Unpaired electrons, spin polarization, and bond orders in radicals from the 2-RDM in orbital spaces: Basic notions and testing calculations



Adopting the second-order reduced density matrix level, the conventional α- and β-spin populations in radicals are split into paired and unpaired or electropon (referring to the simultaneous occurrence of an electron and a hole of opposite spins in an orbital) populations. This analysis gives the possibility to distinguish the (un)favorable for chemical bonding electronic interactions by means of positive or negative Coulomb and/or Fermi correlations of two electropons. To overcome the conceptual difficulties originated from the subtle superposition of unpaired electrons due to spin density and those responsible for chemical bonding, we use the notion of properly unpaired electrons. The quantity describing this notion provides a global picture for the ability of electrons of a given orbital to form covalent bonds with the electrons of all remaining orbitals. More detailed information, concerning the behavior of electrons in two distinct target orbitals, is obtained by means of the two-electropon correlations. As shown, the boundary values of the used quantities are physically meaningful, and the whole theory is tested from various points of view concerning: localized and delocalized radical centers, orthogonal and nonorthogonal orbitals, uncorrelated and correlated levels, Coulomb and Fermi correlations. We also check the electropon based analysis by investigating the spin polarization effects and bond orders in radicals. The tests are achieved for well-known radicals, and to preserve the stability of the numerical results and the invariance of the obtained conceptual pictures, we used natural basis sets introduced within the natural bond orbital methodology. © 2014 Wiley Periodicals, Inc.