Optimal generalized internal vibrational coordinates for symmetrical linear triatomic molecules

The use of generalized internal vibrational coordinates to describe vibrational motions in symmetrical linear triatomic molecules is considered. These coordinates are defined as the magnitudes of two generalized internal vectors and the angle formed between them, and they depend on two parameters which can be properly optimized. We derive an analytical expression which provides the optimal values of these parameters for linear symmetrical triatomic molecules. The validity of this expression is checked by making variational calculations of vibrational energy levels for the CO2 and CS2 molecules.