Reduced masses, force constants and vibrational amplitudes

Reduced masses, force constants and vibrational amplitudes 

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 

Infrared Spectroscopy of H-Bonded Systems Theoretical Descriptions 

We compare the force constants of these two types of modes, taking as an example X-H being HCl, with = 2i6m (m is the mass of an H-atom) and Y being CH3-O-CH3, with MCH3-0-CH3 = 46oth. Eq. (5.A24) shows that the reduced mass of the 

The force constant due to an H-bond is thus weaker than that due to a covalent bond by more than one order of magnitude. 

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