August 15, 2018

Controlling the potential in electrochemical simulations

The Solvated Jellium Method.

Electrocatalytic reactions are promising candidates for producing sustainable fuels such as hydrogen and hydrocarbons. In electrochemical setups the catalytic ability of transition metals can be exploited, while at the same time the driving force of the reactions can be controlled via an applied potential. Experimental studies have a long tradition and the application of electrochemical cells is standardized in a large variety of application areas. However, the microscopic principles and mechanisms of even the simplest reactions are not fully understood to this day. This is due to the fact that the reaction conditions are exceptionally complex, where the electrode surface and composition, the applied potential as well as the nanoscale solid-liquid interface play a major role. Therefore, experiments generally need to rely on computational simulations for resolving mechanistic details.

In a recent article published in the Journal of Physical Chemistry C, we have theoretically studied the energetics involved in the hydrogen evolution reaction (HER), being the cathodic reaction of water electrolysis, from first principles. In order to capture the electrochemical nature of the reaction, the standard scheme of density functional theory (DFT), our simulation method of choice, had to be adapted. DFT is generally bound to the simulation of systems containing a constant number of particles, i.e. ions and electrons. An electric circuit, however, represents an open system for electrons, where the potentiostat regulates the applied potential via introducing or extracting electrons to or from the working electrode. In our scheme, referred to as the Solvated Jellium Method (SJM), we are able to consistently, equilibrate the electrode potential in our simulation while we study the kinetics of an electrode reaction happening in a solvent. This is done by systematically varying the number of electrons in the simulation cell on the reaction pathway. Therefore, it allows us to calculate not only reaction free energies, but also study explicit kinetics of the electrode reactions via constant potential activation energies.

Applying this novel scheme, we were able to study the potential dependence of the Volmer reaction, one of the elementary reactions in HER, on platinum and gold. Platinum is the current "golden" standard, when it comes to the activity for HER. In our work we could explain platinum's high activity on the basis of its low intrinsic activation energy (kinetic barrier), when compared to gold. Furthermore, we could explicitly deduce a fundamental behavior of electrochemical reactions. That is, while we observed a linear change in the reaction energy with varying applied potential, as expected from thermodynamics, for the activation energy we found a quadratic trend. This suggests that the charge transfer at the transition state and the Butler-Volmer transfer coefficient are functions of the applied potential.

The Solvated Jellium Method has now been implemented in GPAW, an open-source electronic structure calculator.