It is shown that for all the essential bond forming and bond breaking reactions on metal surfaces, the reactivity of the metal surface correlates linearly with the reaction energy in a single universal relation. Such correlations provide an easy way of establishing trends in reactivity among the different transition metals.
Keywords Density Functional Theory -Stepped surfaces -Coupling reactions -Bond breaking reactions -BEP relations -Scaling relationsTo bridge the gap between macroscopic properties of a catalyst, such as turn-over rates and selectivity and the microscopic properties obtained from electronic structure methods based on density functional theory (DFT), an in depth understanding of the underlying thermodynamics and kinetics of the corresponding metal surfaces is needed. Today, DFT has reached a level of sophistication where it can be used to describe complete catalytic reactions and hence provide an insight that pinpoints to the origin of the catalytic activity and selectivity. 1,2,3,4,5,6 However, extensive DFT calculations that eventually lead to this understanding are still computationally demanding. A simplification that connects the reactivity and selectivity of a catalytic surface to one or few descriptors is therefore extremely useful. Such a simplification, e.g. the Brønsted-Evans-Polanyi (BEP) relations, is able to show that the transition state energy of a reaction is linearly depending on the reaction energy. 7,8,9,10,11,12 * Corresponding author SLAC-PUB-14285 2 Herein, we investigate the transition state energies of a large number of essential bond breaking and forming reactions that play a key role in the catalytic transformation of a large fraction of base chemicals. The transition state energies investigated include C-C, C-O, C-N, N-O, N-N, and O-O coupling and have been calculated on different stepped surfaces of transition metals such as Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt, and Au. For a dissociation reaction (AB → A+B), the transition state energy (E ts ) is calculated by Equation (1), in which E ts/slab , E slab and E gas are the total energies of the slab with transition states, the clean slab, and the gas phase molecules relevant for the reactions, respectively. The dissociative adsorption energy (E diss ) is calculated by Equation (2), in which E A/slab and E B/slab are the total energies of the slab with adsorbates A and B, respectively.(1)All calculations were performed using the DACAPO plane-wave pseudo potential DFT code. 13 Ionic cores were described by ultrasoft pseudopotentials 14, and the Kohn-Sham one-electron valence states were expanded in a basis of plane wave functions with a cutoff energy up to 340 eV. For most adsorption systems, the surface Brillouin zone was sampled using a Monkhorst-Pack grid of size 4×4×1, while 2×3×1 was used for O 2 , and 8×6×1 was used for N 2 and NO as a test of the parameters. The self-consistent electron density was determined by iterative diagonalization of the Kohn-Sham Hamiltonian. A Fermi distribution for the population of...