Conclusions
We have presented a calibration study of three density functionals, TPSSh, B3LYP and PBE0, for their application in computational Mössbauer spectroscopy. All density functionals were found to perform well for both the isomer shift and the quadrupole splitting prediction; R-values exceeded 0.985 in all cases. We defined trust regions as the double mean absolute deviation of the correlation line and note as exemplary values 0.13 mm s−1 for the isomer shift and 0.45 mm s−1 for the quadrupole splitting obtained with the B3LYP density functional.
Besides the notoriously difficult electronic structures of iron(II) intermediate spin (2S +1 = 3) ions in square-planar coordination geometry, we discuss other cases where an adequate electronic structure description was not found when treating DFT purely as a black-box method. In order to facilitate comparisons of computational data for iron complexes with complicated electronic structures such as those expected in the coordination environment of FeNC catalysts, it is thus strongly recommended to at least report the spin populations on all relevant atoms.
The focus of this study was placed on iron environments similar to those thought to be the active sites in FeNC catalysts, thereby guiding the choice of complexes in the reference set. Despite this intentional constrain, the results are very similar to those of Pápai et al .,21 suggesting that the correlation lines obtained here can be used for other systems as well. The data presented here are made available in an online notebook that allows researchers to obtain predicted Mössbauer parameters and the individual uncertainties from the computed values; the notebook (tinyurl.com/mbs-notebook) is open to submission of additional data points for the computational setups presented here and will accept submissions of entire data sets produced with different methodological choices. In this way, a future-proof and ever-growing calibration of computational Mössbauer spectroscopy is provided that ensures a rigorous and directly comparable statistical analysis of different computational approaches.
In native FeNC catalysts, up to five distinct Mössbauer signatures can be found and several other signals can be produced by different treatments. We discuss the trust regions for isomer shift and quadrupole splitting deduced from the calibration study in the context of the relative positions of these experimental values. From this analysis, it appears probable that appropriate computational models will be able to differentiate between these characteristic spectral features if isomer shift and quadrupole splitting are both considered in the analysis. In other words, through a combination of experimental and computational Mössbauer spectroscopy, one will likely be able to identify the structural and electronic basis for the oxygen reduction reaction in FeNC catalysts.