Theoretical infrared spectral density of H-bonds in liquid and gas phases: Anharmonicities and dampings effects Najeh Rekik a, * , Brahim Oujia a , Marek J. Wójcik b a Laboratoire de Physique Quantique, Faculté des Sciences de Monastir, Route de Kairouan, 5000 Monastir, Tunisia b Laboratory of Molecular Spectroscopy, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Kraków, Poland article info Article history: Received 21 March 2008 Accepted 16 May 2008 Available online 22 May 2008 Keywords: Hydrogen bond Anharmonicity Morse potential Fermi resonance Direct and indirect relaxation Liquid and gas Phases Linear response theory Autocorrelation function Infrared spectral density abstract The main purpose of the present paper is to show how both anharmonicities of the fast and the slow modes, multiple Fermi resonances and damping mechanisms introduced within the strong anharmonic coupling theory, are susceptible to explain some analogies in the infrared spectra of hydrogen bonded systems, when passing from the condensed to the gas phase. The high-frequency mode X— H !  Y described by double well potential is supposed to be anharmonically coupled to the H-bond stretching mode X  —H  Y ! described by Morse potential and to first overtones of some bending modes through Fermi resonances. The relaxation of the fast and bending modes and of the H-bond bridge is incorporated by aid of previous results [N. Rekik, B. Ouari, P. Blaise, O. Henri-Rousseau, J. Mol. Struct. 687 (2004) 125]. The spectral density is obtained as the Fourier transform of the autocorrelation function of the dipole moment operator within linear response theory. Numerical results show that mixing of all these effects results in a broad and complicated structure and expects to provide efficient energy relaxation pathways by using large dampings parameters for the con- densed phase and weaker dampings for the gas one. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Infrared spectroscopy is considered as a powerful tool in the hydrogen bond research, able to deliver a complete information about the complex dynamics of atoms in hydrogen bonds. There- fore, in the state of the art of our knowledge, infrared spectroscopy provides a wealthy data system allowing for deeper understanding of the hydrogen bond nature [1–7]. In the case of IR spectroscopic studies, the most evident effect of hydrogen bonding (H-bond) are the red shift of the high-frequency X—H  Y stretching mode, its intensity increase and band broadening; the latter is often accom- panied by the development of peculiar band-shapes. The large increase of the bandwidth, the band asymmetry, the appearance of subsidiary absorption maxima and minima, such as Evans win- dows, peculiar isotope and temperature effects and the similarity of features of the lineshape when passing from the condensed to the gas phase [8,9] (see Fig. 1) are the challenge for theories of H-bonds. Fig. 1 shows the similarity between the spectra of acetic acid dimers in the gas and liquid phases. This is due to the fact that the mutual interactions of acetic acid dimers in an inert solvent like CCl 4 most probably resemble their interactions in CH 3 COOH vapours and, therefore, the two compared gaseous and liquid phase spectra are very similar. The blurring of the spectra, caused by condensation, was recently shown in thin layer of pure liquid acetic acid by Flakus and Tyl [10]. For about thirty years, it has been assumed that anharmonicity plays a fundamental role in the spectral features of the m X—H line- shapes. That has been confirmed by quantum chemical calculations. The anharmonicity may manifest in different ways: there is the pos- sibility of an anharmonic coupling between the low and high-fre- quency modes [6] (see Table 1). There are also anharmonic coupling between the first excited state of the fast mode and some harmonics or band combinations of some low-frequency bending modes which lead to Fermi resonances [11–19]. Besides, the anhar- monicity of the H-bond is present for the slow and fast modes. The slow mode potential is described by a Morse curve [20] whereas the fast mode potential may be of double well nature (symmetric or not) [21–26]. Besides, there is also the theory of relaxation which is reflecting the irreversible influence of the medium on the H-bond. One distinguishes two possibilities of damping mechanisms: the ‘‘direct” and ‘‘indirect” relaxations. In the first one, the fast mode directly relaxes toward the medium via dipole–dipole inter- actions [27], whereas in the second one, it relaxes via the damped H-bond bridge to which it is anharmonically coupled [28]. There have been some semi-classical approaches of the two relaxation mechanisms dealing either with direct damping [28,29], or with indirect damping [30–32], and, at last, attempts to treat simulta- neously both dampings [33]. But these semi-classical approaches are not susceptible to reproduce the details of the experimental. 0301-0104/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2008.05.009 * Corresponding author. Fax: +216 73 500 278. E-mail address: rekik.najeh@fsm.rnu.tn (N. Rekik). Chemical Physics 352 (2008) 65–76 Contents lists available at ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys