Based on density functional theory and the broken-symmetry approach, the magnetic properties of an azido-Cu(II) complex with isonicotinic acid coligands were studied at the B1LYP/def2-TZVP level. According to the molecular magnetic orbitals and Mulliken spin population analysis, there are strong orbital interactions between the paramagnetic Cu^II/Ni^II ions and the bridging azide ligands and isonicotinic ions. The supposedly empty 4s/4p/4d orbitals of the M^II ions are found to play an important role in the mechanism of magnetic coupling and are probed using NBO analysis. As the number of unpaired electrons on the M^II ions increases, the number of electrons that occupy the empty 4d orbitals with the highest energy and overlap integrals of the magnetic orbitals in the Cu^IIM^II (M = Cu, Ni, Co, Fe, Mn) model complexes increases accordingly, and the magnetic coupling constant gradually decreases.

基于密度泛函理论和断裂对称方法，在B1LYP / def2-TZVP水平研究了具有异烟酸大分子配体的叠氮基-Cu（II）配合物的磁性。根据分子磁性轨道和Mulliken自旋种群分析，顺磁性Cu ^II / Ni ^II离子与桥联叠氮化物配体和等渗离子之间存在强烈的轨道相互作用。发现M ^II离子的所谓空4 s / 4 p / 4 d轨道在磁耦合机理中起着重要作用，并使用NBO分析进行了探测。作为M ^II上未成对电子的数量离子增加，占据最高能量的空4 d轨道的电子数量以及Cu ^II M ^II（M = Cu，Ni，Co，Fe，Mn）模型配合物中磁轨道的重叠积分增加，并且磁耦合常数逐渐减小。