Evaluating model parameters of theκ- andβ′-type Mott insulating organic solids

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We elucidate the model parameters for a series of organic crystals called $\ensuremath{\kappa}$- and ${\ensuremath{\beta}}^{\ensuremath{'}}$-type salts by constructing the maximally localized Wannier orbitals which reproduce the bulk energy band of the first-principles methods based on the density functional theory (DFT). These materials host a dimer Mott insulator, localizing one hole per dimerized ET molecules due to strong on-dimer interaction, ${U}_{\mathrm{d}}$. For all these materials, we evaluate the parameters of the two representative effective lattice models in units of molecule and on dimer, and clarify two issues. First, the conventional relationships between the two models called ``dimer approximation'' does not hold. Second, contrary to the previous semiempirical estimates, the degree of dimerization (which approximates ${U}_{\mathrm{d}}$) does not depend much on materials, and that the overall ground state properties are controlled by the degree of anisotropy of the triangular lattice, denoted as $|{t}_{c}/{t}_{a}|$ in units of dimers. We update the DFT estimates $|{t}_{c}/{t}_{a}|$ of $\ensuremath{\kappa}$-ET${}_{2}$Cu${}_{2}$(CN)${}_{3}$, showing that it falls on a class of regular triangle with the strongest degree of frustration.