Abstract

The nonlinear triatomic molecule of the type $X{Y}_{2}$ has been treated and the expression for the energy of vibration has been obtained when second, third and fourth powers of the coordinates are considered in the potential function. The higher powers of the coordinates have been introduced by the use of first and second order perturbation theory. A method has also been outlined for treating the more complicated types of kinetic energy expressions by a perturbation method. Using the results of this treatment there have been evaluated for the water molecule, from the known spectrum, the primary binding constants and vibration frequencies for infinitesimal amplitudes. Finally, a prediction of the infrared vibration spectrum of the symmetrically substituted heavy water has been made.