From 2011 to 2014, the BESIII experiment collected about 5 fb$^{-1}$ data at
center-of-mass energies around 4 GeV for the studies of the charmonium-like and
higher excited charmonium states. By analyzing the di-muon process
$e^{+}e^{-}
ightarrowgamma_{
m ISR/FSR}mu^{+}mu^{-}$, the center-of-mass
energies of the data samples are measured with a precision of 0.8 MeV. The
center-of-mass energy is found to be stable for most of time during the data
taking.
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