過渡金屬錯合物可透過 d 軌域形成金屬-金屬多重鍵 (Metal-metal multiple bond)，然而由於受限於軌域重疊 (orbital overlap) 的空間位向與金屬原子間的距離，其形成的微弱δ鍵常使此系統具備複雜的多重組態特徵 (Multireference character)。針對此系統，本研究選用合適的密度泛函理論 (Density Functional Theory, DFT) 計算方法，並搭配能量最穩定的自旋態 (spin state) 進行計算，得到與實驗晶體結構相符合的結果。此外，為進一步釐清金屬間的鍵結型態，額外採用內稟鍵軌域 (Intrinsic Bond Orbital, IBO) 分析金屬 d 軌域間電子的交互作用，證實該結構之有效鍵級 (effective bond order) 低於理想的成鍵預期。
為了瞭解本研究中雙鉻錯合物的反應機制，我們利用 DFT 計算探討其反應路徑，並將反應路徑分為兩個階段。第一階段為雙鉻錯合物中橋接的雙氮配位基以獨特的方式脫去，並伴隨金屬中心的還原；第二階段為脫氮後的中間體進行兩步的五元環合環反應，其中首步成環因受取代基立體阻礙 (Steric hindrance) 影響，成為此階段的速率決定步驟 (rate-determining step) ；待首步成環完成且分子構象鎖定後，第二步成環即可迅速發生，最終生成熱力學穩定的雙五元環產物。
綜合而言，本研究完整探討了形成雙鉻多重鍵錯合物的反應路徑，並揭示該雙鉻系統獨特的鍵結模式，這不僅成功解釋了實驗上得到的現象，更為未來開發高活性雙金屬催化材料提供重要的方向。

Transition metal complexes can form metal-metal multiple bonds via d orbitals. However, constrained by the spatial orientation of orbital overlap and the intermetallic distance, the resulting weak δ bonds often impart complex multireference character to these systems. In this study, we selected an appropriate Density Functional Theory computational method. By adopting the lowest-energy spin state for our calculations, we obtained results that are consistent with the experimental crystal structure. Furthermore, to better elucidate the metal-metal bonding modes, Intrinsic Bond Orbital analysis was additionally employed to analyze the electronic interactions between the metal d-orbitals, confirming that the effective bond order of the structure is lower than the ideally expected value.
To understand the reaction mechanism of the dichromium complex, DFT calculations were employed to investigate its reaction pathway, which can be divided into two distinct stages. The first stage involves the unique elimination of the bridging dinitrogen ligand, accompanied by the reduction of the metal centers. The second stage features a two-step cyclization of the denitrogenated intermediate to form two five-membered rings. Due to steric hindrance imparted by the substituents, the initial cyclization is kinetically restricted and serves as the rate-determining step for this stage. Once the first ring is formed and the molecular conformation is locked, the second cyclization step proceeds rapidly, ultimately yielding a thermodynamically stable double five-membered ring product.
Overall, this study comprehensively investigates the reaction pathway for the formation of the dichromium multiple-bonded complex and reveals the unique bonding mode within this dichromium system. These findings not only successfully rationalize the experimental observations but also provide critical insights for the future development of highly active bimetallic catalytic materials.

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