The Strength of a Geometric Simplex Helps Quantify Geometric Affinities of Molecules

Source abstract

All molecules naturally live in a 3-dimensional space, though some of them are linear, like carbon dioxide, or flat, like water or benzene. Molecules were recently classified as clouds of unordered atoms by complete invariants with Lipschitz continuous metrics, all computable in polynomial time. The key ingredient of this new classification is the strength of a geometric simplex. We rigorously prove the Lipschitz continuity of this strength in any dimension and extend this concept to continuously quantify the degeneracy of atomic clouds when they can close to a flat or linear configuration.