Benchmarking Orbital-Free Density-Potential Functional Theory of Electrified Metal-Solution Interfaces

The electrical double layer (EDL) at the metal-solution interface is a nanoscale region where quantum mechanical metal electrons meet almost classical electrolyte species. Describing metal electrons with orbital-free density-functional theory (DFT), the recently developed density-potential functional theoretical (DPFT) model constitutes a computationally efficient approach to modeling the EDL. However, the performance of orbital-free DFT is less studied for interfaces than for bulk phases. Herein, we develop a constant-potential Kohn-Sham-Poisson-Boltzmann theory with exact kinetic energy as a benchmark for DPFT models. Solving Kohn-Sham and Poisson-Boltzmann equations self-consistently, we obtain electron density, electrostatic potential, and double-layer capacitance of the EDL, which are then used to assess DPFT models with Thomas-Fermi-von Weizsäcker (TFvW) or Pauli-Gaussian kinetic energy functional. In general, TFvW outperforms the Pauli-Gaussian kinetic energy functional for modeling EDL. In addition, a much smaller gradient coefficient in the TFvW functional than the default value of 5/3 is suggested for modeling the EDL. These findings are instrumental to the future development of orbital-free DFT for electrochemical interfaces.