  Recent proposals of measuring bipartite Renyi entropy experimentally involve
techniques that hold exactly for non-interacting quantum particles. Here we
consider the difference between such measurements and the actual Renyi entropy
for ground state fermion ab initio molecular systems. To calculate various
entanglement measures we extended several different techniques for use with
variational Monte Carlo, Hartree-Fock and quantum chemistry methods. Our
results show that in systems with strong electron correlations the Renyi
entropy may not be accurately determined with the proposed measurements. In
addition, we find significant physical insight can be gained by calculating
entanglement properties in molecular systems. We see that the Renyi entropy and
the entanglement Hamiltonian encode information about the character of the
covalent bonds in a molecular system and that such information may lead to
better descriptions of bonded systems that have been traditionally hard to
describe with standard techniques. In particular our results for the C$_{2}$
dimer suggests all eight valence electrons play a significant role in covalent
bonding.
