N. Rekik et al., Spectral density of H-bonds. II. Intrinsic anharmonicity of the fast mode within the strong anharmonic coupling theory, CHEM PHYS, 273(1), 2001, pp. 11-37
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
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