Najeh Rekik

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.

A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction

We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.

Explaining the structure of the OH stretching band in the IR spectra of strongly hydrogen-bonded dimers of phosphinic acid and their deuterated analogs in the gas phase: a computational study.

We present a simulation of the OH stretching band in the gas-phase IR spectra of strongly hydrogen-bonded dimers of phosphinic acid and their deuterated analogs [(R(2)POOH(D), with R = CH(2)Cl, CH(3)], which is based on a model for a centrosymmetric hydrogen-bonded dimer that treats the high-frequency OH stretches harmonically and the low-frequency intermonomer (i.e., O···O) stretches anharmonically. This model takes into account the following effects: anharmonic coupling between the OH and O···O stretching modes; Davydov coupling between the two hydrogen bonds in the dimer; promotion of symmetry-forbidden OH stretching transitions; Fermi resonances between the fundamental of the OH stretches and the overtones of the in- and out-of-plane bending modes involving the OH groups; direct relaxation of the OH stretches; and indirect relaxation of the OH stretches via the O···O stretches. Using a set of physically sound parameters as input into this model, we have captured the main features in the experimental OH(D) bands of these dimers. The effects of key parameters on the spectra are also elucidated. By increasing the number and strength of the Fermi resonances and by promoting symmetry-forbidden OH stretching transitions in our simulations, we directly see the emergence of the ABC structure, which is a characteristic feature in the spectra of very strongly hydrogen-bonded dimers. However, in the case of the deuterated dimers, which do not exhibit the ABC structure, the Fermi resonances are found to be much weaker. The results of this model therefore shed light on the origin of the ABC structure in the IR spectra of strongly hydrogen-bonded dimers, which has been a subject of debate for decades.

Some further considerations on deriving matrix elements of non-periodic potentials in the basis of the non-degenerate harmonic oscillator wavefunctions

Abstract Using the properties of the generating function of the Hermite polynomials, we have calculated the matrix elements for the Gaussian-type potential V G (x)=A exp {−B(x−C) 2 } and for the Morse-type potential VM(x)=De[1−exp(−ax)]2 in the basis of the non-degenerate harmonic oscillator wavefunctions. The final forms of these matrix elements are very simple to use and hence suitable for the numerical resolution of the Schrodinger equation for multiple-well potentials or anharmonic oscillators.

Theoretical study of the νO–H IR spectra for the hydrogen bond dimers from the polarized spectra of glutaric and 1-naphthoic acid crystals: Fermi resonances effects

A full quantum theoretical model is proposed to study the nu(O-H) experimental IR line shapes of polarized crystalline glutaric and 1-naphthoic acid dimer crystals at room and liquid nitrogen temperatures. This work is an application of a previous model [M. E-A. Benmalti, D. Chamma, P. Blaise, and O. Henri-Rousseau, J. Mol. Struct. 785 (2006) 27-31] by accounting for Fermi resonances. The approach is dealing with the strong anharmonic coupling, Davydov coupling, multiple Fermi resonances between the first harmonics of some bending modes and the first excited state of the symmetric combination of the two nu(O-H) modes and the quantum direct and indirect relaxation. Numerical results show that mixing of all these effects allows to reproduce satisfactorily the main features of the experimental IR line shapes of crystalline hydrogenated and deuterated glutaric and 1-naphthoic acid crystals and are expected to provide efficient of Fermi resonances effects.

An investigation on the effect of high partial pressure of hydrogen on the nanocrystalline structure of silicon carbide thin films prepared by radio-frequency magnetron sputtering.

The aim of the study reported in this paper is to investigate the role of the high partial pressure of hydrogen introduced during the growth of nanocrystalline silicon carbide thin films (nc-SiC:H). For this purpose, we report the preparation as well as spectroscopic studies of four series of nc-SiC:H obtained by radio-frequency magnetron sputtering at high partial pressure of hydrogen by varying the percentage of H2 in the gas mixture from 70% to 100% at common substrate temperature (TS=500°C). The effects of the dilution on the structural changes and the chemical bonding of the different series have been studied using Fourier transform infrared and Raman spectroscopy. For this range of hydrogen dilution, two groups of films were obtained. The first group is characterized by the dominance of the crystalline phase and the second by a dominance of the amorphous phase. This result confirms the multiphase structure of the grown nc-SiC:H thin films by the coexistence of the SiC network, carbon-like and silicon-like clusters. Furthermore, infrared results show that the SiC bond is the dominant absorption peak and the carbon atom is preferentially bonded to silicon. The maximum value obtained of the crystalline fraction is about 77%, which is relatively important compared to other results obtained by other techniques. In addition, the concentration of CHn bonds was found to be lower than that of SiHn for all series. Raman measurements revealed that the crystallization occurs in all series even at 100% H2 dilution suggesting that high partial pressure of hydrogen favors the formation of silicon nanocrystallites (nc-Si). The absence of both the longitudinal acoustic band and the transverse optical band indicate that the crystalline phase is dominant.

Signature of Congregated Effects of Mechanical and Electrical Anharmonicities, Fermi Resonances, and Dampings on the IR Spectra of Hydrogen Bonded Systems: Quantum Dynamic Study

Theoretical IR spectral density of the high-frequency stretching mode of hydrogen bond (H-bond) systems is reported using a three-dimensional approach. The model, studied within the framework of linear response theory, involves the mechanical anharmonicity of the high-frequency stretching mode by contemplating its potential as an asymmetric double well potential, the mechanical anharmonicity of the H-bond Bridge by contemplating its potential as a Morse potential, Fermi resonances which occur between the high frequency stretching mode and the overtones of the bending modes, the electrical anharmonicity translated by the nonlinearity to second order in the electric dipole moment function of the fast mode, the second order modulation of the angular frequency and the equilibrium position of the fast mode on the slow mode coordinate, and direct and indirect relaxation mechanism. Moreover, the repulsive potential interposing in the fast mode potential is chosen in Gaussian form to account for the asymmetry of the fast mode potential and thereby elucidate the nature of the H-bond. The anharmonic coupling between the fast and slow frequency modes is handled within the strong anharmonic coupling theory. The direct relaxation of the fast mode and the indirect relaxation of the H-bond Bridge are consolidated using previous results [Rekik et al. Chem. Phys. 2008, 352, 65-76]. The infrared spectral density is calculated using the Fourier transform of the autocorrelation function of the transition dipole moment operator of the fast mode. The evolution of the infrared absorption is demonstrated, indicating that mixing of all these effects results in a broadening and complicated distribution of the spectral density. The result of this work underscores the necessity of simultaneously combining the maximum effects in H-bonded complexes for effectively modeling and interpreting their corresponding IR spectra.

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)+=1βtrρB∫0βμ(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, β 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 Witkowskis 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(β){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/β) tr{ρ∫0β[μ(0)}{μ(t + iλℏ)}† 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.