will see that orbital mixing brings about phase diagrams showing different magnetic states when Coulomb interactions on the two types of orbitals are independently varied. In particular, a slight enhancement of mixing in \[Au(tmdt)$_2$\] suggested by experiments [@Zhou_2009IC] results in marked changes from our previous results [@Seo_2008JPSJ]: The involvement of the $pd\sigma$ orbital is suggested.

Section \[sec4\] is devoted to discussions, especially on the magnetic transitions observed in the two compounds. Our results are consistent with the picture that, in \[Cu(tmdt)$_2$\], the $pd\sigma$-MO carries 1D $S$ = 1/2 localized spins, interpreted as a multiband Mott insulator. We discuss possible situations realized in \[Au(tmdt)$_2$\], from the viewpoint of doped Mott insulating systems due to orbital mixing. A summary is given in § \[sec5\].

Effective Model {#sec2}
===============

The wave functions that we chose as basis sets for the effective model of SCMC in our previous work [@Seo_2008JPSJ] are localized on some portions of the molecules. They can be considered as fragments of the MO, and then called the fragment MO (fMO) in refs. , which we follow in this paper as well.

The original motivation to consider such decomposition of MO was the results of first-principles calculations [@Ishibashi_2005JPSJ; @Ishibashi_2008JPSJ]. The spin-dependent 