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Searching for an accurate optical clock which can serve as a better timestandard than the present day atomic clock is highly demanding from severalareas of science and technology. Several attempts have been made to built moreaccurate clocks with different ion species. In this article we discuss theelectric quadrupole and hyperfine shifts in the $5d^{9}6s^{2}^{2}D_{5/2}(F=0,m_{F}=0)\leftrightarrow5d^{10}6s ^{2}S_{1/2}(F=2,m_{F}=0)$clock transition in $ ^{199}Hg^{+}$, one of the most promising candidates fornext generation optical clocks. We have applied Fock-space unitarycoupled-cluster (FSUCC) theory to study the electric quadrupole moment of the$5d^{9}6s^{2} ^{2}D_{5/2}$ state and magnetic dipole hyperfine constants of$5d^{9}6s^{2} ^{2}D_{3/2,5/2}$ and $5d^{10}6s^{1} ^{2}S_{1/2}$ statesrespectively of $ ^{199}Hg^{+}$. We have also compared our results withavailable data. To the best of our knowledge, this is the first time a variantof coupled-cluster (CC) theories has been applied to study these kinds ofproperties of $Hg^{+}$and is the most accurate estimate of these quantities todate.

A relativistic unitary coupled-cluster study of electric quadrupole moment and magnetic dipole hyperfine constants of ^{199}Hg^{+}