Bond Order Conservation Strategies in Catalysis Applied to the NH₃ Decomposition Reaction

On the basis of an extensive set of density functional theory calculations, it is shown that a simple scheme provides a fundamental understanding of variations in the transition state energies and structures of reaction intermediates on transition metal surfaces across the periodic table. The scheme is built on the bond order conservation principle and requires a limited set of input data, still achieving transition state energies as a function of simple descriptors with an error smaller than those of approaches based on linear fits to a set of calculated transition state energies. We have applied this approach together with linear scaling of adsorption energies to obtain the energetics of the NH₃ decomposition reaction on a series of stepped fcc(211) transition metal surfaces. This information is used to establish a microkinetic model for the formation of N₂ and H₂, thus providing insight into the components of the reaction that determines the activity

Examining the Linearity of Transition State Scaling Relations

The dissociation of strong bonds in molecules shows large variations in the geometric structure of the transition state depending on the reactivity of the surface. It is therefore remarkable that the transition state energy can be accurately described through linear relations such as the Brønsted-Evans–Polanyi relations. Linear scaling relations for adsorbates with fixed structure can be understood in terms of bond order conservation but such arguments should not apply to transition states where the geometric structure varies. We have investigated how to relate the concepts from linear adsorption energy scaling to transition state energies. We expect that strong deviations from linearity only occur for very early or very late transition states. According to the Sabatier principle, the rate-limiting step of the best catalysts is not expected to be in either of these regions. Our results therefore support the use of linear transition state scaling relations for the optimization of catalysts

Revealing Local and Directional Aspects of Catalytic Active Sites by the Nuclear and Surface Electrostatic Potential

This work examines the prospects of using the electrostatic potential, V(r), as a descriptor in heterogeneous catalysis. In particular, the subatomic spatial resolution of the property allows for analysis of both directionality and confinement effects in surface adsorption. This feature of V(r) is used to identify adsorption sites, orientations, and energetics for metal surfaces, particles, and nanoclusters upon interactions with catalytically relevant intermediates. The use of V(r) in assessing the 3D nature of catalytic sites in low-temperature and electrocatalysis is highlighted, and future directions in catalysis design are discussed. Ultimately, we provide a critical analysis of the use of V(r) in the predictions of local adsorption susceptibilities, and we address its limitations. The link between V(r) and other established descriptors in catalysis are motivated via physical relations and theoretical derivations; close ties are established between V(r) and the d-band center (εd), as well as the surface site stability (BEM). By comparing the performance of V(r) evaluated on isodensity contours, i.e., the surface electrostatic potential, to that of V(r) evaluated at the nucleus of an atom, we investigate the application space for a directional and an atom-localized version of the V(r) descriptor for catalyst design

Classification of Adsorbed Hydrocarbons Based on Bonding Configurations of the Adsorbates and Surface Site Stabilities

The design of heterogeneous catalysts can be accelerated by identifying relevant descriptors that accurately and effectively link the binding and activation energies to reactivity. Herein, we investigated scaling relations between binding energies of various hydrocarbon-based adsorbates on three different Pt surfaces and metal binding energies estimated via the recently developed α-scheme model. We find that the scaling slopes are similar for certain groups of adsorbates, which then can be classified based on their spatial and electronic structure enabling fast description of binding strengths for each member of the class. Hence, our findings show that the binding energies of simple hydrocarbons CHx, x = {0,1,2,3,4}, and CHCH2 can be used to identify the binding energies of more complex hydrocarbon-based adsorbates. We introduce this classification to establish a generalizable scheme in which complex hydrogenation/dehydrogenation processes of higher hydrocarbons can be predicted via the binding energies of simpler hydrocarbon-based species and ultimately through surface site stabilities

Sintering of Pt Nanoparticles via Volatile PtO₂: Simulation and Comparison with Experiments

It is a longstanding question whether sintering of platinum under oxidizing conditions is mediated by surface migration of Pt species or through the gas phase, by PtO₂(g). Clearly, a rational approach to avoid sintering requires understanding the underlying mechanism. A basic theory for the simulation of ripening through the vapor phase has been derived by Wynblatt and Gjostein. Recent modeling efforts, however, have focused entirely on surface-mediated ripening. In this work, we explicitly model ripening through PtO₂(g) and study how oxygen pressure, temperature, and shape of the particle size distribution affect sintering. On the basis of the available data on α-quartz, adsorption of monomeric Pt species on the support is extremely weak and has therefore not been explicitly simulated, while this may be important for more strongly interacting supports. Our simulations clearly show that ripening through the gas phase is predicted to be relevant. Assuming clean Pt particles, sintering is generally overestimated. This can be remedied by explicitly including oxygen coverage effects that lower both surface free energies and the sticking coefficient of PtO₂(g). Additionally, mass-transport limitations in the gas phase may play a role. Using a parameterization that accounts for these effects, we can quantitatively reproduce a number of experiments from the literature, including pressure and temperature dependence. This substantiates the hypothesis of ripening via PtO₂(g) as an alternative to surface-mediated ripening

Tuning the MoS₂ Edge-Site Activity for Hydrogen Evolution via Support Interactions

The hydrogen evolution reaction (HER) on supported MoS₂ catalysts is investigated using periodic density functional theory, employing the new BEEF-vdW functional that explicitly takes long-range van der Waals (vdW) forces into account. We find that the support interactions involving vdW forces leads to significant changes in the hydrogen binding energy, resulting in several orders of magnitude difference in HER activity. It is generally seen for the Mo-edge that strong adhesion of the catalyst onto the support leads to weakening in the hydrogen binding. This presents a way to optimally tune the hydrogen binding on MoS₂ and explains the lower than expected exchange current densities of supported MoS₂ in electrochemical H₂ evolution studies

Understanding the Reactivity of Layered Transition-Metal Sulfides: A Single Electronic Descriptor for Structure and Adsorption

Density functional theory is used to investigate the adsorption and structural properties of layered transition-metal sulfide (TMS) catalysts. We considered both the (101̅0) M-edge and (1̅010) S-edge terminations for a wide range of pure and doped TMSs, determined their sulfur coverage under realistic operating conditions (i.e, steady-state structures), and calculated an extensive set of chemisorption energies for several important reactions. On the basis of these results, we show that the d-band center, ε_d, of the edge-most metal site at 0 ML sulfur coverage is a general electronic descriptor for both structure and adsorption energies, which are known to describe catalytic activity. A negative linear correlation between adsorbate–S binding and S–metal binding allows ε_d to describe the adsorption of species on both metal and sulfur sites. Our results provide a significant simplification in the understanding of structure–activity relationships in TMSs and provides guidelines for the rational design and large-scale screening of these catalysts for various processes

Surface Tension Effects on the Reactivity of Metal Nanoparticles

We present calculated adsorption energies of oxygen on gold and platinum clusters with up to 923 atoms (3 nm diameter) using density functional theory. We find that surface tension of the clusters induces a compression, which weakens the bonding of adsorbates compared with the bonding on extended surfaces. The effect is largest for close-packed surfaces and almost nonexistent on the more reactive steps and edges. The effect is largest at low coverage and decreases, even changing sign, at higher coverages where the strain changes from compressive to tensile. Quantum size effects also influence adsorption energies but only below a critical size of 1.5 nm for platinum and 2.5 nm for gold. We develop a model to describe the strain-induced size effects on adsorption energies, which is able to describe the influence of surface structure, adsorbate, metal, and coverage