Application of Grand Canonical Density Functional Theory to Electrocatalytic Interfaces

Abstract

Grand canonical DFT (GC-DFT) provides a fundamentally correct and accurate description of electrified interfaces and electrocatalysis. GC-DFT calculates the grand free energy at an arbitrary potential by optimizing the grand free energy while self-consistently solving for the number of electrons that matches the applied potential rather than calculating the electronic energy of the system with a fixed number of electrons. Therefore, this work implements GC-DFT to model electrocatalytic interfaces. We first study the effect of the electrochemical environment on the pure metal surfaces. Then, we utilize CG-DFT to model the electrochemical CO2 reduction to CO on selected metal surfaces and compare the results with the Computational Hydrogen Electrode (CHE) approach which is commonly used to model electrochemical reactions. Lastly, we model the full reaction pathway for CO2 reduction to CO over TiN4C site including transition states and kinetic barriers.

We use GC-DFT to predict the surface energies, Wulff shapes, charge distributions and catalytically active sites of different metal surfaces under electrochemical conditions. We propose a method for computing surface energies from GC-DFT calculations of periodic slab models and use it to compute the surface energies of facets of pure metallic crystals to predict their Wulff shapes under electrochemical conditions. GC-DFT predicts that, for the pure metals studied,solvation only slightly affects the Wulff shape while applied potentials considerably affect the surface energies and corresponding Wulff shapes. We study the effect of the applied potential on the distribution of electron density over the atoms of surfaces of pure metals and alloys. This analysis shows that, under an applied potential, the electron density is unevenly distributed over the surface atoms and that the charges of atoms more exposed to solvent are more sensitive to bias. Our results also show that the most sensitive atom to bias can be used to identify the most favorable adsorption site and thus, the active sites of electrochemical reactions.

Then, we report the results of modeling CO2 reduction (CO2R) to CO over Ag(110) and Cu(211) surfaces at different applied potentials using GC-DFT and we compare it with the CHE approach. We modeled the reaction on the most favorable adsorption sites as obtained from the charge sensitivity to bias. GC-DFT predicts that the geometries of theses reacting systems depend on the applied potential and the Helmholtz free energies vary with the applied potential, which contradicts a central assumption of the CHE approach. The CHE approach neglects the change in the number of electrons on the electrode surface at different applied potentials, which reduces its accuracy as the potential changes from the potential of zero charge (PZC). Our results further demonstrate that the grand free energies of the reaction intermediates not only depend on the value of the applied potential, but also on the metal surface type, adsorption site, and adsorbate. GC-DFT’s ability to predict the effect of the applied potential on adsorbate geometry enables it to evaluate different possible reaction mechanisms at different applied potentials. For instance, GC-DFT predicts that the first step of CO2R likely switches from proton coupled electron transfer to sequential electron transfer then proton transfer at more reducing potentials, a result that cannot be determined by CHE because it assumes all electron transfers are coupled to proton transfers and neglects the effect of the applied potential on the adsorbate geometry.

Finally, we use GC-DFT to model the electrocatalytic CO2R to CO by TiN4C, including the activation energies of the elementary steps at various applied potentials, and the thermodynamics of CO2R to CO catalyzed by TiNxC defects. Based on the thermodynamic barriers, TiN4C and all defect configurations are predicted to be promising catalysts for CO2R to CO at certain applied potential range. We propose a criterion to choose the optimum applied potential for CO2R to CO based on the PZC of the reaction intermediates and the contention that the optimum applied potential for CO2R to CO lies in the range 𝑃𝑍𝐶∗𝐶𝑂<𝑉<𝑃𝑍𝐶∗𝐶𝑂2− that can be generalized to other electrocatalytic systems. Solvating H2O molecules are predicted to form strong hydrogen bonds to *COOH, especially at more oxidizing potentials, which significantly influence the thermodynamic barrier for *COOH protonation. Grand canonical nudged elastic band (GC-NEB) was used to predict the rate determining step (RDS) of CO2R to CO catalyzed by TiN4C. GC-NEB predicts that the RDS is potential dependent where CO desorption and CO2 adsorption are RDS at highly reducing and highly oxidizing potentials, respectively.