Theory of Infrared Bandshapes in Hydrogen-Bonded Crystals

A simple dynamical model is proposed for the X-H stretching vibrations of molecules forming a one-dimensional hydrogen-bonded claim of type X-H...X-H.... The vibration of each X-H molecular unit is assumed to undergo a classical frequency modulation, such that its instantaneous frequency varies linearly with the relative displacement between neighbouring units. This model is used to generate numerical bandshape calculations for the X-H absorption spectrum. At high T(>60 K), the model reproduces the temperature dependence of the O-H bandwidth for crystalline methanol. The low-T behaviour remains problematic.