Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
Joint Center for Artificial Photosynthesis, California Institute of Technology, Pasadena, California 91125, USA.
J Chem Phys. 2017 Mar 21;146(11):114104. doi: 10.1063/1.4978411.
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.
第一性原理计算结合密度泛函理论和连续溶剂化模型，能够对电化学系统进行真实的理论建模和设计。当反应在这样的系统中进行时，系统中被量子力学处理的部分的电子数连续变化，在连续电解质中出现平衡电荷。因此，由电极电势设定的化学势下的电子巨正则系综是直接模拟实验条件的此类系统的理想描述。我们提出了两种不同的算法：自洽场方法和使用辅助哈密顿量的直接变分自由能最小化方法（GC-AuxH），直接在固定电势的巨正则系综中求解电子密度泛函理论的 Kohn-Sham 方程。与针对所需电势的一系列常规固定数量的计算相比，这两种方法都显著提高了性能，而 GC-AuxH 方法还表现出了可靠且平滑的巨自由能的指数收敛。最后，我们将巨正则密度泛函理论应用于含有氯离子的电解质中铜在铂上的欠电势沉积，并表明是氯离子的脱附而不是部分铜单层的形成导致了第二个伏安峰。
