Towards accurate infrared spectral density of weak H-bonds in absence of relaxation mechanisms.

Following the previous theoretical developments to completely reproduce the IR spectra of weak hydrogen bond complexes within the framework of the linear response theory (LRT), the quantum theory of the high stretching mode spectral density (SD) of weak H-bonds is reconsidered. Within the LRT theory, the SD is the one sided Fourier transform of the autocorrelation function (ACF) of the high stretching mode dipole moment operator. In order to provide more accurate theoretical bandshapes, we have explored the equivalence between the SDs given in previous studies with respect to a new quantum one, and revealed that in place of the basic equations used in the precedent works for which the SD IOld(ω)=2Re∫0∞GOld(t)e-iωtdt where the ACF GOld(t) = ⟨µ(0)µ(t)+⟩ = tr {ρ {µ(0)} {µ(t)}+}, one can use a new expression for the SD, given by INew(ω)=2ωRe∫0∞GNew(t)e-iωtdt where GNew(t)=µ(0)µ(t)+=1ßtrρB∫0ßµ(0)µ(t+iλℏ)+dλ. Here ρB is the Boltzmann density operator, µ(0) the dipole moment operator at initial time and µ(t) the dipole moment operator at time t in the Heisenberg picture, ℏ is the Planck constant, ß is the inverse of the Boltzmann factor kBT where T is the absolute temperature and kB the Boltzmann constant. Using this formalism, we demonstrated that the new quantum approach gives the same final SD as used by previous models, and reduces to the Franck-Condon progression appearing in the Maréchal and Witkowski's pioneering approach when the relaxation mechanisms are ignored. Results of this approach shed light on the equivalence between the quantum and classical IR SD approaches for weak H-bonds in absence of medium surroundings effect, which has been a subject of debate for decades.

Equivalence between the Classical and Quantum IR Spectral Density Approaches of Weak H-Bonds in the Absence of Damping.

The aim of this paper is to overhaul the quantum elucidation of the spectral density (SD) of weak H-bonds treated without taking into account any of the damping mechanisms. The reconsideration of the SD is performed within the framework the linear response theory. Working in the setting of the strong anharmonic coupling theory and the adiabatic approximation, the simplified expression of the classical SD, in the absence of dampings, is equated to be ICl(ω) = Re[∫0∞GCl(t)e-iΩt dt] in which the classical-like autocorrelation function (ACF), GCl(t), is given by GCl(t) = tr{ρ(ß){µ(0)}{µ(t)}†}. With this consideration, we have shown that the classical SD is equivalent to the line shape obtained by F(ω) = ΩICl(ω), which in turn is equivalent to the quantum SD given by IQu(ω) = Re[∫0∞GQu(t)e-iΩt dt], where GQu(t) is the corresponding quantum ACF having for expression GQu(t) = (1/ß) tr{ρ∫0ß[µ(0)}{µ(t + iλℏ)}†â€¯dλ}. Thus, we have shown that for weak H-bonds dealt without dampings, the SDs obtained by the quantum approaches are equivalent to the SDs geted by the classical approach in which the incepation ACF is, however, of quantum nature and where the line shape is the Fourier transform of the ACF times the angular frequency. It is further shown that the classical approach dealing with the SD of weak H-bonds leads identically to the result found by Maréchal and Witkowski in their pioneering quantum treatment where they ignored the linear response theory and dampings.

Electrical anharmonicity in hydrogen bonded systems: complete interpretation of the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH3)2OHCl complex.

Following the previous developments to simulate the fully infrared spectra of weak hydrogen bond systems within the linear response theory, an extension of the adiabatic model is presented here. A general formulation including the electrical anharmonicities in the calculation of the damped autocorrelation function of weak H-bonds is adopted to facilitate the support of the additional properties, and thus the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH3)2OHCl complex. We have explored the origins of the broadening of the Cl-H[combining right harpoon above] stretching band. We found that the main features of the lineshape are attributed to electrical anharmonicity as a consequence of the large mixed second derivatives of the dipole moment with respect to the Cl-H[combining right harpoon above] bond and of the intermonomer elongations . In addition to providing more accurate theoretical band shapes, inclusion of the electrical anharmonicity in the present model paves the way for a more complete interpretation by generating three new Franck-Condon superposed distributions.

Extended diffusion in a double well potential: transition from classical to quantum regime.

The transition between the classical and quantum regimes in the diffusion of a particle in a 2-4 double-well potential is treated via the strong collision model in the high-temperature limit. Both the classical and semiclassical position correlation functions, their spectra, and correlation times are evaluated using the memory function formalism. It is shown that even in the high temperature limit, marked classical-quantum transition effects appear in the observables when collisions are rare.

Polarized infrared spectra of the H(D) bond in 2-thiophenic acid crystals: a spectroscopic and computational study.

Polarized IR spectra of the hydrogen bond in 2-thiophenic acid crystals, isotopically neat and of mixed H/D isotopic content, are measured at 298 and 77 K in the "residual" nuO-H and nuO-D band frequency ranges. This crystalline system provides spectra in these band frequency ranges that differ considerably in intensity distribution from the spectra of other H-bonded centrosymmetric dimeric species. This change in the spectral properties of the crystals is probably due to the influence of the sulfur atoms from the thiophene aromatic rings, which are directly linked to the (COOH)2 or (COOD)2 cycles. The magnitude of this effect correlates with the net electronic charge distribution at the 2- and 3-positions of substituted thiophene rings, which in a different way influences the electron charge density in the hydrogen bonds of the two thiophenic acid isomers. The experimental results for spectral structures are compared to predictions obtained with theoretical calculations involving the combined effects of anharmonicities, Davydov coupling, Fermi resonances, and direct and indirect relaxations within the framework of the linear response theory. Numerical results show that mixing of all these effects allows satisfactory reproduction of the main features of the experimental IR line shapes of crystalline H- and D-bonded 2-thiophenic acid at room and liquid-nitrogen temperatures.

Theoretical interpretation of the line shape of crystalline adipic acid.

A general quantum theoretical approach of the upsilon(X-H) IR line shape of cyclic dimers of weakly H-bonded species in the crystal state 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. Quantum indirect damping and Fermi resonances are taken into account. The present model reduces satisfactorily to many models in the literature dealing with more special situations. It has been applied to the cyclic dimers of adipic acid in the crystal phase. It correctly fits the experimental line shape of the hydrogenated compound and predicts satisfactorily the evolution in the line shapes with temperature and the change in the line shape with isotopic substitution.

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

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.