  A recent development in quantum chemistry has established the quantum mutual
information between orbitals as a major descriptor of electronic structure.
This has already facilitated remarkable improvements of numerical methods and
may lead to a more comprehensive foundation for chemical bonding theory.
Building on this promising development, our work provides a refined discussion
of quantum information theoretical concepts by introducing the physical
correlation and its separation into classical and quantum parts as distinctive
quantifiers of electronic structure. In particular, we succeed in quantifying
the entanglement. Intriguingly, our results for different molecules reveal that
the total correlation between orbitals is mainly classical, raising questions
about the general significance of entanglement in chemical bonding. Our work
also shows that implementing the fundamental particle number superselection
rule, so far not accounted for in quantum chemistry, removes a major part of
correlation and entanglement previously seen. In that respect, realizing
quantum information processing tasks with molecular systems might be more
challenging than anticipated.
