Detailed state-of-the-art ab initio and Density functional theory (DFT) calculations have been undertaken to understand both Single-Molecule Magnetic (SMM) and Single-Molecule Toroic (SMT) behavior of fascinating 3d-4f;{M3Ln3} triangular complexes having a molecular formula [MII3LnIII3(O2)L3(PyCO2)3](OH)2(ClO4)2·8H2O (when M = Zn; Ln = Dy (1), Tb (2) & Gd (3) and M = Cu; Ln = Dy (4), Tb (5) & Gd (6)) and [Ni3Ln3(H2O)3(mpko)9(O2)(NO3)3](ClO4)·3CH3OH·3CH3CN] (Ln = Dy (7), Tb (8), and Gd (9)) [mpkoH = 1-(pyrazin-2-yl)ethanone oxime]. All these complexes possess a peroxide ligand that bridges the {LnIII3} triangle in µ3–η3:η3 fashion and the oxygen atoms/oxime of co-ligands that connect each MII ion to the {LnIII3} triangle. Through our computational studies, we tried to find the key role of the peroxide bridge and how that helps in the SMM and SMT behavior of these complexes. Primarily, ab initio Complete Active Space Self-Consistent Field (CASSCF) SINGLE_ANISO+RASSI-SO+POLY_ANISO calculations were performed on 1, 2, 4, 5, 7, and 8 to study the anisotropic behavior of each Ln(III) ion, to derive the magnetic relaxation mechanism and to calculate the LnIII−LnIII and CuII/NiII−LnIII magnetic coupling constants. DFT calculations were also performed to validate those exchange interactions (J) by computing the GdIII−GdIII, CuII/NiII−GdIII interactions in 3, 6, and 9. The experimental magnetic relaxation process and the magnetic exchange interactions for all complexes were explained by our calculations, which also strongly imply that the peroxide bridge plays a role in observing SMM behavior in these systems. On the other hand, this peroxide bridge does not support the SMT behavior. To investigate the effect of bridging ions in {M3Ln3} systems, we modeled a {ZnII3DyIII3} (complex 1a) with hydroxide ion replacing the bridged peroxide ion in complex 1 and considered a hydroxide-bridged {CoIII3DyIII3} (10) complex having a formula of [Co3Dy3(OH)4(OOCCMe3)6(teaH)3(H2O)3](NO3)2·H2O. We discovered that as compared to the LoProp charges of peroxide ion, the greater negative charges on the bridging hydroxide ion reduce quantum tunneling of magnetization (QTM) effects, enabling more desired SMM characteristics and also leading to good SMT behavior.

中文翻译：

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过氧化物桥双三角{MII3LnIII3}（M = Ni、Cu 和Zn；Ln = Gd、Tb 和Dy）配合物中单分子磁性和单分子环形行为的理论探索


我们进行了详细的最先进的从头计算和密度泛函理论 (DFT) 计算，以了解迷人的 3d-4f;{M3Ln3} 三角形的单分子磁性 (SMM) 和单分子环面 (SMT) 行为分子式为 [MII3LnIII3(O2)L3(PyCO2)3](OH)2(ClO4)2·8H2O 的配合物（当 M = Zn；Ln = Dy (1)、Tb (2) & Gd (3) 和 M = Cu；Ln = Dy (4)、Tb (5) & Gd (6)) 和 [Ni3Ln3(H2O)3(mpko)9(O2)(NO3)3](ClO4)·3CH3OH·3CH3CN] (Ln = Dy (7)、Tb (8) 和 Gd (9)) [mpkoH = 1-(吡嗪-2-基)乙酮肟]。所有这些配合物都具有过氧化物配体，以 µ3–η3:η3 方式桥接 {LnIII3} 三角形，以及将每个 MII 离子连接到 {LnIII3} 三角形的辅助配体的氧原子/肟。通过计算研究，我们试图找出过氧化物桥的关键作用以及它如何帮助这些复合物的 SMM 和 SMT 行为。首先，对 1、2、4、5、7 和 8 进行从头算完整活性空间自洽场 (CASSCF) SINGLE_ANISO+RASSI-SO+POLY_ANISO 计算，以研究每个 Ln(III) 离子的各向异性行为，推导磁弛豫机制并计算 LnIII−LnIII 和 CuII/NiII−LnIII 磁耦合常数。还进行了 DFT 计算，通过计算 3、6 和 9 中的 GdIII−GdIII、CuII/NiII−GdIII 相互作用来验证这些交换相互作用 (J)。所有配合物的实验磁弛豫过程和磁交换相互作用解释为我们的计算，这也强烈暗示过氧化物桥在观察这些系统中的 SMM 行为中发挥着作用。另一方面，这种过氧化物桥不支持 SMT 行为。 为了研究桥接离子在 {M3Ln3} 系统中的影响，我们模拟了 {ZnII3DyIII3}（配合物 1a），其中氢氧根离子取代了配合物 1 中桥接的过氧化物离子，并考虑了氢氧根桥接的 {CoIII3DyIII3} (10) 配合物，其结构式为[Co3Dy3(OH)4(OOCCMe3)6(teaH)3(H2O)3](NO3)2·H2O。我们发现，与过氧化物离子的 LoProp 电荷相比，桥接氢氧根离子上更大的负电荷减少了磁化量子隧道 (QTM) 效应，从而实现了更理想的 SMM 特性，并导致良好的 SMT 行为。