Using the example of a proton adsorption process, we analyze and compare two prominent modeling approaches in computational electrochemistry at metallic electrodes─electronically canonical, constant-charge and electronically grand-canonical, constant-potential calculations. We first confirm that both methodologies yield consistent results for the differential free energy change in the infinite cell size limit. This validation emphasizes that, fundamentally, both methods are equally valid and precise. In practice, the grand-canonical, constant-potential approach shows superior interpretability and size convergence as it aligns closer to experimental ensembles and exhibits smaller finite-size effects. On the other hand, constant-charge calculations exhibit greater resilience against discrepancies, such as deviations in interfacial capacitance and absolute potential alignment, as their results inherently only depend on the surface charge and not on the modeled charge vs potential relation. The present analysis thus offers valuable insights and guidance for selecting the most appropriate ensemble when addressing diverse electrochemical challenges.

中文翻译：

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收敛发散路径：计算电化学中的恒定电荷与恒定电势能量学

以质子吸附过程为例，我们分析和比较了金属电极计算电化学中两种著名的建模方法——电子正则恒电荷计算和电子大正则恒电位计算。我们首先确认这两种方法对于无限单元尺寸限制中的微分自由能变化产生一致的结果。该验证强调，从根本上来说，这两种方法同样有效且精确。在实践中，大规范、恒势方法显示出卓越的可解释性和尺寸收敛性，因为它更接近实验系综并表现出更小的有限尺寸效应。另一方面，恒定电荷计算对差异（例如界面电容和绝对电势对准的偏差）表现出更大的弹性，因为它们的结果本质上仅取决于表面电荷，而不取决于建模的电荷与电势关系。因此，本分析为在解决各种电化学挑战时选择最合适的整体提供了宝贵的见解和指导。