  We characterize both entanglement and quantum coherence in a molecular system
by connecting the linear entropy of electronic-nuclear entanglement with
Wigner-Yanase skew information measuring vibronic coherence and local quantum
uncertainty on electronic energy. Linear entropy of entanglement and
quantifiers of quantum coherence are derived for a molecular system described
in a bipartite Hilbert space H=Hel x Hvib of finite dimension Nel x Nv, and
relations between them are established. For the specific case of the
electronic-vibrational entanglement, we find the linear entropy of entanglement
as having a more complex informational content than the von Neumann entropy. By
keeping the information carried by the vibronic coherences in a molecule,
linear entropy seizes vibrational motion in the electronic potentials as
entanglement dynamics. We analyze entanglement oscillations in an isolated
molecule, and show examples for the control of entanglement dynamics in a
molecule through the creation of coherent vibrational wave packets in several
electronic potentials by using chirped laser pulses.
