AI 中文总结
本研究针对分子构象光谱的测量问题，提出依赖测量模型的可识别性框架，结合贝叶斯误差图、秩与约束Fisher准则，经实验验证拉曼窗口可消除正戊烷的非镜像商歧义。
AI 中文摘要
构象归属仅在测量能区分候选结构时才有意义。我们将构象光谱表述为依赖测量模型的可识别性问题，其中每种模态定义了带有明确实验和理论不确定性的观测规律。观测规律的等价性定义了精确类，当添加模态时这些类会细化，而有限分辨率的歧义是非传递的，由贝叶斯误差图表示。我们还给出了从未归一化加性光谱中恢复总体的秩和约束Fisher准则。该框架应用于经审核的B3LYP-D3(BJ)/def2-TZVP系综，涉及1,2-二氟乙烷、乙二醇和正戊烷。在声明的共享协方差工作模型下，红外光谱（IR）可区分所有非镜像对，仅留下在手性观测映射下完全简并的镜像对。这一方法内结果不意味着红外光谱具有普适充分性：在六案例PBE0-to-B3LYP诊断中，固定校准可恢复1个预期代表，而带有保守跨方法协方差的尺度-偏移分析可恢复5个代表和全部6个非手性类。在组合压力测试协方差下，正戊烷出现1个非镜像商歧义，3个单独拉曼（Raman）窗口可消除该歧义，而所有测试的红外窗口均无法做到。在校准尺度工作模型下，镜像折叠类的总体仍可识别且条件良好，而从非手性加性光谱中无法识别分开的镜像伙伴总体。
英文摘要
Conformer assignment is meaningful only when the measurement can distinguish the candidate structures. We formulate conformer spectroscopy as a measurement-model-dependent identifiability problem in which each modality defines an observation law with explicit experimental and theoretical uncertainty. Equality of observation laws defines exact classes that refine as modalities are added, whereas finite-resolution ambiguity is non-transitive and is represented by a Bayes-error graph. We also give rank and constrained-Fisher criteria for population recovery from unnormalized additive spectra. The framework is applied to audited B3LYP-D3(BJ)/def2-TZVP ensembles of 1,2-difluoroethane, ethylene glycol, and n-pentane. Under the declared shared-covariance working model, IR separates all non-mirror pairs, leaving only mirror pairs that are exactly degenerate under the achiral observation maps. This within-method result does not imply general IR sufficiency: in a six-case PBE0-to-B3LYP diagnostic, fixed calibration recovers one intended representative, whereas scale-and-shift profiling with a conservative cross-method covariance recovers five representatives and all six achiral classes. Under a combined stress-test covariance, n-pentane develops one non-mirror quotient ambiguity. Three individual Raman windows remove it, while no tested IR window does. Mirror-collapsed class populations remain identifiable and well conditioned under the calibrated-scale working model, whereas separate mirror-partner populations are exactly unidentifiable from achiral additive spectra.
Comments46 pages, 5 figures, and 5 tables. Includes 25 pages of supplementary material as an ancillary file. Reproducibility archive: https://doi.org/10.5281/zenodo.21712522
