Finite-resolution conformer assignment from vibrational spectra: Uncertainty-aware distinguishability and measurement design

Conformer assignment from vibrational spectra depends not only on whether calculated spectra differ but also on whether those differences exceed the combined uncertainty of experiment and theory. We formulate this question as a finite-resolution pairwise distinguishability problem for infrared (IR) and Raman spectroscopy. Calculated conformer spectra are passed through an explicit measurement model that includes instrumental resolution, measurement noise, spectral-model discrepancy, and frequency uncertainty. The resulting separation is converted to a model-conditional Bayes error that identifies conformer pairs that remain unresolved at a stated tolerance and tests which additional spectral measurement would resolve them. We apply the method to conformer ensembles of 1,2-difluoroethane, ethylene glycol, and n-pentane computed at the B3LYP-D3(BJ)/def2-TZVP level. Under the working covariance, all chemically distinct pairs are separated by IR after spectroscopically equivalent mirror partners are collapsed. Under a deliberately conservative combined stress test, however, IR no longer resolves the gauche–gauche (gg) and gauche–trans (gT) families of n-pentane. Raman resolves this ambiguity, and the 500–1000, 1000–1800, and 2800–3800 cm−1 regions are individually sufficient under the stated model. The added discrimination arises primarily from conformer-dependent redistribution of Raman activity rather than large frequency shifts. Region-dependent cross-functional frequency residuals preserve the same IR-vs-Raman design conclusion, while gas-phase comparisons show the limitations of a single global frequency scale and of scoring a conformer mixture as a pure conformer. The method therefore links explicit spectral uncertainty to conformer distinguishability and measurement selection.