Small-angle rigid-unit modes requiring linear strain compensation

Group-theoretical and linear-algebraic methods and tools have recently been developed that aim to exhaustively identify the small-angle rotational rigid-unit modes (RUMs) of a given framework material. But in their current form, they fail to detect RUMs that require a compensating lattice strain which grows linearly with the amplitude of the rigid-unit rotations. Here, we present a systematic approach to including linear strain compensation within the linear-algebraic RUM-search method, so that any geometrically possible small-angle RUM can be detected.