Theoretical study of the influence of resonance relaxation on infrared band shapes

The resonance coupling between an active and an inactive ir transition and the influence of this mechanism on relaxation of the vibrational energy is discussed. An explicit expression is derived for the band shape in terms of a one-dimensional integral which is valid for arbitrary profiles of the uncoupled bands. Assuming Lorentzian profiles of these bands, a simple analytical formula is obtained, comprising the phenomenon of transmission windows as a special case. The band shape is discussed in terms of its Fourier transform, the autocorrelation function of the electric dipole moment. Two relaxation times are obtained which may be interpreted by resonance exchange of excitation energy between the coupled oscillators. A sharp separation of weak and strong coupling exists at exact resonance. The correlation function which oscillates with the frequency of the allowed transition is exponentially damped in the weak coupling case, whereas a multiple energy exchange occurs with strong coupling, resulting in a modulation of the correlation function with the exchange frequency. The theory is applied to the asymmetric OCO stretching band of acetate ions in methanol.