Size-Dependent π + π Combination Band Intensities of Polyynes CH ( = 1-9) Analyzed by the Local CCH Bending and the Linear Response Functions.

Polyynes (CH) show the unusually strong π + π combination bands in the infrared absorption spectra. We calculated them as the first overtone of the local CCH bending; the strong intensities are interpreted as a consequence of the large-amplitude bending vibration of the acidic acetylenic hydrogen combined with the size-dependent π electron conjugation. Our theoretical calculations show that the absorption intensity increases steadily and their increase rate is gradually slowed down by increasing the number of acetylene units up to = 9. However, the calculated vibrational wavenumber converges quickly in agreement with the experimental observation. The second-order electron density deformation caused by the local CCH bending was analyzed using the linear response functions, including the linear and nonlinear contributions, to explain the dependence. The easily polarizable π electron density caused two kinds of deformation-dominant but dark δ type and minor but bright σ type. Both of them exhibit interesting zigzag sign alternations, consistent with the law of alternating polarity of Coulson and Longuet-Higgins. The electron density polarization in these intra- and interacetylene units induces a large axial component molecular dipole moment, contributing to the intensity that increases with . The difference between the curvilinear and rectilinear bending coordinates is interpreted within the present theoretical scheme.