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#### A theoretical analysis of chemical bonding, vibronic coupling, and magnetic anisotropy in linear iron(II) complexes with single-molecule magnet behavior

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##### Citation

Atanasov, M., Zadrozny, J. M., Long, J. R., & Neese, F. (2013). A theoretical analysis
of chemical bonding, vibronic coupling, and magnetic anisotropy in linear iron(II) complexes with single-molecule magnet behavior.* Chemical Science,* *4*(1), 139-156. doi:10.1039/C2SC21394J.

Cite as: http://hdl.handle.net/21.11116/0000-0007-B728-E

##### Abstract

The electronic structure and magnetic anisotropy of six complexes of high-spin Fe

^{II}with linear FeX_{2}(X = C, N, O) cores, Fe[N(SiMe_{3})(Dipp)]_{2}(1), Fe[C(SiMe_{3})_{3}]_{2}(2), Fe[N(H)Ar′]_{2}(3), Fe[N(H)Ar*]_{2}(4), Fe[O(Ar′)]_{2}(5), and Fe[N(t-Bu)_{2}]_{2}(7) [Dipp = C_{6}H_{3}-2,6-Pr^{i}_{2}; Ar′ = C_{6}H_{3}-2,6-(C_{6}H_{3}-2,6-Pr^{i}_{2})_{2}; Ar* = C_{6}H_{3}-2,6-(C_{6}H_{2}-2,4,6-Pr^{i}_{2})_{2}; Ar^{#}= C_{6}H_{3}-2,6-(C_{6}H_{2}-2,4,6-Me_{3})_{2}], and one bent (FeN_{2}) complex, Fe[N(H)Ar^{#}]_{2}(6), have been studied theoretically using complete active space self-consistent field (CASSCF) wavefunctions in conjunction with N-Electron Valence Perturbation Theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for the treatment of magnetic field and spin-dependent relativistic effects. Mössbauer studies on compound 2 indicate an internal magnetic field of unprecedented magnitude (151.7 T) at the Fe^{II}nucleus. This has been interpreted as arising from first order angular momentum of the^{5}Δ ground state of Fe^{II}center (J. Am. Chem. Soc. 2004, 126, 10206). Using geometries from X-ray structural data, ligand field parameters for the Fe-ligand bonds were extracted using a 1 : 1 mapping of the angular overlap model onto multireference wavefunctions. The results demonstrate that the metal–ligand bonding in these complexes is characterized by: (i) strong 3d_{z2}–4s mixing (in all complexes), (ii) π-bonding anisotropy involving the strong π-donor amide ligands (in 1, 3–4, 6, and 7) and (iii) orbital mixings of the σ–π type for Fe–O bonds (misdirected valence in 5). The interplay of all three effects leads to an appreciable symmetry lowering and splitting of the^{5}Δ (3d_{xy}, 3d_{x2−y2}) ground state. The strengths of the effects increase in the order 1 < 5 < 7 ∼ 6. However, the differential bonding effects are largely overruled by first-order spin–orbit coupling, which leads to a nearly non-reduced orbital contribution of L = 1 to yield a net magnetic moment of about 6 μ_{B}. This unique spin–orbital driven magnetism is significantly modulated by geometric distortion effects: static distortions for the bent complex 6 and dynamic vibronic coupling effects of the Renner–Teller type of increasing strength for the series 1–5.Ab initio calculations based on geometries from X-ray data for 1 and 2 reproduce the magnetic data exceptionally well. Magnetic sublevels and wavefunctions were calculated employing a dynamic Renner–Teller vibronic coupling model with vibronic coupling parameters adjusted from the ab initio results on a small Fe(CH_{3})_{2}truncated model complex. The model reproduces the observed reduction of the orbital moments and quantitatively reproduces the magnetic susceptibility data of 3–5 after introduction of the vibronic coupling strength (f) as a single adjustable parameter. Its value varies in a narrow range (f = 0.142 ± 0.015) across the series. The results indicate that the systems are near the borderline of the transition from a static to a dynamic Renner–Teller effect. Renner–Teller vibronic activity is used to explain the large reduction of the spin-reversal barrier U_{eff}along the series from 1 to 5. Based upon the theoretical analysis, guidelines for generating new single-molecule magnets with enhanced magnetic anisotropies and longer relaxation times are formulated.