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In this study, we investigated theoretically the Mott-insulating phase of adeficient spinel chalcogenide GaV$_4$S$_8$, which is known to form atetrahedral V$_4$S$_4$ cluster unit that results in molecular orbitals (MOs)with a narrow bandwidth in the noninteracting limit. We used a clusterextension of charge self-consistent embedded dynamical mean-field theory tostudy the impact of strong intra-cluster correlations on the spectralproperties as well as the structural degrees of freedom of the system. We foundthat the strong tetrahedral clustering renders the atomic Mott pictureineffective, and that the resulting MO picture is essential to describe theMott phase. It was also found that, while the spectral properties can bequalitatively described by the truncation of the Hilbert space down to thelowest-energy MO, a proper description of the structural degrees of freedomrequires the inclusion of multi-MO correlations that span a larger energywindow. Specifically, we found that the lowest-energy MO descriptionoveremphasizes the clustering tendency, while the inclusion of the Hund'scoupling between the lower- and higher-energy MOs corrects this tendency,bringing the theoretically predicted crystal structure into good agreement withthe experiment.

Molecular Mott state in the deficient spinel GaV$_4$S$_8$