Experimental and theoretical study of the polarized infrared spectra of the hydrogen bond in 3‐thiophenic acid crystal

This article presents the results of experimental and theoretical studies of the v_{O H} and v_{O D} band shapes in the polarized infrared spectra of 3‐thiophenic acid crystals measured at room temperature and at 77 K. The line shapes are studied theoretically within the framework of the anharmonic coupling theory, Davydov coupling, Fermi resonance, direct and indirect damping, as well as the selection rule breaking mechanism for forbidden transitions. 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 via the resonant exchange between the fast‐mode excited states of the two moieties. The spectral density is obtained within the linear response theory by Fourier transform of the damped autocorrelation functions. The approach 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. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Theoretical study of the polarized infrared spectra of the hydrogen bond in 2‐furoic acid crystal dimer

This work presents a theoretical simulation of ν_{O? H} and ν_{O? D} band shapes in the polarized infrared spectra of 2‐furoic acid dimer crystals measured at liquid‐nitrogen temperature. The line shapes are studied theoretically within the framework of the anharmonic couplings between low‐frequency hydrogen‐bond vibrations and degenerate excited states of high‐frequency hydrogen vibrations in hydrogen‐bonded dimers and the anharmonic coupling between the first excited state of the fast mode and the harmonics or band combinations of some low‐frequency bending modes, which lead to Fermi resonances.This approach takes into account the adiabatic approximation, the intrinsic anharmonicity of the low‐frequency mode through a Morse potential, Davydov coupling triggered by resonance exchange between the excited states of the fast modes of the two hydrogen bonds involved in the cyclic dimer, and the direct and indirect damping of the fast‐stretching modes of the hydrogen bonds and of the bending modes. The infrared spectral density was calculated within the linear response theory by Fourier transform of the autocorrelation function of the transition dipole moment operator of the fast mode. 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‐furoic acid at liquid‐nitrogen temperature and for different polarizations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

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 ν_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 ν_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.     

Theoretical study of hydrogen and deuterium bond in glutaric acid crystal dimer

In the spirit of the work of Blaise et al. [J Chem Phys, 2005, 122, 64306], we have extended their quantum theoretical approach by accounting for the intrinsic anharmonicity of the slow frequency mode, which is described by a Morse potential to reproduce the polarized infrared line shapes of glutaric acid dimer and its deuterium derivative at different temperatures. In this approach, the adiabatic approximation 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. Working within the strong anharmonic coupling theory, according to which the high‐frequency mode is anharmonically coupled to the H‐bond bridge, this approach incorporated the Davydov coupling between the excited states of the two moieties, the quantum direct and indirect dampings and the intrinsic anharmonicity of the H‐bond bridge. The spectral density was obtained within the linear response theory by Fourier transform of the damped autocorrelation functions. The numerical results show that the theoretical line shapes of the glutaric acid dimer are in fairly good agreement with the experimental ones. Using a minimum number of independent parameters, this theoretical approach fits correctly the experimental line shapes of the glutaric acid dimer. The effects of deuteration and temperature have been successfully reproduced by our calculations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Determination of vibrational parameters of methanol from matrix-isolation infrared spectroscopy and ab initio calculations. Part 2 – Theoretical treatment including a perturbative approach of the resonances within the methyl group

Ab initio calculations of the potential energy surface of methanol have been developed for the determination of vibrational parameters and their comparison with vibrational data reported in the first part of this work. The strong resonances between the methyl bending and stretching modes, giving rise to polyads of levels P_n in the ranges 3000–2800 (P₂), 4500–4250 (P₃) and 6000–5600 cm⁻¹ (P₄), have been treated by solving for each polyad two Hamiltonian matrices containing off-diagonal terms including both Fermi and Darling-Dennison anharmonic contributions. These terms were calculated from the ab initio determination of the potential energy surface developed up to the quartic terms using the Möller–Plesset 2 method. The choice of the basis set was made to minimize the problem of divergence of the Darling-Dennison constants. Their determination requires however the omission of the terms in which the difference between the harmonic frequencies of the symmetrical methyl stretching and the sum of the two A′ bendings (ω₃–ω₄–ω₅) appears in the denominator. Then, by adjustment of the diagonal elements of the Hamiltonian matrices, it becomes possible to propose a realistic assignment of the matrix spectra.     

Theory of profiles of hydrogen stretching infrared bands of hydrogen-bonded solids. Multi-Fermi resonance effects and strong coupling between the high-frequency hydrogen stretching vibration and low-frequency phonons

A theory is developed to describe the profiles of hydrogen stretching infrared bands of hydrogen-bonded solids taking into account the anharmonic coupling between the high-frequency stretching vibration, ν(XH), and low-frequency lattice phonons, Ω_i, as well as multi-Fermi resonances between states involving the ν(XH) stretching and overtones or combinations of some internal modes. The theory has been constructed in the framework of the extended molecular exciton Davydov approach. Model calculations show that the strong couplings between the high frequency ν(XH) and low-lattice vibration frequencies, Ω_i, generate the broadness of the ν(XH) band but the multi-Fermi resonances between the ν(XH) state and overtones or combinations of internal modes generate the complicated substructure band which is observed experimentally.     

Fermi resonance and strong anharmonic effects in the absorption spectra of the ν-OH (ν-OD) vibration of solid H- and D-benzoic acid

The vibrational spectra of polycrystalline benzoic acid (BA) and its deuterated derivative were studied over the wide frequency region 4000–10 cm⁻¹ by IR and Raman methods. A theoretical analysis of the hydrogen bond frequency region and calculations at the B3LYP/6-311++G(2d, 2p) level for the benzoic acid cyclic dimer in the gas phase were made. In order to study the dynamics of proton transfer two formalisms were applied: Car–Parrinello Molecular Dynamics (CPMD) and Path Integrals Molecular Dynamics (PIMD). It was shown that the experimentally observed very broad ν-OH band absorption is the result of complex anharmonic interaction: Fermi resonance between the OH-stretching and bending vibrations and strong interaction of the ν-OH stretching with the low frequency phonons. The theoretical analysis in the framework of such an approach gave a good correlation with experiment. From the CPMD calculations it was confirmed that the O–HO bridge is not rigid, with the OO distance being described by a large amplitude motion. For the benzoic acid dimer we observed stepwise (asynchronous) proton transfer.     

Entropic functionals of Laguerre polynomials and complexity properties of the half‐line Coulomb potential

The stationary states of the half‐line Coulomb potential are described by quantum‐mechanical wavefunctions, which are controlled by the Laguerre polynomials L(x). Here, we first calculate the qth‐order frequency or entropic moments of this quantum system, which is controlled by some entropic functionals of the Laguerre polynomials. These functionals are shown to be equal to a Lauricella function F(${1 \over q}$ ,…,,${1 \over q}$ ,1) by use of the Srivastava‐Niukkanen linearization relation of Laguerre polynomials. The resulting general expressions are applied to obtain the following information‐theoretic quantities of the half‐line Coulomb potential: disequilibrium, Renyi and Tsallis entropies. An alternative and simpler expression for the linear entropy is also found by means of a different method. Then, the Shannon entropy and the LMC shape complexity of the lowest and highest (Rydberg) energetic states are explicitly given; moreover, sharp information‐theoretic‐based upper bounds to these quantities are found for general physical states. These quantities are numerically discussed for the ground and various excited states. Finally, the uncertainty measures of the half‐line Coulomb potential given by the information‐theoretic lengths are discussed. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011