Theoretical analysis of weak adjacent substituent effect on the overtone intensities of XH (X = C, O) stretching vibrations

It is known that the overtone intensities of some set of OH and CH stretching vibrations show only a weak dependence on the adjacent substituent, in sharp contrast to the much stronger dependence of their fundamental intensities. To understand this characteristic, we calculated the fundamental and overtone intensities of the Δv = 1-6 transitions for the OH stretching of alcohols and acids and the CH stretching of hydrocarbons with different types of hybridization. Based on the local-mode model, from the three components of the dipole moment function (DMF) of each molecule, a one-component effective DMF that recovered about 95% of the total intensity for the Δv = 1-6 transitions was constructed and expressed as a sixth-order polynomial of the bond displacement ΔR, with the leading expansion coefficients M ₁, M₂, and M₃ for the linear, quadratic, and cubic terms, respectively. When these coefficients for each molecule were represented as points in the coordinate system O-M₁M ₂M₃, the points for some set of molecules were found to lie on a straight line. Interestingly, the line had a direction cosine such that the resultant transition moments exhibited a small substituent dependence of the overtone intensities. Moreover, the slope of the line could be well approximated by the Morse exponential parameter and the bond distance. These characteristics of the DMFs can be rationalized by using the calculated transition moments and the wave function expansion method with the eigenfunction of the Morse potential. It was also verified by the quasiclassical method of Medvedev that these characteristics of the DMFs are the intrinsic reason for the weak substituent dependence of the overtone intensities. It is emphasized that the graphical representation of the DMF parameters provides a comprehensive tool for discussing various aspects of vibrational intensities.