Order of Coulomb and Fermi pairs: application in a π-system

The order of electron pairs with anti-parallel (Coulomb) and parallel (Fermi) spins, existing in a molecule, is quantified and compared. Information entropies, providing a measure of the (dis)order of Coulomb and Fermi pairs, are defined. The corresponding probabilities are calculated in orbital spaces appropriate for population analysis, as the natural atomic orbitals. The π-bonding of butadiene molecule is considered as a model system, and the (dis)order of electron pairs is examined in both Hartree–Fock and CI levels. It turns out that chemical bonding imposes an increase of the order of both Coulomb and Fermi pairs; however, Fermi pairs are more ordered, that is involve more structure than the Coulomb ones; this holds remarkably in all approximation levels.