Maximally localized Wannier function within linear combination of pseudo-atomic orbital method: Implementation and applications to transition-metal-benzene complex

Construction of maximally localized Wannier functions (MLWFs) has been implemented within the linear combination of pseudo-atomic orbital (LCPAO) method. Detailed analysis using MLWFs is applied to three closely related materials, single benzene (Bz) molecule, organometallic Vanadium-Bz infinite chain, and V$_2$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 V$_2$Bz$_3$, an important role played by the difference in the orbital energy between the edge Bzs and the middle Bz is newly 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 V$_2$Bz$_3$.