Magnetic and Electrochemical Properties of Lantern-Type Dinuclear Ru(II,III) Complexes with Axial Chloride Ions or Water Molecules

Abstract

By using [Ru₂(O₂CC₃H₇)₄Cl]_n (1) as a starting material, ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] (ⁿBu₄N⁺ = tetra(n-butyl)ammonium cation) (2) and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ (3) were prepared. The lantern-type dinuclear structures with axial chloride ions or water molecules were confirmed for 2 and 3 by X-ray crystal structure analyses. The crystal structures of 2 and 3 were compared with that of 1. In the crystal of 2, there were three crystallographically different dinuclear units; the Ru–Ru distances of each unit were 2.3094(3), 2.3046(4), and 2.3034(4) Å, respectively, which were longer than those of 1 (2.281(4) Å) and 3 (2.2584 (7) Å). Temperature dependent magnetic susceptibility measurements were performed for 1 and 2 as well as 3. The effective magnetic moments (µ_eff) at 300 K were 3.97 (for 1), 4.00 (for 2), and 3.97 µ_B (for 3), respectively. The decreases in the µ_eff value were confirmed for all of the complexes due to the large zero-field splitting (D): D = 68 cm⁻¹ for 1, 78 cm⁻¹ for 2, and 60 cm⁻¹ for 3. Cyclic voltammograms measured in CH₂Cl₂ with a electrolyte of ⁿBu₄N(BF₄) showed the Ru₂⁵⁺/Ru₂⁴⁺ process at −0.2–−0.4 V (vs. SCE) and the Ru₂⁶⁺/Ru₂⁵⁺ one at 1.3–1.4 V (vs. SCE), of which potentials were confirmed by the DFT calculation for ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂].

1. Introduction

There has been much interest devoted to lantern-type dinuclear complexes with a direct metal–metal (M–M) interaction giving a wide range of remarkable physical–chemical properties based on the direct M–M interaction [1,2,3,4,5]. In the case of the ruthenium dinuclear complexes, the crystal structure was first reported in 1969 by Cotton and co-workers for [Ru₂(O₂CC₃H₇)₄Cl]_n (1), where the mixed-valent diruthenium(II,III) dinuclear (Ru₂⁵⁺) units are linked by axial chloride ions to give a zig-zag chain structure with a Ru–Cl_ax–Ru bond angle of 125.4°, as shown in Scheme 1 [6].

Temperature-dependent magnetic susceptibility was later reported for [Ru₂(O₂CC₃H₇)₄Cl]_n (1) by Telser et al., showing a large zero-field splitting (D = 76.8 cm⁻¹) with g = 2.10 with the support of EPR (electron paramagnetic resonance) spectral data [7]. In the study, they did not mention the interaction through the axial Cl⁻ ions between the paramagnetic dinuclear units (S = 3/2), although we have lately described the importance of the axial bond through interaction to understand the magnetic behaviors of the polymer complexes of Ru₂⁵⁺ units linked by axial ligands [5]. An electrochemical study has been also performed for [Ru₂(O₂CC₃H₇)₄Cl]_n (1); the complicated electrochemical behaviors found in CV (cyclic voltammogram) with two redox waves for Ru₂⁵⁺/Ru₂⁴⁺ at E_1/2 = 0.00 V (vs. SCE) and −0.34 V (vs. SCE) in dichloromethane containing 0.1 M tetrabutylammonium perchlorate (ⁿBu₄N(ClO₄)) were interpreted in terms of equilibrium [Ru₂(O₂CC₃H₇)₄]⁺ + nCl⁻ ↔ [Ru₂(O₂CC₃H₇)₄Cl_n]⁽ⁿ⁻¹⁾⁻ [8]. That is, the Ru₂⁵⁺/Ru₂⁴⁺ redox waves were observed at E_1/2 = 0.00 V for [Ru₂(O₂CC₃H₇)]⁺ and −0.34 V for {Ru₂(O₂CC₃H₇)₄Cl_n}(^n−l)⁻, respectively. The axial coordination of chloride ions is considered to magnetically and electrochemically affect the properties of the Ru₂⁵⁺ complexes. However, systematic investigation has not been conducted by changing the number of axial chloride ions. In this study, the dinuclear complexes ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] (2) and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ (3) were prepared, characterized, and compared with [Ru₂(O₂CC₃H₇)₄Cl]_n (1) for their crystal structures, magnetic properties, and electrochemical properties. Furthermore, DFT calculations were also performed to estimate the redox potentials for the Ru₂⁵⁺ complexes.

