Molecular Vibrations and the Reaction Coordinate

When choosing between possible deformation types of the molecular framework in the course of a reaction, one may compare the corresponding force constants or vibration frequencies. The most likely type of deformation will correspond to a minimal vibration frequency. 

for example, known that the dehydrohalogenation of vinyl halogenides XXVIII proceeds preferably by the mechanism of trans-elimination. The stereoselectivity can be explained as follows [84]. The structure of bent acetylene emerging upon trans-elimination of the hydrohalogen elements transforms much more readily into an equilibrium linear form than the structure forming in the case of a cis-elimination. The frequency of the symmetrical normal vibration Ttg, which corresponds to the deformations of XXIX, equals 612cm which is much less than the value of 729 cm for the antisymmetrical vibration 7c of the structure XXX  

However, only in the initial reaction phase the form of normal vibration can approximate the reaction coordinate whose typical feature is its correspondence with the imaginary vibration frequency (Sect. 1.3.3). A more rigorous approach based on the data on the force constants of a reacting molecule describes the reaction coordinate in terms of the so-called interaction displacement coordi-nates 0) [85], 

These coordinates represent changes of (n — 1) internal coordinates Rp the changes which minimize the potential energy of the system for a given displacement of Ri (compare with the method of reaction coordinate). The method uses the force constants of molecular vibrations (interaction compliance) calculated somewhat differently than in Eq. (1.4), namely as the forces that need to be applied to achieve measurable distortions in with the potential energy minimized with respect to other coordinates  

The reaction coordinate Ri corresponding to the MERP is calculated for some fixed displacements of each of n internal coordinates R as  

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