Theory of weak damped H-bonds: relative influence of relaxation mechanisms on IR spectra

Abstract

We revisit numerically the roles played by relaxation mechanisms on the line shapes of the IR spectral density of weak H-bonds. This is performed by means of three theories already published. The tools common to these theories are the strong anharmonic coupling theory (between the high- and low-frequency stretching modes of the H-bond), and the linear response theory (according to which the spectral density is the Fourier transform of the autocorrelation function). The theories are those of: (1) G. Robertson and J. Yarwood [Chem. Phys. 32 (1978) 267], taking into account (semiclassically) indirect damping; (2) N. Rösch and M. Ratner [J. Chem. Phys. 61 (1974) 3444] dealing (quantum mechanically) with direct damping; and (3) B. Boulil, J.-L. Déjardin, N. El-Ghandour, O. Henri-Rousseau [J. Mol. Struct. (Theochem) 314 (1994) 83] involving (quantum mechanically) slow-mode damping. The quantum direct damping induces a broadening, and the quantum slow-mode damping (in contrast with the semiclassical indirect relaxation) a weak narrowing, when they are both occurring. The direct damped quantum spectral density leads to Lorentzian (fast modulation limit) or Gaussian (slow modulation limit) shapes as does the spectral density of the semiclassical model of indirect relaxation. The dephasing of the fast mode should be predominant for line shapes with broadened sub-bands (obeying the Franck–Condon progression law), or without sub-bands (but with nearly symmetric profiles intermediate between Gaussian and Lorentzian). Both the dephasing of the fast mode and the damping of the slow mode should occur by similar amounts if the line shapes are without sub-bands but with asymmetry, or with sub-bands but with intensity anomalies in the Franck–Condon progression.