(370c) A Descriptor Based Approach Towards Understanding the Effect of Functionals on Reducible Oxide Reaction Kinetics

Density Functional Theory (DFT) is the workhorse for the computational design of catalysts. The inherent errors within this theory and the effect of the functional on macroscopic observables, such as reaction rates, are well documented for transition metals ^{[1]- [3]}, but there have been fewer studies focused on reducible metal oxides. Herein, using methanol oxidation on MoO₃(010) as a prototypical example, we demonstrate the effect of the functional on competition between methanol oxidation and redox steps involving oxygen vacancies, within a Mars van Krevelen mechanism. A direct correspondence between reaction kinetics and the degree of binding, a descriptor for DFT functionals, is presented. Adsorption energies of 21 covalently bound intermediates that participate in the catalytic cycle, calculated with the BEEF-vdW functional, (a functional constructed for surface science), follow linear scaling with binding energies computed using a series of GGA and GGA-vdW functionals. The linear relationships have a slope of 1±0.03, and an intercept, termed as the degree of binding (δ), representing an average difference in adsorption strengths between a given XC functional and the reference functional (BEEF-vdW). Unlike adsorption energies, however, the activation energies of elementary steps for all functionals are nearly equal. GGA-vdW functionals have a more negative degree of binding (δ values of -0.50, -0.40 and -0.23 eV for optB88-vdW, optPBE-vdW, and PBE-vdWDF2, respectively) as compared with pure GGA functionals (δ values of -0.02 and 0.39 eV for PBE and RPBE, respectively). Using scaling relationships, the kinetic and thermodynamic barriers with a given functional are expressed in terms of those calculated using BEEF-vdW and the descriptor, δ (MAE of ±0.12 eV). By inputting these relationships into a detailed microkinetic model, it is found that the apparent activation energy of the reaction exhibits a parabolic dependence with δ. Hence, higher activation energies are observed for functionals with extreme values of δ. Rate determining steps and methanol/oxygen orders remain fairly constant as δ decreases from 0.39 eV to -0.23 eV. For δ below -0.23 eV, the rate determining steps shift from those associated with methanol oxidation to steps related to oxidation of vacancies. Thus, although rates and apparent activation energies show a strong dependence on δ, shifts in the reaction mechanism are observed for only those functionals with very negative values of δ (optB88-vdW and optPBE-vdW). From these observations, we propose that it may be possible to generate very accurate microkinetic models of kinetics on reducible oxides by fitting just one parameter, δ, to very limited series of experimental data.

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2. Liu, B.; Cheng, L.; Curtiss, L.; Greeley, J.; Surf. Sci. 2014, 622, 51-519.

3. Wellendorff, J.; Silbaugh, T.; Garcia-Pintos, D.; Nørskov, J. K.; Bilgaard, T.; Studt, F.; Campbell, C.T.; Surf. Sci. 2015, 640, 36-44.