Previous Attempts of Defining Internal Vibrational Modes

PREVIOUS ATTEMPTS OF DEFINING INTERNAL VIBRATIONAL MODES 

The column vectors of C, c , can be chosen to represent the internal displacement vectors Vr,  

The c-vectors are implicitly used when expressing normal vibrational modes in terms of internal coordinates or when applying the potential energy distribution (PED) analysis to describe vibrational modes [25-27]. However, they have never been used explicitly to define internal modes of a molecule in the sense of Eq. (22). Since c-vectors are associated with internal coordinates qn, and each of the latter describes a molecular fragment tin, they seem to be the natural choice for internal modes. However, it has been shown that v = Cn is not a satisfactory choice of an internal vibration [19]. 

However, using Eq. (21) it is easy to show that such an assumption is strictly valid only for the case where 

both the choice of c-vectors as internal mode vectors v and the typical assumption 1 = Cn are not suited to provide an analysis of vibrational spectra in terms of internal modes [18,19]. Therefore, in the next section we will discuss a different approach that is based on a physically reasonable definition of internal modes. 

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