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.