  Entanglement is one of the most fascinating concepts of modern physics. In
striking contrast to its abstract, mathematical foundation, its practical side
is, however, remarkably underdeveloped. Even for systems of just two orbitals
or sites no faithful entanglement measure is known yet. By exploiting the spin
symmetries of realistic many-electron systems, we succeed in deriving a closed
formula for the relative entropy of entanglement between electron orbitals. Its
broad applicability in the quantum sciences is demonstrated: (i) in light of
the second quantum revolution, it quantifies the true physical entanglement by
incorporating the crucial fermionic superselection rule (ii) an analytic
description of the long-distance entanglement in free electron chains is found,
refining Kohn's locality principle (iii) the bond-order wave phase in the
extended Hubbard model can be confirmed, and (iv) the quantum complexity of
common molecular bonding structures could be marginalized through orbital
transformations, thus rationalizing zero-seniority wave function ansatzes.
