Ab initio size-consistent calculations of effective exchange interactions in mesoscopic magnetic clusters composed of triplet methylenes and quartet nitrogen atoms

The electronic structures of linear magnetic clusters composed of eleven triplet methylenes, eleven quartet nitrogen atoms, and five triplet methylenes plus six quartet nitrogen atoms were investigated by the unrestricted Hartree-Fock (UHF), post UHF and their spin-projected wavefunctions in combination with the Heisenberg model. The effective:ve exchange integrals (J(ab)) in the Heisenberg model were calculated by the difference between the total energies of the highest spin (HS) and lowest spin (LS) UHF-based wavefunctions of the clusters. The J(ab) values by the UHF-based and spin-polarized DFT methods were compared with those of the SO-Cl, MRSDCI, CASSCF, CASPT2, and MRMP2 calculations in the case of small linear clusters, such as a triplet methylene dimer. The spin-polarized density functional (BLYP and B3LYP) calculations followed by the size-consistent spin projection were carried out for dimer, trimer, and clusters with eleven magnetic sites to obtain the J(ab) values, since the DFT methods were heavily utilized in solid state physics. It was found that all of the methods, except for DFT, provide similar J(ab) values in the magnetic region of the dimer, where the interatomic distance is longer than 3.0 Angstrom. However, the spin crossover from the LS state to the HS state occurs at a larger distance in the cases of MRSDCI and MRMP2. The spin projection for LS spin-polarized wavefunctions becomes less important in the case of long linear clusters, such as (CH2)(11). The DFT results are generally biased to stabilize low-spin states. The implications of the calculated results are discussed in relation to the molecular magnetisms in mesoscopic molecular aggregates.