  Electronic properties of quasi-two-dimensional molecular conductors
$X$[Pd(dmit)$_2$]$_2$ are studied theoretically. We construct an effective
model based on the fragment molecular orbital scheme developed recently, which
can describe the multi-orbital degree of freedom in this system. The
tight-binding parameters for a series of $\beta'$-type compounds with different
cations $X$ are evaluated by fitting to first-principles band calculations. We
find that the transfer integrals within the dimers of Pd(dmit)$_2$ molecules,
along the intramolecular and intermolecular bonds including the diagonal ones,
are the same order, leading to hybridization between different molecular
orbitals. This results in charge disproportionation within each molecule, as
seen in our previous ab initio study [T. Tsumuraya et al, J. Phys. Soc. Jpn.
82, 033709 (2013)], and also to a revised picture of an effective dimer model.
Furthermore, we discuss broken-symmetry insulating states triggered by
interaction effects, which show characteristic features owing to the
multi-orbital nature. The on-site Coulomb interaction induces antiferromagnetic
states with intramolecular antiparallel spin pattern, while electron-lattice
couplings stabilize non-magnetic charge-lattice ordered states where two kinds
of dimers with different charge occupation arrange periodically. These states
showing different spatial patterns compete with each other as well as with the
paramagnetic metallic state.
