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

Theoretical elucidation of the IR spectra of 4-bromo-3, 5-dimethylpyrazole crystals and their deuterium-bonded analogues: Multi-objective analysis from a quantum modeling perspective

In the field of medicine, compounds that contain pyrazole and their derivatives are recognized as some of the earliest anti-inflammatory and analgesic agents. Consequently, the development of novel pyrazole-containing synthons represents a promising avenue in the quest for new biologically active substances. The supramolecular aspect plays a crucial role in comprehending the chemistry of pyrazoles. The primary driving force behind the self-assembly of pyrazolyl molecules is attributed to hydrogen bonds. In this context, we propose a quantum theoretical approach to hydrogen bonding in order to elucidate the infrared (IR) spectra of 4-bromo-3,5-dimethylpyrazole (4-Br,3,5-DMPz) crystals. Our ultimate objective is to elucidate the hydrogen-bond dynamics and illustrate the main mechanisms that govern the generation of the IR band contours. The approach addresses the impact of the anharmonic vibrational coupling within the dimeric units, the Davydov coupling and the combined influences of damping mechanisms on theυSX-H IR band contours. The exchange interaction between the two hydrogen bonds of the dimeric units is analyzed through the non-adiabatic coupling framework. The direct damping mechanism is addressed within the theoretical framework established by Rösch and Ratner, while the indirect damping associated with the two hydrogen-bonded bridges is integrated using non-Hermitian Hamiltonians. The contours of the IR bands are obtained through linear response theory by applying a Fourier transform to the dipole moment operator autocorrelation function associated with the high-frequency mode. This theoretical framework reverts to the model proposed by Maréchal and Witkowski regarding Davydov coupling in damping lack, and aligns with the foundational quantum approach of indirect damping when Davydov coupling is not present. The methodology is applied to the study the IR spectra of crystals of 4-Br,3,5-DMPz and their deuterium-bonded analogues at 293 K and 77 K. Numerical simulations demonstrate that the congregated influence of Davydov coupling, the linear interaction within the dimeric units, and the various damping mechanisms can effectively account for the intricate characteristics of the experimental IR band contours. The notable distinctions identified in the fine structure patterns of theυSX-H(D) band contours, along with the temperature effects in these crystals, have been clarified and interpreted from a physical perspective.

Deciphering the abnormal IR spectral density of phthalic acid dimer crystals: Unveiling the role of the dynamical effects of the Davydov coupling and the mechanisms of relaxation

To consistently determine the anomalous characteristics of phthalic acid crystal (PAC) derivatives, we performed quantum dynamics simulations of the infrared spectral density of the h6-PAC and d6-PAC isotopomers that show up in the H/D isotopic frequency domain at two different temperatures viz. 77 and 298 K. A theoretical framework explaining the dynamical cooperative interactions within the hydrogen bonds (HBs) in the PAC crystals across a simulation of IR spectral density of the stretching band was developed. The model presupposes HBs from the nearby (COOH)2 cycles to have exceptionally strong dynamical cooperative contacts. The approach precisely hinges upon on a model that consider the dimer as centrosymmetric in which the low-frequency intermonomer mode (that is, O⋯O) stretches anharmonically and committing the O-H vibrational mode, associated with the high-frequency mode, to stretch harmonically. The approach considers also the following effects: Davydov coupling arising from the interference between the two HBs in the dimer; strong anharmonic coupling between the two stretching modes within the same HB; direct relaxation mechanism of the high stretches in the HB; and indirect relaxation mechanism that is devoted to the high stretches via the slow stretches. Using this approach, the principal characteristics of the O-H(D) experimental bands of the isotopomers studied herein with their peculiarities are simulated by selecting physically sound parameters that uniquely identify the onset of the specific features of the IR spectral densities. The impacts of the important parameters, characterizing the different leading mechanisms within this approach on the spectra, are revealed. The contrast of the emerging simulated spectra with the experimental ones reveals decent agreement for the studied isotopomers. By congregating the different mechanisms employed herein within the pioneering context of the linear response theory of Kubo, the obtained results strongly demonstrate and identify the main effects responsible for the generation of the experimental O-H and O-D bands. Through an examination of the effect of each mechanism involved within the h 6-PAC and d4-PAC isotopomers, it is possible to relate the emergence of IR spectral density to an interplay between the Davydov coupling and the relaxation dynamics.

