  We report the first measurements of the moments -- mean ($M$), variance
($\sigma^{2}$), skewness ($S$) and kurtosis ($\kappa$) -- of the net-charge
multiplicity distributions at mid-rapidity in Au+Au collisions at seven
energies, ranging from $\sqrt {{s_{\rm NN}}}$= 7.7 to 200 GeV, as a part of the
Beam Energy Scan program at RHIC. The moments are related to the thermodynamic
susceptibilities of net-charge, and are sensitive to the proximity of the QCD
critical point. We compare the products of the moments, $\sigma^{2}/M$,
$S\sigma$ and $\kappa\sigma^{2}$ with the expectations from Poisson and
negative binomial distributions (NBD). The $S\sigma$ values deviate from
Poisson and are close to NBD baseline, while the $\kappa\sigma^{2}$ values tend
to lie between the two. Within the present uncertainties, our data do not show
non-monotonic behavior as a function of collision energy. These measurements
provide a distinct way of determining the freeze-out parameters in heavy-ion
collisions by comparing with theoretical models.
