Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1 , 45470 Mülheim an der Ruhr , Germany.
J Chem Theory Comput. 2019 Feb 12;15(2):938-948. doi: 10.1021/acs.jctc.8b00969. Epub 2019 Jan 28.
Face-sharing octahedral dinuclear Cr(III) compounds with d-d electronic configurations represent nontrivial examples of electronic complexity, posing particular challenges for theoretical and computational studies. A tris-hydroxy-bridged Cr(III)-Cr(III) system has proven to be a richly rewarding target for studies of magnetism and electron paramagnetic resonance spectroscopy. It was also reported to be a peculiarly difficult system to treat with density functional theory (DFT). In this work the magnetic coupling problem for this dimer is approached with broken-symmetry (BS)-DFT and multireference calculations that utilize the density matrix renormalization group (DMRG) to handle full-valence active spaces. BS-DFT is shown to recover the correct ordering and energy spacing of Heisenberg spin states if used in conjunction with appropriate spin projection procedures, albeit with pronounced functional sensitivity. The contrasting conclusions of previous studies are traced to incorrect inclusion of electronically excited configurations. Analysis of the direct and differential overlap of corresponding orbital pairs from the BS-DFT solution indicates that metal-metal through-space interaction is the dominant contributor to antiferromagnetic coupling. At the DFT level a procedure that utilizes pseudopotential substitution is demonstrated that allows evaluation of the direct exchange vs superexchange contributions. A complementary description is obtained with DMRG-SCF calculations that enable state-averaged CASSCF calculations with both metal and bridge orbitals in the active space. A localized orbital subspace analysis supports the DFT conclusions that in contrast to doubly bridged isoelectronic analogues, antiferromagnetic coupling in the chromium dimer arises primarily from direct metal-metal interaction but is significantly enhanced by ligand-mediated superexchange.
具有 d-d 电子构型的共享面八面体双核 Cr(III)化合物是电子复杂性的重要实例，对理论和计算研究构成了特殊挑战。三羟桥联 Cr(III)-Cr(III)体系已被证明是研究磁学和电子顺磁共振光谱学的丰富目标。据报道，该体系也是用密度泛函理论（DFT）进行处理的一个特别困难的体系。在这项工作中，使用具有不对称自旋（BS）-DFT 和利用密度矩阵重整化群（DMRG）处理全价活性空间的多参考计算来处理该二聚体的磁耦合问题。如果与适当的自旋投影程序一起使用，BS-DFT 可以恢复 Heisenberg 自旋态的正确排序和能隙，尽管具有明显的功能敏感性。以前研究的相反结论可以追溯到不正确地包含电子激发态构型。对 BS-DFT 解的对应轨道对的直接和微分重叠的分析表明，金属-金属的贯穿空间相互作用是反铁磁耦合的主要贡献者。在 DFT 水平上，展示了一种利用赝势取代的程序，可以评估直接交换与超交换贡献。通过 DMRG-SCF 计算获得了互补描述，该计算允许在活性空间中同时包含金属和桥轨道进行平均态 CASSCF 计算。局部轨道子空间分析支持 DFT 的结论，即与双桥联等电子类似物相反，铬二聚体中的反铁磁耦合主要来自直接的金属-金属相互作用，但通过配体介导的超交换得到显著增强。
