Intramonomer vibrations

Dynamic quantities such as spectroscopic constants (frequencies or wavenumbers of various vibrations) are obtained from IR or Raman spectra. IR spectra are by far the most precise method to measme such quantities related to intramonomer vibrations (vibrations of X-H component, which are for some of them described in Chs. 4 and 5, are highly sensitive to the establishment of a H-bond X-H Y), which contain a lot of information on H-bonds themselves. Raman spectra are more useful for intermonomer vibrations that are found in a region of smaller wavenumbers, where the quality of IR spectra becomes poorer. They also have been useful in the case of liquid water and aqueous media which give such intense signals in IR spectra that... 

Intramonomer vibrations are found inside the X H or Y molecules. They consequently exist even in the absence of an H-bond between these two molecules, in opposition to intermonomer bands we have seen above, which exist due to the formation of the H-bond. An H-bond has, however, marked effects on some intramonomer vibrations. It has a spectacular effect on the stretching vibration of the H-atom of X H that establishes the H-bond. 

The other vibrational coordinates of X-H - Y are those related to the other two intermonomer vibrations, those related to internal vibrations in X-H and Y, and those of the centre of gravity of the whole system, which separates from all other coordinates. When this complex is isolated, these coordinates of the centre of gravity do not appear in the potential energy. They can consequently be discarded as they are independent of the other ones. The coordinates of internal vibrations are driven by force constants due to covalent bonds within molecules X-H and Y. They are, as seen in the following, much greater than the force constants due to H-bonds that drive the intermonomer vibrations. These much faster intramonomer vibrations consequently hardly mix with intermonomer vibrations, even if cross terms between these two kinds of coordinate appear in the potential energy they are well out of resonance, that is each of them displays vibration frequencies that are different, and the effect of these possible cross terms remains small in aU cases. We are then left with two kinds of normal modes of the complex those that are mainly composed... 

TABLE III Intramonomer Vibrational Frequencies of Hydrogen Halides (In cm ). 

We find, in the case of the above-considered complex Cl-H- 0(0113)2 at 300K, the ratio of vibrational amplitudes for the intramonomer Cl-H - stretching mode and the intermonomer C1-H- - -0(CH3)2 stretching mode... 

It means that the vibrational amplitudes are comparable for intramonomer and intermonomer modes. At very low temperatures it falls in the vicinity of 1 and decreases when temperature is raised because intermonomer modes see their amplitude increased when becomes comparable to hD,, whereas faster intramonomer modes are temperature independent. Let us calculate the absolute value of this amplitude. Following eq. (5.A28), the mean square vibrational amplitude of the stretching mode of the H-atom in this complex is, with... 

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