Equivalence between perturbatively calculated transition moments

We have shown that equivalence between dipole length and dipole velocity transition moments is obtained in an order by order polarization propagator calculation of excitation energies and transition moments. Also, the Thomas–Reiche–Kuhn sum rule is shown to be fulfilled order by order. Numerical examples show good agreement between dipole length and velocity transition moments both in first and second order polarization propagator calculations using finite basis sets with approximately 50 Slater type orbitals for atoms and diatomic molecules.