Abstract
Here we explored the performance of M06, M06-L, M11, and M11-L Minnesota functionals on predicting core-level 1s binding energies (BEs) and BE shifts (ΔBEs) for a set of 20 organic molecules containing main-group elements C → F (39 core levels in total). The broadly used Hartree–Fock (HF) and Becke–Lee–Yang–Parr (B3LYP) methods have also been studied for comparison. A statistical analysis comparing with X-ray photoelectron spectroscopy (XPS) experimental values shows that overall BEs estimations only deviate a small percentage from the experimental values, yet the absolute deviations are generally too large, with the different methods over/underestimating the reported values. However, taking the contribution of relativistic effects of BEs into account leads to larger differences. Overall, the performance of the explored Minnesota functionals is not satisfactory, with errors of up to 1 eV, except for the M06-L meta-GGA functional. In this case, the mean absolute deviation is below 0.1 eV and thus within XPS chemical resolution. Hence, M06-L poses itself as a rather accurate and computational expense-wise method for estimating BEs of organic molecules. Nevertheless, the observed deviations almost cancel when considering ΔBEs with respect to some arbitrary reference, with errors within 0.2–0.3 eV, indicating that these are largely systematic, which in turn implies that the corresponding methods have room for improvement.
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Acknowledgments
The authors are very much indebted to Paul S. Bagus for providing the relativistic values for the core-level binding energies of atoms C to F and for many highlighting and inspiring discussions. This work has been supported by Spanish MINECO CTQ2012-30751 grant and, in part, by Generalitat de Catalunya grants 2014SGR97 and XRQTC. F.V. thanks MINECO for a postdoctoral Ramón y Cajal (RyC) research contract (RYC-2012-10129). We acknowledge Consorci de Serveis Universitaris de Catalunya (CSUC; former CESCA) for providing access to computational resources.
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Published as part of the special collection of articles “CHITEL 2015 - Torino - Italy”.
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Appendix
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Pueyo Bellafont, N., Álvarez Saiz, G., Viñes, F. et al. Performance of Minnesota functionals on predicting core-level binding energies of molecules containing main-group elements. Theor Chem Acc 135, 35 (2016). https://doi.org/10.1007/s00214-015-1787-3
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DOI: https://doi.org/10.1007/s00214-015-1787-3