**Open Journal of Inorganic Chemistry** Vol.1 No.3(2011), Article ID:8153,6 pages DOI:10.4236/ojic.2011.13005

Magnetic analyses of isosceles tricobalt(II) complexes containing two types of octahedral high-spin cobalt(II) ions

^{1}Department of Material and Biological Chemistry, Faculty of Science, Yamagata University, Kojirakawa, Japan;

^{2}Department of Chemistry, The University of Sheffield, Sheffield, UK;

^{3}Department of Chemistry, Faculty of Science, Kyushu University, Fukuoka, Japan.

Email: ^{*}saki@sci.kj.yamagata-u.ac.jp

Received 5 September 2011; revised 5 October 2011; accepted 20 October 2011.

**Keywords:** Tricobalt(II) Complex; Magnetic Properties; Spin-Orbit Coupling; Exchange Interaction

ABSTRACT

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_{A} and Co_{B}) in the shape of an isosceles triangle (Co_{A1}-Co_{B}-Co_{A2}), and the contribution of the orbital angular momentum is significant. The exchange interaction between the Co_{A} and Co_{B} ions is practically negligible (J = ~ 0), whereas the interaction between the Co_{A1} and Co_{A2} ions is ferromagnetic (J’ > 0) for both complexes.

1. 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 (Co_{A2}-Co_{B}-Co_{A2}), 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 [Co_{3}(L1)_{2}(OCOMe)_{2}(NCS)_{2}] (1) and [Co_{3}(L2)_{2}(OCOMe)_{2}(NCS)_{2}] (2) (see Figure 1), whose crystal structures and magnetic data were previously reported [15].

2. EXPERIMENT

Magnetic Analysis

The entire calculation was performed on a Power Macintosh 7300/180 computer using the MagSaki(T) program

Figure 1. Chemical structures of L1^{–} (R = C_{2}H_{5}) and L2^{–} (R = n-C_{3}H_{7}).

developed by Sakiyama. Nine independent parameters κ_{A},λ_{A}, Δ_{A}, κ_{B}, λ_{B}, Δ_{B}, 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 κ_{A}, λ_{A}, Δ_{A}, κ_{B}, λ_{B}, and Δ_{B}, 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 DISCUSSION

3.1. 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 ^{4}T_{1}(^{4}F) 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 = H_{LF} + H_{LS}+ H_{ZE}+ H_{ex}, where H_{LF}, H_{LS}, H_{ZE}, and H_{ex} are the ligand field term, LS coupling term, Zeeman term, and the exchange term of the Hamiltonian, respectively. The Hamiltonians H_{LF}, H_{LS}, and H_{ZE} are as follows: (see Equations (1)-(3))

(1)

Figure 2. Isosceles tricobalt(II) core.

(2)

If we assume isotropic exchange interactions between local true spins (S_{A1} = S_{A2} = S_{B} = 3/2), the exchange part of the Hamiltonian can be written as

(4)

Since the local ^{4}T_{1} ground term is split by spin-orbit coupling larger than the exchange interactions, the local effective spins (s_{A1} = s_{A2} = s_{B} = 1/2) for the local lowest Kramers doublets are introduced [2,8].

(U = A1, A2, and B) (5)

Assuming axial symmetry for local effective spins (β_{U} = α_{U} and s_{U,y} = s_{U,x}), the exchange Hamiltonian can be rewritten as

, (6)

whereand.

The coefficients α_{U} and γ_{U} (U = A1, A2, and B) can be expressed by the local parameters κ_{U}, λ_{U}, and Δ_{U} [2,8], where κ_{U} is the orbital reduction factor, λ_{U} is the spin-orbit coupling parameter, and Δ_{U} is the axial splitting parameter. The zero-field splitting parameter (D_{quin}) within an effective quintet state, generated from the three local effective spins (1/2), can be expressed as D_{quin} = D_{eff}/3 + D’_{eff}/6 [16].

