Uncertainty quantification is applied in theoretical spectroscopy to obtain error bars accounting for the structural sensitivity of calculated spectra.

The deconvolution of impedance data to their respective distribution of relaxation times (DRT) is accompanied by an increase in the resolution of the frequency domain and is, thus, advantageous. Yet, most of the techniques used for computing DRT spectra from experimental data are valid only for impedance spectra that solely show polarization processes. Therefore, most experimental electrochemical impedance spectra must be corrected from perturbing inductive, capacitive, or diffusive contributions. This preprocessing is time consuming, and its quality has an enormous impact on the obtained DRT spectra. It also prohibits using the DRT method within an automated impedance evaluation. In this work, we propose a software-aided approach for deriving optimal preprocessing. For this purpose, we first introduce a quality indicator that reflects the quality of a certain preprocessing. Based on this quality indicator, we furthermore introduce a new batch fitting approach for deriving the optimal equivalent electrical circuit within the preprocessing of experimental impedance spectra. Besides, the batch fitting displays the optimal frequency range for modeling the unwanted impedance fractions. Based on this information, the considered impedance data can finally be optimally corrected from any non-polarization processes. The new methods and their application are tested for simulated data and experimental impedance data of a lithium-ion cell.

Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill-posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions.The Tikhonov algorithm is a widespread method for computing DRT data, but it leads to unlikely spectra due to necessary boundaries. Therefore, we introduce the application of three alternative algorithms (Gold, Richardson Lucy, Sparse Spike) for the determination of stable DRT solutions and compare their performances. As the promising Sparse Spike deconvolution has a limited scope when using one single regularization parameter, we furthermore replaced the scalar regularization parameter with a vector. The resulting method is able to calculate well-resolved DRT spectra.

Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems such as batteries and fuel cells. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill-posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions. Different algorithms exist to find the best solution for this regularization. The following work tests and shows unconventional algorithms for the calculation of the DRTs. This manuscript is related to Poster SOFC-0064.

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. Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. 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. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. 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. 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 with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy.