  Optical atomic clocks using highly-charged ions hold an intriguing promise of
metrology at the 19th significant figure. Here we study transitions within the
$4f^{12}$ ground-state electronic configuration of highly charged ions. We
consider isotopes lacking hyperfine structure and show that the detrimental
effects of coupling of electronic quadrupole moments to gradients of trapping
electric field can be effectively reduced by using specially chosen virtual
clock transitions. The estimated systematic fractional clock accuracy is shown
to be below $10^{-19}$.