2. Results and Discussion

2.1. Synthesis and Characterizations

The addition of an excess amount of ⁿBu₄NCl to the dinuclear units of [Ru₂(O₂CC₃H₇)₄Cl]_n (1) with stirring at room temperature for 24 h in dichloromethane solution gave a dichloridodiruthenium(II,III) complex ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] (2) with a yield of 85% (based on Ru₂⁵⁺ unit of 1). On the other hand, the axial chloride ligand of 1 could be removed by the reaction with AgBF₄ in THF at room temperature for 24 h with stirring to give a diaquadiruthenium(II,III) complex [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ (3) with a yield of 69%. Their chemical formula were confirmed by elemental analyses. The IR spectra of 2 and 3 showed the COO vibrations as a set of two distinctive bands (ν_asym (COO) 1465 cm⁻¹ and ν_sym (COO) 1426 cm⁻¹ for 2; ν_asym (COO) 1455 cm⁻¹ and ν_sym (COO) 1428 cm⁻¹ for 3) in a similar energy region to those of 1 (ν_asym (COO) 1462 cm⁻¹ and ν_sym (COO) 1425 cm⁻¹). These facts suggest that the dinuclear skeleton is preserved in the above-mentioned reactions to 2 and 3. The stretching vibrations of BF₄⁻ appear as a broad band around 1090 cm⁻¹ in 3, which indicate no coordination of the ion to the Ru₂⁵⁺ core [9].

