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# Theory and applications of surface micro‐kinetics in the rational design of catalysts using density functional theory calculations

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Rational design of catalysts has long been an important and challenging goal in heterogeneous catalysis. To achieve this target, density functional theory (DFT) calculations and micro‐kinetics are two of the cornerstones. The DFT calculations make it possible to obtain microscopic properties of catalytic systems by computational simulations, and the micro‐kinetic modeling of surface reactions provides a tool to link quantum‐chemical data with macroscopic behaviors of the systems. In this review, we focus on the basic concepts and latest theoretical progresses of strategies for the catalysts design, including Brønsted−Evans−Polanyi relation, the volcano curve, and the activity window. Among the progresses, the theory of chemical potential kinetics in heterogeneous catalysis and its implications on catalysts design, which was developed by our group, are described in detail with extensive derivations. Furthermore, the applications of this method on screening low‐cost counter electrodes for dye‐sensitized solar cells are presented with experimental evidences. WIREs Comput Mol Sci 2017, 7:e1321. doi: 10.1002/wcms.1321

• Structure and Mechanism > Reaction Mechanisms and Catalysis
• Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics
Schematic diagram of the volcano curves associated with reactions in which the adsorption (red) and desorption (blue) are rate determining, together with the real volcano curve (black) (left). The right side of the figure shows the energy profiles on three typical catalysts. μ R and μ P are the chemical potentials of the gaseous reactants and products, respectively. Reprinted from Ref with permission from American Chemical Society.
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Searching for good catalysts by means of the involved chemical potentials. The chemical potentials of reactant and product (μ R and μ P) set the boundaries for the chemical potential of the surface intermediate (μ I, blue zone). On good catalysts, this zone can only be slightly relaxed for the standard chemical potential of the surface intermediate ($μ I o$, red zone). Thus, surfaces of catalysts related to $μ I , C o$ and $μ I , D o$ are very likely to be good catalysts, whereas surfaces related to $μ I , A o$ and $μ I , B o$ cannot be good catalysts. Adapted from Ref with permission from Wiley‐VCH.
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Energy diagram of a model for heterogeneous catalytic reactions. The black curve stands for the profile of total energies calculated from density functional theory (DFT), and the red curve represents the profile of chemical potentials. TS1 and TS2 are the transition states (TSs) of adsorption and desorption, respectively. E tot is the total energy, and μ is the chemical potential (subscripts R, I, and P refer to reactant, intermediate, and product, respectively). $E R tot , ≠$ and $μ R ≠ , o$ are the total energy and standard chemical potential of the TS of adsorption, respectively; $E P tot , ≠$ and $μ P ≠ , o$ have the same meanings for the TS of desorption. The correction of the chemical potential because of the temperature effect is given by Δμ. The thermal corrections for gaseous molecules (Δμ R and Δμ P) are quite large because of large entropy effects, whereas the corrections for surface species are much smaller. RTln(θi /θ* ) is the coverage‐dependent term in the expression of the chemical potential of surface species, and likewise RTln(p/p o) is the pressure‐dependent term for gaseous molecules. Unlike intermediate state, the standard chemical potentials for the TSs appear in the profile of chemical potentials. Adapted from Ref with permission from Wiley‐VCH.
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Schematic profile of a two‐step model taking into consideration the dissociative adsorption of reactants and associative desorption of products on a heterogeneous catalyst surface. ΔH is the enthalpy change of the overall reaction. E R and E P are total energies of the gaseous reactants and products, respectively. E ad,R and E ad,P are the adsorption energies of the reactants and the products, respectively. $E R dis$ and $E P dis$ are the barriers for the adsorption and desorption processes. E I is the energy of the intermediate state. Adapted from Ref with permission from American Chemical Society.
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Schematic representation of the Sabatier's principle and the volcano curve.
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(a–c) Pt(111) surface structure in the presence of CH3CN solvent, I adsorption structure, and the transition‐state structure. (d–f) For the α‐Fe2O3(012) surface, similar with (a–c). (g) Energy profiles of the whole CE reaction on Pt(111), Fe2O3(104), and Fe2O3(012), respectively, which were calculated at U = 0.61 V versus standard hydrogen electrode. Reprinted from Ref with permission from Nature Publishing Group.
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(a) Illustration of calculated E a dis of I 2 dissociation (red dots) and E a des for I* desorption (black squares) in a neutral system (U ext = 0 V) as a function of E ad I. (b) Calculated volcano curves for IRR as a function of E ad I under different external voltages U ext (dashed line, under open‐circuit condition, U ext = 0 V; solid line, 0.54 V), in which three different transfer coefficients for the I* desorption step are considered (blue, 0; green, 0.5; yellow, 1). Adapted from Ref with permission from American Chemical Society.
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Calculated adsorption energy of I atom in the gas phase or in the CH3CN solvent using density functional theory (DFT) method. Blue triangles indicate the reported active materials; black squares represent the unreported materials, which were predicted to be less catalytically active; red pentagons stand for the materials tested in our research. For materials on which the adsorption of iodine atom is endothermic, solvent effects were not considered any more. Adapted from Refs with permission from the Nature Publishing Group.
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Demonstration of range estimation model for the suitable electrodes in terms of the adsorption energy of I atom. TΔS I2 is the entropy correction term of I 2 in gas phase, $Δ μ I 2$ is the chemical potential difference of I 2 molecule in between gas phase and CH3CN solvent at 298 K and ΔG 0 is the Gibbs free‐energy change of half reaction I 2(sol) + 2e → 2I (sol). Reprinted from Ref with permission from the Nature Publishing Group.
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