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

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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 νt, the far-infrared transition νσ, the normal-infrared transition νs, and the combination bands νs ± νσ 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.