As one of the most widely used chemical concepts whose origin can be traced back to Lewis theory of bonding a century ago, a covalent bond involves sharing one or more pairs of electrons between atoms. A strong covalent interaction (SCI) is such a covalent bond that two or more electron pairs are shared, yielding a double, triple, quadruple, or even higher bond order. Despite its ubiquity and usefulness, a robust and generally applicable approach to accurately identify strong covalent interactions and determine their bond orders is still lacking. In this work, an SCI index is proposed from density functional theory using the Pauli energy, which is the contribution of the Pauli exclusion principle to the kinetic energy. Illustrative examples from organic, inorganic, and organometallic systems were provided. Its close relationship with the electron localization function (ELF) was elucidated. Both ELF and SCI generate similar results. Two complexes with a quintuple metal–metal bond have been confirmed. A stronger than quintuple bond has been showcased. This work should provide a robust approach to determine bond orders for strong covalent interactions in complex systems, pinpoint the physiochemical origin of strong covalent interactions, and rationalize the usefulness of both SCI and ELF. These tools should be able to be applied to other systems in different fields to effectively appreciate strong covalent interactions.

中文翻译：

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识别与Pauli Energy的强共价相互作用

作为最广泛使用的化学概念之一，其起源可以追溯到一个世纪前的刘易斯（Lewis）的键合理论，共价键涉及在原子之间共享一对或多对电子。强共价相互作用（SCI）是这样的共价键，两个或多个电子对被共享，从而产生双键，三键，四倍甚至更高的键序。尽管它无处不在和有用，但仍然缺少一种可靠且普遍适用的方法来准确识别强共价相互作用并确定其键序。在这项工作中，使用保利能量从密度泛函理论提出了SCI指数，这是保利排除原理对动能的贡献。提供了来自有机，无机和有机金属体系的说明性实例。阐明了它与电子定位功能（ELF）的密切关系。ELF和SCI都产生相似的结果。已经确认了具有五重金属-金属键的两个络合物。已经展示出比五重债券更强大的债券。这项工作应提供一种确定复杂系统中强共价相互作用的键序的稳健方法，查明强共价相互作用的理化起源，并使SCI和ELF的实用性合理化。这些工具应该能够应用于不同领域的其他系统，以有效地了解强大的共价相互作用。这项工作应提供一种确定复杂系统中强共价相互作用的键序的稳健方法，查明强共价相互作用的理化起源，并使SCI和ELF的实用性合理化。这些工具应该能够应用于不同领域的其他系统，以有效地了解强大的共价相互作用。这项工作应提供一种确定复杂系统中强共价相互作用的键序的稳健方法，查明强共价相互作用的理化起源，并使SCI和ELF的实用性合理化。这些工具应该能够应用于不同领域的其他系统，以有效地了解强大的共价相互作用。