text: The transition dipole moment is useful for determining if transitions are allowed under the electric dipole interaction. For example, the transition from a bonding  orbital to an antibonding  orbital is allowed because the integral defining the transition dipole moment is nonzero. Such a transition occurs between an even and an odd orbital; the dipole operator, , is an odd function of , hence the integrand is an even function.  The integral of an odd function over symmetric limits returns a value of zero, while for an even function this is not necessarily the case.  This result is reflected in the parity selection rule for electric dipole transitions. The transition moment integral
  of an electronic transition within similar atomic orbitals, such as s-s or p-p, is forbidden due to the triple integral returning an ungerade (odd) product. Such transitions only redistribute electrons within the same orbital and will return a zero product. If the triple integral returns a gerade (even) product, the transition is allowed.