Metaphenylene-based nitroxide diradicals: a protocol to calculate intermolecular coupling constant in a one-dimensional chain.

Intramolecular magnetic exchange coupling constants are determined for seven isolated metaphenylene-based dinitroxide diradicals by unrestricted density functional methodology (UDFT) using a number of hybrid functionals such as B3LYP, B3LYP-D3, M06-2X, HSE, and LC-ωPBE. Geometry optimizations for both triplet and broken symmetry solutions are performed with the 6-311G(d,p) basis set for all the molecules. In all cases, B3LYP somewhat overestimates the coupling constant, and M06-2X produces a more realistic value. The range-separated HSE and LC-ωPBE functional yield large deviations from experiment. The nature of spin coupling agrees with the spin alternation rule and the calculated spin densities, in conjunction with the McConnell rule. It can also be explained in terms of the nondisjoint Single Occupied Molecular Orbital effect. Furthermore, it correlates with the calculated NICS(1) isotropic and zz and hyperfine coupling constants. We also put forward a method for the determination of the intramolecular (J) and intermolecular (J') coupling constants from quantum chemical calculations on a one-dimensional chain of weakly bound diradicals. Two expressions are derived for the energies of different spin states in terms of J and J'. Exemplary UDFT computations are done on the N-mers (N = 2-6) of two diradicals for which the crystal coordinates are available. The intramolecular and intermolecular coupling constants are determined from the calculated UDFT energies. These are indeed in general agreement with the measured coupling constants.