Revisiting magnetic coupling in transition-metal-benzene complexes with maximally localized Wannier functions

Construction of maximally localized Wannier functions (MLWFs) has been implemented within the linear combination of pseudoatomic orbital method. Detailed analysis using MLWFs is applied to three closely related materials, single benzene (Bz) molecule, organometallic vanadium-Bz infinite chain, and ${\text{V}}_2{\text{Bz}}_3$ sandwich cluster. Two important results come out from the present analysis: (1) for the infinite chain, the validity of the basic assumption in the mechanism of Kanamori and Terakura for the ferromagnetic (FM) state stability is confirmed; (2) for ${\text{V}}_2{\text{Bz}}_3$, an important role played by the difference in the orbital energy between the edge Bzs and the middle Bz is revealed: the on-site energy of $p\delta$ states of edge Bzs is higher than that of middle Bz, which further reduces the FM stability of ${\text{V}}_2{\text{Bz}}_3$.