  We report ab initio relativistic correlation calculations of potential curves
and electric dipole transition moments for ten low-lying electronic states,
effective electric field on the electron, hyperfine constants and radiative
lifetimes for the $^3\Delta_1$ state of cation of the heavy transition metal
fluoride HfF$^+$, which it is suggested to be used in experiments to search for
the electric dipole moment of the electron. It is obtained 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 as the relatively long-lived, with
lifetime equal to about 0.4 s.,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 $5.84*10^{24} Hz/{e*cm}$. The obtained hyperfine
constants are $A_{\parallel}= -1239$ MHz for the $^{177}$Hf nucleus and
$A_{\parallel}= -58.1$ MHz for the $^{19}$F nucleus.
