Density open-shell character

The dimerisation energy for derivatives of 2 (ca. 35 kJ mol-1) is considerable, particularly in relation to the strength of intermolecular forces and some persistence is required in order to isolate derivatives of 2 which do not form 7T —7r dimers in the solid state. A survey of the monomeric derivatives has been published recently.26 Since the spin density distribution in 2 is rather insensitive to chemical tuning, approaches to inhibit dimerisation rely exclusively on structural modifications, which affect the nature of the intermolecular forces. Inclusion of sterically demanding groups, such as 13, 14 and 15 has proved partially successful (in the case of the diradical 14 one ring is involved in formation of a dimer, while the other retains its open shell character). 

So far, we have encountered the spin density as a variable both in the description of electronic structures of open-shell character and in the analysis of local quantities such as local spins or bond orders. For an accurate treatment of open-shell molecules, spin-spin interactions and chemical bonding, reliable spin densities are thus mandatory. However, the determination of rehable spin density distributions can be a difficult task in quantum chemistry [199, 200]. Examples of such difficult cases are iron nitrosyl complexes containing salen or porphyrin ligands for which DFT spin densities considerably depend on the approximate exchange-correlation functional [87,199]. 

We believe this behavior to be indicative of a calculation with open-shell character. The swapping of the HOMO positions between pairs of subsystems is actually equivalent to the exchange of electrons between these subsystems. On average, the situation probably amounts to the creation of unpaired electrons in two or more subsystems. The pseudo closed-shell density matrix formula in equation (14) is not equipped to deal with unpaired electrons, so convergence is difficult to achieve, and any results are nonphysical. 

Other properties in magnetic resonance may be mentioned here, for example, hyperfine couplings. As the isotropic hyperfine coupling also depends crucially on the spherical spin-density distribution around the nucleus in question, s-character in bonding and, thus, hybridization defects will be important. Obviously, for open-shell radicals the s-character of the singly occupied MO(s) is the most cmcial aspect, but spin polarization of doubly occupied MOs with core or valence s-character may also be relevant (e.g., when the singly occupied molecular orbital is of pure p-character at the given atom). 

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