Negative Linear Compressibility in [NHNH]Co(HCOO) and Its Structural Origin Revealed from First Principles.

First-principles density functional theory computations are used to predict negative linear compressibility in hybrid organic-inorganic perovskite [NHNH][Co(HCOO)]. Negative linear compressibility is a rare exotic response of a material to pressure associated with expansion along one or two lateral directions. Detailed structural analysis revealed that [NHNH][Co(HCOO)]  responds to pressure through tilting of its relatively rigid units, CoO polyhedra, and (HCOO) ligand chain. The (HCOO) units form a "wine-rack" geometry which is well described with the "strut-hinge" model. Within the model, the struts are formed by the rigid units, while hinges are their relatively flexible interconnects. Under pressure, the hinge angle increases which leads to the expansion along the direction subtended by the angle. Interestingly, at zero pressure the linear compressibilities in [NHNH][Co(HCOO)]  are all positive. As pressure increases, the lowest linear compressibility value turns negative and increases in magnitude. Comparison with the literature suggests that such a trend is likely to be common to this family of materials. Mechanical properties of [NHNH][Co(HCOO)]  are highly anisotropic.