Algorithmic construction and exploitation of topology-constrained refinement models for semiexperimental equilibrium structures

Semiexperimental equilibrium structures combine high-resolution rotational spectroscopy with computed vibrational and electronic corrections. Although the least-squares solution is well established, constructing the inverse model still requires expert choices of coordinates, symmetry, constraints, and parameter classes. We introduce MORPHEUS (Model Optimization and Refinement from Perceived Hierarchy, Equivalence, Uncertainty, and Symmetry), a reproducible framework that makes these choices explicit and tests them against topology, symmetry, rank, isotope coverage, and external reference information. Starting from Cartesian geometry, it builds non-redundant internal coordinates and a refinement model before fitting. Two alternative active spaces are supported: symmetry-adapted generalized internal coordinates and symmetry-adapted Cartesian displacements with translations and rotations removed. Across acyclic, cyclic, planar, fused, bridged, and flexible molecules, the workflow recovers effective dimensions, residuals, structural parameters, and uncertainties without manual construction of the active coordinate model. In camphor, the chemically validated model gives sub-milliangstrom bond corrections and remains stable under basis changes, robust losses, predicate-width scans, and multi-starts. A 49-atom testosterone demonstration shows how QC geometries, accelerated vibrational corrections, and class-constrained refinement models can be combined when isotope-rich data are unavailable.