Emergence of quasi-one-dimensional physics in Mo${}_3$S${}_7$(dmit)${}_3$, a nearly-isotropic three-dimensional molecular crystal

We report density functional theory calculations for Mo${}_3$S${}_7$(dmit)${}_3$. We derive an ab initio tight-binding model from overlaps of Wannier orbitals; finding a layered model with interlayer hopping terms $\sim 3\mathrm{/}4$ the size of the in-plane terms. The in-plane Hamiltonian interpolates the kagom'e and honeycomb lattices. It supports states localized to dodecahedral rings within the plane, which populate one-dimensional (1D) bands and lead to a quasi-1D spin-one model on a layered honeycomb lattice once interactions are included. Two lines of Dirac cones also cross the Fermi energy.