A subtle aspect of the derivative couplings is that of translational invariance. As noted by Fatehi et al., expressions for h JK obtained from straightforward application of the pseudo-wavefunction approach are not translationally invariant, which is is problematic for nonadiabatic molecular dynamics simulations, and certain "electronic translation factors" were introduced to restore translational invariance. It was noted that the terms violating translational invariance arise from a kind of "Pulay force", meaning derivatives of the overlap matrix in an atom-centered Gaussian basis set. It was later demonstrated by Zhang and Herbert that the electronic translation factors introduced in Ref. 59 precisely annihilate the non-Hellmann-Feynman parts of h JK . The translationally-invariant Hellmann-Feynman expression is easy to state, at least in schematic form. Within the TDA, it is