Towards an Understanding of Linear Scaling Relations Through Energy Decomposition Analysis

The discovery of linear scaling relations has fundamentally changed the field of heterogeneous catalysis. While the scaling relations have been rationalized based on a separation of sp and d electron contributions to adsorption energies, a full understanding of such a separation would require one to further break the adsorp- tion energy into distinct energy components such as electrostatics, polarization, charge transfer, and van der Waals components, and examine the sp and d contributions to each of them. As a first step in this direction, we analyze the interaction energy between CHx adsorbates and fcc(100) transition metal surfaces (M = Cu, Ag, Au, Rh, and Pt), with the surfaces represented both as slabs in plane-wave density functional theory (pw-DFT) calculations and as atomic clusters in atomic-orbital basis density functional theory (ao-DFT) calculations. Through an absolutely-localized molecular orbital (ALMO) based energy decomposition analysis of the ao- DFT adsorption energy, each of the interaction energy components (electrostatics, polarization, van der Waals, and charge transfer) was found to follow its own scaling relations, with an intricate in- terplay among these energy components yielding the overall scaling relations for the total adsorption energies. Using the recently in- troduced ALMO-based polarization and charge-transfer analysis schemes, we further dissected polarization into metal surface and adsorbate contributions, and charge transfer into metal→adsorbate and adsorbate→metal contributions. The contributions from the sp and d electrons of metal to these terms were further quantified. These analysis results shed light on how CHx adsorbates interact with metal surfaces and reveal the physical origin of the scaling relations.