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The lacunar spinel GaNb$_4$Se$_8$ is a tetrahedral cluster Mott insulatorwhere spin-orbit coupling on molecular orbitals and Jahn-Teller energy scalesare competitive. GaNb$_4$Se$_8$ undergoes a structural and anti-polar orderingtransition at T$_Q$ = 50 K that corresponds to a quadrupolar ordering ofmolecular orbitals on Nb$_4$ clusters. A second transition occurs at T$_M$ = 29K, where local distortions on the Nb$_4$ clusters rearrange. We present asingle crystal x-ray diffraction investigation these phase transitions andsolve the crystal structure in the intermediate T$_M$ < T < T$_Q$ and low T <T$_M$ temperature phases. The intermediate phase is a primitive cubic P2$_1$3structure with a staggered arrangement of Nb4 cluster distortions. A symmetrymode analysis reveals that the transition at TQ is continuous and described bya single Jahn-Teller active amplitude mode. In the low temperature phase, thesymmetry of Nb$_4$ clusters is further reduced and the unit cell doubles intoan orthorhombic P2$_1$2$_1$2$_1$ space group. Nb$_4$ clusters rearrange throughthis transition to form a staggered arrangement of intercluster dimers,suggesting a valence bond solid magnetic state.

Jahn-Teller driven quadrupolar ordering and spin-orbital dimer formation in GaNb$_{4}$Se$_{8}$