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

A quantum theoretical 2-D approach of the IR v(X-H) spectral density (SD) f or symmetric or asymmetric intermediate or strong H-bonds is proposed. The presented model is based on the linear response theory; the strong anharmon ic coupling theory (SACT) beyond the adiabatic approximation is used. The f ast mode potential is described by an asymmetric double-well potential, whe reas the slow mode is assumed to be harmonic. The slow and fast modes are a ssumed to be anharmonically coupled as in the SACT. The intrinsic anharmoni city 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 mech anics, without any semiclassical assumption. The relaxation is supposed giv en by a direct damping mechanism. When the barrier of the double-well asymm etric 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 o f our precedent more simple approaches, dealing with weak H-bonds and worki ng beyond the adiabatic approximation [Chem. Phys. 243 (1999) 229]. It redu ces, within the adiabatic approximation, to the Franck-Condon progression o f Rosch-Ratner (RR) [J. Chem. Phys. 61 (1974) 3444], and, in turn, to that of Marechal-Witkowski (MW) [J. Chem. Phys. 48 (1968) 2697] when in this adi abatic approximation the damping is missing. When the anharmonic coupling b etween the slow and fast mode is missing, the behavior of the SDs is in goo d agreement with that which may be waited for a situation involving a 1-D a symmetric double well and thus the possibility of tunnelling. When the barr ier is low, and the asymmetry is missing or weak, the changes induced by th e 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 resona nces or the Davydov coupling are acting. The model reproduces satisfactoril y the increase in low frequency shift when passing from weak to strong H-bo nds. The isotope effect due to the D-substitution of the H-bond bridge lead s, in agreement with experiment, to a low frequency shift and a narrowing o f the line shapes and simultaneously to deep changes in the features. (C) 2 001 Elsevier Science B.V. All rights reserved.