Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry

2017/01/31 by Ravishankar Sundararaman, William A. Goddard III, William A. Goddard +2
Chemistry · Energy · Engineering · Mathematics · Physics and Astronomy · #Canonical ensemble #Chemistry #Computational chemistry #Density functional theory #Electrocatalysts for Energy Conversion #Electrochemistry #Electrode #Electrolyte #Electron #Grand canonical ensemble #Grand potential #Materials science #Mathematics #Molecular Junctions and Nanostructures #Physical chemistry #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #cond-mat.mtrl-sci #physics.chem-ph #physics.comp-ph

paper · pdf · doi:10.1063/1.4978411

published as J. Chem. Phys. 146, 114104 (2017) · 15 pages, 12 figures

arxiv created 2017/02/28 · openalex publication_date 2017/03/16 · arxiv updated 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solve the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Finally, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.

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