  We study a LiCs strongly-interacting molecular gas loaded into an
one-dimensional optical lattice at quarter filling. The molecules are in the
lowest electronic and vibrational state, $X^{1}\Sigma$ ($\nu=0$). Due to the
large intermolecular distance and low filling, dipole-dipole interaction in the
nearest-neighbor approximation governs the dynamics of the rotational
excitations. For low DC electric field strengths, the full set of rotational
levels $N=0,1$ must be taken into account, nevertheless, our calculations show
that very weak fields act as field-selectors disclosing two- and three-level
systems out of the original four-level one. The dynamics and the generated von
Neumann entanglement entropy among the internal rotational states throughout
the evolution are presented for low, moderate and strong fields . We observe a
sharp and monotonous growth of the entanglement as the dynamics take place
showing the potential of these molecular systems to be used in quantum
information protocols. The numerical simulations are performed by means of the
Time-Evolving Block Decimation algorithm based on the Matrix Product State
formalism and the Susuki-Trotter decomposition.