IR absorption band of weak H-Bonded systems: Showcasing the signature of the quantum indirect damping within the framework of a new approach using non-Hermitean Hamiltonian formalism

Herein, we investigate the effects of the irreversible action of the medium on the theoretical elucidation of the IR spectrum of weakly H-bonded systems, a prototypical model which provides a rigorous treatment of the relaxation mechanisms impacts on the IR spectral density. The attention will be focused particularly on the effect of indirect damping on the IRυS(X-H⃗) spectrum beyond the harmonic and adiabatic approximations. The ultimate objective of the present investigation is the treatment of the action of the surrounding of the intermonomer modes of H-bonded systems, which must induce a broadening of the Dirac delta peaks, the nature of which, as shown by Maréchal and Witkowski theory, is a Franck-Condon progression. The quantum treatment of the IR absorption band reveals that quantum relaxation of the intermonomer mode of H-bonded complexes could be successfully approached by a non-Hermitian Hamiltonian formalism. Motivated by development of a second method that will be able to validate the first approach, a computationally efficient algorithm was proposed for elucidating the quantum indirect relaxation using Hermitean Hamiltonians. The real eigenvalues, corresponding to different energies of the system are considered to be complex by adjunction of the imaginary parts, which reflects the action of the indirect irreversible action of the medium. These two crude approaches may pave the way for the incorporation of the mechanism of indirect relaxation in more physical and complex situations dealing, particularly, with tunnelling effects in strong H-bonded species, Fermi resonances, and Davydov coupling for cyclic H-bonds dimers beyond the harmonic and adiabatic assumptions.

Elucidating the Infrared Spectral Properties of Succinic Molecular Acid Crystals: Illustration of the Structure and the Hydrogen Bond Energies of the Crystal and Its Deuterated Analogs

Herein, the infrared spectroscopic properties of molecular succinic acid crystals (SA) and their four isotopic analogs [C₂H₄(COOH)₂, h₆-SA; C₂H₄(COOD)₂, d₂-SA; C₂D₄(COOH)₂, d₄-SA; C₂D₄(COOD)₂, d₆-SA] are reported. The correlation between the structure of succinic acid molecules and their corresponding hydrogen bond energies is elucidated. The effects related to the isotopic dilution as well as the changes in the spectrum recording temperature on the fine structures of the v_O-H and v_O-D bands are interpreted. The infrared spectral anomalies detected in the spectra of isotopically neat succinic nanocrystal acids are confirmed by theoretical calculations using density functional theory (DFT). According to previous spectroscopic studies of succinic acid and those carried out for α,ω-dicarboxylic acids, a decent agreement between the experimental results and the theoretical DFT simulations is obtained. Moreover, the spectra of single crystals of the h₆ and d₄ succinic acid variants prove that the vibrational coupling mechanism between the (COOH)₂ cycles is rigorously convergent to that detected in the spectra of aromatic carboxylic acids, suggesting thereby that the promotion of symmetry-forbidden high stretching IR transitions plays a crucial role. Furthermore, the obtained experimental results reveal that the succinic acid shows a spectral behavior significantly different from that characteristic of hydrogen associations of other acids of homologous series, such as the glutaric, adipic, malonic, and pimelic acid crystals. The results obtained herein shed light on the way to explore the revealed structure of isotopic derivatives of succinic acid crystals and may prove to be useful results for understanding the nature of unconventional interactions as well as the macroscopic energy effects directing the development of hydrogen associations.

Lack of the 'long-distance' dynamical co-operative interactions due to low symmetry of hydrogen-bonded malonic acid aggregates in molecular crystals

The paper explains the relationship between the energy of hydrogen bonds and the distance between associated carboxyl groups of malonic acid (MA) molecules by means of infrared spectroscopic studies of crystals of its four isotopic varieties [CH₂(COOH)₂, h₄-MA; CH₂(COOD)₂, d₂^c-MA; CD₂(COOH)₂, d₂^m-MA; CD₂(COOD)₂, d₄-MA]. The effects associated with impact on the isotopic dilution and changes in the temperature of spectrum registration on the fine structures of the ν_O-H and ν_O-D bands were analyzed. MA molecular crystals are characterized by a tendency to spontaneous H/D isotopic exchange both within centrosymmetric hydrogen bond cycles and methylene groups. The mono- and polycrystalline spectra obtained in the infrared range of isotopically neat and isotopically diluted by deuterons do not indicate the occurrence of anomalous temperature evolution in the course of lowering their registration temperature to 77 K. Theoretical calculations did not give clear confirmation of the nature of the phenomena analyzed.

