Investigation of the nuclear magnetic quadrupole moment (MQM) is an excellent way to reveal the new physics in the hadron sector of matter. Therefore, we investigate the violation of parity (P) and time-reversal (T) invariance induced by the MQM of the( 201) Hg nucleus in the HgH molecule, which has been proposed as a very promising candidate for the experimental search of the electric dipole moment of electron [M. G. Kozlov and A. Derevianko, Phys. Rev. Lett. 97, 063001 (2006)]. We report the precise value of the molecular parameter, W-M, associated with the P, T-odd nuclear MQM-electron interaction in (HgH)-Hg-201 using the four-component relativistic coupled-cluster method. This parameter is required to interpret the experimental P, T-odd frequency shift in terms of the MQM of nuclei. Furthermore, the magnetic hyperfine structure (HFS) constants of the molecule are computed at the same level of theory. We also study the role of core-correlating functions and the virtual energy functions in the calculations of the HFS constant and W-M. The most reliable value of W(M )in HgH is obtained as 3.22 x 10 (33) Hz/e cm (2) with an uncertainty of around 6%.

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