電化學系統和反應在現代能源轉換應用、電合成和傳感器中無處不在。它們的關鍵特性是通過施加電極電位來控制反應熱力學和動力學。在實驗中，工作電極的電位通過外部電壓源控制，這提供了一種直接操縱電極電位（電極材料內部電子的電化學電位）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.

恒定電極電位實驗對應于電子池電化學電位的控制以及系統電位對電子池電化學電位的響應。盡管實驗通常在恒定電位條件下進行，并且相對于定義良好的參比電極進行參考，但實現恒定電位的原子尺度模擬一直是非常具有挑戰性的。恒定電位和巨正則系綜（GCE）模擬對于揭示電極電位功能的電化學過程的屬性是不可或缺的。

Fig. 2 A schematic illustration of the CIP.

目前，在密度泛函理論（DFT）水平上進行的GCE計算需要在模擬單元內固定費米能級。當模擬外球反應和雙電極電池時，這種方法是不足勝任的。在這些系統中，從DFT計算得到的費米能級并不準確地代表實驗控制的電極電位或描述GCE-DFT中的熱力學獨立變量。

來自芬蘭于韋斯屈萊大學化學系的Marko M. Melander等，提出了一種更一般的GCE-DFT方法，其中電子池電化學電位（而不是DFT的費米能級）被直接控制，開發并實現了一個恒內勢（CIP）DFT方法，實現了恒定電位或偏置電壓條件下電化學系統的GCE-DFT模擬。

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

該方法是金屬系統進行恒勢從頭算模擬領域的一種通用的、理論上嚴格的方法。CIP-DFT可模擬多種電化學系統，并將GCE-DFT模擬的范圍從單個金屬電極和球內反應，擴展到球外反應和偏置雙電極單元。CIP-DFT方法有望被廣泛應用于各種有趣的電化學系統。該文近期發布于npj?Computational Materials10:?5?(2024)。

Editorial Summary

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.?

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.?

Marko M. Melander et al. from the Department of Chemistry, University of Jyv?skyl?, 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及其翻譯

Constant inner potential DFT for modelling electrochemical systems under constant potential and bias (恒定電位和偏壓下電化學系統的恒內勢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?電化學系統在清潔能源轉換等方面發揮著決定性作用，但理解其復雜化學反應仍然是一個未解決的挑戰。恒定電位和巨正則系綜（GCE）模擬對于揭示電化學過程中與電極電位成函數變化的屬性是不可或缺的。目前，在密度泛函理論（DFT）水平上進行的GCE計算需要在模擬單元內固定費米能級。在本文中，我們展示了當模擬外球反應和雙電極電池時，這種方法是不足勝任的。在這些系統中，從DFT計算得到的費米能級并不準確地代表實驗控制的電極電位或描述GCE-DFT中的熱力學獨立變量。為了解決這個限制，我們開發并實現了一個恒內勢（CIP）方法，為在恒定電位或偏置電壓條件下電化學系統的GCE-DFT模擬提供了一種更穩健和通用的方法。CIP的主要優勢是它使用局部電極內部電位作為電極電位的熱力學參數，而不是全局費米能級。通過數值和分析研究，我們證明了CIP和費米能級GCE-DFT方法對于金屬電極和內層反應是等價的。然而，CIP更具有通用性，因為它可以應用于外層和雙電極系統，解決了在這些情景中恒定費米能級方法上的限制。總而言之，CIP方法作為一種從第一原理模擬電化學界面的通用且高效的GCE-DFT方法，脫穎而出。