Controlling potential difference between electrodes based on self-consistent-charge density functional tight binding

A proper understanding and description of the electronic response of the electrode surfaces in electrochemical systems are quite important because the interactions between the electrode surface and electrolyte give rise to unique and useful interfacial properties. Atomistic modeling of the electrodes requires not only an accurate description of the electronic response under a constant-potential condition but also computational efficiency in order to deal with systems large enough to investigate the interfacial electrolyte structures. We thus develop a self-consistent-charge density functional tight binding based method to model a pair of electrodes in electrochemical cells under the constant-potential condition. The method is more efficient than the (ab initio) density functional theory calculations so that it can treat systems as large as those studied in classical atomistic simulations. It can also describe the electronic response of electrodes quantum mechanically and more accurately than the classical counterparts. The constant-potential condition is introduced through a Legendre transformation of the electronic energy with respect to the difference in the number of electrons in the two electrodes and their electrochemical potential difference, through which the Kohn-Sham equations for each electrode are variationally derived. The method is applied to platinum electrodes faced parallel to each other under an applied voltage. The electronic response to the voltage and a charged particle is compared with the result of a classical constant-potential method based on the chemical potential equalization principle.