case of \[Au(tmdt)$_2$\], localized spins appear on the antibonding orbital of dimerized L sites. In contrast, in the case of \[Cu(tmdt)$_2$\] spins appear on each of the L sites as well as of the M$\sigma$ sites as a result of orbital mixing.

![(Color) Mean field ground-state phase diagrams for \[Au(tmdt)$_2$\]. The parameters used are fitted results for (a) room-temperature ($T$) structure, (b) low-$T$ structure, and (c) room-$T$ structure but with reduced $\Delta_{\textrm{M}\sigma}^0 \rightarrow \Delta_{\textrm{M}\sigma}^0 - 0.1$ eV. Dashed lines are guides for the eyes. The legend symbols are shown in (d); colors are appointed for distinctions between orbitals showing spin moments as red (L), green (M$\sigma$), and blue (both L and M$\sigma$), while filled symbols represent insulating states. []{data-label="fig6"}](fig6a.eps "fig:"){width="5.8cm"}\
![(Color) Mean field ground-state phase diagrams for \[Au(tmdt)$_2$\]. The parameters used are fitted results for (a) room-temperature ($T$) structure, (b) low-$T$ structure, and (c) room-$T$ structure but with reduced $\Delta_{\textrm{M}\sigma}^0 \rightarrow \Delta_{\textrm{M}\sigma}^0 - 0.1$ eV. Dashed lines are guides for the eyes. The legend symbols are shown in (d); colors are appointed for distinctions between orbitals showing spin moments as red (L), green (M$\sigma$), and blue (both L and M$\sigma$), while filled symbols represent insulating states. []{data-label="fig6"}](fig6b.eps "fig:"){width="5cm"}

![(Color) Parameter 