Symmetry-based study of molecular electronic, vibrational, rotational, and nuclear-spin states

The electronic, vibrational, rotational, and nuclear-spin states of a molecule are discussed in terms of the symmetry, one of the most fundamental ideas in physics. First, the author shows how to correctly build up the electronic terms of a diatomic molecule with use of the three conventional ways characterized by the electronic configuration, separated atoms, and united atom. In particular, the transformation properties of terms under reflection are focused on. Next, the difference in symmetry lowering upon vibration between diatomic and polyatomic molecules is clarified, and specific infrared-inactive modes of the latter molecules are shown to absorb infrared light owing to the high order terms in the Taylor expansion of the dipole operator with respect to the normal coordinates. Finally, the author relates the molecular symmetry to the existence of the identical nuclei and shows how their permutation symmetry yields coupling of rotational and nuclear-spin states. After the description of the molecular rotation in a symmetric crystalline field, the author reviews a recent infrared-spectroscopic investigation of nuclear spin conversion in H₂O trapped by crystalline Ar, where temperature dependence of its conversion rate is discussed on the basis of a new model of the phonon-mediated relaxation. (author)