The theory of transformation relations between states of Born Oppenheimer and weak coupling approximations is developed for polyatomic molecules. The relations are a generalization of frame transformation relations used by Chang and Fano for symmetric-top molecules, and they lead to a more convenient symmetry labeling system than was previously available. A key internal symmetry label (named "soul") is defined so that it remains a constant label for frame transformation relations, and is conserved during vibronic transitions, ionization, and even dissociation provided the nuclear spin-rotation interaction is relatively small. Various nomograms, graphs, and tableaus associated with the soul label make it easy to predict and visualize the form of many types of complex high-resolution spectra. Simplified procedures are given for obtaining selection rules, statistical weights, and matrix elements of multipole operators for common molecules having various point symmetries. Simplifications of computational theory using the new level cluster bases for high $J$ are discussed.

DOI:https://doi.org/10.1103/RevModPhys.50.37