  Highly charged liquid droplets are unstable above the critical charge
squared-to-volume ratio given by the Rayleigh limit. The instability leads to
ion ejection from jets formed on the droplet's surface. Despite the many
experiments that have been performed to capture the jet formation the precise
fission mechanism has not yet been observed because of its brief transient
nature. Here, we present the first atomistic simulations that reveal the
mechanism of Rayleigh fission. We demonstrate that ion ejection takes place
through a drop's deformation from a spherical into a distinct shape that
contains a conical protrusion. We assert that the latter state is a free energy
minimum along an order parameter that measures the degree of droplet
asphericity. The charged droplet's long-time evolution proceeds by alternating
between the two minima above and below the critical value that are reached
through solvent evaporation and ion ejection, respectively. For the first time,
this mechanism allows one to explain the nature of the progeny droplets and the
percentage of charge lost during fission. We determine that the cone half-angle
is close to the value predicted from the solution of the electrostatic equation
for the dielectric liquid. It is found that the conical deformation is
independent of the effect of electrohydrodynamic forces reported in
experiments. Contrary to the experimental observations of two diametrically
opposite jets for droplets suspended in the electric field, we found that a
single jet is formed at the Rayleigh limit. This indicates that super-charged
droplet states may have been detected in the experiments.
