  We compute, from first-principles, the frequency of the E2g, Gamma phonon
(Raman G-band) of graphene, as a function of the charge doping. Calculations
are done using i) the adiabatic Born-Oppenheimer approximation and ii)
time-dependent perturbation theory to explore dynamic effects beyond this
approximation. The two approaches provide very different results. While, the
adiabatic phonon frequency weakly depends on the doping, the dynamic one
rapidly varies because of a Kohn anomaly. The adiabatic approximation is
considered valid in most materials. Here, we show that doped graphene is a
spectacular example where this approximation miserably fails.
