widths of the four bands are about 1.7 eV ($M=$ Ni) $>$ 1.6 eV (Au) $>$ 1.3 eV (Cu).

The fitted tight-binding parameters together with the orbital occupancies per site calculated from ${\cal H}_0$, i.e., $\langle n_i^{\textrm{o}} \rangle \equiv
 \bar{n}_{\textrm{o}}$ ($\textrm{o}=$ M$\sigma$, L, M$\pi$), are listed in Table \[table1\]. The listed orbital energies, $\Delta_{\textrm{M}\sigma}^0$, and $\Delta_{\textrm{M}\pi}^0$, are obtained by fitting the energy dispersions of ${\cal H}_0$. By noting that the first-principles band structures are obtained self-consistently including the Hartree contributions within the interactions, we can make a correspondence between the fitted values and the orbital energies in eq. (\[eq:H\]) as [@Seo_2008JPSJ; @Tsuchiizu_2012JCP; @Misawa_2011JPSJ] $$\begin{aligned}
\Delta_{\textrm{M}\sigma}^0 &=
 \Delta_{\textrm{M}\sigma} 
 +U_{\textrm{M}\sigma} \bar{n}_{\textrm{M}\sigma}/2 
 +U'_{\textrm{M}} \bar{n}_{\textrm{M}\pi} 
 -U_{\textrm{L}} \bar{n}_{\textrm{L}}/2,\label{eq:orbene1}\\ 
\Delta_{\textrm{M}\pi}^0 &=
 \Delta_{\textrm{M}\pi} 
 +U_{\textrm{M}\pi} \bar{n}_{\textrm{M}\pi}/2 
 +U'_{\textrm{M}} \bar{n}_{\textrm{M}\sigma} 
 -U_{\textrm{L}} \bar{n}_{\textrm{L}}/2.\label{eq:orbene2}\end{aligned}$$

The transfer integrals $t_{lm}$ show more or less similar values for all three members [@noteTransvalue], which is due to the fact that they are isostructural, as noted in our previous work [@Seo_2008JPSJ]. The M$\sigma$ orbitals have a large $t_{lm}$ only for the A bonds along the \[100\] direction: they show a 1D structure. The L orbitals, on the other hand, possess a two-dimensional network, where the [*inter*]{}-molecular dimers are formed by B bonds. Their network is schematically shown 