Olivier Henri-Rousseau

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.

IR THEORY OF WEAK H-BONDS : DAVYDOV COUPLING, FERMI RESONANCES AND DIRECT RELAXATIONS. I. BASIS EQUATIONS WITHIN THE LINEAR RESPONSE THEORY

Abstract Infrared and Raman spectral densities of cyclic H-bonded dimers, such as encountered in carboxylic acids, are obtained in a full quantum mechanical way by introducing relaxation effects towards the surroundings in the model of Wojcik [Mol. Phys. 36 (1978) 1757] which accounts for the possibility of simultaneous Davydov coupling (between the two hydrogen bonds involved in a cyclic dimer) and Fermi coupling (between each hydrogen bond and one or several bending modes). The relaxations of the fast stretching modes of the H-bonds and of the bending modes are assumed to be of direct type, and are taken into account in the spirit of the Green formalism by insertion of imaginary damping parameters in the effective hamiltonians. Then, the spectral density is obtained within the framework of the linear response theory by Fourier transform of the time-dependent autocorrelation function either of the dipole moment operator, in the infrared case, or of the tensor of the polarizabilities in the Raman case. Extension to non-resonant fast stretching and bending modes, and to several Fermi resonances is also performed according to Henri-Rousseau and Chamma [Chem. Phys. 229 (1998) 37]. In the undamped case, the equivalence of the present work is established with the theory of Marechal and Witkowski [J. Chem. Phys. 48 (1968) 3697] by neglecting the Fermi resonances. Moreover, one-to-one correspondences are also shown with the work of Henri-Rousseau and Chamma [Chem. Phys. 229 (1998) 37] by ignoring Davydov coupling, and with that of Rosch and Ratner [J. Chem. Phys. 61 (1974) 3344] by neglecting both Davydov and Fermi couplings. Finally, the use of the symmetry properties which appear in cyclic dimers when neglecting the Fermi resonances, initially performed by Marechal and Witkowski [J. Chem. Phys. 48 (1968) 3697], is discussed, showing the equivalence with the results of the non-symmetrized treatment.

Infrared spectra of hydrogen bonded species in solution

Abstract The ν s (XH) hydrogen bond IR spectrum in liquid phase is studied by starting from the full quantum mechanical theory of Witkowski and Marechal, and handling the dephasing process of the ν s (XH) mode by taking into account the random modulation resulting from the anharmonic coupling of the ν s (XH) with the ν s (XH…Y) mode. It is subject to intermolecular resonance energy exchange with the molecules of the inert solvent. The approach allows to obtain the spectral density of the ν s (XH) mode in terms of the following parameters: (i) the frequency of the fast mode in the absence of hydrogen bond, (ii) the frequency of the slow ν s (XH…Y) mode, (iii) a dimensionless parameter characterizing the anharmonic coupling between the fast ν s (XH) and the slow ν s (XH…Y) mode, and (iv) a damping parameter related to the strength of the resonant energy exchange between the ν s (XH…Y) mode and the molecules of the solvent. The model leads to results which are in agreement with experiment. It allows to connect the Witkowski and Marechal approach in the gas phase with that of Bratos, and of Robertson and Yarwood in the liquid phase.

IR theory of weak H-bonds: Davydov coupling, Fermi resonances and direct relaxations. II. General trends, from numerical experiments

Abstract The theoretical model proposed in the precedent paper [Chem. Phys. 248 (1999) 53] which was dealing with the X- H → ⋯ Y stretching mode of a cyclic dimer susceptible of Davydov coupling, and involving weak H-bonds and Fermi resonances, is applied. The basis of this theory was an extension of the quantum model of Wojcik [Mol. Phys. 36 (1978) 1757] in which has been incorporated the direct damping of the fast mode and that of the bending mode involved in the Fermi resonance mechanism. The Fourier transform of the autocorrelation function of the dipolar moment operator is computed as a function of nine basic physical parameters. Fermi resonances ought to be an universal phenomenon for H-bonded dimers, since the lineshape is sensitive to the Fermi coupling over a frequency range that is one order of magnitude greater than the Fermi coupling parameter. The spectral lineshapes exhibit a rich polymorphism, mainly with respect to the coupling and damping parameters, which was some unpredictable and must lead to be extremely cautious in the interpretation of experimental spectra. In contrast, the details of the lineshapes appear to be very stable with respect to large temperature changes, even if the half width is smoothly increased by around 12% by raising the temperature from 10 to 300 K, that is in qualitative agreement with experiment.