A unified quantum model susceptible to elucidate the dissimilarity of IR spectral density of dicarboxylic acid crystals: Phthalic and terephthalic acid crystals cases

Over the last decades, several approaches have been developed for elucidating the infrared spectral density of dicarboxylic acid crystals, which has been served as prototype for determining hydrogen bonds dynamics. These approaches differ in how accurately the simulated spectra can superimpose the experimental ones. In this study, we present a superdimer quantum approach susceptible to elucidate the infrared spectral properties of some particular dicarboxylic acid crystals using a newly proposed algorithm, which favors the rule of Davydov coupling in the generation of the spectra. The approach, which is herein effectively applied to terephthalic and phthalic acid dimer crystals, ascribes the non-conventional IR spectral properties of these particular acid crystals to the existence of superdimer structure in their lattices. In this superdimer structure, a strong vibronic coupling mechanism, namely Davydov coupling, takes place between the proton stretching vibrations in the (COOH)₂ cycles. This strong coupling exciton, generated by the resonance arising in the two coupled (COOH)₂ cycles of the aromatic rings of the superdimer, in conjunction with the strong anharmonic coupling between the fast and slow modes of each hydrogen bonds provide a strong support basis for a common explanation of the physical properties of these two different crystalline systems. The numerical simulations, involving the implications of the superdimer model, are systematically correlated with the experimental spectra. A decent agreement between the evaluated spectra and the experimental bandshapes of terephthalic and phthalic dicarboxylic acid crystals was obtained using a set of physically sound parameters as inputs in the theoretical formulation. The superdimer quantum approach thereby underscore the potential of the dynamical cooperative interactions between "Davydov coupling" and "strong anharmonic coupling" mechanisms in the generation of the spectral features of terephthalic and phthalic dicarboxylic acid crystals, suggesting that the congregated effects of these two mechanisms can be considered as the most reliable source of the non-conventional IR spectral properties observed. It is therefore expected that this novel algorithm reduces the discrepancies between the simulated spectra compared to the experimental one and simplify the computation of spectra in more complex hydrogen bonded systems.

Computational analysis of vibrational frequencies and rovibrational spectroscopic constants of hydrogen sulfide dimer using MP2 and CCSD(T)

Previous studies have shown that the weakly bonded H₂S dimer demands high level quantum chemical calculations to reproduce experimental values. We investigated the hydrogen bonding of H₂S dimer using MP2 and CCSD(T) levels of theory in combination with aug-cc-pV(D,T,Q)Z basis sets. More precisely, the binding energies, potential energy curves, rovibrational spectroscopic constants, decomposition lifetime, and normal vibrational frequencies were calculated. In addition, we introduced the local mode analysis of Konkoli-Cremer to quantify the hydrogen bonding in the H₂S dimer as well as providing for the first time the comprehensive decomposition of normal vibrational modes into local modes contributions, and a decomposition lifetime based on rate constant. The local mode force constant of the H₂S dimer hydrogen bond is smaller than that of the water dimer, in accordance with the weaker hydrogen bonding in the H₂S dimer.

How far the vibrational exciton interactions are responsible for the generation of the infrared spectra of oxindole crystals?

Oxindole (indolin-2-one, Ox) is a unique and a crucial molecular system in spectroscopic studies. Indole is the core structure of many substances found in the human body (tryptophan, serotonin) and the indole alkaloids have highly differentiated pharmacological properties such as analgesic, anti-fever and anti-inflammatory. The Ox's structural results given in the Cambridge Structural Database revealed the existence of only one crystalline form of Ox, referred to the α-form. However, we have experimentally noticed the existence of two polymorphic forms during the crystallization of Ox. Furthermore, the significant spectral differences that we have observed in the solid state infrared spectra of these two forms additionally confirm the existence of the polymorphism phenomenon. Of the four polymorphic forms of Ox, two of them - α - and β-forms - were of particular interest. In the crystalline lattices of both polymorphs, we observed a similar pattern of molecular arrangements giving rise to the supramolecular synthon according to the terminology of Etter. Moreover, hydrogen bonds in the dimer of the α-form are found to be non-equivalent (non-centrosymmetric dimers), having a length of 2797 Å and 2979 Å, respectively. Comparatively, in the most densely packed crystalline structure of Ox, the β-form, the dimer is formed by a pair of almost identical intermolecular hydrogen bonds and consequently the crystals of β-form exhibited spectral properties typical to centrosymmetric hydrogen bond dimers. In addition, the spectroscopic studies that we have conducted to polymorphic forms of Ox, isotopically diluted with deuterium, show the dramatic influence of isotopic substitution in the hydrogen bridge on the infrared spectra of hydrogen bonding. Thus, the main goal of this work is the proposition of a theoretical approach that can describe the main features of the crystalline infrared spectra of the Ox polymorphs. The proposed approach is based on the phenomenon of the exciton coupling results directly from intermolecular interactions in the vibrationally excited state which leads to the delocalization of the excitation over the molecules in the lattice and to the Davydov splitting effect in the crystalline spectra.

