Agreement Is Not Assignment: Dynamic Observables and the Limits of Structural Validation

Agreement between experiment and calculation is indispensable for structural interpretation, but agreement alone does not identify the structure sampled by a measurement. When spectroscopic accuracy is sought, the measured observable may be a vibrational average around a minimum, a tunneling average, or an above-barrier average rather than the property of a single equilibrium geometry. Here we introduce a diagnostic framework that combines newly generated high-accuracy equilibrium structures, perturbative anharmonic corrections for regular modes, one-dimensional variational treatments of selected low-barrier coordinates, and isotope-resolved residual patterns to identify the structural object probed by rotational spectroscopy. The central result is that improved numerical agreement changes the interpretation of agreement itself: once equilibrium-structure errors are reduced to the few-milliangstrom scale required by high-resolution spectroscopy, the remaining discrepancies are no longer generic electronic-structure failures but signatures of the vibrational treatment, the chosen structural reference, or both. Distinct structural-assignment regimes then emerge from the combined isotope-resolved experiment-theory residual pattern. The decisive numerical signatures are residual-collapse factors of 1.5-36 for minimum-connected systems, values larger than 5 for glycine conformer II and larger than 8 for malonaldehyde, with isotope balance recovered only after the appropriate dynamic averaging. Compact covalent frameworks remain minimum-connected, selected hydrogen-bond separations require higher structural levels, and glycine conformer II, malonaldehyde, and the formic acid dimer require dynamic comparison targets. Corannulene and corannulene-water extend the diagnostic to symmetry and high-accuracy structural-parameter reduction in a noncovalent complex, while the example of the hyperfine coupling constants for the glycine radical shows that the same ambiguity is not confined to rotational constants. Agreement becomes chemically meaningful only after the nuclear-motion regime sampled by the experiment has been identified.