Raman intensities of C=C stretching vibrational frequencies of polyenes: Nodal mode analysis

Abstract

It is not clearly understood how and why the Raman intensity increases drastically with an increasing chain length of polyenes. We therefore investigated the vibrational intensities of the C=C stretching vibrational modes of four polyene systems of X–(HC=CH)n–Y, where X/Y=H/H, H/NH2, H/NO2, and NH2/NO2. The investigation was done using nodal mode analysis (based on the number of nodes formed by the alternations of stretches and contractions) combined with ab initio frequency calculations. The C=C stretching/contracting mode without node is found to have the strongest Raman intensities regardless of polyene systems because of the long-range cooperation effect by the concurrent stretch/contraction motion of all C=C bonds. The corresponding IR spectra have also the strongest intensities for the nonsymmetric polyene systems, whereas are inactive for the symmetric polyenes (by the exclusion rule). The intensities of the nonconcurrent C=C stretching/contracting modes (particularly for the Raman spectra) tend to decrease drastically (in proportion to [n/(m+1)]4) with increasing node number m, though weak (or zero) intensities appear somewhat alternately because the molecules have approximate (or exact) centrosymmetry.