Spectral density of H-bonds. II. Intrinsic anharmonicity of the fast mode within the strong anharmonic coupling theory Original Research Article

A quantum theoretical 2-D approach of the IR νX–H spectral density (SD) for symmetric or asymmetric intermediate or strong H-bonds is proposed. The presented model is based on the linear response theory; the strong anharmonic coupling theory (SACT) beyond the adiabatic approximation is used. The fast mode potential is described by an asymmetric double-well potential, whereas the slow mode is assumed to be harmonic. The slow and fast modes are assumed to be anharmonically coupled as in the SACT. The intrinsic anharmonicity of the fast mode and the anharmonicity related to the coupling between the slow and the fast modes are taken in an equal foot within quantum mechanics, without any semiclassical assumption. The relaxation is supposed given by a direct damping mechanism. When the barrier of the double-well asymmetric fast mode potential is very high, i.e. when the H-bond becomes weak, the computed theoretical SD reduces, as required, to that obtained in one of our precedent more simple approaches, dealing with weak H-bonds and working beyond the adiabatic approximation [Chem. Phys. 243 (1999) 229]. It reduces, within the adiabatic approximation, to the Franck–Condon progression of Rösch–Ratner (RR) [J. Chem. Phys. 61 (1974) 3444], and, in turn, to that of Maréchal–Witkowski (MW) [J. Chem. Phys. 48 (1968) 2697] when in this adiabatic approximation the damping is missing. When the anharmonic coupling between the slow and fast mode is missing, the behavior of the SDs is in good agreement with that which may be waited for a situation involving a 1-D asymmetric double well and thus the possibility of tunnelling. When the barrier is low, and the asymmetry is missing or weak, the changes induced by the asymmetric potential in the features of the Franck–Condon progression of the RR and MW model are more important than those in which the Fermi resonances or the Davydov coupling are acting. The model reproduces satisfactorily the increase in low frequency shift when passing from weak to strong H-bonds. The isotope effect due to the D-substitution of the H-bond bridge leads, in agreement with experiment, to a low frequency shift and a narrowing of the line shapes and simultaneously to deep changes in the features.