Performance of Minnesota functionals on predicting core-level binding energies of molecules containing main-group elements

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 (Delta BEs) 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 Delta BEs 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.