  We present a critical analysis of the popular fragment-orbital
density-functional theory (FO-DFT) scheme for the calculation of electronic
coupling values. We discuss the characteristics of different possible
formulations or 'flavors' of the scheme which differ by the number of electrons
in the calculation of the fragments and the construction of the Hamiltonian. In
addition to two previously described variants based on neutral fragments, we
present a third version taking a different route to the approximate diabatic
state by explicitly considering charged fragments. In applying these FO-DFT
flavors to the two molecular test sets HAB7 (electron transfer) and HAB11 (hole
transfer) we find that our new scheme gives improved electronic couplings for
HAB7 (-6.2% decrease in mean relative signed error) and greatly improved
electronic couplings for HAB11 (-15.3% decrease in mean relative signed error).
A systematic investigation of the influence of exact exchange on the electronic
coupling values shows that the use of hybrid functionals in FO-DFT calculations
improves the electronic couplings, giving values close to or even better than
more sophisticated constrained DFT calculations. Comparing the accuracy and
computational cost of each variant we devise simple rules to choose the best
possible flavor depending on the task. For accuracy, our new scheme with
charged-fragment calculations performs best, while numerically more efficient
at reasonable accuracy is the variant with neutral fragments.
