Superexchange effects play an important role in the determination of crystal structures; however, there has been much less reported on how they determine the stability of clusters. Using evolutionary search strategies and DFT+U (density functional theory with the Hubbard U correction) calculations, we investigate the global minimum-energy structures of Fe₁₂O_n clusters. Among predicted Fe₁₂O_n clusters, a cage-shaped Fe₁₂O₁₂ cluster with unexpected stability was observed. In addition, the bare Fe₁₂O₁₂ cluster is shown to possess an extremely large energy gap (2.00 eV), which is greater than that of C₆₀, Au₂₀ and Al₁₃−clusters. Using a Heisenberg model, we traced the origin of the unexpected stability of the bare Fe₁₂O₁₂ cluster to magnetic competition between the nearest-neighbor exchange constant J₁ and the next-nearest neighbor exchange constant J₂ that was induced by the superexchange interactions. The bare Fe₁₂O₁₂ cluster is thus a unique molecule that is stable and chemically inert.

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超交换效应在晶体结构的确定中起着重要作用。但是，关于它们如何确定星团稳定性的报道很少。使用进化搜索策略和DFT + U（带有Hubbard U校正的密度泛函理论）计算，我们研究了Fe ₁₂ O _n团簇的整体最小能级结构。在预测的Fe ₁₂ O _n团簇中，观察到具有出乎意料的稳定性的笼形Fe ₁₂ O ₁₂团簇。另外，显示出裸露的Fe ₁₂ O ₁₂簇具有非常大的能隙（2.00 eV），该能隙大于C ₆₀，Au的能隙。₂₀和Al _13-团簇。使用Heisenberg模型，我们追踪了Fe ₁₂ O ₁₂裸簇的意外稳定性的起因，这是由超交换相互作用引起的最近邻居交换常数J ₁和下一个邻居交换常数J ₂之间的磁竞争。。因此，裸露的Fe ₁₂ O ₁₂簇是稳定且化学惰性的独特分子。

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