Gradual hydrogen uptake into Zr2Cu intermetallic leads to crystal symmetry changes from tetragonal Zr2CuH2 to monoclinic Zr2CuH5. This experimental finding is explained here from cohesive energies computed within quantum DFT for Zr2CuHx (x = 1, 2, 3, 4, 5) models in both structures. The threshold is found at 2 < x < 3 in agreement with experiment. Beside structural crossover, electronic properties, chemical bonding, and mechanical behavior are also analyzed. Metal-H interactions arising from increasingly H presence in Zr2Cu lead to more and most cohesive and harder Zr2CuH2 and Zr2CuH5 respectively.