推进电化学模拟：恒内势DFT

电化学系统和反应在现代能源转换应用、电合成和传感器中无处不在。它们的关键特性是通过施加电极电位来控制反应热力学和动力学。在实验中，工作电极的电位通过外部电压源控制，这提供了一种直接操纵电极电位（电极材料内部电子的电化学电位）的方法。

Fig. 1 Depiction of a two-electrode cell with the relevant electrochemical potentials. The dotted rectangle shows the system explicitly treated in (GCE-)DFT simulations.

恒定电极电位实验对应于电子池电化学电位的控制以及系统电位对电子池电化学电位的响应。尽管实验通常在恒定电位条件下进行，并且相对于定义良好的参比电极进行参考，但实现恒定电位的原子尺度模拟一直是非常具有挑战性的。恒定电位和巨正则系综（GCE）模拟对于揭示电极电位功能的电化学过程的属性是不可或缺的。

Fig. 2 A schematic illustration of the CIP.

目前，在密度泛函理论（DFT）水平上进行的GCE计算需要在模拟单元内固定费米能级。当模拟外球反应和双电极电池时，这种方法是不足胜任的。在这些系统中，从DFT计算得到的费米能级并不准确地代表实验控制的电极电位或描述GCE-DFT中的热力学独立变量。

Fig. 3 Analysis of the inner sphere reaction.

来自芬兰于韦斯屈莱大学化学系的Marko M. Melander等，提出了一种更一般的GCE-DFT方法，其中电子池电化学电位（而不是DFT的费米能级）被直接控制，开发并实现了一个恒内势（CIP）DFT方法，实现了恒定电位或偏置电压条件下电化学系统的GCE-DFT模拟。

Fig. 4 Illustration and results for the molecular dynamics simulations.

该方法是金属系统进行恒势从头算模拟领域的一种通用的、理论上严格的方法。CIP-DFT可模拟多种电化学系统，并将GCE-DFT模拟的范围从单个金属电极和球内反应，扩展到球外反应和偏置双电极单元。CIP-DFT方法有望被广泛应用于各种有趣的电化学系统。该文近期发布于npj Computational Materials10: 5 (2024)。

Fig. 5 A schematic illustration of the electrochemical potential of the Au(111) electrode and the adiabatic free energy level (redox potential) of the Ru[NH3]63+/2+ redox couple on the absolute electrode potential scale3.

Editorial Summary

Advancing Electrochemical Modeling: Constant Inner Potential DFT

Electrochemical systems and reactions are ubiquitous in modern energy conversion applications, electrosynthesis, and sensors, to name but a few. Their key property is the ability to control reaction thermodynamics and kinetics through the application of an electrode potential. In experiments, the potential of a working electrode is controlled from the backside of an electrode through connections to an external voltage source. This provides a direct way to manipulate the electrode potential, i.e. the electrochemical potential of electrons within the bulk of the electrode material. Constant electrode potential experiments correspond to controlling the electrochemical potential of an electron reservoir and the system potential, responds to the change in the electrochemical potential. While experiments are routinely performed under constant potential conditions and referenced against well-defined reference electrodes, realizing constant potential atomistic simulations has been very challenging.

Fig. 6 Ru[NH3]63+ on the Au(111) surface.

Constant potential and grand canonical ensemble (GCE) simulations are indispensable for unraveling the properties of electrochemical processes as a function of the electrode potential. Currently, GCE calculations performed at the density functional theory (DFT) level require fixing the Fermi level within the simulation cell. This method is inadequate when modeling outer sphere reactions and a biased two-electrode cell. For these systems, the Fermi level obtained from DFT calculations does not accurately present the experimentally controlled electrode potential or describe the thermodynamic independent variable in GCE-DFT.

Fig. 7 Results for the two-electrode setup within CIP-DFT.

Marko M. Melander et al. from the Department of Chemistry, University of Jyväskylä, presented a more general GCE-DFT approach, in which the electrochemical potential rather than Fermi level is explicitly controlled. The authors developed and implemented a constant inner potential (CIP) method, offering a more robust and general approach to conducting GCE-DFT simulations of electrochemical systems under constant potential or bias conditions. They illustrated that this approach offers a versatile and theoretically rigorous approach for conducting constant potential ab initio simulations for metallic systems. CIP-DFT emerges as a universal approach for simulating a wide variety of electrochemical systems and expands the scope of the GCE-DFT simulations from a single metallic electrode and inner-sphere reactions to outer-sphere reactions and biased two-electrode cells. CIP-DFT methods may be broadly applied and applicable to a wide variety of interesting electrochemical systems. This article was recently published in npj Computational Materials 10: 5 (2024).

原文Abstract及其翻译

Constant inner potential DFT for modelling electrochemical systems under constant potential and bias (恒定电位和偏压下电化学系统的恒内势DFT)

Marko M. Melander, Tongwei Wu, Timo Weckman & Karoliina Honkala

Abstract Electrochemical systems play a decisive role in, e.g. clean energy conversion but understanding their complex chemistry remains an outstanding challenge. Constant potential and grand canonical ensemble (GCE) simulations are indispensable for unraveling the properties of electrochemical processes as a function of the electrode potential. Currently, GCE calculations performed at the density functional theory (DFT) level require fixing the Fermi level within the simulation cell. Here, we illustrate that this method is inadequate when modeling outer sphere reactions and a biased two-electrode cell. For these systems, the Fermi level obtained from DFT calculations does not accurately present the experimentally controlled electrode potential or describe the thermodynamic independent variable in GCE-DFT. To address this limitation, we developed and implemented a constant inner potential (CIP) method offering a more robust and general approach to conducting GCE-DFT simulations of electrochemical systems under constant potential or bias conditions. The primary advantage of CIP is that it uses the local electrode inner potential as the thermodynamic parameter for the electrode potential, as opposed to the global Fermi level. Through numerical and analytical studies, we demonstrate that the CIP and Fermi level GCE-DFT approaches are equivalent for metallic electrodes and inner-sphere reactions. However, CIP proves to be more versatile, as it can be applied to outer-sphere and two-electrode systems, addressing the limitations of the constant Fermi-level approach in these scenarios. Altogether, the CIP approach stands out as a general and efficient GCE-DFT method simulating electrochemical interfaces from first principles.

摘要 电化学系统在清洁能源转换等方面发挥着决定性作用，但理解其复杂化学反应仍然是一个未解决的挑战。恒定电位和巨正则系综（GCE）模拟对于揭示电化学过程中与电极电位成函数变化的属性是不可或缺的。目前，在密度泛函理论（DFT）水平上进行的GCE计算需要在模拟单元内固定费米能级。在本文中，我们展示了当模拟外球反应和双电极电池时，这种方法是不足胜任的。在这些系统中，从DFT计算得到的费米能级并不准确地代表实验控制的电极电位或描述GCE-DFT中的热力学独立变量。为了解决这个限制，我们开发并实现了一个恒内势（CIP）方法，为在恒定电位或偏置电压条件下电化学系统的GCE-DFT模拟提供了一种更稳健和通用的方法。CIP的主要优势是它使用局部电极内部电位作为电极电位的热力学参数，而不是全局费米能级。通过数值和分析研究，我们证明了CIP和费米能级GCE-DFT方法对于金属电极和内层反应是等价的。然而，CIP更具有通用性，因为它可以应用于外层和双电极系统，解决了在这些情景中恒定费米能级方法上的限制。总而言之，CIP方法作为一种从第一原理模拟电化学界面的通用且高效的GCE-DFT方法，脱颖而出。