  The high effective electric field ($E_\mathrm{eff}$) experienced by the
unpaired electron in an atom or a molecule is one of the key ingredients in the
success of electron electric dipole moment (eEDM) experiment and its precise
calculation require a very accurate theory. We, therefore, employed the
Z-vector method in the relativistic coupled-cluster framework and found that
HgH has a very large $E_\mathrm{eff}$ value (123.2 GV/cm) which makes it a
potential candidate for the next generation eEDM experiment. Our study also
reveals that it has a large scalar-pseudoscalar ${\mathcal{P,T}}$-violating
interaction constant, $W_\mathrm{s}$ = 284.2 kHz. To judge the accuracy of the
obtained results we have calculated parallel and perpendicular magnetic HFS
constants and compared with the available experimental values. The results of
our calculation are found to be in nice agreement with the experimental values.
Therefore, by looking at the HFS results we can say that both $E_\mathrm{eff}$
and $W_\mathrm{s}$ values are also very accurate. Further, We have derived the
relationship between these quantities and the ratio which will help to get
model independent value of eEDM and S-PS interaction constant.
