FREQUENCIES OF STRETCHING AND BENDING VIBRATIONS FOR TWO-DIMENSIONAL H-BOND MODEL IN IR SPECTRA

Abstract

On the base of one-dimensional Morse potential for the first time the surface of the two-dimensional asymmetric potential for proton of hydrogen bond have been received $\begin{array}{lll}U&=&U_{0} \{\exp (- 2a [(R/2-x)^{2} + (y+y_{0})^{2}]^{1/2}-x_{0}) + \exp (-2a [(R/2+x)^{2} + (y-y_{0})^{2}]^{1/2}-x_{0})\\ &&- 2\exp (-a [(R/2-x)^{2} + (y+y_{0})^{2}]^{1/2}-x_{0}) - 2\exp (-a [(R/2+x)^{2} + (y-y_{0})^{2}]^{1/2}-x_{0})\},\end{array}$ where $U_{0}, a, x_{0}$ and $y_{0}$ are parameters of the one-dimensional one-minimum potential. According to this potential and the method been developed $previously^{1}$ the free energy F of the H-bond chain system has been calculated. From minimality condition of F the system of a two equations for the both proton frequencies has been received. The dependencies of this frequencies on the crystal temperature and on the length of H-bond were obtained. In the calculations the mutual influence of the stretching and bending vibrations was taken into account, which is of special interest near the H-bond critical length. The agreement of the theory and experimental data was obtained. It was shown that the dependence of the bending vibrations on H-bond length has an opposite character as compared with that of the stretching $one^{2}$. 1. S. Tanaka, Phys. Rev. B42, 10488 (1990). 2. E. A. Shadchin and A. I. Barabash, J. Mol. Struc. 325, 65 (1994).