Vibrational Spectra of Different Molecules

As indicated for 1 and 2, the CNM analysis in terms of adiabatic internal modes makes it rather simple to correlate the vibrational spectra of related molecules and to discuss the influence of substituents, heteroatoms, and structural changes in terms of the internal mode frequencies. In the following section, we will provide further examples how vibrational spectra of different molecules can be correlated with the help of the CNM analysis. 

The CNM analysis in terms of adiabatic internal modes has been carried out to correlate the calculated vibrational spectra of the three dehydrobenzenes, namely ortho- (3), meta- (4) and para-henzyne (5), with the vibrational spectrum of benzene (6). Investigation of dehydrobenzenes with the help of infrared spectroscopy is of considerable interest at the moment since these molecules have been found to represent important intermediates in the reaction of enediyne anticancer drugs with DNA molecules [34-37]. Both 4 and 5 are singlet biradicals and, therefore, they are so labile that they can only be trapped at low temperatures in an argon matrix upon photolytic decomposition of a suitable precursor [38-40]. 

A positive identification of the dehydrobenzenes in the matrix requires, besides an expert set up of the experiment, high level ab initio calculations of the infrared spectra of the compounds trapped so that comparison between measured and calculated spectra becomes meaningful. In this way, both 4 and 5 have been identified and investigated in the matrix [38,39]. To further understand the electronic nature and the relationship of the three dehydrobenzenes, a correlation of their calculated vibrational spectra is desirable. 

Kraka and co-workers [41] have calculated the vibrational spectra of 3, 4, and 5 at the GVB(l)/6-31G(d,p) level of theory where in each case the biradical nature of the dehydrobenzenes was described by the two-configuration approach of GVB. In Tables 4, 5, and 6, a CNM analysis of the calculated spectra based on calculated adiabatic internal modes is presented. 

With the CNM analyses presented in Tables 4, 5, and 6 and a similar analysis for benzene, it is straightforward to correlate the vibrational spectra of the three benzynes with each other and with that of benzene. This is done in Tables 7, 8, and 9, which should be read considering that benzene has 30 normal modes while the benzynes have only 24. Hence, not all normal modes of benzene can be correlated with normal modes of the benzynes. 

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There are immediately a number of applications of adiabatic internal modes that lead to a new dimension in the analysis of vibrational spectra. For example, the adiabatic vectors ap are perfectly suited to present a set of localized internal modes that can be used to analyze delocalized normal modes. This has led to the CNM analysis (Sections 7 and 8) of calculated vibrational spectra of molecules as was discussed in Section 9. With the CNM analysis it is rather easy to correlate the vibrational spectra of different molecules (Section 10). With the help of perturbation theory and calculated normal modes, the determination of adiabatic modes and the CNM analysis can be extended to experimental spectra (Section 12). 

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