Twin growth in hexagonal close-packed zirconium is investigated at the atomic scale by modeling the various disconnections that can exist on twin boundaries. Thanks to a coupling with elasticity theory, core energies are extracted from atomistic simulations and the formation energy of isolated disconnection dipoles is defined. For twin systems where several disconnections can exist, because of this core contribution, the most stable disconnection is not always the one with the smallest Burgers vector. Crystallographic parameters of the disconnection with the lowest formation energy correlate well with twin modes observed experimentally. On the other hand, disconnection migration, characterized here by computing their migration energy and Peierls stress, does not appear critical for twin mode selection.