Additive Decomposition of the Physical Components
of the Magnetic Coupling from Broken Symmetry Density Functional Theory
Calculations
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Abstract
The procedure to extract and identify
from broken-symmetry density
functional theory (BS-DFT) calculations the various components of
the magnetic couplings in diradicals [<i>J. Chem. Phys.</i> <b>2012</b>, <i>137</i>, 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 <i>M</i><sub>S</sub> = 1 and <i>M</i><sub>S</sub> = 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