2.2. Crystal Structures

Crystals of 2 and 3 suitable for X-ray crystal structure analyses were obtained by recrystallizations from dichloromethane–diethyl ether and dichloromethane–benzene mixed solvents, respectively. The crystal packing diagram of ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] (2) is shown in Figure 1. In this crystal, there are crystallographically different dinuclear (Cl–Ru–Ru–Cl) anionic units designated as (Cl1–Ru1–Ru2–Cl2), (Cl3–Ru3–Ru3″–Cl3″), and (Cl4–Ru4–Ru4‴–Cl4‴), respectively, while ⁿBu₄N⁺ counter cations exist among the (Cl–Ru–-Ru–-Cl)⁻ anionic units without any important short contacts with the (Cl–Ru–Ru–Cl) units in the crystal. The crystallographical inversion centers are located at the centers of the (Cl3–Ru3–Ru3″–Cl3″) and (Cl4–Ru4–Ru4‴–Cl4‴) dinuclear units. The ORTEP drawing for one of the anionic dinuclear units, (Cl1–Ru1–Ru2–Cl2), is depicted in Figure 2. Including the other dinuclear units, (Cl3–Ru3–Ru3″–Cl3″) and (Cl4–Ru4–Ru4‴–Cl4‴), of which structures are shown in Figures S1 and S2, respectively, the lantern-type dinuclear structures with axial chloride ligands are basically the same as those reported for ⁿBu₄N[Ru₂(O₂CCH₃)₄Cl₂] (4) [10]. The Ru–Ru and Ru–Cl^ax bond distances were 2.3094(3) (for Ru1–Ru2), 2.3046(4) (for Ru3–Ru3″), 2.3034(4) Å (Ru4–Ru4‴), 2.5344(6) (for Ru1–Cl1), 2.5524(6) (for Ru2–Cl2), 2.5335(6) (for Ru3–Cl3), and 2.5127(6) Å (for Ru4–Cl4), respectively. The Ru–Ru and Ru–Cl bond distances were similar to those for 4 (Ru–Ru = 2.3019(4) and 2.3006(5) Å; Ru–Cl^ax = 2.5316(6) and 2.5181(7) Å). The Ru–Ru bond distances of 2 seemed to be large when compared with that of 1 (2.281(4)Å), while the Ru–Cl^ax distances of 2 were rather small when compared with that of 1 (2.587(5) Å). The ORTEP drawing of the cationic unit of [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ (3) is depicted in Figure 3. The crystallographic inversion center exists at the center of the lantern-type dinuclear Ru₂⁵⁺ core. The Ru1–Ru1′ and Ru1–O5 bond distances were 2.2584(7) and 2.267(3) Å, respectively, which were comparable to the corresponding distances for the previously reported lantern-type Ru₂⁵⁺ complexes with axial water molecules, [Ru₂(O₂CCH₃)₄(H₂O)₂]BF₄ (Ru–Ru = 2.248(1) Å and Ru–O^ax = 2.34(1) and 2.27(1) Å) [11], [Ru₂(O₂CCH₃)₄(H₂O)₂]PF₆•3H₂O (Ru–Ru = 2.2648(9) Å and Ru–O^ax = 2.279(4) Å) [12], [Ru₂{O₂CC(CH₃)₃}₄(H₂O)₂]BF₄ (Ru–Ru =2.259(1) Å and Ru–O^ax = 2.280(5) and 2.323(5) Å), and [Ru₂{O₂CC(CH₃)₃}₄(H₂O)₂]BF₄•CH₂Cl₂ (Ru–Ru = 2.256(1) Å and Ru–O^ax = 2.330(5) and 2.248 (4) Å) [13]. As depicted in the crystal packing diagram (Figure 4), the BF₄⁻ counter anions are located among the dinuclear Ru₂⁵⁺ units without any important contacts between them. Alternatively, there are hydrogen bonds between an axially coordinating water molecule and a bridging butanoate oxygen within the neighboring dinuclear unit as shown by dashed line (O5---O3″ = 2.800 Å) in Figure 4 where the hydrogen bonds connect to Ru₂⁵⁺ to give a zig-zag chain. This is in contrast to the hydrogen bonds between the axially coordinated water molecules and BF₄⁻ anions that were found for [Ru₂{O₂CC(CH₃)₃}₄(H₂O)₂]BF₄ and [Ru₂{O₂CC(CH₃)₃}₄(H₂O)₂]BF₄•CH₂Cl₂ (O(water)---F (BF₄⁻) = 2.742~2.960 Å), leading to two-dimensional sheets [13].

2.3. Magnetic Properties

The temperature dependences of magnetic susceptibilities and effective magnetic moments of 1, 2, and 3 are shown in Figure 5, Figure 6 and Figure 7, respectively. The magnetic moments at 300 K were 3.97 (for 1), 4.00 (for 2), and 3.97 µ_B (for 3), respectively, indicating the existence of three unpaired electrons within the dinuclear Ru₂⁵⁺ cores like the other lantern-type tetrakis(carboxylato)diruthenium(II,III) with a formal electron configuration of σ²π⁴δ²(δ*π*)³ (i.e., S = 3/2 ground state) [1]. All of the complexes showed decreases in the moments by lowering the temperature due to the strong zero-field splitting (D). The magnetic behaviors were simulated using the Equations (1)–(3) [3,5,7,14]:

χ = (χ_// + 2χ_⊥)/3,

(1)

where χ is the magnetic susceptibility and χ_// and χ_⊥ are magnetic susceptibility terms defined as follows:

χ_// = (Ng²µ_B²/kT){1 + 9exp(−2D/kT)}/4{1 + exp(−2D/kT)},

(2)

χ_⊥ = (Ng²µ_B²/kT)[4 + (3kT/D){1 − exp(−2D/kT)}]/4{1 + exp(−2D/kT)}.