Chemical Compounds of Malacca Leaf (Phyllanthus emblica) after Triple Extraction with N-Hexane, Ethyl Acetate, and Ethanol

Malacca (Phyllanthus emblica) is one of the plants that is often by the community in the Aceh Besar district of Indonesia as a traditional medicine for the treatment of various diseases such as antimicrobial, antibacterial, antifungals, antivirals, antimutagenic, antimalaria, and antiallergic. This research was conducted to analyze the content of chemical compounds in the ethanol extract of the Malacca leaf (EEDM) using a gas chromatography-mass spectrophotometer (GC-MS). Malacca leaves were extracted by the maceration method using n-hexane, ethyl acetate, and ethanol. The GC-MS analysis showed EEDM contained 22 chemical compounds. The highest chemical content of EEDM is octadecanoic acid reaching 22.93%, 9,12-octadecanoic acid 14.99%, octadecanoic acid 7.59%, 9-hexadecenoic acid 6.17%, octadecanoic acid 5.95%, octadecanal 5.59%, 9,12-octadecanoic acid 5.06%, 3-eicosyne 4.75%, 1-hexadecenoic acid 4.08%, 11-tetradecen-1-ol 2.92%, 2-furanmethanol 2.83%, delta-guaiene 2.43%, cyclohexane 2.13%, hexadecanoic acid 1.99%, sativen 1.87%, octadecanoic acid 1.52%, 1H-cyclopropaanaphthalene 1.40%, tetradecanoic acid 1.40%, 3,7,11-tridecatrienenitrile 1.20%, caryophellene 1.11%, 2H-pyran 1.07%, and trans-caryophellene 1.03%. This study clearly shows the presence of fatty acids which play a major role in the efficacy of these traditional medicines particularly as antioxidant and antimalarial.

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 I_Old(ω)=2Re∫₀^∞G_Old(t)e^-iωtdt where the ACF G_Old(t) = ⟨μ(0)μ(t)⁺⟩ = tr {ρ {μ(0)} {μ(t)}⁺}, one can use a new expression for the SD, given by I_New(ω)=2ωRe∫₀^∞G_New(t)e^-iωtdt where G_New(t)=μ(0)μ(t)⁺=1βtrρ_B∫₀^βμ(0)μ(t+iλℏ)⁺dλ. Here ρ_B 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 k_BT where T is the absolute temperature and k_B 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 Witkowski's 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 I_Cl(ω) = Re[∫₀^∞G_Cl(t)e^-iΩt dt] in which the classical-like autocorrelation function (ACF), G_Cl(t), is given by G_Cl(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) = ΩI_Cl(ω), which in turn is equivalent to the quantum SD given by I_Qu(ω) = Re[∫₀^∞G_Qu(t)e^-iΩt dt], where G_Qu(t) is the corresponding quantum ACF having for expression G_Qu(t) = (1/β) tr{ρ∫₀^β[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.

Electrical anharmonicity in hydrogen bonded systems: complete interpretation of the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH3)2OHCl complex

Following the previous developments to simulate the fully infrared spectra of weak hydrogen bond systems within the linear response theory, an extension of the adiabatic model is presented here. A general formulation including the electrical anharmonicities in the calculation of the damped autocorrelation function of weak H-bonds is adopted to facilitate the support of the additional properties, and thus the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH₃)₂OHCl complex. We have explored the origins of the broadening of the Cl-H[combining right harpoon above] stretching band. We found that the main features of the lineshape are attributed to electrical anharmonicity as a consequence of the large mixed second derivatives of the dipole moment with respect to the Cl-H[combining right harpoon above] bond and of the intermonomer elongations . In addition to providing more accurate theoretical band shapes, inclusion of the electrical anharmonicity in the present model paves the way for a more complete interpretation by generating three new Franck-Condon superposed distributions.

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

Theoretical infrared line shapes of H‐bonds within the strong anharmonic coupling theory and Fermi resonances effects

In this article, we extend a previous work toward presenting a theoretical study of the effects of Fermi resonances and the fundamental anharmonic coupling parameter α between the high‐frequency mode and the H‐bond bridge. The model incorporates (i) both intrinsic anharmonicities of the fast mode (double well potential) and the H‐bond Bridge (Morse potential), (ii) strong anharmonic coupling theory, (iii) Fermi resonances by the aid of an anharmonic coupling between the fast mode and one or several harmonic bending modes, (iv) quadratic modulation of both the angular frequency and the equilibrium position of the X$\vec H$…Y stretching mode on the intermonomer $\vec X$H…$\vec Y$ motions, and (v) the quantum direct (fast and bending modes) and indirect dampings (slow mode). The IR spectral density is obtained by Fourier transform of the autocorrelation function of the transition dipole moment operator of the XH bond. The numerical calculation shows that Fermi resonances generate very complicated profiles with multisubstructure and also provide a direct evidence of Fermi resonances which were predicted to be a major feature of H‐bonds. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Theoretical modeling of infrared spectra of the hydrogen and deuterium bond in aspirin crystal

