  We study minimum-energy pathways (MEPs) between the branches of metastable
helical structures in chiral nematic liquid crystals (CNLCs)subjected to the
electric field applied across the cell. By performing stability analysis we
have found that, for the branches with non-vanishing half-turn number, the
threshold (critical) voltage of the Freedericksz transition is an increasing
function of the free twisting wave number. The curves for the threshold voltage
depend on the elastic anisotropy and determine the zero-field critical free
twisting number where the director out-of-plane fluctuations destabilize the
CNLC helix. For each MEP passing through a first order saddle point we have
computed the energy barrier as the energy difference between the saddle-point
and the initial structures at different values of the applied field. In our
calculations, where the initial approximation for a MEP at the next step was
determined by the MEP obtained at the previous step, the electric field
dependence of the energy barrier is found to exhibit the hysteresis. This is
the hysteresis of electrically driven transition of the saddle-point
configuration between the planar and the tilted structures involving
out-of-plane director deformations. It turned out that, by contrast to the
second-order Freedericksz transition, this transition is first order and we
have studied how it depends on the zenithal anchoring energy strength.
