  The quantum superposition principle has been extensively utilized in the
quantum mechanical description of the bonding phenomenon. It explains the
emergence of delocalized molecular orbitals and provides a recipe for the
construction of near-exact electronic wavefunctions. On the other hand, its
existence in composite systems may give rise to nonclassical correlations that
are regarded now as a resource in quantum technologies. Here, we approach the
electronic ground states of three prototypical molecules from the point of view
of fermionic information theory. For the first time in the literature, we
properly decompose the pairwise orbital correlations into their classical and
quantum parts in the presence of superselection rules. We observe that quantum
orbital correlations can be stronger than classical orbital correlations though
not often. Also, quantum orbital correlations can survive even in the absence
of orbital entanglement depending on the symmetries of the constituent
orbitals. Finally, we demonstrate that orbital entanglement would be
underestimated if the orbital density matrices were treated as qubit states.
