On the mechanism of the broadening of the proton vibrational IR band in weak hydrogen bonds. Double adiabatic approximation

It is proposed that broadening of the ν_s (AH) IR band is due to the ν_s (AH) and ν_σ (AH…B) mode coupling and to the stochastic variation of the equilibrium distance R_e (A…B) modulating the proton vibration. The R_e disordering variation is caused by a coupling of the ν_σ mode with the low frequency oscillators (ν_Q) of the medium and of the complex as such. Besides, the (ν_σ, ν_Q) and (ν_s, ν_σ) couplings cause a ν_s frequency shift. Both the band broadening and the frequency shift increase with higher force constants responsible for (ν_σ, ν_Q) mode coupling. Furthermore the Q_i low frequency stochastic vibrations directly modulate the ν_σ (AH…B) vibration and the free AH groups stretching vibration (ν^o_s) causing some broadening at their bands which is however several times smaller than the ν_s band broadening in the complex. Several examples are reported to confirm the proposed model.