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In this review paper the definition of the elements of the molecular point group are carefully considered. It is shown that certain terms in the molecular Hamiltonian are not invariant to these operations and, hence, these terms can break the point group symmetry. The symmetry labelling of the energy levels of H2, H2O and CH4 are studied in detail in order to demonstrate this point. It is shown that the rotational energy levels of molecules can be satisfactorily labelled using the Complete Nuclear Permutation Inversion Group or the Molecular Symmetry Group as appropriate.

Ten rotation–vibration transitions in the ν2 (bending) fundamental band of CH2 in its 3B1 ground electronic state have been measured and assigned using the technique of intracavity CO2 laser magnetic resonance (LMR) spectroscopy in the region 880–1090 cm−1. Using the present data, and the microwave and far‐infrared LMR measurements of pure rotational transitions, an effective bending potential energy curve has been derived for CH2 using the semirigid bender Hamiltonian. The bending frequency of CH2 is determined to be ν2=963.0987(4) cm−1, which is considerably lower than previous theoretical and experimental estimates.

Thirteen pure rotational transitions of CH2 in its X 3B1 ground vibronic state have been measured and assigned using the technique of far‐infrared laser magnetic resonance (LMR) spectroscopy. The energy levels thus determined led to the prediction and subsequent detection by microwave spectroscopy of a further rotational transition 404–313, at lower frequency (∼70 GHz). The analysis of these observations yields precise rotational constants as well as spin–spin, spin‐rotation, and hyperfine interaction parameters for gas phase CH2. Its rotational spectrum may enable interstellar CH2 to be detected by radio astronomy. Two rotaional transitions within the v1=1 excited vibrational state have also been identified in the LMR spectrum. Future observations of vibrationally excited CH2 may afford a means of determining the singlet–triplet splitting in methylene, and studies of CD2 and CHD will result in improved structural determinations.