Chemists have a strong language describing and defining idealized polyhedra P and symmetry point groups G, but no efficient measure to correlate these to real molecular structures Q. The Continuous Symmetry operation Measure changes this by providing automated symmetry determination and a yardstick for quantifying deviations from symmetry. Symmetry and structure have been ascribed through experience, but this approach is error-prone and provides no measure that can correlate molecular structure to molecular properties. The Continuous Symmetry operation Measure tool solves this issue as it can quantify the symmetry of any structure that can be described as a list of points in space. Here, we compare the Continuous Symmetry Measure, the Continuous Shape Measure, and the Continuous Symmetry operation Measure approaches and demonstrate how the Continuous Symmetry operation Measure can be used as a tool to determine the molecular structure, the coordination geometry, and the symmetry of water, organic molecules, transition metal complexes, and lanthanide compounds. We conclude that the Continuous Symmetry operation Measure is not limited by any of the restrictions present in the other methods and allows a detailed analysis of e.g. phase changes and luminescence.
Nielsen et al. (2025) studied this question.