Through bond interaction of two radical centers: Analysis of the spin polarization and related mechanisms in linear π diradicals

Linear π diradicals are treated as a through-bond interaction of two radical centers. The ferromagnetic or antiferromagnetic electron coupling is examined by means of an analytic study of the interaction of two methylene groups (the radical centers) through a butadiene (the bridge). The interaction of each radical center with the bridge is treated at the Hartree–Fock level; the obtained NBMO’s (or magnetic orbitals) A and B are of two types: (i) A and B are of the same parity (i.e., with common delocalization coefficients on the same AO’s of the bridge) for the first class of polyenes with m=m*±2 (m and m* are the unstarred and starred positions). (ii) A and B are of a different parity for the second class of polyenes with m=m*. The method of the direct calculation of the singlet–triplet transition energy is used at configuration interaction level, in order to elucidate the ferromagnetic or antiferromagnetic behavior of the various electronic mechanisms. Numerical calculations show that double spin polarization (DSP) controls the whole singlet–triplet energy difference; this is then analyzed exhaustively in the framework of RHF plus CI methods; a clear physical interpretation is then given in the language of UHF methods. The two spin densities induced in the bridge from the two radical centers are: (i) in phase, for the triplet state of the first class of polyenes and for the singlet state of the second class; the two spin polarizations are additive and the spin fluctuations very high; (ii) out of phase for the singlet state of the first class of polyenes and for the triplet state of the second class; the two spin polarizations are competitive without high spin fluctuations. The analytical study generalizes our conclusions for the ferromagnetic or antiferromagnetic behavior of any dimethylene linear-polyene system.