Force constants, correlation with coupling

Table 3 presents the values of the force constants corresponding to the C skeleton vibrations of s-trans-1,3-butadiene obtained at several levels of calculation. The computed values are very sensitive to the inclusion of electron correlation. Stretching C=C and C—C force constants decrease when electron correlation is taken into account. This effect is generally larger for basis sets without polarization functions than for those with polarization functions23. On the contrary, the values of the C=C/C—C and C=C/C=C coupling constants do not vary much upon increasing the level of calculation of electron correlation. 

It may be possible to test this supposition by looking for a correlation between the magnitudes of the coupling constants and the radial components of the vibrational modes involved. This, of course, requires knowledge of the eigenfunctions associated with the normal modes. These may be obtained using the 13k model and so we leave this as an exercise for a later date when a clearer indication of the true force constants within the molecule has been found. 

FIGURE 35. Correlation between 1, /(-9Si—7yS() coupling constants and Si—Si valence force constants f(SiSi) (N/m) in oligosilanes. Reprinted from Reference 269. Copyright 1995, with permission from Elsevier Science... 

The fact that the second derivative, d U/db in Eq. [24], contains a slight contamination from nonbonded interactions and third-order terms is an example of how parameter correlation can arise because it is not a pure bond stretch. If this derivative were simply used as the bond-stretching force constant, as in spectroscopic force fields, it would not be transferable to other molecules where the coupling or nonbonded interaction may differ. This problem is a general one and can be quite serious. As already discussed in previous sections, one possible resolution of this problem lies in the use of many molecular environments to determine all contributing terms. If we simultaneously fit many different alkanes, i.e., ethane, propane, butane, etc., with the full force field and assume... 

According to the scheme above, the total driving force of the reaction will be given by the applied potential and also by the M(III)/M(II) formal potential of the catalyst, so the catalytic activity could be correlated with the formal potential of the catalyst. Many authors have discussed this issue and it is yet not clear what sort of correlation should be expected. Reduction should occur at the potential of reduction of the M(III)02 adduct and not at the potential of the M(III)/(II) couple. The latter should only be observed if the reaction were outer sphere. For the particular case of iron phthalocyanines and other iron macrocyclics, O2 reduction starts at potentials very close to the Fe(III)/(II) couple ". In contrast, for cobalt macrocyclics reduction of O2 begins at potentials much more negative than those corresponding to the Co(III)/(II) couple . Several authors have reported correlations between activity (measured as potential at constant current) and the M(III)/(II) formal potential and volcano-shaped curves have been obtained -see for... 

The band positions associated with the various vibrations are primarily dependent on mass- and force-constant effects. They are sensitive to small, but highly specific perturbations, induced by effect of stereo chemistry, mechanical coupling, intramolecular electrical effects, and intermolecular interaction. Thus, the physical state of the compound, liquid, amorphous solid, crystalline solid (including polymorphism) may alter the frequency of absorption. When using band-by-band correlation with a standard compound for identification of an unknown, these factors should be considered. More detailed information appears in the textbooks on infrared spectroscopy (48-53). 

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