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MV$_2$Ga$_4$ (M = Sc, Zr, Hf) compounds belong to an emerging class ofmaterials showing a unique combination of unusual superconducting behavior withextended linear chains in the crystal structure. In order to gain insights{into} its mechanical and thermal properties, we have performedfirst-principles electronic-structure calculations in the framework of theDensity Functional Theory (DFT). From the calculated second-order elasticconstants, we have systematically shown that the extended linear vanadium chainsubstructures indeed give rise to an anisotropic regime in the elastic andmechanical moduli. The high density of valence and conduction electrons alongthe linear vanadium chains leads to a directional dependence of the reciprocallinear compressibility, Young's modulus and shear modulus. Poisson's ratio forseveral elongation directions is also drastically affected by the presence ofextended V chains. If the elongation is along the V chains, all compoundsexhibit {practically} the same Poisson ratio in directions perpendicular to it,further highlighting the importance of the V chains to the mechanicalproperties. Moreover, based on our results, we have discussed the possibleconsequences of the elastic anisotropy on the superconducting properties of thecompounds. Finally, using the Debye-Gr\"uneisen approximation, our calculationsof thermal properties show {a good agreement with the available experimentallow temperature heat capacity data above the superconducting criticaltemperature.

Elastic anisotropy and thermal properties of extended linear chain compounds MV$_2$Ga$_4$ (M = Sc, Zr, Hf) from ab-initio calculations