The
simulation of electrochemical reaction dynamics from first principles remains
challenging, since over the course of an elementary step, an electron
is either consumed or produced by the electrode. For example, the
hydrogen evolution reaction begins with a simple proton discharge
to a metal surface, but with conventional electronic structure methods,
the simulated potential, which is manifested as the metal’s
workfunction, varies over the course of the simulation as the electron
is consumed in the new metal–hydrogen bond. Here, we present
a simple approach to allow the direct control of the electrochemical
potential via charging of the electrode surface. This is achieved
by changing the total number of electrons in the self-consistent cycle,
while enforcing charge neutrality through the introduction of a jellium
counter charge dispersed in an implicit solvent region above the slab.
We observe that the excess electrons localize selectively at the metal’s
reactive surface and that the metal workfunction responds nearly linearly
to the variation in electronic count. This linear response allows
for control of the potential in simulations with a minimal computational
penalty compared to standard electronic structure calculations. This
scheme can be straightforwardly implemented with common electronic
structure calculators (density functional theory in the present work),
and we find this method to be compatible with the commonly used computational
hydrogen electrode model, which we expect will make it useful in the
construction of potential-dependent free-energy diagrams in electrochemistry.
We apply this approach to the proton-deposition (Volmer) step on both
Au(111) and Pt(111) surfaces and show that we can reliably control
the simulated electrode potential and thus assess the potential dependence
of the initial, transition, and final states. Our method allows us
to directly assess the location along the reaction pathway with the
greatest amount of charge transfer, which we find to correspond well
with the reaction barrier, indicating this reaction is a concerted
proton–electron transfer. Interestingly, we show that the Pt
electrode has not only a more favorable equilibrium energy with adsorbed
hydrogen but also a lower intrinsic barrier under thermoneutral conditions.