Deformation potential approximation, hydrogen

Deformation density maps have been used to examine the effects of hydrogen bonding on the electron distribution in molecules. In this method, the deformation density (or electrostatic potential) measured experimentally for the hydrogen-bonded molecule in the crystal is compared with that calculated theoretically for the isolated molecule. Since both the experiment and theory are concerned with small differences between large quantities, very high precision is necessary in both. In the case of the experiment, this requires very accurate diffraction intensity measurements at low temperature with good thermal motion corrections. In the case of theory, it requires a high level of ab-initio molecular orbital approximation, as discussed in Chapter 4. 

It Is a familiar observation in vibrational spectroscopy that a hydrogen bending or deformation vibration has a fundamental frequency approximately half that of the hydrogen stretching modes. It may then happen that cubic enharmonic interaction terms in the potential couple the stretching mode to the overtone of the bending mode. The terms concerned will be of the type... 

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