Theoretical Studies of the Defect Structures for Cu(en)₃²⁺ and Ru(en)₃³⁺ Clusters in Tris(Ethylenediamine) Complexes

1 Introduction

Ethylenediamine (en) and the relevant complexes have broad applications in a diverse range of fields. Ethylenediamine can improve enzymatic digestibility of corn stover for the production of fermentable sugars [1] and act as a vapour phase crosslinking agent for Matrimid films in the range of 0.35–0.55 μm under ambient conditions for alcohol penetrant transport [2]. In particular, the various ethylenediamine complexes can be used as fluorescent sensors [3] and fluorescence probes for detecting Hg²⁺ in water [4], as well as fluffy porous carbon nanotube composites for isolation of clenbuterol from pork [5]. On the other hand, ruthenium (e.g. Ru³⁺) and ruthenium complexes not only can act as an electrogenerated chemiluminescence label for highly sensitive detection of DNA methylation and assay of methyltransferases activity [6], but also exhibit giant magnetoresistance [7]. Moreover, the tris(ethylenediamine)ruthenium (III) (4d⁵) complex, Ru(en)₃³⁺, can be adopted as a water oxidation catalyst for the cooperative catalysis of the bimolecular decomposition with high concentrations in aqueous solution [8] and the chemically modified electrodes in chemical sensors [9]. Copper (Cu²⁺, 3d⁹) is a vital transition-metal element in cofactor for protein enzymes [10], antimicrobial activity against the bacteria Salmonella paratyphi [11], modification of DNA [12], and high T_C superconductivity [13]. Furthermore, both Cu²⁺ and Ru³⁺ under octahedra exhibit orbitally degenerated ground states and thus experience the Jahn–Teller distortions through the vibration interaction [14], [15], [16]. These systems may demonstrate unique structural properties that are of special scientific significance.

As the single crystals of transition-metal complexes in the form of M(en)₃ⁿ⁺ are ideal host lattices for the studies of the local structures and electronic properties, considerable researches have been conducted by means of electron paramagnetic resonance (EPR) [17], [18], reversible phase transitions [19], and the circularly polarised luminescence spectra [20] and vibrational dichroism spectroscopy [21]. Especially, EPR is a very informative method to probe the delicate local distortions of the active transition-metal centres, characterised by the spin Hamiltonian parameters (SHPs), i.e. g factors and hyperfine structure constants. Electron paramagnetic resonance spectra were measured for the trigonally distorted Ru(en)₃³⁺ in the uniaxial [Rh(en)₃Cl₃]₂NaCl ⋅ 6H₂O single crystal doped with the single-crystal chloride salt [Ru(en)₃]Cl₃ ⋅ 4H₂O at 4 K and the two tetragonally elongated octahedral Cu(en)₃²⁺ clusters in Zn(en)₃(NO₃)₂:Cu²⁺ polycrystalline powder at 4.2 K and room temperature (RT), respectively [17], [18]. Regretfully, these experimental results of EPR spectra have not been theoretically analysed until now; neither has the quantitative formation about the local structures of these clusters been obtained. In view of the importance of the mechanisms of the SHPs and the local structural information for the above Cu(en)₃²⁺ and Ru(en)₃³⁺ clusters, which have been rather scarcely studied so far, it is worthy to perform further investigations on their SHPs and local structures in a uniform way so as to achieve deep understanding of the structures and properties for ethylenediamine complexes containing transition-metal impurities. In this work, the SHPs and local structures of these transition-metal clusters are theoretically and systematically investigated based on the perturbation formulae of the SHPs for trigonally distorted octahedral 4d⁵ and tetragonally elongated octahedral 3d⁹ clusters. The reasonableness of the results and the local structures of the various Ru(en)₃³⁺ and Cu(en)₃²⁺ clusters are discussed.

2 Theoretical Calculations

2.1 Local Structures of the Cu(en)₃²⁺ and Ru(en)₃³⁺ Clusters

For the Cu(en)₃²⁺ clusters in the Zn(en)₃(NO₃)₂ polycrystalline powder, the octahedral Cu²⁺ is coordinated to six nitrogen atoms (from three en groups) and forms two tetragonally elongated octahedral centres at 4.2 K (centre I) and RT (centre II) [18], respectively. As Cu²⁺(3d⁹) is a Jahn–Teller ion, the Cu(en)₃²⁺ clusters may undergo the significant Jahn–Teller effect through the vibration interactions and generate six magnetically nonequivalent sites. As a result, both copper centres exhibit the tetragonal elongation distortions, responsible for the feature of the observed g factors (g_∥ > g_⊥ ≥ 2 [18]). The energy level structure for a Cu²⁺(3d⁹) ion under ideal octahedra can be described as a ground orbital doublet ²E_g and an excited orbital triplet ²T_2g [22], [23]. Subject to the tetragonal elongation distortion, the two-fold orbital degeneracy of the cubic ²E_g ground state can be lifted by the Jahn–Teller effect and separated into two orbital singlets ²B_1g and ²A_1g, with the former lying lowest [24], [25]. Therefore, the local impurity–ligand bond lengths (R_∥ and R_⊥) parallel and perpendicular to the C₄ axis may be conveniently characterised by a relative tetragonal elongation ΔZ (Fig. 1a).

