Didier Chamma

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.

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.

Infrared spectra of medium strength H-bonds: beyond an adiabatic description of Fermi resonances

Abstract We extend a quantum non-adiabatic treatment of damped weak H-bonds involving Fermi resonances (D. Chamma, O. Henri-Rousseau, Chem. Phys. 248 (1999) 91–104) in order to account for stronger H-bonds. For this purpose, we introduce in the model the quadratic dependence of both the angular frequency and the equilibrium position of the X – H → ⋯ Y stretching mode on the intermonomer X ← – H ⋯ Y → motions. We obtain the spectral density corresponding to this Hamiltonian by Fourier transform of the autocorrelation function of the dipole moment of the fast stretching mode. This paper goes beyond a step toward a more comprehensive theory of infrared bandshapes of H-bonded systems. Further development should lead to the release of a modeling software in this field.

Infrared spectra of weak H-bonds: Fermi resonances and intrinsic anharmonicity of the H-bond bridge

Abstract The present quantum theory is a new step in our attempt to obtain a flexible tool susceptible to be used by experimentalists working in the realm of the infrared spectra of the ν S ( X – H → ⋯Y) mode of weak strength hydrogen bonds. We take into account the intrinsic anharmonicity of the hydrogen bond stretching mode X ← –H⋯ Y → through a Morse potential by starting from a previous model [Chem. Phys. 248 (1999) 91] which described a weak hydrogen bond subject to a Fermi resonance and which included relaxation phenomena within a quantum treatment, but which considered this mode as an harmonic oscillator. The IR spectral density is studied within the linear response theory by Fourier transform of the autocorrelation function of the transition dipole moment operator of the X–H bond. The main feature brought by the anharmonicity of the H-bond bridge X–H⋯Y is the increase of the average frequency of the ν S ( X – H → ⋯Y) IR band upon a temperature rising. Then, this theory reproduces successfully the experimental behavior of both the first and second moments of this band which is observed when varying the temperature as well as upon isotopic substitution.

IR spectral density of weak H-bonds involving indirect damping. Part II: Davydov coupling

Abstract A non-perturbative approach of the quantum indirect damping for cyclic dimers of weak H-bonds susceptible to involve Davydov coupling is proposed. The effective non-Hermitian Hamiltonians describing the damped H-bond bridge obtained in Part I [Chem. Phys. (2003) submitted] following the basic quantum model of the indirect damping [Chem. Phys. 126 (1988) 263], is introduced in the model of Marechal and Witkowski [J. Chem. Phys. 48 (1968) 3637]. A result which is equivalent to an infinite order expansion of a precedent perturbative approach [J. Mol. Struct. (Theochem.) 314 (1994) 101] is obtained. It allows us to obtain, within the linear response theory, the infrared lineshape of the ν X–H stretching mode. The fine structure of the high frequency tail appears to be more smoothed than that of the low frequency one.

IR spectral density of weak H-bonds involving indirect damping. Part III: application to situations with multiple Fermi resonances

Abstract The IR spectral density (SD) 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 ⋯ Y and the low frequency X – H ⋯ Y modes is treated inside the strong anharmonic coupling theory, whereas Fermi resonances are introduced in the spirit of the work of Witkowski and Wojcik [Chem. Phys. 1 (1973) 9]. The relaxation of the fast and bending modes (direct damping) is treated as usual, whereas the indirect damping is incorporated by aid of our results of part I [Chem. Phys. 293 (2003) 9], dealing with the quantum theory of driven damped quantum harmonic oscillator. The IR SD is obtained by Fourier transform of the autocorrelation function of the dipole moment operator of the fast mode.