  The electric quadrupole moment for the $4d ^2D_{5/2}$ state of
$\mathrm{^{88}Sr^+}$, one of the most important candidates for an optical
clock, has been calculated using the relativistic coupled-cluster theory. The
result of the calculation is presented and the important many-body
contributions are highlighted. The calculated electric quadrupole moment is
$(2.94\pm0.07)ea_{0}^{2}$, where $a_{0}$ is the Bohr radius and $e$ the
electronic charge while the measured value is $(2.6\pm0.3)ea_{0}^{2}$. This is
so far the most accurate determination of the electric quadrupole moment for
the above mentioned state.
