(1D) spin-$1/2$ Heisenberg model with AF exchange coupling of about 150 meV [@Zhou_2010IC], which is consistent with the $^1$H-NMR nuclear spin-lattice relaxation rate ($T_1^{-1}$) indicating 1D spin dynamics [@Takagi_2012PRB]. In this compound, in contrast with the discussions above, a $pd\sigma$-type MO centered at the metal site is suggested to lie close to the two ligands $p\pi$ orbitals, and mix substantially. The charge transfer from the $p\pi$-MO results in a nearly half-filled $pd\sigma$-band [@Ishibashi_2012Crystals]. Then, the magnetic properties of \[Cu(tmdt)$_2$\] are attributed to localized spins appearing on the $pd\sigma$-MO [@Zhou_2010IC; @Takagi_2012PRB].

In fact, the possibility that more than the two $p\pi$-MO are involved in the electronic states of SCMC was first proposed for \[Au(tmdt)$_2$\] on the basis of first-principles band calculations [@Ishibashi_2005JPSJ; @Ishibashi_2008JPSJ]: The $pd\sigma$- and $p\pi$-MO mix slightly when forming the electronic band structure, whereas the latter plays the major role near $\epsilon_{\rm F}$. However, more recently, it has been inferred from experiments that the orbital energy difference between these MO is modified upon cooling by an unusual structural variation, enhancing the mixing [@Zhou_2009IC].

Such multi-MO characters in SCMC can be captured by the effective model approach based on tight-binding approximation, which has been successful in describing the electronic properties 