A comprehensive analysis of low coverage CO adsorption on Ni and Cu low-index miller surfaces - (100), (110), and (111) - over all the possible adsorption sites is presented. Systems are theoretically studied within an accurate adsorption model using RPBE density functional calculations to obtain electronic and geometrical structure predictions along with their corresponding adsorption energy computations. Based on the surface- and site-dependent comparisons of the adsorption mechanisms, we were able to grasp trends that point to the factors that determine the final C-O structure upon adsorption. The resulting C-O bond length is found to be directly dependent on structural parameters, such as depth of adsorption and metal-adsorbate bonding distances, and the quantity of charge transferred from the surface to the CO molecule. Those factors are collated into a formula that defines the final C-O bond: the "C-O formula". For each adsorption site, the final C-O bond length is calculated using this formula and compared with the DFT predictions, where consistent matching results are obtained. Deeper analysis of the adsorbed C-O molecule is also presented from a molecular orbital level. Density of states (DOS) charts were exploited to investigate the perturbations in the 3σ and 1π orbitals that hold the internal C-O bond. From this analysis, a consistent link between the degree of destabilization of the orbitals and the final C-O bond length is found, obtaining a more profound understanding of the final adsorbate structure. Energetically, adsorptions on Cu and Ni surfaces are compared within the Blyholder-Nilsson and Petersson (B-NP) model. The frontier (5σ and 2π*) orbital energies relative to the d-band center of the metal surfaces are displayed, which implicitly defines the adsorption energy. The controversial repulsive nature of the σ-interaction proposed in the NP model has been tested by tracking the charge redistribution within the metallic states, including the broad sp-states. The nature of σ-interaction is, however, found to be dependent on the substrate type; repulsive σ-interaction is concluded for Ni, while for Cu, a rather dual nature is found, including both partial repulsive and attractive behavior, with a dominant and overall repulsive nature, in agreement with the NP model. The degree of σ repulsion/attraction is also found to be dependent on the metal coordination. Finally, spin-polarized DFT calculations were repeated for Ni surfaces and compared with the previous Ni results without spin-polarization. The reported results confirmed the absence of correlation between adsorption energetics and the final adsorbate structure, and verified the factors presented in the "C-O formula" as the main descriptors for the adsorbate structure.
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