(3)

The simulation results provided the following parameter values: g = 2.06, D = 68 cm⁻¹ for 1, g = 2.08, D = 78 cm⁻¹ for 2, and g = 2.05, D = 60 cm⁻¹ for 3. Large D values are common for the lantern-type Ru₂⁵⁺ complexes [1,2,3,4,5] and are in the range of D = 50–100 cm⁻¹. Although the magnetic interactions between dinuclear units can be estimated using zJ, which means the exchange energy multiplied by the number of interacting neighboring units and is defined by χ’ = χ/{1 − (2zJ/Ng²µ_B²)χ}, when a molecular field approximation is applied [3,5,7,14], the temperature-dependent profiles of magnetic susceptibilities and moments of 1–3 could all be reproduced well without the zJ term. That is, the magnetic interactions were negligible for the complexes (zJ = 0 cm⁻¹). This is reasonable for 2 and 3 because the X-ray crystal structural data showed that the Ru₂⁵⁺ units were distant from each other without any axial linkers mediating the interaction. As for 1, the antiferromagnetic interaction could be possible through an axial chloride linker ligand. The negligible interaction may be due to the zig-zag chain structure with a smaller Ru–Cl^ax-Ru bond angle (125.4°). According to an empirical linear relationship between zJ and the structural parameter Ru–X/Ru–X–Ru, which was proposed for lantern-type Ru₂⁵⁺ complexes with axial halide (X⁻) linkers by Delgado-Martinez et al., smaller Ru–X–Ru bond angles decrease the antiferromagnetic interaction [15]. Although the Ru–X/Ru–X–Ru value of 1 (2.587/125.4 = 0.0206) seems to be for weak antiferromagnetic interaction (zJ = −2 ~ −4 cm⁻¹), we expect that the negligible interaction comes from the small Ru–Cl^ax-Ru bond angle (125.4°). A similar explanation has been presented in terms of MO overlap by Cukiernik et al. for zJ = 0 cm⁻¹ of [Ru₂(O₂CC₃C₇)₄Cl]_n (1) [16]. The magnetic simulation has been reported for 1 as g_// = 2.02, g_⊥ = 2.14 (g_av = 2.10), and D = 76.8 cm⁻¹ by Telser et al. as well as g_// = 2.14, g_⊥ = 2.25 (g_av = 2.21), and D = 69 cm⁻¹ by Cukiernik et al. Although the g values shown by Cukiernik et al. were rather large, our results for the g, D, and zJ values obtained in this study for complex 1 were not against the previously reported results.

The EPR spectra measured at 5 K in solid for 1–3 are given in Figure 8, Figures S3 and S4. The signal intensities were strong enough for 2 and 3 to analyze the spectra. Despite the weak signal intensities for 1, the g values were barely estimated. The estimated g values were g_// = 2.040 and g_⊥ = 4.390 for 1; g_// = 1.980 and g_⊥ = 4.385 for 2; and g_// = 1.975 and g_⊥ = 4.335 for 3. For the S =3/2 system with D >> gβH, the estimated effective g values (g^e = hν/βH) are g_//^e ≈ g_// and g_⊥^e ≈ 2g_⊥ [7,17]. Thus obtained g values (g_// = 2.040 and g_⊥ = 2.195 for 1; g_// = 1.980 and g_⊥ = 2.1925 for 2; g_// = 1.975 and g_⊥ = 2.168 for 3) are typical of the lantern-type Ru₂⁵⁺ complexes [3,7,8,10,17]. The axial signal pattern was observed in 1:1 toluene/CH₂Cl₂ at 3.4 K for 1 (g_// = 1.9465 and g_⊥ = 4.400) [7].

