Understanding active sites and mechanism of oxygen reduction reaction on FeN4–doped graphene from DFT study

First-principle density functional theory (DFT) calculations are performed to study the active sites in FeN₄G electrocatalysts, as well as ORR activity and mechanism. The possible intermediates and transition states existing in the possible reaction paths from Langmuir-Hinschelwood (LH) mechanism are investigated. The results show that the associative pathways of OOH1 formation is prior to that of O₂1 dissociation. The condition of proton adsorbed on top N sites (T2) is more beneficial to the reduction of O-contained species adsorbed on top Fe site (T1) compared to the conditions of proton adsorbed on top C sites (T3). However, the dissociation of O₂1, OOH1 and H₂O₂1 is more likely to occur on the paired T1-T3 sites, since their lower energy barriers compared to other paired sites. The most favorable four-electron reduction pathway follows the mechanisms: O₂1→ OOH1→ O1+H₂O→ OH1+H₂O→ 2H₂O. The rate determining step for ORR on FeN₄G is the reduction of O1 into OH1 (barrier, 0.47 eV). The most feasible pathway for ORR is downhill at a high electrode potential (0.76 V vs. SHE at pH = 0) according to the free energy diagram. Compared to the ideal catalyst, the adsorption energy of OOH1 on FeN₄G is much lower in free energy, while those of OH1 and O1 are slightly higher. Additionally, the elementary reaction rate for OOH1→O1+H₂O is much larger than that of OOH1→H₂O₂ based on the parameter of activation barrier. Therefore, the formation of H₂O₂ (l) is unfavorable on FeN₄G catalysts.     

Mechanisms insight into oxygen reduction reaction on sulfur-doped Fe–N2 graphene electrocatalysts

The density functional theory (DFT) calculations were performed to investigate the stability of the S-doped Fe–N₂G electrocatalysts, as well as ORR mechanism and activity. The most stable configuration is the Fe–N₂S1G because of forming a strong bond structure of Fe–S. In addition, the structures of Fe–N₂S3G and Fe–N₂S4G also exhibit the higher stability compared to the undoped Fe–N₂G. According to the distinct charge difference on the surface, the O-contained intermediates would like to adsorb on the active sites of Fe–N₂ complex active sites. The binding strength of OH on these different catalysts follows the increasing order of Fe–N₂S4G < Fe–N₂S3G < FeN₂G < Fe–N₂S1G < Fe–N₂S5G < Fe–N₂S2G < Fe–N₂S6G < Fe–N₂S7G, implying the opposite order of the catalytic activity. The calculations of the free energy diagrams show that all elementary reaction steps on Fe–N₂S4G, Fe–N₂S3G, FeN₂G and Fe–N₂S1G are downhill. Besides, the rate determining step (RDS) for these catalysts (excluded Fe–N₂S4G) is the fourth reduction step (OH*+H⁺+e⁻→H₂O+*). The study of the reaction mechanisms predicted that the direct 4-electron reduction process is the favorable ORR pathway, and the alternative reaction pathways containing the formation of OH* + OH* co-adsorbate also process without the formation of H₂O₂ for these catalysts. Particularly, Fe–N₂S4G also exhibits the outstanding performance for H₂O₂ reduction. In general, since the higher stability and working potential for ORR, Fe–N₂S4G is predicted to be the prior candidate site for ORR among S-doped FeN₂G catalysts.     

移样离散傅里叶变换在重磁勘探中的应用

基于移样离散傅里叶变换理论,以严谨的数学演绎将高斯节点积分引入傅里叶变换数值计算。演绎结果证明,一个傅里叶积分可用数个移样离散傅里叶变换的加权求和高精度逼近,其权系数为高斯求积系数的1/2,偏移量为高斯节点坐标的1/2加0.5。这一结论为保证重磁勘探中波数域正演问题的精度提供了严谨的理论依据。由于移样离散傅里叶变换理论和高斯节点积分理论的充分条件都是有界函数,基于上述结论的高斯FFT算法的应用领域可拓展到任意有界函数的正、反傅里叶变换。