Two-Dimensional Double-Minimum Model of Hydrogen Bonding: The Symmetric Case

Abstract

A linear AH···A model, representing hydrogen bonding, which incorporates a double minimum in the potential energy, and interaction between the symmetric and antisymmetric stretching motion, is examined. Using harmonic‐oscillator functions as a basis for expansion, solutions of the two‐dimensional wave equation are obtained. Three tests for the convergence of the matrix expansion are satisfied. Using ranges of parameters appropriate to hydrogen‐bonded systems, the combined effects of tunneling and vibrational interaction on the tunneling transition ${\nu }_t$ , the far‐infrared transition ${\nu }_{\sigma }$ , the normal‐infrared transition ${\nu }_s$ , and the combination bands ${\nu }_s{\mathrm{\hspace{0.17em}\pm \hspace{0.17em}\nu }}_{\sigma }$ are determined. The effect of replacement of H by D is also examined. The validity of applying the Stepanov approximation to these systems is tested.