Size-Dependent π_g + π_u Combination Band Intensities of Polyynes C_2nH₂ (n = 1–9) Analyzed by the Local CCH Bending and the Linear Response Functions

Abstract

Polyynes (C 2n H 2 ) show the unusually strong π g + π u 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 largeamplitude 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 n = 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 n dependence. The easily polarizable π electron density caused two kinds of deformationdominant but dark δ xx−yy 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 n. The difference between the curvilinear and rectilinear bending coordinates is interpreted within the present theoretical scheme.