2.4. Reflectance and Absorption Spectra

The diffuse reflectance spectra for the powder samples of 1–3 are given in Figure 9. All of the complexes showed a distinctive band at 430–490 nm with a discernible shoulder band at 550–690 nm and a broad band at 1030–1150 nm. These spectral features seem to be typical of lantern-type Ru₂⁵⁺ dinuclear complexes [1]. In fact, [Ru₂{O₂CC(CH₃)₃}₄]BF₄ has been reported as having corresponding bands; a band at 427 nm with a shoulder band at 545 nm and a band at 990 nm in the diffuse reflectance spectrum [18], which were assigned as π (Ru–O, Ru₂) → π* (Ru₂), δ*/π* (Ru₂) → δ* (Ru–O), and δ(Ru₂) → δ* (Ru₂), respectively, according to their assignment in the literature [19]. Absorption spectra (measured in CH₂Cl₂) are shown in Figure 10. Absorption peaks are found in the near-ultraviolet (450–470 nm) and near-infrared region (1000–1150 nm) for all complexes. The similarity in the spectral features between the reflectance and absorption spectra indicates that the Ru₂⁵⁺ dinuclear skeletons were maintained in the solution.

2.5. Cyclic Voltammogram (CV)

Cyclic voltammograms (CVs) were obtained in the dichloromethane solutions containing ⁿBu₄N(BF₄) (Figure 11). All complexes showed the Ru₂⁵⁺ → Ru₂⁴⁺ process at −0.2–−0.4 V and the Ru₂⁵⁺ → Ru₂⁴⁺ one at 1.3–1.4 V, respectively. Cotton et al. reported that [Ru₂(O₂CC₃H₇)₄Cl]_n exhibited a two-step Ru₂⁵⁺ → Ru₂⁴⁺ reduction process (E_1/2 = 0.00 and −0.34 V (vs. SCE) in CH₂Cl₂ containingⁿBu₄N(ClO₄)) although a one-step reduction was observed at E_1/2 = −0.34 V when ⁿBu₄NCl was used as the electrolyte, which was due to the existence of equilibrium shown by [Ru₂(O₂CC₃H₇)₄]⁺ + n(Cl⁻) ↔ [Ru₂(O₂CC₃H₇)₄Cl_n]⁽ⁿ⁻¹⁾⁻ [8]. It seems reasonable that the bis-adduct species [Ru₂(O₂CC₃H₇)₄Cl₂]⁻ is predominant in the CH₂Cl₂ solution containing ⁿBu₄NCl, and the observed redox couple at E_1/2 = −0.34 V can be attributed to that of the Ru₂⁵⁺ → Ru₂⁴⁺ process of the bis-adduct species. We confirmed that ⁿBu₄N[Ru₂(O₂CCH₃)₄Cl₂] (4) exhibited a redox couple attributed to the Ru₂⁵⁺ → Ru₂⁴⁺ process at E_1/2 = −0.34 V in a CH₂Cl₂ solution with an electrolyte ⁿBu₄N(ClO₄); in addition, the redox wave observed at E_1/2 = −0.32 V for [Ru₂(O₂CCH₃)₄Cl]_n dissolved in a CH₂Cl₂ solution with an electrolyte ⁿBu₄NCl [10]. That is, the axial coordination of Cl⁻ to the Ru₂⁵⁺ unit was kept in the measured CH₂Cl₂ solution containing the ⁿBu₄N(ClO₄) electrolyte. Hence, the axial chloride ligations of 2 could also be considered as kept in the measured CH₂Cl₂ solution, although the reversibility of the redox couple (E_pc = −0.46 V and E_pa = −0.14 V) was not good when compared with that of 4 (E_pc = −0.40 V and E_pa = −0.28 V) [10]. We performed DFT calculations to estimate the redox potentials (E^calc_1/2) for Ru₂⁵⁺ → Ru₂⁴⁺ as well as the Ru₂⁶⁺ → Ru₂⁵⁺ processes for [Ru₂(O₂CC₃H₇)₄Cl₂]⁻ by using our previous treatment for [Ru₂(O₂CCH₃)₄Cl₂]⁻ [10]. The calculated values were E^calc_1/2 (for Ru₂⁵⁺ → Ru₂⁴⁺) = −0.42 V and E^calc_1/2 (for Ru₂⁶⁺ → Ru₂⁵⁺) = 1.25 V. The results support the assignment of the Ru₂⁵⁺ → Ru₂⁴⁺ process at –0.2– –0.4 V and the Ru₂⁶⁺ → Ru₂⁵⁺ one at 1.3–1.4 V for 2. We further performed calculations on [Ru₂(O₂CC₃H₇)₄Cl] and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]⁺ as the model compounds of 1 and 3, respectively. The calculated E^calc_1/2 (for Ru₂⁵⁺ → Ru₂⁴⁺) and E^calc_1/2 (for Ru₂⁶⁺ → Ru₂⁵⁺) values were −0.05 and 2.09 V for [Ru₂(O₂CC₃H₇)₄Cl], and 0.34 and 2.77 V for [Ru₂(O₂CC₃H₇)₄(H₂O)₂]⁺. At present, it is difficult to explain the reason why complexes 1–3 showed redox waves at similar potentials of −0.2– −0.4 V and 1.3–1.4 V. Many factors such as the coordination of the Cl⁻ ion and BF₄⁻ ion of the electrolyte ⁿBu₄N(BF₄) as well as the oligomerization of Ru₂⁵⁺ dinuclear units should be taken further into consideration.

