  Electron exchange and correlations emerging from the coupling between ionic
vibrations and electrons are addressed. Spin-dependent electron-phonon coupling
originates from the spin-orbit interaction, and it is shown that such
electron-phonon coupling introduces exchange splitting between the spin
channels in the structure. By application of these results to a model for a
chiral molecular structure mounted between metallic leads, the chirality
induced spin selectivity is found to become several tens of percents using
experimentally feasible parameters.
