1 In many cases, structural information can only be extracted from experimental spectra by combining them with computations.

1 Introduction The quantum-chemical calculation of molecular spectra has nowadays become an essential tool for determining the structure of molecules. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy. We show that with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is applied to the calculation of X-ray emission spectra of iron carbonyl complexes, of the electronic excitation spectrum of a coumarin dye, and of the infrared spectrum of alanine. We show that by performing a principal component analysis, the most influential collective distortions can be identified, which allows for the construction of surrogate models that are amenable to a statistical analysis of the propagation of uncertainties in the molecular structure to uncertainties in the calculated spectrum. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. Here, we explore the application of methods from uncertainty quantification to theoretical spectroscopy, with the ultimate goal of providing systematic error bars for calculated spectra.

Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. Molecular spectra calculated with quantum-chemical methods are subject to a number of uncertainties ( e.g., errors introduced by the computational methodology) that hamper the direct comparison of experiment and computation.

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