An extended quantum theoretical approach of the nu(X-H) IR lineshape of cyclic dimers of weakly H-bonded species is proposed. We have extended a previous approach [M.E.-A. Benmalti, P. Blaise, H.T. Flakus, O. Henri-Rousseau, Chem. Phys. 320 (2006) 267] by accounting for the anharmonicity of the slow mode which is described by a "Morse" potential in order to reproduce the polarized infrared spectra of the hydrogen and deuterium bond in acetylsalicylic acid (aspirin) crystals. From comparison of polarized IR spectra of isotopically neat and isotopically diluted aspirin crystals it resulted that centrosymmetric aspirin dimer was the bearer of the crystal main spectral properties. In this approach, the adiabatic approximation is performed for each separate H-bond bridge of the dimer and a strong non-adiabatic correction is introduced into the model via the resonant exchange between the fast mode excited states of the two moieties. Within the strong anharmonic coupling theory, according to which the X-H...Y high-frequency mode is anharmonically coupled to the H-bond bridge, this model incorporated the Davydov coupling between the excited states of the two moieties, the quantum direct and indirect dampings and the anharmonicity for the H-bond bridge. The spectral density is obtained within the linear response theory by Fourier transform of the damped autocorrelation functions. The evaluated spectra are in fairly good agreement with the experimental ones by using a minimum number of independent parameters. The effect of deuteration has been well reproduced by reducing simply the angular frequency of the fast mode and the anharmonic coupling parameter.

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.

Anharmonic effects on theoretical IR line shapes of medium strong H(D) bonds

We extend a quantum nonadiabatic treatment of damped H‐bonds involving combined effects of anharmonicities of both the fast and the slow modes, Fermi resonances and relaxation [Rekik et al., J Mol Liq (in press)] in order to account for stronger H‐bonds. For this purpose, we introduce, in the model, the quadratic modulation of both the angular frequency and the equilibrium position of theX−$\mathop H\limits^{\rightarrow}$…Ystretching mode on the intermonomer$\mathop X\limits^{\leftarrow}- H \ldots \mathop Y\limits^{\rightarrow}$motions to refine the structure of the spectrum, whereas we have considered in our previous work only the linear modulation of the angular frequency of the fast mode. In this approach, the strong anharmonic coupling theory is used through second‐order expansion in the slow‐mode coordinateQof the angular frequency and the equilibrium position of the fast mode. The relaxations of the fast mode (direct damping) and of the H‐bond bridge (indirect damping) are incorporated by aid of previous results [Rekik et al., J Mol Struct 2004, 687, 125]. The spectral density is obtained by Fourier transform of the autocorrelation function of the dipole moment of the fast stretching mode. The numerical calculation shows that the modulation of the angular frequency of the fast mode and its equilibrium position by the slow mode coordinate generate an improvement of the fine structure of the spectrum and also provide a direct evidence of the increase of the level density and the spectral broadening. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Relaxation and anharmonic couplings of the O-H stretching vibration of asymmetric strongly hydrogen-bonded complexes

We present infrared transient grating measurements of complexes of formic acid with pyridine and pyrazine at four excitation frequencies within the broad proton-stretching band. These experiments investigate the mechanism of the line broadening of the O-H stretching vibration. The transients show coherent oscillations that decay within a few hundred femtoseconds and population relaxation on two time scales. We fit the data using a simple model of three coupled oscillators that relax via sequential kinetics through an intermediate state. Based on this model, we conclude that the coherent oscillations result from superpositions of Fermi-resonance-coupled states involving formic acid overtone and combination states.

On the Contribution of Vibrational Anharmonicity to the Binding Energies of Water Clusters

The second-order vibrational perturbation theory method has been used together with the B3LYP and MP2 electronic structure methods to investigate the effects of anharmonicity on the vibrational zero-point energy (ZPE) contributions to the binding energies of (H2O)n, n = 2-6, clusters. For the low-lying isomers of (H2O)6, the anharmonicity correction to the binding energy is calculated to range from -248 to -355 cm(-1). It is also demonstrated that although high-order electron correlation effects are important for the individual vibrational frequencies, they are relatively unimportant for the net ZPE contributions to the binding energies of water clusters.