On the choice of shape and size for truncated cluster-based x-ray spectral simulations of 2D materials

Truncated cluster models represent an effective way for simulating x-ray spectra of 2D materials. Here, we systematically assessed the influence of two key parameters, the cluster shape (honeycomb, rectangle, or parallelogram) and size, in x-ray photoelectron (XPS) and absorption (XAS) spectra simulations of three 2D materials at five K-edges (graphene, C 1s; C₃N, C/N 1s; h-BN, B/N 1s) to pursue the accuracy limit of binding energy (BE) and spectral profile predictions. Several recent XPS experiments reported BEs with differences spanning 0.3, 1.5, 0.7, 0.3, and 0.3 eV, respectively. Our calculations favor the honeycomb model for stable accuracy and fast size convergence, and a honeycomb with ∼10 nm side length (120 atoms) is enough to predict accurate 1s BEs for all 2D sheets. Compared to all these experiments, predicted BEs show absolute deviations as follows: 0.4-0.7, 0.0-1.0, 0.4-1.1, 0.6-0.9, and 0.1-0.4 eV. A mean absolute deviation of 0.3 eV was achieved if we compare only to the closest experiment. We found that the sensitivity of computed BEs to different model shapes depends on systems: graphene, sensitive; C₃N, weak; and h-BN, very weak. This can be attributed to their more or less delocalized π electrons in this series. For this reason, a larger cluster size is required for graphene than the other two to reproduce fine structures in XAS. The general profile of XAS shows weak dependence on model shape. Our calculations provide optimal parameters and accuracy estimations that are useful for x-ray spectral simulations of general graphene-like 2D materials.