Does the Total Energy Difference Method for Modelling Core Level Photoemission Fail for Bigger Molecules?

The $\Delta$ -self-consistent-field ( $\Delta$ SCF) method permits calculations of core electron binding energies in materials and molecules at a modest computational cost. However, it has been reported that whilst this method works well for small molecules, its accuracy drops off dramatically when larger systems are considered. Particularly large errors have been reported for the anthrone molecule, which consists of 25 atoms. In this work, the gas-phase photoelectron spectrum of anthrone is revisited both computationally and experimentally. The measured C 1s binding energies in anthrone differ markedly from previously published values, and the new experimental results are in good agreement with $\Delta$ SCF calculations. In addition, the performance of the $\Delta$ SCF method is evaluated for a dataset of 44 core electron binding energies from medium-sized molecules containing between 10 and 40 atoms. Both SCAN and B3LYP yield a mean absolute error of 0.19 eV for this dataset. This level of accuracy is comparable to the results of previous computational benchmarks. Overall, these results and general theoretical considerations indicate that the $\Delta$ SCF method is suitable for modelling localized excitations in both small and large molecules, and applications to other extended systems are also promising.