analysis of the perfluoroethyl radical was performed and the valence force field of C2F5 was calculated (Snelson et al., 1981). 

A normal coordinate analysis was carried out (55) for CIF2O+ assuming the following geometry Bcio = 1.41 A rciF = 1-62 A, /5(0C1F) = 108° and a(FClF) = 93°. A modified valence force field was computed, and the results are given in Table X. As can be seen from Table I, the CIO-... 

This type of representation of the potential energy in terms of the internal (valence) degrees of freedom is called a Valence Force Field. Valence force fields have long been used in vibrational spectroscopy in order to carry out normal mode analysis[j ]. Basically what the terms in equation (2) express are the energies required to deform each internal coordinate from some unperturbed... 

Chemisorption is of the following four types ion exchange, complexation, coordination, and chelation. It is the adsorption in which the forces involved are valence forces of the same kind as those operating in the formation of chemical compounds. Some features that are useful in recognizing chemisorption include... 

Force constant calculations are facilitated by applying symmetry concepts. Group theory is used to find the appropriate linear combination of internal coordinates to symmetry-adapted coordinates (symmetry coordinates). Based on these coordinates, the G matrix and the F matrix are factorized, which makes it possible to carry out separate calculations for each irreducible representation (c.f. Secs. 2.133 and 5.2). The main problem in calculating force constants is the choice of the potential function. Up until now, it has not been possible to apply a potential function in which the number of force constants corresponds to the number of frequencies. The number of remaining constants is only identical with the number of internal coordinates (simple valence force field SVFF) if the interaction force constants are neglected. If this force field is applied to symmetric molecules, there are often more frequencies than force constants. However, the values are not the same in different irreducible representations, a fact which demonstrates the deficiencies of this force field (Becher, 1968). 

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