Theoretical Studies of Magnetic Interactions in Mn(II)(hfac)₂{di(4-pyridyl)phenylcarbene} and Cu(II)(hfac)₂{di(4-pyridyl)phenylcarbene}

Bis(hexafluoroacetylacetonato(hfac))manganese(II) coordinated with di(4-pyridyl)phenylcarbene, Mn(II)(hfac)₂{di(4-pyridyl)phenylcarbene} (1a) and its copper analogue Cu(II)(hfac)₂{di(4-pyridyl)phenylcarbene} (2a) have attracted great interest from the viewpoint of photoinduced magnetism. The complexes 1a and 2a are regarded as the new d−π−p conjugated systems containing transition metal ion and carbene as spin sources. The magnetic measurements demonstrated antiferromagnetic and ferromagnetic effective exchange interactions for 1a and 2a, respectively. Here, we have performed UHF and UHF plus DFT hybrid calculations (UB3LYP) to elucidate the nature of the through-bond effective exchange interaction between Mn(II) (or Cu(II)) ion and triplet carbene sites in 1a (or 2a) and their model complexes. The natural orbital analysis of the UHF and UB3LYP solutions and CASCI calculations for the simplest models of 1a and 2a are performed to elucidate relative contributions of spin polarization (SP) and spin delocalization (SD) (or superexchange (SE)) interactions for determination of the sign of J_ab values. Mn(II) carbene complex 1a shows an antiferromagnetic interaction because of the π-type antiferromagnetic SE effect and the π-type SP effect, while the positive J_ab value for Cu(II) carbene complex 2a can be explained by the fact that ferromagnetic SE and SP interactions due to orbital orthogonality are more effective than the σ-type antiferromagnetic SE interaction. The ligand coordination effects of both 4-pyridylcarbene and hfac play crucial roles for determination of the J_ab values, but the ligand coordination effect of hfac is more important for the active control of charge or spin density distributions than that of 4-pyridylcarbene. The spin alignment mechanisms of 1a and 2a are indeed consistent with SE plus SP rule, which is confirmed with the shape and symmetry of natural orbitals, together with charge and spin density distributions.