Computation of electronic transition moments: the length versus the velocity representation

Summary We have compared transition moments (TMs) obtained using the length and velocity representations for transitions from the ground state of H₂ to the lowest two¹ _u and two¹ _u ⁺ Rydberg states, theA ¹–X ¹⁺ transition in BH, and theA ¹ _u –X ¹ _g ⁺ transition in C₂. For H₂, the TMs in the length and velocity representations agree well even in cases where the one-particle basis is incomplete and the TM has not converged. For BH and C₂ the TM in the length representation converges rapidly with improvements in the one-particle basis set and is insensitive to inner-shell correlation. In contrast, in the velocity representation convergence with improvements in the one-particle basis is much slower, especially for C₂, and the TMs are significantly changed by inner-shell correlation. Thus the difference between the TMs in the length and velocity representations would not appear to be a viable diagnostic of TM convergence.