Term Structure of the Non-Collinear Triatomic Molecule of TypeX2Y

Group theory methods are applied to the molecule of type $X_{2}Y$ (e.g., ${\mathrm{H}}_2$O, S${\mathrm{O}}_2$) in which the equilibrium configuration of the nuclei is assumed to be that of an isosceles triangle. Electronic motion, vibration of the nuclei and rotation are successively taken into account, and symmetry with respect to interchange of the two equal nuclei, and with respect to inversion at the origin, is considered. Tables are given which allow one to determine, when the electronic, vibrational and rotational symmetries are known, the symmetry of a given term with respect to interchange of nuclei and inversion. Selection rules for all of the types of symmetry except rotational, are given; the selection rules of the asymmetrical rotator are then obtained from these, with the aid of the tables.