Theoretical interpretation of the line shape of the gaseous acetic acid cyclic dimer

Abstract

A general quantum theoretical approach of the nu(X-H) IR line shape of cyclic dimers of weakly H-bonded species in the gas phase is proposed. In this model, the adiabatic approximation (allowing to separate the high frequency motion from the slow one of the H-bond bridge), is performed for each separate H-bond bridge of the dimer and a strong nonadiabatic correction is introduced into the model via the resonant exchange between the fast mode excited states of the two moieties. The present model reduces satisfactorily to many models in the literature dealing with more special situations. It has been applied to the cyclic dimers (CD(3)CO(2)H)(2) and (CD(3)CO(2)D)(2) in the gas phase. It correctly fits the experimental line shape of the hydrogenated compound and predict satisfactorily the evolution in the line shapes, to the deuterated one by reducing simply the angular frequency of the H-bond bridge and the anharmonic coupling parameter by the factor 1/ square root of 2.

Theoretical Simulation of the Infrared Absorption Spectrum of the Strong Hydrogen and Deuterium Bond in 2-Pyridone Dimer

“…The values obtained here are also in satisfactory agreement with the experimental data reported by Odinokov, et al [36] for complexes of carboxylic acids with various bases and are comparable to those found in our recent work dealing with the H/D isotopic effects in H-bond spectra [33]. However, these ratios are different from those used by Blaise, et al [37] since in their approaches dealing with theoretical interpretation of the IR line shapes of liquid and gaseous acetic acid [38] and gaseous propynoic and acrylic acid dimers [29], low and high-frequency hydrogen stretching vibrations in individual hydrogen bonds are assumed to be harmonic whereas in the present work we use a Morse potential in order to describe the anharmonicity of the H-bond Bridge. Recall that the removal of the harmonic approximation for the slow modes by introducing Morse potential in place of harmonic one has been done by Leviel and Maréchal [39] in a model similar to the present one, involving cyclic dimer, however without damping.…”

“…The direct relaxation is included following quantum treatment of Rösch and Ratner [22] whereas the indirect one was taken into account via the approach of Louisell and Walker [42] dealing with the relaxation of driven damped quantum oscillators studied initially by Feynman and Vernon [43] and later by Louisell [44]. The values of the direct and indirect relaxation parameters reflecting the effect of the medium used presently for alpha-phase 2-pyridone are of the same magnitude as those used by Blaise, et al [29,37,38] in their study dealing with acetic acid in the gas phase, whereas the indirect damping at 298 K for acetic acid in crystalline state is γ = 1 cm -1 . One may ask whether the indirect damping used for crystalline state is weaker than that used for the gaseous phase since the indirect relaxation is ought to be larger in the solid state.…”

“…The present theory was developed in the framework of the adiabatic approximation [25]. The adiabatic approximation of the N-H stretching vibrations leads to the description of each moiety by effective Hamiltonians of the H-bond Bridge: for a single H-bond bridge, this effective Hamiltonian is either that of a harmonic oscillator, if the fast mode is in its ground state, or that of a driven harmonic oscillator if the fast mode is excited.…”

“…It is important to note that in the majority of recent works, the slow-frequency mode was assumed as harmonic [25].…”

“…In the presence of Davydov coupling, the autocorrelation function (ACF) of the dipole moment operator of the fast mode may be written [25]:…”