Additive Decomposition of the Physical Components of the Magnetic Coupling from Broken Symmetry Density Functional Theory Calculations

The procedure to extract and identify from broken-symmetry density functional theory (BS-DFT) calculations the various components of the magnetic couplings in diradicals [J. Chem. Phys. 2012, 137, 114106] is re-examined. It is shown that this previous decomposition scheme fails for systems exhibiting large core polarization effects and hence becomes not additive in such cases. At variance, the new scheme which differs from the previous one in the assessment of the polarization effects is perfectly additive. As done previously, the direct exchange is calculated from the M-S = 1 and M-S = 0 restricted solutions. We show that allowing first the delocalization of the magnetic orbitals in the field of the closed shell frozen core furnishes a good evaluation of the kinetic exchange contribution to the magnetic exchange coupling, i.e. the intersite delocalization of the magnetic electrons in the low-spin state. In a second step, allowing the polarization of the core to take place in the field of the so-revised magnetic orbitals practically leads to the same total value of the magnetic coupling obtained by the brute-force BS-DFT calculation. The success of this decomposition is illustrated on a representative series of inorganic and organic diradicals. The obtained quasi-additivity of the effects is rationalized thanks to a careful theoretical analysis of the broken-symmetry solutions.