The observed magnetic data for two isosceles tricobalt(II) complexes have been successfully analyzed, considering the axial distortion around each cobalt(II) ion, the local spin-orbit coupling, the anisotropic exchange interactions, and the intermolecular exchange interactions. The complexes each contains two types of octahedral high-spin cobalt(II) ions (Co<sub>A</sub> and Co<sub>B</sub>) in the shape of an isosceles triangle (Co<sub>A1</sub>–Co<sub>B</sub>–Co<sub>A2</sub>), and the contribution of the orbital angular momentum is significant. The exchange interaction between the Co<sub>A</sub> and Co<sub>B</sub> ions is practically negligible (<i>J</i> = ~ 0), whereas the interaction between the Co<sub>A1</sub> and Co<sub>A2</sub> ions is ferromagnetic (<i>J</i>’ > 0) for both complexes.
Tricobalt(II) Complex; Magnetic Properties; Spin-Orbit Coupling; Exchange Interaction1. INTRODUCTION
Magnetic analysis of multinuclear octahedral high-spin cobalt(II) complexes is a challenging subject because the orbital angular momentum makes the theoretical treatment difficult [1]. One of the most difficult points is that the local spin-orbit coupling is much larger than the exchange interactions [2]. Another difficult point is that the effect of local distortion is generally too large to be ignored, and that the anisotropic treatment is necessary [2,3].
For mononuclear octahedral high-spin cobalt(II) complexes, Lines [2] and Figgis [3] solved the problem, considering the axial distortion and spin-orbit coupling. For dinuclear complexes containing two equivalent octahedral high-spin cobalt(II) ions, Lines [4] developed a magnetic susceptibility equation for pure octahedral coordination geometries, and Sakiyama [5-10] developed susceptibility equations for distorted octahedral geometries considering the local axial distortion, local spin-orbit coupling, and isotropic/anisotropic exchange interaction. Palii et al. [11-13] derived analytical expressions for the components of the exchange parameter, the g-tensor, and the temperature independent paramagnetism (TIP), based on the application of irreducible tensor operator technique. Recently, Lloret et al. [14] proposed an empirical expression.
In spite of progress in the theoretical treatment of dinuclear high-spin cobalt(II) complexes, magnetic analysis of the trinuclear octahedral high-spin cobalt(II) complexes had not been successfully performed. In this study, a magnetic susceptibility equation was obtained for tricobalt(II) complexes in the shape of an isosceles triangle (CoA2-CoB-CoA2), considering local distortions, local spinorbit couplings, exchange interactions, and the intermolecular exchange interactions. Magnetic analyses were successfully performed for two trinuclear high-spin cobalt(II) complexes [Co3(L1)2(OCOMe)2(NCS)2] (1) and [Co3(L2)2(OCOMe)2(NCS)2] (2) (see Figure 1), whose crystal structures and magnetic data were previously reported [15].
2. EXPERIMENTMagnetic Analysis
The entire calculation was performed on a Power Macintosh 7300/180 computer using the MagSaki(T) program
developed by Sakiyama. Nine independent parameters κA,λA, ΔA, κB, λB, ΔB, J, J’, and θ were determined as described below. First, the susceptibility data above 50 K (or 100 K) were fitted using six local parameters κA, λA, ΔA, κB, λB, and ΔB, excluding the effect of exchange interactions between cobalt(II) ions. Secondly, fixing the six local parameters, the susceptibility data in the entire temperature range (2 - 300 K) were fitted to determine the remaining parameters J, J’, and θ, and finally all the parameters were optimized.
3. RESULTS AND DISCUSSION3.1. Magnetic Susceptibility Equation for Isosceles Tricobalt(II) Complexes
In a trinuclear octahedral high-spin cobalt(II) complex, each cobalt(II) ion (O symmetry) has a local 4T1(4F) ground term, which is split into six Kramers doublets due to a spin-orbit coupling. When the cobalt(II) ion is axially distorted, the order of the six Kramers doublets changes; however, the second-lowest doublet is always more than 100 cm–1 higher than the lowest doublet [2]. Since the local spin-orbit coupling is much larger than the exchange interactions, the exchange interaction is effective only between the lowest doublets of cobalt(II) ions. Therefore, it is appropriate to assume that the exchange interaction causes no effect to the higher doublets [2,5].
Here we want to obtain a magnetic susceptibility equation for an isosceles tricobalt(II) core, as shown in
Figure 2. Full Hamiltonian is written as H = HLF + HLS+ HZE+ Hex, where HLF, HLS, HZE, and Hex are the ligand field term, LS coupling term, Zeeman term, and the exchange term of the Hamiltonian, respectively. The Hamiltonians HLF, HLS, and HZE are as follows: (see Equations (1)-(3))
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