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

Anton Z. Ni, Adam Rettig, Joonho Lee

TL;DR

This work presents a periodic, Gaussian-basis grand canonical DFT (GCDFT) framework with implicit solvation for electrochemical modeling, enabling direct minimization of the grand potential $\Omega$ with respect to the density matrix while updating the electron number $N$ within SCF iterations. It implements two cavity-based solvation models, LPCM and CANDLE, to account for dielectric and ionic effects, solving the linearized Poisson–Boltzmann equation with minimal memory overhead. The method demonstrates superior SCF convergence and modest solvation overhead, and validates the approach by reproducing known results for silver corrosion under constant potential, aligning with plane-wave-based solvation benchmarks. Overall, the GTO-based GCDFT+solvation framework affords efficient, electrochemistry-relevant simulations and lays the groundwork for future wavefunction-based enhancements in operando conditions.

Abstract

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 wavefunction-based simulations beyond DFT under electrochemical operando conditions.

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

TL;DR

This work presents a periodic, Gaussian-basis grand canonical DFT (GCDFT) framework with implicit solvation for electrochemical modeling, enabling direct minimization of the grand potential with respect to the density matrix while updating the electron number within SCF iterations. It implements two cavity-based solvation models, LPCM and CANDLE, to account for dielectric and ionic effects, solving the linearized Poisson–Boltzmann equation with minimal memory overhead. The method demonstrates superior SCF convergence and modest solvation overhead, and validates the approach by reproducing known results for silver corrosion under constant potential, aligning with plane-wave-based solvation benchmarks. Overall, the GTO-based GCDFT+solvation framework affords efficient, electrochemistry-relevant simulations and lays the groundwork for future wavefunction-based enhancements in operando conditions.

Abstract

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 wavefunction-based simulations beyond DFT under electrochemical operando conditions.

Paper Structure

This paper contains 28 sections, 51 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theoretical Framework and Implementation
  3. Grand Canonical Density Functional Theory
  4. Implicit Solvation Framework
  5. Solvated DFT energy
  6. Cavity functions
  7. Coulomb energy correction
  8. Dielectric free energy
  9. Ionic free energy
  10. Nonelectrostatic energy
  11. Implementation details
  12. Computational Details
  13. Results and Discussion
  14. Verification of Implemented Solvation Models
  15. Grand canonical SCF convergence
  16. ...and 13 more sections

Figures (8)

  • Figure 1: Surface charge as a function of electrode potential relative to PZC at 0.1 M ionic concentration with a computational unit cell height of 60.8 Å for LPCM and CANDLE.
  • Figure 2: Energy ($\Delta E$) and charge ($\Delta Q$) convergence plot with CANDLE for two systems: (a) Cu(111) at 1 V SHE and (b) Pt(111) at 0 V SHE. The convergence is compared with results from JDFTx, which implements the auxiliary Hamiltonian method for minimization of the grand canonical free energy.sundararaman2017
  • Figure 3: Timing breakdown as a function of (a) number of $\mathbf k$-points and (b) the number of atoms in the unit cell. The slab used was a Cu(100) slab with 15 Å vacuum layer with the PBE functional. The sum of the blue (Fock) and orange (CG) represents the net solvation overhead.
  • Figure 4: Potentials of zero charge predicted from LPCM and CANDLE along with the linear fit. Data points were obtained with (100), (110), (111) facets of Cu, Ag, and Au.
  • Figure 5: Potential energy curves for silver corrosion at different potentials relative to the computational SHE. The dashed lines shown are the results reported by Kang and coworkers.kang2024feb All calculations were performed with the RPBE functional with a GPW plane-wave cutoff of 4800 eV except for at 1.00 V, where a GPW plane-wave cutoff of 6000 eV was used.
  • ...and 3 more figures