Stretching constant

The values of stretching constant E that Crowley quoted in his original paper were substantially underestimated. As a result, his estimates of were in better agreement with experiment. However, did not depend on E and reached the same subnormal value. It must be noted that critical thinning I — almost universally reaches 30-40% for various models of the elastic energy [7],... 

Data from microwave spectra on the centrifugal effect of rotational transitions of selenophene and its deuterium-substituted derivatives have been determined experimentally and compared with the calculated theoretical values of the centrifugal stretching constants by means of the force constants determined from the solution of the inverse vibrational problem.26 The two sets of values show good agreement, indicating that the system of force constants obtained for selenophene correctly reflects the characteristic features of the force field of the molecule. 

Stretching constants in mdyn/A, deformation constants in mdyn A/ radian , and stretch-bend interaction constants in mdyn/radian. 

FC = force constant EQV =equilibrium value stretch constants in kcal/mol/A bend constants in kcaVmol/rad ... 

Kuchitsu and co-workers5 7 were the first to introduce what is perhaps the simplest and most generally useful model, in which they assume all anharmonic force constants in curvilinear co-ordinates to be zero with the exception of cubic and quartic bond-stretching constants. These may be estimated from the corresponding diatomics, or from a Morse function, or they may be adjusted to give the best fit to selected spectroscopic constants to which they make a major contribution. This is often called the valence-force model. It is clear from the results on general anharmonic force fields quoted above that this model is close to the truth, and in fact summarizes 80 % of all that we have learnt so far about anharmonic force fields. 

Stretching constants have the dimension N/m or N/cm. In the latter case, the same numerical value is obtained as with the dimension mdyn/A, which continues to be used. A dimension of deformation constants is N cm/rad. However, deformation constants are often given in the same dimension as stretching constants. In this case the dimension is adjusted by dividing it by 1 cm /rad. ... 

Poisson ratio o, and thickness x. The second term is for pad stretching, modeled [61] as a supported beam problem for a material with stretching constant fcstretch crossing a gap of width X. Both of these terms are proportional to the dishing height h. 

The square planar structure was also found to be consistent with the infrared and Raman spectra of several compounds containing Se " (93). A normal coordinate analysis yielded a value of 2.2 mdynes for the Se-Se stretching constant, which is somewhat greater than the value of 1.67 mdynes obtained for the single Se-Se bond in (CH3)2Se2. 

Since the strength of the metal-ligand bond is directly related to the metal-ligand stretching constant, it is expected that the v(M—O) vibrations will be in the order Al, Ga, In > alkali earth > alkali metals . Correlations were found between the stability constants... 

The recent inclusion of a specific stretch-bend interaction in calculations of molecular geometry and energy by Allinger et al. 22) did not necessitate major revisions as far as the stretching constants or zq are concerned. It is known from vibrational analyses of alkanes and cycloalkanes that when force fields specifically include Urey-Bradley forces, this must be accompanied by a vast reduction of the C—C stretching constant in order to reproduce the experimental C—C stretching frequencies. However, reduction of kcc also necessitates a substantial reduction of zo(CC) in calculation of geometry because the balance between the sum of the non-... 

ST0-3G Genarally poor results stretching constants 20-30% overestimated erratic behavior of the other constants 387 407, 419... 

X 10 dyne. cm whereas Crawford and Brinkley obtained 4 94 X 10. In general the values obtained for bond stretching constants depend on the force field assumed. It is therefore doubtful whether force constants obtained in this wa have any clearly defined significance. 

Doi and Ohta (1991) derived very similar expressions for cri2, A/i, N2 for the elastic stresses of emulsions in step shearing strains. Larson (1997) has shown that Eqs. (9-57a) and (9-57b) can be derived as an approximation from a general phenomenological film model for affinely stretching, constant-tension interfaces thus cti2, N, and N2 can all be represented by the simple tensor expression... 

As pointed out by Kuchitsu and Morino53 it is a fair approximation to neglect all force constants of V except the stretching constant, frrr. The order of magnitude of this can be estimated assuming a Morse potential for the individual C—C stretchings,... 

Units mdyn/A for stretch and stretch, stretch constants mdyn for stretch, bend constants and mdyn A for all others. 

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,... 

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