The ISOTILT software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units.

A user-friendly web-based software tool called 'ISOTILT' is introduced for detecting cooperative rigid-unit modes (RUMs) in networks of interconnected rigid units (e.g. molecules, clusters or polyhedral units). This tool implements a recently described algorithm in which symmetry-mode patterns of pivot-atom rotation and displacement vectors are used to construct a linear system of equations whose null space consists entirely of RUMs. The symmetry modes are first separated into independent symmetry-mode blocks and the set of equations for each block is solved separately by singular value decomposition. ISOTILT is the newest member of the ISOTROPY Software Suite. Here, it is shown how to prepare structural and symmetry-mode information for use in ISOTILT, how to use each of ISOTILT's input fields and options, and how to use and interpret ISOTILT output.

An algebraic approach to cooperative rotations in networks of interconnected rigid units.

Crystalline solids consisting of three-dimensional networks of interconnected rigid units are ubiquitous amongst functional materials. In many cases, application-critical properties are sensitive to rigid-unit rotations at low temperature, high pressure or specific stoichiometry. The shared atoms that connect rigid units impose severe constraints on any rotational degrees of freedom, which must then be cooperative throughout the entire network. Successful efforts to identify cooperative-rotational rigid-unit modes (RUMs) in crystals have employed split-atom harmonic potentials, exhaustive testing of the rotational symmetry modes allowed by group representation theory, and even simple geometric considerations. This article presents a purely algebraic approach to RUM identification wherein the conditions of connectedness are used to construct a linear system of equations in the rotational symmetry-mode amplitudes.