Gaussian-Based Periodic Grand Canonical Density Functional Theory with Implicit Solvation for Computational Electrochemistry

We present a numerical method for grand canonical density functional theory (DFT) tailored to solid-state systems, employing Gaussian-type orbitals as the primary basis. Our approach directly minimizes the grand canonical free energy using the density matrix as the sole variational parameter, while self-consistently updating the electron number between self-consistent field iterations. To enable realistic electrochemical modeling, we integrate this approach with implicit solvation models. Our solvation scheme introduces less than 50% overhead relative to gas-phase calculations. Compared to existing plane wave-based implementations, our method shows improved robustness in grand canonical simulations. We validate the approach by modeling corrosion at silver surfaces, finding excellent agreement with previous studies. Our method is implemented in the quantum chemistry software Q-Chem. This work lays the groundwork for future wave function-based simulations beyond DFT under electrochemical operando conditions.