SONIC: Symmetry-Oriented Non-redundant Internal Coordinates

Abstract

Internal coordinates are the natural language of molecular structure, but automatic non-redundant constructions remain difficult for fused rings, high coordination, molecular symmetry, and weakly bound fragments. We present SONIC (Symmetry-Oriented Non-redundant Internal Coordinates), implemented in SMITH, as a deterministic construction of localized, symmetry-adapted generalized internal coordinates. SMITH accepts a frozen molecular state, supplied topology or primitives, or Cartesian input through a revision-pinned standalone perception kernel. It classifies ordinary primitives, adds chemically typed special and composite families, protects ring and fragment coordinates, and performs block-local rank reduction using analytic Wilson B rows. Local pseudosymmetry orders center, ring, and bond domains, while exact molecular point-group projection is applied within homogeneous blocks. The output is a frozen coordinate contract with human-readable decompositions, symmetry and rank diagnostics, analytic first derivatives, and optional Gaussian 16 serialization. Optimization, internal-to-Cartesian realization, force fields, and higher-order Hessian transformations remain downstream responsibilities. Validation covers acyclic, fused, bridged, high-coordinate, non-covalent, and eta3 metal-complex cases, including rotation/permutation invariance, Python/Fortran checks, and independent GIC evaluation.