Vibration-rotation theory and isotopic substitution in nonlinear triatomic molecules

In the interpretation of high-resolution data it is helpful to be able to relate the experimentally determined molecular constants, such as rotational constants, centrifugal distortion constants, and vibration-rotation interaction constants of a given molecule to those of its isotopically substituted variants. Results concerning the symmetric nonlinear triatomic molecule (XYX) have been given through the second order of approximation by previous workers. In this paper, extensions of the work to the fourth order of approximation and to the nonsymmetric nonlinear triatomic molecule (XYZ) are considered. These extensions are found to increase the algebraic complexity of the problem considerably, and results can generally be given in implicit form only. The approach used is one that emphasizes the isotopic invariants of the problem, i.e., those expressions which remain unchanged when applied to the various isotopic modifications of a given molecule under the assumption that the molecular force field and the molecular geometry remain unchanged under isotopic substitution.