Graphene nanosheets have been considered as robust support materials for metal nanoparticles and clusters with prominent applications to heterogeneous catalysis. In this study, by using the density functional theory, we performed a systematic investigation of the binding energetics, electronic charge analysis, and migratory surface barriers of free and solvated Pd₃ and Pd₄ clusters over pristine and defect-ridden graphene. Intrinsic as well as extrinsic defects were considered. In intrinsic defects, Stone–Wales defect, single-vacancy defect, and double-vacancy defect were considered, while in extrinsic defects, boron-, nitrogen-, and oxygen-doped systems were considered. Our investigation highlighted double-vacancy-defected graphene and B-doped graphene as excellent materials providing strong traps for Pd₃ and Pd₄ clusters, which not only immobilized the Pd clusters on them but also hindered their surface migration, thereby making them potential candidates for heterogeneous catalytic applications. With a particular reference to the prevalent application of Pd–graphene systems to the catalysis of hydrogenation reactions, we also studied the stability of the clusters in the presence of H₂. Our calculations showed that the stability of the clusters was retained in the presence of H₂, making them suited for the catalysis of hydrogenation reactions.

中文翻译：

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Pd3 和 Pd4 纳米团簇在有缺陷的石墨烯上固定和受阻表面迁移的密度泛函理论研究：对多相催化的影响

石墨烯纳米片已被认为是金属纳米颗粒和簇的强大支撑材料，在多相催化方面具有突出的应用。在这项研究中，我们使用密度泛函理论对游离和溶剂化 Pd ₃和 Pd ₄的结合能量学、电荷分析和迁移表面势垒进行了系统研究。原始和缺陷缠身的石墨烯上的簇。考虑了内在和外在缺陷。在固有缺陷中，考虑了 Stone-Wales 缺陷、单空位缺陷和双空位缺陷，而在外在缺陷中，考虑了硼、氮和氧掺杂系统。我们的研究强调双空位缺陷石墨烯和 B 掺杂石墨烯是为 Pd ₃和 Pd ₄提供强陷阱的优秀材料簇，这不仅将 Pd 簇固定在其上，而且还阻碍了它们的表面迁移，从而使它们成为非均相催化应用的潜在候选者。特别参考 Pd-石墨烯系统在氢化反应催化中的普遍应用，我们还研究了在 H ₂存在下簇的稳定性。我们的计算表明，在 H ₂存在下，团簇的稳定性得以保持，使其适用于催化氢化反应。