compounds. Our model Hamiltonian including local Coulomb interactions reads:$$\begin{aligned}
&{\cal H} = {\cal H}_0 + {\cal H}_{\rm int},\label{eq:H}\\
&{\cal H}_0 =\sum_{\langle l,m \rangle} \sum_s t_{lm} \left( c^\dagger_{ls} c_{ms}^{} + \mathrm{h.c.} \right) \nonumber\\
 &\hspace{3em} 
+ \sum_{i} \left( \Delta_{\textrm{M}\sigma} \ n_i^{\textrm{M}\sigma} 
 + \Delta_{\textrm{M}\pi} \ n_i^{\textrm{M}\pi} \right),\label{eq:H0}\\
&{\cal H}_{\rm int} = \sum_{i} \left\{ U_{\textrm{L}} 
    \left( n_{i\uparrow}^\textrm{L1} n_{i\downarrow}^\textrm{L1} +n_{i\uparrow}^\textrm{L2} n_{i\downarrow}^\textrm{L2} \right) \right.   + U_{\textrm{M}\sigma} \ n_{i\uparrow}^{\textrm{M}\sigma} n_{i\downarrow}^{\textrm{M}\sigma} \nonumber\\
 &\hspace{3em} 
+  U_{\textrm{M}\pi} \ n_{i\uparrow}^{\textrm{M}\pi} n_{i\downarrow}^{\textrm{M}\pi}   + \left. U'_\textrm{M} \ n_i^{\textrm{M}\sigma} n_i^{\textrm{M}\pi} \right\},\label{eq:Hint}
$$ where ${\cal H}_0$ and ${\cal H}_{\rm int}$ represent the one-particle part, determining the band structure, and the on-site interaction, respectively. In the first term of eq. (\[eq:H0\]), $t_{lm}$ denotes the transfer integrals between fMO, where the sum is taken for inter-fMO pairs $\langle l,m \rangle$ including intra- and inter-molecular ones, and $c_{ls}$ ($c^\dagger_{ls}$) denotes the annihilation (creation) operator for all kinds of orbitals with fMO site index $l$ and spin $s=\uparrow$ or $\downarrow$. In the second term of eq. (\[eq:H0\]), $\Delta_{\textrm{M}\sigma}$ and $\Delta_{\textrm{M}\pi}$ are the orbital energies of the M$\sigma$ and M$\pi$ orbitals, with respect to the L level. The sum here, as well as in eq. (\[eq:Hint\]), is taken for the molecule index $i$, where the number operators are $n_{is}^\textrm{o}={c^{\textrm{o}}_{is}}^\dagger c^{\textrm{o}}_{is}$ 