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Motivated by the intriguing suggestion of realizing SU(8) Dirac semi-metalwith $J=3/2$ electrons on a honeycomb lattice, we provide a systematic study ofthe interplay of various hopping pathways and atomic spin-orbit coupling forthe low energy electrons in candidate d$^1$ transition metal halides MX$_3$(M=Ti, Zr, Hf; X=F, Cl, Br). By combining first principle calculations andminimal hopping Hamiltonian, we uncover the role of dominant direct metal-metalhopping on top of indirect metal-halide-metal hopping. This sets up a hierarchyof hopping pathways that centrally modify the SU(8) picture for the abovematerials. These hopping interactions, along with the spin-orbit coupling, leadto a plethora of exactly compensated metals instead of the SU(8) Diracsemi-metal. Remarkably the same can be understood as descendants of atopological insulator obtained by gapping out the SU(8) Dirac semi-metallicphase. The resultant compensated metals have varied Fermi surface topology andare separated by Lifshitz phase transitions. We discuss the implications of theproximate Lifshitz transition, which may be accessed via strain, in the contextof the relevant materials.

Ab-initio Insights on the Fermiology of $d^1$ Transition metals in Honeycomb lattice : Hierarchy of hopping pathways and spin-orbit coupling