Constant Potential Thermodynamic Integration for Obtaining the Free Energy Profile of Electrochemical Reaction.

In this work, we advanced an efficient free energy sampling method based on constrained ab initio molecular dynamics (cAIMD) with a fully explicit solvent layer to depict the electrochemical reaction process at constant surface charge density, named the "Constant-Potential Thermodynamic Integration (CPTI)" method. For automatically adjusting surface charge density at different states, we built an "on-the-fly" procedure which is capable of managing all the necessary steps during cAIMD simulations, including the system pre-equilibrium, surface charge density updating, and force sampling. We applied it to predict the potential-dependent free energy profiles of CO2 adsorption on a single-atom catalyst. The results show that our method can not only account for changes in electrostatic potential energy associated with potential but also consider the potential-induced solvation effects. Our approach enables the accurate simulation of electrochemical environment by presenting the complete solid-liquid interface and efficient computation of electrocatalytic reaction energetics based on a robust potential descriptor.

Continuous constant potential model for describing the potential-dependent energetics of CO2RR on single atom catalysts.

In this work, we have proposed a Continuous Constant Potential Model (CCPM) based on grand canonical density functional theory for describing the electrocatalytic thermodynamics on single atom electrocatalysts dispersed on graphene support. The linearly potential-dependent capacitance is introduced to account for the net charge variation of the electrode surface and to evaluate the free energetics. We have chosen the CO2 electro-reduction reaction on single-copper atom catalysts, dispersed by nitrogen-doped graphene [CuNX@Gra (X = 2, 4)], as an example to show how our model can predict the potential-dependent free energetics. We have demonstrated that the net charges of both catalyst models are quadratically correlated with the applied potentials and, thus, the quantum capacitance is linearly dependent on the applied potentials, which allows us to continuously quantify the potential effect on the free energetics during the carbon dioxide reduction reaction instead of confining it to a specific potential. On the CuN4@Gra model, it is suggested that CO2 adsorption, coupled with an electron transfer, is a potential determining step that is energetically unfavorable even under high overpotentials. Interestingly, the hydrogen adsorption on CuN4@Gra is extremely easy to occur at both the Cu and N sites, which probably results in the reconstruction of the CuN4@Gra catalyst, as reported by many experimental observations. On CuN2@Gra, the CO2RR is found to exhibit a higher activity at the adjacent C site, and the potential determining step is shifted to the *CO formation step at a wide potential range. In general, CCPM provides a simple method for studying the free energetics for the electrocatalytic reactions under constant potential.

Realistic Modeling of the Electrocatalytic Process at Complex Solid-Liquid Interface.

The rational design of electrocatalysis has emerged as one of the most thriving means for mitigating energy and environmental crises. The key to this effort is the understanding of the complex electrochemical interface, wherein the electrode potential as well as various internal factors such as H-bond network, adsorbate coverage, and dynamic behavior of the interface collectively contribute to the electrocatalytic activity and selectivity. In this context, the authors have reviewed recent theoretical advances, and especially, the contributions to modeling the realistic electrocatalytic processes at complex electrochemical interfaces,  and illustrated the challenges and fundamental problems in this field. Specifically, the significance of the inclusion of explicit solvation and electrode potential as well as the strategies toward the design of highly efficient electrocatalysts are discussed. The structure-activity relationships and their dynamic responses to the environment and catalytic functionality under working conditions are illustrated to be crucial factors for understanding the complexed interface and the electrocatalytic activities. It is hoped that this review can help spark new research passion and ultimately bring a step closer to a realistic and systematic modeling method for electrocatalysis.