Experimental studies of the oxygen reduction reaction (ORR) at nitrogen-doped graphene electrodes have reported a remarkably low overpotential, on the order of 0.5 V, similar to Pt-based electrodes. Theoretical calculations using density functional theory have lent support to this claim. However, other measurements have indicated that transition metal impurities are actually responsible for the ORR activity, thereby raising questions about the reliability of both the experiments and the calculations. To assess the accuracy of the theoretical calculations, various generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are employed here and calibrated against high-level wave-function-based coupled-cluster calculations (CCSD(T)) of the overpotential as well as self-interaction corrected density functional calculations and published quantum Monte Carlo calculations of O adatom binding to graphene. The PBE0 and HSE06 hybrid functionals are found to give more accurate results than the GGA and meta-GGA functionals, as would be expected, and for a low dopant concentration, 3.1%, the overpotential is calculated to be 1.0 V. The GGA and meta-GGA functionals give a lower estimate by as much as 0.4 V. When the dopant concentration is doubled, the overpotential calculated with hybrid functionals decreases, while it increases in GGA functional calculations. The opposite trends result from different potential-determining steps, the *OOH species being of central importance in the hybrid functional calculations, while the reduction of *O determines the overpotential obtained in GGA and meta-GGA calculations. The results presented here are mainly based on calculations of periodic representations of the system, but a comparison is also made with molecular flake models that are found to give erratic results due to finite size effects and geometric distortions during energy minimization. The presence of the electrolyte has not been taken into account explicitly in the calculations presented here but is estimated to be important for definitive calculations of the overpotential.

中文翻译：

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评估密度泛函计算氮掺杂石墨烯上的氧还原反应的准确性

氮掺杂石墨烯电极的氧还原反应 (ORR) 的实验研究表明，其过电位非常低，约为 0.5 V，类似于 Pt 基电极。使用密度泛函理论的理论计算为这一主张提供了支持。然而，其他测量表明过渡金属杂质实际上是造成 ORR 活性的原因，从而引发了对实验和计算可靠性的质疑。为了评估理论计算的准确性，各种广义梯度近似 (GGA)、元 GGA、和混合泛函在这里使用，并根据高水平的基于波函数的耦合簇计算 (CCSD(T)) 的过电位以及自相互作用校正的密度泛函计算和已发表的 O 原子绑定的量子蒙特卡罗计算进行校准到石墨烯。发现 PBE0 和 HSE06 混合泛函比 GGA 和元 GGA 泛函给出更准确的结果，正如预期的那样，对于低掺杂浓度（3.1%），计算出的过电位为 1.0 V。GGA 和元-GGA 泛函给出的估计值低达 0.4 V。当掺杂浓度加倍时，使用混合泛函计算的过电位会降低，而在 GGA 泛函计算中会增加。相反的趋势源于不同的潜在决定步骤，*OOH 物质在混合函数计算中至关重要，而 *O 的减少决定了 GGA 和元 GGA 计算中获得的过电位。此处提供的结果主要基于系统周期性表示的计算，但也与分子薄片模型进行了比较，发现由于能量最小化过程中的有限尺寸效应和几何变形，这些模型会给出不稳定的结果。此处介绍的计算中并未明确考虑电解质的存在，但估计对于过电位的确定计算很重要。此处提供的结果主要基于系统周期性表示的计算，但也与分子薄片模型进行了比较，发现由于能量最小化过程中的有限尺寸效应和几何变形，这些模型会给出不稳定的结果。此处介绍的计算中并未明确考虑电解质的存在，但估计对于过电位的确定计算很重要。此处提供的结果主要基于系统周期性表示的计算，但也与分子薄片模型进行了比较，发现由于能量最小化过程中的有限尺寸效应和几何变形，这些模型会给出不稳定的结果。此处介绍的计算中并未明确考虑电解质的存在，但估计对于过电位的确定计算很重要。