A note on obtaining vibrational mixing parameter from average bending energy criterion

An analytical expression is given for the mixing parameter that characterizes the vibrational eigen vector matrix in the second-order case based on the criterion of minimization of average bending energy of molecular vibration. The expression, which is derived on the assumption that the parameter is small, contains only molecular geometry and the two normal frequencies of the vibrational species. Bent symmetric XY₂ molecular system is treated as an example and the calculated values of the parameter are in good agreement with the standard results.