  Searching for an accurate optical clock which can serve as a better time
standard than the present day atomic clock is highly demanding from several
areas of science and technology. Several attempts have been made to built more
accurate clocks with different ion species. In this article we discuss the
electric 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 for
next generation optical clocks. We have applied Fock-space unitary
coupled-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 $5d^{10}6s^{1} ^{2}S_{1/2}$ states
respectively of $ ^{199}Hg^{+}$. We have also compared our results with
available data. To the best of our knowledge, this is the first time a variant
of coupled-cluster (CC) theories has been applied to study these kinds of
properties of $Hg^{+}$and is the most accurate estimate of these quantities to
date.
