The selection rule of electronic multipole transitions derived from symmetry analysis

There is an only possibility to derive the symmetrical wave function, i.e. the symmetrized basis function, for each irreducible representation based on the group analysis, and so is for the selection rule for electronic multipole transitions: E1, E2 and E3. The present work devotes to derive the selection rule for electronic multipole transitions for group C_2V and D_2h. The selection rule derived from angular momentum is one of special cases. It is in agreement with the calculations of H₂O and CC molecules by method SAC-CI/6-31G. (authors)