Bond-bending frequencies

Also the product ratio observed for donor molecules with other leaving groups than protons can be understood under the above mentioned aspects. So for the compounds of trimethylbenzylsi-lane and of sulphide type, the product distribution of FET depends on the mobility of the critical bond (bending frequency and activation barrier of this motion). Details of these observations should be taken from the publications cited in the last column of Table 1. 

Different motions of a molecule will have different frequencies. As a general rule of thumb, bond stretches are the highest energy vibrations. Bond bends are somewhat lower energy vibrations and torsional motions are even lower. The lowest frequencies are usually torsions between substantial pieces of large molecules and breathing modes in very large molecules. 

In Eq. (6.1) 1 is the unit operator, there is one state /> associated with each lattice site, and l and l A A = 1, 2, 3, 4) label a molecule and its nearest neighbors in the tetrahedral lattice. Weare and Alben show also that the theorem remains valid when small distortions away from tetrahedrality exist, hence it can be used to describe a random amorphous solid derived from a tetrahedral parent lattice. Basically, the density of states of the amorphous solid is a somewhat washed out version of that of the parent lattice. The general shape of the frequency spectrum is not much altered by the inclusion of a non zero bond-bending force constant provided the ratio of it to the bond stretching force constant is small relative to unity. 

These estimations engage the assumption that any additional effects due to bending vibrations will tend to contribute relatively weakly to the isotope effect. In fact, however, the above estimates are probably only ball park estimates, in that coupling of molecular vibrations of multiatomic molecules is ignored Another key point is that a covalent bond need not be completely broken in the transition state, and two isotopic isomers may behave slightly differently in the transition state. Jencks discusses this matter as well as the problem of nonlinear transition states, a condition that takes into account the fact that bending frequencies often lessen the developed magnitude of isotope effects. 

The application of Stepanov s theory to intramolecular F bonded systems has been criticized [42], In this case the low frequency vibration described above as vXH Y is also partly constrained by a more nearly harmonic vibration involving skeletal bending motions of the rest of the molecule, and the X, H, and Y atoms are not collinear. These factors would seem to suggest that (I) the vXll Y type of vibration will be of higher frequency than in the usual case (perhaps 200-300 cm"1 rather than 100-200 cm"1) so that the sub-bands will be more widely spaced and may not be recognised as part of the rXH band (2) the motion of the H atom will have less effect on rXY and (3) H-bond bending vibrations may also couple considerably with vXH. The observation of rather smaller frequency shifts for vXR and narrower absorption bands w such cases are in reasonable agreement with this picture,... 

If, in addition, the bending frequencies of the reacting bond also vanish in the transition state, we obtain the relation ... 

SB = Values calculated taking into account the difference in the stretching and bending frequencies between the C-H and C-D bonds. 

---