The interaction between nickel (Ni²⁺), copper (Cu²⁺), and zinc (Zn²⁺) ions and 1-methylimidazole has been studied by exploring the geometries of eleven crystal structures in the Cambridge Structural Database (CSD). The coordination behavior of the respective ions was further investigated by means of density functional theory (DFT) methods. The gas-phase complexes were fully optimized using B3LYP/GENECP functionals with 6-31G^∗ and LANL2DZ basis sets. The Ni²⁺ and Cu²⁺ complexes show distorted tetrahedral geometries around the central ions, with Zn²⁺ being a perfect tetrahedron. Natural bond orbital (NBO) analysis and natural population analysis (NPA) show substantial reduction in the formal charge on the respective ions. The interaction between metal d-orbitals (donor) and ligand orbitals (acceptor) was also explored using second-order perturbation of the Fock matrix. These interactions followed the order Ni²⁺ > Cu²⁺ > Zn²⁺ with Zn²⁺ having the least interaction with the ligand orbitals. Examination of the frontier orbitals shows the stability of the complexes in the order Ni²⁺ > Cu²⁺ < Zn²⁺ which is consistent with the Irving–Williams series.

中文翻译：

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四面体1-甲基咪唑配合物中Ni2 +，Cu2 +和Zn2 +的配位行为：DFT / CSD研究。

通过在剑桥结构数据库（CSD）中探索11种晶体结构的几何形状，研究了镍（Ni ²⁺），铜（Cu ²⁺）和锌（Zn ²⁺）离子与1-甲基咪唑之间的相互作用。借助密度泛函理论（DFT）方法进一步研究了各个离子的配位行为。使用B3LYP / GENECP功能和6-31G ^*和LANL2DZ基集对气相配合物进行了全面优化。Ni ²⁺和Cu ²⁺配合物在中心离子周围显示扭曲的四面体几何形状，而Zn ²⁺成为完美的四面体。天然键轨道（NBO）分析和天然种群分析（NPA）显示相应离子的形式电荷显着降低。还使用Fock矩阵的二阶扰动来探索金属d轨道（供体）和配体轨道（受体）之间的相互作用。这些相互作用遵循Ni ²⁺  > Cu ²⁺  > Zn ²⁺的顺序，其中Zn ²⁺与配体轨道的相互作用最小。前沿轨道的检查显示了配合物的稳定性，顺序为Ni ²⁺  > Cu ²⁺  <Zn ²⁺，与Irving–Williams系列一致。