IR spectral density of the υ S ( Cl – H → ) band in gaseous ( CH 3 ) 2 O … HCl complex: Phase decoherence due to the anharmonic coupling theory and the bending mode effects

Highlights: • Spectroscopic features of the ${\upsilon }_S(\mathrm{Cl}–\overrightarrow{H})$ band in gaseous ${\left({\text{CH}}_3\right)}_2\text{O}\dots \text{HCl}$ complex are studied. • A quantum approach susceptible to reproduce theoretically these features is proposed. • A good agreement between the simulated and experimental lineshapes is illustrated. -- Abstract: The elucidation of Fermi resonances impact on the IR spectral density (SD) of weak hydrogen bonded systems is still subject of an ongoing debate. We present, in this paper, a simple quantum approach that may illumine the contribution of Fermi resonances, resulting from the interaction between the high stretching and bending modes, on the SD of the ${\upsilon }_S(\mathrm{Cl}–\overrightarrow{H})$ band in gaseous ${\left({\text{CH}}_3\right)}_2\text{O}\dots \text{HCl}$ Complex and address the question whether there is Fermi resonances phenomenon in such weak hydrogen bonded complexes. We analyzed the problem by considering a quantum approach taking into account the following hypotheses: (i) the low frequency stretching mode (slow mode) of the hydrogen bond is represented by a Morse potential, (ii) the high stretching mode (fast mode) is considered to harmonic, (iii) the ${\upsilon }_S(\mathrm{Cl}–\overrightarrow{H})$ phase coherence is lost because of the coupling between the fast and slow modes, and because of the coupling between the fast and the bending mode, (iv) the SD is obtained within the framework of Kubo's theory, according to which the SD is the Fourier transform of the transition dipole moment autocorrelation function which characterises the lineshape of the mid infrared ${\upsilon }_S(\mathrm{Cl}–\overrightarrow{H})$ absorption band, (v) the direct relaxation mechanism of the ${\upsilon }_S(\mathrm{Cl}–\overrightarrow{H})$ stretching band is incorporated by aid of the quantum treatment of Rosch and Ranter for which for the autocorrelation function decays exponentially on time, (vi) the indirect relaxation mechanism of the bending mode is introduced by aid of complex energy levels' method for which the Hamiltonian eigenvalues of the H-bonded system, computed in the absence of damping, imaginary parts reflecting the irreversible influence of the medium on the bending mode. Using a set of physically reasonable parameters as input into the presented approach, the numerical experimentations have shown the capability of this simple model, which anharmonically couple the high stretching mode together with the slow and bending modes, to explain the main spectroscopic features of the ${\upsilon }_S(\mathrm{Cl}–\overrightarrow{H})$ band in gaseous ${\left({\text{CH}}_3\right)}_2\text{O}\dots \text{HCl}$ Complexes. A good agreement between the simulated and experimental lineshapes is illustrated and a deep study of the role of each mechanism on the ${\upsilon }_S(\mathrm{Cl}–\overrightarrow{H})$ band is elucidated.