Pushing the Limits of the Mean Field Model: Quantifying and Predicting the Coverage Dependence of Complex Aromatics on Pd(111)

Mean-field models describing coverage-dependent adsorption energies were developed for 12 aromatics of varying complexity on Pd(111). All systems are accurately captured by first-order linear regressions, yielding low errors even as molecular complexity increases. However, to better represent the low-coverage regime, a quadratic dependence provides a more accurate description of the coverage effect. The net lateral interactions are strongly influenced by the functional group type, where more complex aromatics (i.e., those with multiple functional groups) exhibit smaller net lateral interactions. Closed-shell aromatics display increasingly repulsive interactions with higher coverage, while open-shelled aromatics show minimal dependence on coverage due to their high instability in the gas-phase. The spacing between functional groups on the same molecule significantly impacts the interactions between the adspecies, with farther-spaced groups behaving more like single-functional aromatics. The largest deviations of the mean field model come from adsorbates with multiple functional groups but with root mean squared errors below 100 meV/molecule. Each aromatic/metal combination is governed by both surface-mediated and through-space interactions, where the former depends on the metal and the latter on the aromatic structure. Using minimal data and key descriptors, linear regression models are developed to predict the coverage-dependent energies for all aromatics on Pd(111), achieving an accuracy within 50 meV/molecule Root-Mean-Square Error. These models include a newly developed correction factor to account for the behavior of open-shelled aromatics and highlights the importance of understanding coverage-dependent adsorbate behavior.