Figure 1:

Local structures of the tetragonally elongated octahedral Cu(en)₃²⁺ (a) and the trigonally distorted octahedral Ru(en)₃³⁺ (b) clusters characterised by the relative tetragonal elongation ΔZ and the angular variation Δβ, respectively.

The Ru(en)₃³⁺ cluster is formed in the diamagnetic and uniaxial solvent [Rh(en)₃Cl₃]₂NaCl ⋅ 6H₂O doped with the single-crystal chloride salt [Ru(en)₃]Cl₃ ⋅ 4H₂O, which may tend to conserve the original trigonal (D_3d) symmetry [17]. As Ru³⁺ (4d⁵) is also a Jahn–Teller ion with the ground orbital triplet ²T_2g in an ideal octahedron, the Ru(en)₃³⁺ cluster can undergo the Jahn–Teller distortion through the vibration interaction and bring forward some modification in the local structure [26], [27], [28], [29]. In addition, slightly different environments for the Ru(en)₃³⁺ cluster in the solvent of [Rh(en)₃Cl₃]₂NaCl ⋅ 6H₂O single crystal may also lead to some influence on the local structure related to that in the solute [Ru(en)₃]Cl₃ ⋅ 4H₂O. Under trigonally elongated octahedra, the cubic ground ²T_2g state of low spin (S = 1/2) may split into one orbital singlet ²A_1g and one doublet ²E_g, with the later lying lowest [22], [30]. The above energy separation is often defined as the trigonal field parameter V [22], [30], [31]. Moreover, the spin–orbit coupling interactions may induce the further splittings of these states into three Kramers doublets. In view of the host metal–ligand bonding angle β_H (≈57.32° [17], [32]) of Ru³⁺ site in the solute [Ru(en)₃]Cl₃ ⋅ 4H₂O, the structural modifications of this trigonal centre can be suitably described as the angular variation Δβ (=β − β_H) of the local Ru³⁺–N³⁻ bonding angle β in the solvent related to the host bonding angle β_H in the solute (Fig. 1b).

3 Discussion

Table 2 reveals that the calculated SHPs for all the Cu(en)₃²⁺ and Ru(en)₃³⁺ clusters based on the local lattice distortions (i.e. the relative tetragonal elongations ΔZ and the local angular variation Δβ) agree well with the measured results at various temperatures. Thus, the EPR spectra and local structures for these Cu(en)₃²⁺ and Ru(en)₃³⁺ clusters are systematically in a uniform manner.

(A) In general, the microscopic mechanisms of the local structural modifications for the Cu(en)₃²⁺ and Ru(en)₃³⁺ clusters related to the host lattices may be explained as the Jahn–Teller effect and size mismatch. For the Cu(en)₃²⁺ clusters (centres I and II), the positive relative tetragonal elongations ΔZ in (5) are in accordance with the expectation based on the positive anisotropies Δg (= g_∥ − g_⊥) of the experimental g factors [17]. Despite the original trigonal point symmetry of host Zn²⁺ site in Zn(en)₃(NO₃)₂ single crystal, the impurity Cu²⁺ ion tends to exhibit tetragonal elongation distortion because of the Jahn–Teller effect through the vibration interactions, which can completely remove the two-fold orbital degeneracy of the cubic ground state ²E_g. Comparatively, the influence of the size mismatch can be much weaker than the Jahn–Teller effect due to the very small difference in ionic radius between Cu²⁺ and Zn²⁺. Nevertheless, the tetragonal elongations ΔZ of both copper centres I and II are much smaller than those (0.08 ∼ 0.3 Å) [35], [54], [55] of other similar copper centres in some tetragonally elongated octahedra [e.g. AgCl, NaCl, alkali lead tetraborate 90R₂B₄O₇ ⋅ 9PbO ⋅ CuO (R = Li, Na, and K) glasses and LaSrGa_0.995Cu_0.005O₄ ceramics] of the same Jahn–Teller nature. This point may be illustrated as the stronger CFs and hence larger force constant of the copper-ligand bonds in present Cu(en)₃²⁺ clusters, based on the spectrochemical series [23]. Moreover, the slightly larger axial elongation ΔZ of copper centre II than centre I can be suitably attributed to be more intense vibration interactions at RT. On the other hand, the significant angular variation (decrease) by about 2° for the Ru(en)₃³⁺ cluster is mainly attributable to the Jahn–Teller effect. Notably, the local angular variation Δβ for present Ru(en)₃³⁺ cluster in uniaxial [Rh(en)₃Cl₃]₂NaCl ⋅ 6H₂O single crystal doped with [Ru(en)₃]Cl₃ ⋅ 4H₂O is slightly smaller in magnitude than those for the similar trigonal (D_3d) Ru³⁺ centres in the garnets [26]. This is understandable in view of the local angular variations arising from both the Jahn–Teller effect and the significant size mismatch between the impurity Ru³⁺ (≃0.87 Å [40]) and host Al³⁺ (≃0.54 Å [40]) or Ga³⁺ (≃0.62 Å [40])

