  In order to realize more sensitive eEDM measurement, it would be worthwhile
to find some new laser-cooled molecules with larger internal effective electric
field (E$_{eff}$), higher electric polarizability and longer lifetime of the
eEDM measurement state. Here we explore the merits of mercuric monofluoride
($^{202}Hg^{19}F$, X$^ 2 {\Sigma}_{1/2}$) for its potential of laser cooling
and eEDM measurement. We theoretically investigated the electronic,
rovibrational and hyperfine structures and verified the highly diagonal
Franck-Condon factors (FCFs) of the main transitions by the Rydberg-Klein-Rees
inversion (RKR) method and the Morse approximation. Hyperfine manifolds of the
X$^ 2 {\Sigma}_{1/2} (\nu=0$) rotational states were examined with the
effective Hamiltonian approach and a feasible sideband modulation scheme was
proposed. In order to enhance optical cycling, the microwave remixing method
was employed to address all the necessary levels. The Zeeman effect and the
hyperfine structure magnetic g factors of the X$^ 2 {\Sigma}_{1/2}
(\nu=0$,$\mathit{ N } $=1) state were studied subsequently. Finally, its
statistical sensitivities for the eEDM measurement were estimated respectively
to be about $9\times 10^{-31} e\bullet cm $ (the laser cooled transverse beam
experiment), $2\times 10^{-31} e\bullet cm$ (the fountain experiment) and
$1\times 10^{-32}$ e\bullet cm (experiment with trapped cold molecules),
indicating that $^{202}Hg^{19}F$ might be another promising eEDM candidate when
compared with the most recent ThO result of $d_{ e } = (4.3 \pm 3.1_{ stat }
\pm 2.6_{ syst })\times 10^{-30} e\bullet cm$ (Nature, 562, 355 (2018)). In
addition, the possibility of direct Stark decelerating of the HgF radical was
also discussed.
