The rotation of octahedra (octahedral tilting) is common in ABO3 perovskites and relevant to many physical phenomena, ranging from electronic and magnetic properties, metal-insulator transitions to improper ferroelectricity. Hydrostatic pressure is an efficient way to tune and control octahedral tiltings. However, the pressure behavior of such tiltings can dramatically differ from one material to another, with the origins of such differences remaining controversial. In this work, we discover several new mechanisms and formulate a set of simple rules that allow to understand how pressure affects oxygen octahedral tiltings, via the use and analysis of first-principles results for a variety of compounds. Besides the known A-O interactions, we reveal that the interactions between specific B-ions and oxygen ions contribute to the tilting instability. We explain the previously reported trend that the derivative of the oxygen octahedral tilting with respect to pressure (dR/dP) usually decreases with both the tolerance factor and the ionization state of the A-ion, by illustrating the key role of A-O interactions and their change under pressure. Furthermore, three new mechanisms/rules are discovered. We further predict that the polarization associated with the so-called hybrid improper ferroelectricity could be manipulated by hydrostatic pressure, by indirectly controlling the amplitude of octahedral rotations.
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