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Among the layered material transition metal dichalcogenides, MoTe₂ shows a complex phase diagram and many interesting properties such as magnetoresistance, superconductivity, and potentially Weyl semimetal property. If synthesized by furnace cooling, MoTe₂ is stabilized in a hexagonal phase (2H). Quenching from above 1000 °C results in a metastable monoclinic phase (1T’), which becomes orthorhombic (Td) in a first order phase transition when cooled below room temperature. The phase transition is accomplished through layer shifting along the monoclinic tilting direction, and the structure within each layer is not changed. The reported crystal structures indicate that the layer shifting from 1T’ (P2₁/m) to Td (Pnm2₁) breaks the inversion symmetry and allows the Weyl physics to emerge. Single crystal neutron diffraction performed at SNS, ORNL provided evidence on a lower symmetry (P2₁) in the 1T’ phase which is non-centrosymmetric. Ab initio calculations and molecular dynamics simulations based on the refined structure will be discussed.