At this stage, the susceptibility equation can be expressed as follows:

, (7)

where θ is the Weiss constant to describe the intermolecular exchange interactions. This interaction is actually temperature-dependent, but it is approximated as a constant in this study. The zero-field energies and firstand second-order Zeeman coefficients for each cobalt(II) ion, , , , , and (n = ±1 - ±6) can be expressed using equations reported previously [5,6].

(3)

(8)

(9)

(10)

3.2. Structural Features of 1 and 2

The crystal structures of 1 and 2 have been reported previously [15]; thus, only the structural features are briefly mentioned here. Both 1 and 2 have tricobalt(II) structures as shown in Figure 3, and the structures are very similar. Both ligands L1^{–} and L2^{–} have an N_{2}O coordination site and an NO site (see Figure 1). The N_{2}O site of a ligand incorporates a cobalt(II) ion (Co_{A}), and another cobalt(II) ion (Co_{B}) is incorporated by two NO sites of the two ligands, forming a trinuclear structure in the shape of an isosceles triangle. Co_{A} and Co_{B} are bridged by a phenolic oxygen atom of the ligand and an oxygen atom from an external acetate ion. Two Co_{A} ions (Co_{A1} and Co_{A2}) are bridged by two pairs of syn-anti bidentate oxygen atoms of two acetate ions. The coordination geometry for each cobalt(II) ion is distorted octahedral.

3.3. Magnetic Data Analysis

Magnetic data for complexes 1 and 2, as well as the preparations and crystal structures, were reported earlier [15], but no theoretical analysis of the data was made. The temperature dependencies of χ_{M} and µ_{eff} for the Co_{3} unit for 1 and 2 are shown in Figures 4 and 5, respectively. The µ_{eff} values for the Co_{3} unit for 1 and 2 at room temperature are 8.36 and 8.45 µ_{B}, respectively. These values are larger than the spin-only value of the high-spin cobalt(II) ion (6.71 µ_{B}; µ_{SO} = [3{4S(S+1)}]^{1/2}; S = 3/2) but close to the value expected when the spin momentum and orbital momentum exist independently [9.00 µ_{B}; µ_{LS} = [3{L(L+1)+ 4S(S+1)}]^{1/2}; L = 3, S = 3/2]. This indicates a contribution of the orbital angular momentum typical of the local ^{4}T_{1} ground term. Moreover, the characteristic slopes of µ_{eff} curves are typical for the result of spin-orbit coupling. Therefore, the data were analyzed using the equation in Section 3.1, considering the local axial distortions, the local spin-orbit couplings, the anisotropic exchange interactions, and the intermolecular exchange interactions. The obtained parameters are summarized in Table 1.

The orbital reduction factor κ corresponds to the delocalization of unpaired electrons from metal ions to ligand, but it also contains the admixture of the upper ^{4}T_{1}(^{4}P) state into the ^{4}T_{1}(^{4}F) ground state. The κ value is known to be ~0.93 for the free cobalt(II) ion [4,17], and the obtained κ_{A} and κ_{B} values for both complexes are close to the free ion value. Comparing the axial splitting parameters Δ_{A} and Δ_{B}, Δ_{B} is larger than Δ_{A} for both complexes. All the Δ values for both complexes are normal for octahedral high-spin cobalt(II) complexes (~ 200 - ~ 800 cm^{–1}) [3]. The spin-orbit coupling parameter λ for the free cobalt(II) ion is theoretically expected to be ~ –172 cm^{–1} [18], but is generally smaller in the complexes. For complex 1, the λ_{A} value is normal (~70% of the free ion value), whereas the λ_{B} value is slightly smaller than the normal value. This occurs presumably because the assumed symmetry is less suitable for Co_{B}. That is, the local distortion axes are assumed to be parallel in this studyand this assumption may not be adequate. A similar tendency is also seen for complex 2.

The magnetic susceptibility below 50 K cannot be fitted without consideration of the exchange interactions. If we assume that there is no exchange interaction (J = 0.00 cm^{–1}, J’ = 0.00 cm^{–1}, and θ = 0.00 K), the calculated susceptibility curves are lower than the observed susceptibility below ~50K for both complexes as shown in

Figure 3. Schematic drawing of the tricobalt(II) structure for 1 (R = C_{2}H_{5}) and 2 (R = n-C_{3}H_{7}).

