We report ab initio relativistic correlation calculations of potential curves for ten low-lying electronic states, the effective electric field on the electron, and hyperfine constants for the Δ13 state of a cation of the heavy transition metal fluoride Hf F+, which it is suggested can be used in experiments to search for the electric dipole moment of the electron. It is shown that Hf F+ has a deeply bound Σ+1 ground state; its dissociation energy is De =6.4 eV. The Δ13 state is obtained as the relatively long-lived first excited state lying about 0.2 eV higher. The calculated effective electric field Eeff = Wd Ω acting on an electron in this state is 5.84× 1024 Hze cm.