Using a combination of single-crystal and powder X-ray diffraction measurements, we study temperature- and pressure-driven structural distortions in zinc(II) cyanide (Zn(CN)(2)) and cadmium(II) imidazolate (Cd(im)(2)), two molecular frameworks with the anticuprite topology. Under a hydrostatic pressure of 1.52 GPa, Zn(CN)(2) undergoes a first-order displacive phase transition to an orthorhombic phase, with the corresponding atomic displacements characterized by correlated collective tilts of pairs of Zn-centered tetrahedra. This displacement pattern sheds light on the mechanism of negative thermal expansion in ambient-pressure Zn(CN)(2). We find that the fundamental mechanical response exhibited by Zn(CN)(2) is mirrored in the temperature-dependent behavior of Cd(im)(2). Our results suggest that the thermodynamics of molecular frameworks may be governed by considerations of packing efficiency while also depending on dynamic instabilities of the underlying framework topology.