Figure 4. Temperature dependencies of χ_{M} (O) and µ_{eff} (∆) of complex 1. Solid curves are drawn with the parameters κ_{A} = 0.93, λ_{A} = –151 cm^{–1}, Δ_{A} = 604 cm^{–1}, κ_{B} = 0.93, λ_{B} = –101 cm^{–1}, Δ_{B} = 714 cm^{–1}, J = +0.01 cm^{–1}, J’ = +1.51 cm^{–1}, and θ = –0.61 K. The dashed curve in the insert is drawn with the parameters κ_{A} = 0.93, λ_{A} = –151 cm^{–1}, Δ_{A} = 604 cm^{–1}, κ_{B} = 0.93, λ_{B} = –101 cm^{–1}, Δ_{B} = 714 cm^{–1}, J = 0.00 cm^{–1}, J’ = 0.00 cm^{–1}, and θ = 0.00 K.

Figure 5. Temperature dependencies of χ_{M} (O) and µ_{eff} (∆) of complex 2. Solid curves are drawn with the parameters κ_{A} = 0.93, λ_{A} = –136 cm^{–1}, Δ_{A} = 531 cm^{–1}, κ_{B} = 0.93, λ_{B} = –115 cm^{–1}, Δ_{B} = 674 cm^{–1}, J = +0.01 cm^{–1}, J’ = +1.76 cm^{–1}, and θ = –1.08 K. The dashed curve in the insert is drawn with the parameters κ_{A} = 0.93, λ_{A} = –136 cm^{–1}, Δ_{A} = 531 cm^{–1}, κ_{B} = 0.93, λ_{B} = –115 cm^{–1}, Δ_{B} = 674 cm^{–1}, J = 0.00 cm^{–1}, J’ = 0.00 cm^{–1}, and θ = 0.00 K.

Figures 4 and 5. This indicates the existence of ferromagnetic interaction in both complexes. Considering both the intramolecular and intermolecular interactions, the data were successfully analyzed. The result indicated that the exchange interaction between Co_{A} (Co_{A1} and Co_{A2}) and Co_{B} is practically negligible (J = ~ 0), but the interaction between Co_{A1} and Co_{A2} is ferromagnetic (J’ > 0). As mentioned above, Co_{A} and Co_{B} are bridged by a phenolic oxygen atom and an oxygen atom of an acetate

Table 1. Magnetic parameters and discrepancy factors for complexes 1 and 2.

ion, whereas Co_{A1} and Co_{A2} are bridged by two pairs of syn-anti bidentate oxygen atoms of two acetate ions. Since an exchange interaction parameter is described as the sum of the ferromagnetic and antiferromagnetoic components and a phenolate bridge generally contributes to an antiferromagnetic interaction, the result (J’ > J) is consistent with this idea.

Judging from the obtained parameters, we can explain the temperature dependencies as follows. The magnetic moments decrease with decreasing the temperature, and the decrease above 50 K is mainly due to the thermal population on the Kramers doublets generated from the local ^{4}T_{1} ground term by the spin-orbit coupling. Below 50 K, the ferromagnetic interaction between Co_{A1} and Co_{A2} appears, and the drop below 10 K is due to the intermolecular antiferromagnetic interaction.

4. CONCLUSIONS

In this study, a new magnetic susceptibility equation was developed for trinuclear octahedral high-spin cobalt(II) complexes in the shape of an isosceles triangle considering the local axial distortion, the spin-orbit coupling, the exchange interactions, and the intermolecular exchange interactions. Using the equation, the magnetic data for two tricobalt(II) complexes 1 and 2 were successfully analyzed. For both complexes, ferromagnetic interaction between Co_{A1} and Co_{A2} ions and practically negligible interaction between Co_{A} and Co_{B} ions were observed.

5. ACKNOWLEDGMENTS

This work was supported by the Saneyoshi Scholarship Foundation.

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