Quantifying similarity for spectra with a large number of overlapping transitions: Examples from soft X-ray spectroscopy

Theoretical simulations are frequently used to assign electronic and geometric structure from spectral fingerprints. However, such assignments are prone to expectation bias. Bias can be reduced by using numerical measures of the similarity between calculated and experimental spectra. However, the commonly used pointwise comparisons cannot handle larger deviations in peak position. Here a weighted cross-correlation function is used to evaluate similarity scores for soft X-ray spectra of first-row transition metals. These spectra consist of hundreds of overlapping resonances, which makes spectral decomposition difficult. They are also challenging to model, leading to significant errors in both peak position and intensity. It is first shown how the choice of weight-function width can be related to the modeling errors. The method is then applied to evaluate the sensitivity of multiconfigurational wavefunction and charge-transfer multiplet simulations to model choices. The approach makes it possible to assess the reliability of assignments from spectral fingerprinting.