(B) The characteristic of the SHPs for these clusters can be further illustrated as follows. First, the observed positive g anisotropy Δg for copper centre I arises from the lowest ²B_1g state due to the tetragonal elongation. The average g_iso of g factors (and also the average |A| for hyperfine structure constants) for copper centre II is slightly higher than centre I, owing to the slightly weaker covalence at RT in the former. Of course, the presently calculated g factors for centre II remain to be further checked with experimental measurements. Second, although the sign of the average of hyperfine structure constants was not determined experimentally in [18] at RT, the results A_∥ < 0 and A_⊥ > 0 in current calculations are consistent with various experimental values and theoretical expectations [35], [49], [56] for tetragonally elongated octahedral Cu²⁺ centres. The negative A_∥ is due to the positive anisotropic terms for hyperfine structure constants smaller than the magnitudes of the negative isotropic terms related to κ, arising from the Fermi contact interactions due to the Cu²⁺ 3d–3s (or –4s) configuration interactions. And, the positive A_⊥ is attributable to the negative isotropic terms slightly lower in magnitude than the positive anisotropic ones (1). Meanwhile, the slightly larger magnitude of hyperfine structure constants of centre II than centre I could be ascribed to the higher N and κ of the former. Third, the positive anisotropy Δg for the Ru(en)₃³⁺ cluster is due to the trigonal elongation distortion, which is much larger than the Ru³⁺ site in host [Ru(en)₃]Cl₃ ⋅ 4H₂O. This indicates that the Jahn–Teller effect may tend to yield trigonal elongation distortion of the ligand octahedron for a Ru³⁺ cluster. This is somewhat similar to the Ru³⁺ centres in the garnets except much stronger influence arising from the size mismatch in the latter [26].

(C) The much larger anisotropy Δg of the Ru(en)₃³⁺ cluster than the Cu(en)₃²⁺ clusters can be further illustrated here. First, the orbital angular momentum shows larger contribution to Δg for the cubic ground triplet ²T_2g of the Ru(en)₃³⁺ cluster than that for the cubic ground doublet ²E_g of the Cu(en)₃²⁺ cluster. Of course, both systems exhibit significant anisotropic contributions to g factors due to the axial symmetrical distortion and spin–orbit coupling interactions, as compared with the cases of cubic orbital singlets (e.g. ⁴A_2g and ³A_2g ground states for octahedral 3d³ and 3d⁸ clusters [22], [23]). Second, different axial symmetries (i.e. trigonality and tetragonality) for the Ru(en)₃³⁺ and Cu(en)₃²⁺ clusters may involve dissimilar mechanisms of the contributions to Δg. In detail, the g anisotropy arises from the first-order and second-order perturbation terms for the Ru(en)₃³⁺ and Cu(en)₃²⁺ clusters ((6) and (1)), respectively, which leads to the much larger Δg in the former. Finally, the more significant axial distortion Δβ for the Ru(en)₃³⁺ cluster than the much smaller ΔZ for the Cu(en)₃²⁺ clusters may also induce much larger Δg in the former.

4 Conclusion

The SHPs and the local structures for the tetragonally elongated Cu(en)₃²⁺ clusters and the trigonally elongated Ru(en)₃³⁺ cluster at various temperatures are theoretically studied by using the perturbation computations. The Cu²⁺ centres I and II are found to experience the slight relative tetragonal elongations ΔZ of about 0.005 and 0.007 Å along the C₄ axis due to the Jahn–Teller effect at 4.2 K and RT, respectively. In the Ru(en)₃³⁺ clusters, the impurity–ligand bonding angle β suffers the significant decrease Δβ by about 1.85° related to the host [Ru(en)₃]Cl₃ ⋅ 4H₂O owing to the Jahn–Teller effect at 4 K. The calculated g factors and hyperfine structure constants based on the above local structural parameters (the relative tetragonal elongation ΔZ and the angular distortion Δβ) agree well with the measured values. Present theoretical studies would be helpful to understand the local structural properties and may establish an improved scheme for the systematic apprehending of the unique behaviours for various Jahn–Teller impurities (e.g. 3d⁹ and 4d⁵ ions) in ethylenediamine and the relevant complexes (or other similar crystals [57], [58], [59]).