  We investigate the entanglement between electronic and vibrational degrees of
freedom produced by a vibronic coupling in a molecular system described in the
Born-Oppenheimer approximation. Entanglement in a pure state of the Hilbert
space $\cal{H}$$=$$\cal{H}$$_{el}$$\bigotimes$$\cal{H}$$_{vib}$ is quantified
using the von Neumann entropy of the reduced density matrix and the reduced
linear entropy. Expressions for these entanglement measures are derived for the
$2 \times N_v$ and $3 \times N_v$ cases of the bipartite entanglement, where 2
and 3 are the dimensions of the electronic Hilbert space $\cal{H}$$_{el}$, and
$N_v$ is the dimension of $\cal{H}$$_{vib}$. We study the entanglement dynamics
for two electronic states coupled by a laser pulse (a $2 \times N_v$ case),
taking as an example a coupling between the $a^3\Sigma_{u}^{+} (6s,6s)$ and
$1_g(6s,6p_{3/2})$ states of the Cs$_2$ molecule. The reduced linear entropy
expression obtained for the $3 \times N_v$ case is used to follow the
entanglement evolution in a scheme proposed for the control of the vibronic
dynamics in a Cs$_2$ cold molecule, implying the $a^3\Sigma_{u}^{+}(6s,6s)$,
$0_g^-(6s,6p_{3/2})$, and $0_g^-(6s,5d)$ electronic states, which are coupled
by a non-adiabatic radial coupling and a sequence of chirped laser pulses.