IR SPECTRAL DENSITY OF WEAK H-BONDED COMPLEXES INVOLVING DAMPED FERMI RESONANCES. I. QUANTUM THEORY

Abstract The IR spectral density of the high frequency stretching mode of weak H-bonded complexes involving Fermi resonances is studied within the linear response theory from a full quantum mechanical point of view: the anharmonic coupling between the high frequency X–H and the low frequency X–H⋯Y modes is treated inside the strong anharmonic coupling theory. Following Witkowski and Wojcik [A. Witkowski, M. Wojcik, Chem. Phys. 1 (1973) 9.], the Fermi resonance between the first excited state of the fast mode and the first harmonic of single or several bending modes is introduced. Besides, the direct relaxation involved by the fast and bending modes are incorporated, in the spirit of the reduced Green formalism, by aid of imaginary damping terms. The spectral density is obtained by the Fourier transform of the autocorrelation function of the dipole moment operator of the fast mode, in which time dependent terms appear that are solution of a set of coupled linear differential equations. It reduces in the special situation where the Fermi coupling is ignored to that obtained by Rosch and Ratner [N. Rosch, M. Ratner, J. Chem. Phys. 61 (1974) 3344.]. Furthermore, when the anharmonic coupling between the slow and fast modes is neglected, it reduces to the spectral density that may be obtained in the framework of the Giry et al. [M. Giry, B. Boulil, O. Henri-Rousseau, C.R. Acad. Sci. Paris 316 s.II (1993) 455; B. Boulil, M. Giry, O. Henri-Rousseau, Phys. status solidi (b) 158 (1990) 629.] approach. At last, it reduces to the Witkowski and Wojcik [A. Witkowski, M. Wojcik, Chem. Phys. 1 (1973) 9.] approach, when the relaxation disappears. A generalization to several Fermi resonances is also proposed. Numerical tests of the theory and physical discussions are reported in the following paper [D. Chamma, O. Henri-Rousseau, Chem. Phys. 229 (1998) 51].

IR spectral density of weak H-bonded complexes involving damped Fermi resonances. II. Numerical experiments and physical discussion

Abstract The IR absorption band profile of the X–H stretching mode of weak H-bonded complexes involving Fermi resonances between the high frequency mode and some bending modes, all these modes being damped, have been computed within the linear response theory, by aid of the Fourier transform of the autocorrelation function of the dipole moment operator of the high frequency mode [O. Henri-Rousseau, D. Chamma, Chem. Phys. 229 (1998) 37]. As it appears the probability to observe realistic and noticeable modifications of the experimental lineshapes by Fermi resonances is strongly enhanced by the presence of an hydrogen bond, leading to the conclusion that Fermi resonances must play a very general role in the lineshapes of H-bonds.

Quantum theory of the spectral density of the hydrogen bond in solution Part 2. A study of dimeric hydrogen-bond systems by perturbative method

Abstract A methodological approach is proposed for the spectral density in solution of symmetric dimers involving hydrogen-bonded species for which Witkowski has shown that the full effective hamiltonian of the slow modes involves hamiltonians of driven oscillators perturbed by the parity operator. The driven damped quantum harmonic oscillator perturbed by the parity operator and embedded in a solvent is studied in the framework of the time-dependent perturbation theory involving the time evolution operator. Advantage is taken of the closed approach we have obtained (B. Boulil, J.-L. Dejardin, N. El Ghandour and O. Henri-Rousseau, J. Mol. Struct. (Theochem), 314 (1994) 83) for the autocorrelation function of a simple hydrogen bond. This allows us to extract a zeroth-order time evolution operator, which is then used in the interaction picture to obtain by perturbative expansion the autocorrelation function of the dimer.

THEORY OF WEAK DAMPED H-BONDS : RELATIVE INFLUENCE OF RELAXATION MECHANISMS ON IR SPECTRA

Abstract We revisit numerically the roles played by relaxation mechanisms on the line shapes of the IR spectral density of weak H-bonds. This is performed by means of three theories already published. The tools common to these theories are the strong anharmonic coupling theory (between the high- and low-frequency stretching modes of the H-bond), and the linear response theory (according to which the spectral density is the Fourier transform of the autocorrelation function). The theories are those of: (1) G. Robertson and J. Yarwood [Chem. Phys. 32 (1978) 267], taking into account (semiclassically) indirect damping; (2) N. Rosch and M. Ratner [J. Chem. Phys. 61 (1974) 3444] dealing (quantum mechanically) with direct damping; and (3) B. Boulil, J.-L. Dejardin, N. El-Ghandour, O. Henri-Rousseau [J. Mol. Struct. (Theochem) 314 (1994) 83] involving (quantum mechanically) slow-mode damping. The quantum direct damping induces a broadening, and the quantum slow-mode damping (in contrast with the semiclassical indirect relaxation) a weak narrowing, when they are both occurring. The direct damped quantum spectral density leads to Lorentzian (fast modulation limit) or Gaussian (slow modulation limit) shapes as does the spectral density of the semiclassical model of indirect relaxation. The dephasing of the fast mode should be predominant for line shapes with broadened sub-bands (obeying the Franck–Condon progression law), or without sub-bands (but with nearly symmetric profiles intermediate between Gaussian and Lorentzian). Both the dephasing of the fast mode and the damping of the slow mode should occur by similar amounts if the line shapes are without sub-bands but with asymmetry, or with sub-bands but with intensity anomalies in the Franck–Condon progression.

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

Abstract A quantum theoretical 2-D approach of the IR ν X–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 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 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.

Quantum theory of the spectral density of the hydrogen bond in solution Part 1. A closed autocorrelation function

Abstract A novel formulation of the quantum theory of the spectral density of the hydrogen bond in solution is proposed. It leads to a compact form for the autocorrelation function to be Fourier transformed in order to get the spectral density. An approximation concerning the modelization of the damping that was performed in our initial approach is avoided, leading to an autocorrelation function that is more physical. The compact form of the autocorrelation function provides an understanding of how our model reduces to that of Witkowski and Marechal in the absence of relaxation and what the differences are between our model and the classical model of Robertson which involves damping. It is also shown that it is not possible to find an equivalent formulation of the spectral density in terms of the density operator formalism, which eliminates the possibility of treating more complex hydrogen bonds with the aid of the perturbation theory using the density operator formalism. Finally, we underline the importance of the recent work of Witkowski on the coupling between slow and fast movements which gives a physical basis for understanding the unexplained coupling between the slow and fast modes of hydrogen bonds, which is at the basis of all the explanations of the features of hydrogen bonds.