Force constant for bending

In these equations, m is the mass of an element (a CHa group), kc is the force constant for stretching of a C—C bond, ka is the force constant for bending of the CCC angle, and

phase difference between the motions of adjacent elements of the chain. Since we are interested only in the factor group modes, i.e those in which the vibrations of corresponding elements in neighboring unit cells are in phase, we require that... 

In our original calculations (,9) we found the AlOH bond of HAIOH to be linear but with a relatively small force constant for bending. In the calculations on the other hydroxyhydrldes the MOH group was restricted to be linear. In very recent work,... 

Models for the low-frequency motions of a semiflexible linear molecule usually treat the system as an elastic wire with force constants for bending and stretching. The model of Harris and Hearst (1966) has been extensively applied to the light-scattering problem by Fujime (1972). In this model the chain is represented by a space vector r which is a... 

From Eq. (4.7), we can deduce that a C—C bond vibrates at a lower wavenumber than a C=C bond, because the force constant for the C—C bond is smaller than that for C=C. For example, C—C vibrates at 1200 cm and C=C vibrates at 1650 cm . In general, force constants for bending vibrations are lower than stretching vibrations. Resonance and hybridization in molecules also affect the force constant for a given bond. 

When the same energy terms are used in two force helds, it may be acceptable to transfer bond-stretching and angle-bending terms. These are fairly stiff motions that do not change excessively. The force constants for these terms vary between force helds, much more than the unstrained lengths and angles. 

Changes in observed CH (CD) stretching frequencies on going from reactant to product are found to be too small and in the wrong direction to account for the observed kinetic isotope effect, and the effect is suggested to be due to increased force constants for lower frequency vibrations, such as for bending (Kaplan and Thornton, 1967). This is consistent with a steric explanation. 

Table 1. Block diagonalized G and F matrices for tetrahedral XY4 and octahedral XYn molecules, using the modified Urey-Bradley force field. Adapted from Nakmoto (1997). nix and nij are the masses of atoms ofX and Y, and r is the length of the X-Y bond. K, H, and are force constants for bond stretching, bond-angle bending, and non-bonded repulsion, respectively.

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