  We develop an analytic-gradient based method for relativistic coupled-cluster
calculations of effective electric field, $\mathcal{E}_{\text{eff}}$, with
improved efficiency and robustness over the previous state of the art. The
enhanced capability to calculate this time-reversal symmetry violation
sensitivity parameter enables efficient screening of candidate molecules for
the electron electric dipole moment (eEDM) search. As examples, the
|$\mathcal{E}_{\text{eff}}$| values of metal methoxides including BaOCH$_3$,
YbOCH$_3$, and RaOCH$_3$ are shown to be as large as those of the corresponding
fluorides and hydroxides, which supports the recent proposal of using these
symmetric-top molecules to improve the sensitivity of eEDM measurements. The
computational results also show that molecules containing late actinide
elements, NoF, NoOH, LrO, and LrOH$^+$, exhibit particularly large
|$\mathcal{E}_{\text{eff}}$| values of around 200 GV/cm.
