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

The electronic structure and magnetic anisotropy of six complexes of high-spin Fe-II with linear FeX2 (X = C, N, O) cores, Fe[N(SiMe3)(Dipp)](2) (1), Fe[C(SiMe3)(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 = C6H3-2,6-Pr-2(i); Ar' = C6H3-2,6-(C6H3-2,6-Pr-2(i))(2); Ar* = C6H3-2,6-(C6H2-2,4,6-Pr-2(i))(2); Ar-# = C6H3-2,6-(C6H2-2,4,6-Me-3)(2)], and one bent (FeN2) 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. Mossbauer 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)Delta 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) pi-bonding anisotropy involving the strong pi-donor amide ligands (in 1, 3-4, 6, and 7) and (iii) orbital mixings of the sigma-pi 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)Delta (3d(xy), 3d(x2-y2)) ground state. The strengths of the effects increase in the order 1 < 5 < 7 similar to 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 mu(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(CH3)(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.