Paul Blaise

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.

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.

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.

Spectral density of medium strength H-bonds. Direct damping and intrinsic anharmonicity of the slow mode. Beyond adiabatic approximation

Abstract The present 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 spectra of the infrared ν X–H⋯Y mode of weak and medium strength hydrogen bonds: the spectral density is studied within the linear response theory by Fourier transform of the autocorrelation function of the transition dipole moment of the fast mode. The strong anharmonic coupling theory is used through second-order expansion in the slow-mode coordinate Q of the angular frequency and the equilibrium position of the fast mode. The theory is working beyond the adiabatic approximation. It takes into account the intrinsic anharmonicity of the low frequency mode through Morse potential, and assumes a direct damping of the fast mode. At last, indirect damping, Fermi resonances and Davydov coupling are ignored. When the Morse potential is expanded up to the harmonic approximation, the theoretical spectral density reduces [O. Henri-Rousseau, P. Blaise, Chem. Phys. 250 (1999) 249]. The theory reproduce not only the experimental features obtained in this previous paper but also the increase in magnitude of the first moment with temperature.

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.

Linear response theory and IR spectral density of direct damped weak H-bonds: validity of adiabatic approximation

Abstract The adiabatic approximation (AA) involved in the quantum theory of the IR lineshapes (νX–H stretching mode) of weak H-bonds, is revisited. This is performed directly by looking at the spectral density obtained by Fourier transform of the direct damped autocorrelation function of the transition dipole moment. The spectral densities computed according to the AA are compared to those obtained directly through the diagonalization of the representative matrix of the Hamiltonian involving the anharmonic coupling between the high- and low-frequency modes. At 300 K, when the anharmonic parameter remains small (α°≤1), the AA lineshape reduces to the exact one, whereas beyond (α°≥1), the AA is less and less satisfied since its spectral density differs progressively from the exact. Introduction in the AA of effective angular frequency and effective anharmonic parameter, allows us for α°≈1.5 to fit sensitively the exact curve except for the spectrum tails. Connection between the two approaches is established through effective Hamiltonians (operators and matrices) by means of the wave operator.

Anharmonic effects on theoretical IR line shapes of H-bonds

Abstract In the spirit of Y. Marechal and A. Witkowskis [J. Chem. Phys. 48 (1968) 2697] work, one revisits, for weak H-bonds, the dependence of the angular frequency ω and of the equilibrium position q e of the υ X–H high frequency mode q , on the position coordinate Q of the low frequency υ X–H⋯Y mode. One considers: ω = ω o + bQ + cQ 2 and q e = gQ + fQ 2 . That leads to the anharmonic potential U : U = k 1 q 2 +∑ k r Q r +∑∑ k nm q n Q m + k 15 qQ 5 . Here k r and k mn ( r =2–5, n =1,2 and m =1–4) are interrelated through b , c , g and f . By aid of the Hamiltonian involving U , we find the direct damped auto correlation function of υ X–H , which, by Fourier transform, gives the IR spectral density (SD). When only b ≠0, the SD is nothing but that given in a previous paper [P. Blaise, O. Henri-Rousseau, Chem. Phys. 243 (1999) 229]. When the adiabatic approximation is performed, this SD becomes that of N. Rosch and M. Ratner [J. Chem. Phys. 61 (1974) 3444] which reduces in turn to that of Marechal and Witkowski in the absence of damping. With respect to b ≠0, c produces a narrowing of the SD if c >0 and a subtle broadening if c g induces the same narrowing for g >0 and g f gives subtle changes very sensitive to the sign of f and to the values of b , c and g . The situation b f >0 which is physically the most probable, leads to SDs which are the most evoking experimental profiles.

IR spectral density of weak H-bonds involving indirect damping. I. A new approach using non-Hermitean effective Hamiltonians

Abstract A new approach of the combined effects of quantum direct and indirect dampings (within the adiabatic approximation) on the infrared lineshapes of the ν X–H stretching mode of simple and single weak H-bonds is proposed. The approach is based on our precedent model dealing only with bare weak H-bonds [B. Boulil, O. Henri-Rousseau , P. Blaise Chem. Phys. 126 (1988) 263; B. Boulil, J.-L. Dejardin, N. El-Ghandour, O. Henri-Rousseau, J. Mol. Struct. (Theochem) 314 (1994) 83]. As in this initial model, the indirect relaxation of the H-bond bridge is described by the aid of the driven damped quantum harmonic oscillator model [W. Louisell, L. Walker, Phys. Rev. 137 (1965) 204]. It is shown that the Hamiltonian characterizing the driven damped quantum harmonic oscillator may be obtained in a non-Hermitean reduced form, allowing, contrarily to the initial approach, the possibility of generalizations to more complex situations than those of bare H-bonds.