The Concept of Localized Internal Vibrational Modes

Chemists have learned to understand geometry and conformation of a molecule in terms of (localized) internal coordinates such as bond lengths, bond angles, and torsional angles. Therefore, it would be chemically useful to discuss 

The information on the various bonds in a molecule should be hidden somewhere in infrared and Raman spectra and it is only a question how to unravel it from experimentally obtained or calculated vibrational spectra. To obtain this information, one has to specify exactly what kind of internal vibrational mode is needed [18-23]  

An internal mode should be fully characterized by only one internal coordinate qn. The internal coordinate qn should be the parameter that leads the internal mode and, therefore, it can be called the leading parameter of the internal mode [18]. The internal mode should be localized in the fragment () nOf 

An analogy to molecular orbital (MO) theory may help to clarify further what is needed. Chemists prefer to discuss chemical problems in terms of localized MOs rather than in terms of (canonical) delocalized MOs resulting from Hartree-Fock (HF) based quantum chemical calculations. The localized MOs are obtained from the delocalized ones by a transformation ( localization ), which in most cases yields MOs directly related to the bonds of a molecule. The same should be true with regard to localized modes associated with a particular internal coordinate q. The question is only How can we transform from delocalized normal modes to localized internal modes To answer this question we will first summarize the basic theory of vibrational spectroscopy. 

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