molecule embedded in the ligands (see ref. ). There are two of them in one molecule, i.e., L1 and L2, one for each ligand; they are equivalent due to the inversion center at the metal site.

In isolated molecules, the M$\sigma$ orbital does not mix with other orbitals from their symmetry; thus, it is a MO itself, i.e., the $pd\sigma$-MO mentioned in § \[sec1\]. As can be seen in Fig. \[fig1\], the other three MO can roughly be described as linear combinations of L and M$\pi$ orbitals [@Seo_2008JPSJ] as $\phi_{\rm L1}-\phi_{\rm L2}+c_1\phi_{\textrm{M}\pi}$, $\phi_{\rm L1}+\phi_{\rm L2}$, and $\phi_{\rm L1}-\phi_{\rm L2}-c_2\phi_{\textrm{M}\pi}$, where $c_1$ and $c_2$ are some coefficients [@Bonnet_2010JCP] (we omit renormalization factors).

In the fMO scheme, we consider these three kinds of orbitals as a basis set composing the band structures, and then for the low-energy effective model. The two-MO case mentioned in § 1 corresponds to the situation where only the L orbitals are considered. In ref. , we chose {L, M$\pi$} for \[Ni(tmdt)$_2$\] and {M$\sigma$, L} for \[Au(tmdt)$_2$\] to reproduce the first-principles band structures near $\epsilon_{\rm F}$. Here, all {M$\sigma$, L, M$\pi$} are taken into account as a common set, in order to provide a systematic view of the 