  We report first ab initio relativistic correlation calculations of potential
curves for ten low-lying electronic states, effective electric field on the
electron and hyperfine constants for the ^3\Delta_1 state of cation of a heavy
transition metal fluoride, HfF^+, that is suggested to be used as the working
state in experiments to search for the electric dipole moment of the electron.
It is shown that HfF^+ has deeply bound ^1\Sigma^+ ground state, its
dissociation energy is D_e=6.4 eV. The ^3\Delta_1 state is obtained to be the
relatively long-lived first excited state lying about 0.2 eV higher. The
calculated effective electric field E_eff=W_d|\Omega| acting on an electron in
this state is 5.84*10^{24}Hz/(e*cm)
