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The molecular solids $\beta^\prime$-$X$[Pd(dmit)$_2$]$_2$ (where $X$ represents a cation) are typical compounds whose electronic structures described by single-orbital Hubbard-type Hamiltonians with geometrical frustration. Using the $ab$ $initio$ downfolding method, we derive low-energy effective for available room- and low-temperature structures. We find that amplitudes of Coulomb interactions anisotropy hopping parameters in sensitive to changes lattice constants induced lowering temperature. obtained analyzed using exact diagonalization method boundary-condition average. significant reduction antiferromagnetic ordered moment occurs Hamiltonian $\beta^\prime$-EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ structure. is consistent quantum spin liquid behavior observed experiments. comprehensive derivations exact-diagonalization analyses them will clarify microscopic origins exotic states matter found such as behavior.