3. Materials and Methods

3.1. General Aspects

All reagents and solvents were used as received. The complex [Ru₂(O₂CC₃H₇)₄Cl]_n (1) was prepared according to a published procedure [8].

Elemental analyses for carbon, hydrogen, and nitrogen were performed using a Yanako CHN Corder MT-6. Infrared spectra (KBr pellets) were measured with a JASCO FT/IR-4600. Absorption spectra and diffuse reflectance spectra were obtained using JASCO V-670 and Shimadzu UV-3100 spectrometers, respectively. The temperature dependent magnetic susceptibilities were measured over the temperature range of 2–300 K at the constant field of 0.5 T with a Quantum Design MPMS XL-5. The measured data were corrected for diamagnetic contributions [20]. EPR spectra were measured at 5 K in solid by a BRUKER ELEXSYS E500 equipped with OXFORD ESR900 and OXFORD ITC503 attachments. The EPR simulation was conducted using the “Hyperfine Spectrum” program with spin Hamiltonian, H_s = βB•gS [21]. Cyclic voltammograms (CVs) were measured in dichloromethane containing ⁿBu₄N(BF₄) on a BAS ALS-DY2325 electrochemical analyzer. A glassy carbon disk (1.5 mm radius), platinum wire, and saturated calomel electrodes were used as the working, counter, and reference electrodes, respectively. All of the potential values are described versus SCE.

3.2. Syntheses of Complexes

3.2.1. Synthesis of ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] (2)

A suspension of [Ru₂(O₂CC₃H₇)₄Cl]_n (50 mg, 0.085 mmol (based on Ru₂ dinuclear unit)) was stirred with ⁿBu₄NCl (29.5 mg, 0.11 mmol) in dichloromethane (20 mL) for 24 h at room temperature. The resulting solution was concentrated to a small portion and stood to give a brown precipitation, which was collected by suction and dried under vacuum overnight. The yield was 62.9 mg (85% based on [Ru₂(O₂CC₃H₇)₄Cl] unit). Anal. Found: C, 44.93; H, 7.38; N, 2.00%. Cacld. for C₃₂H₆₄Cl₂NO₈Ru₂, C, 44.49, H, 7.47; N, 1.62%. IR (KBr disk, cm⁻¹): 2964 s, 2936 m, 2874 m, 1465 s, 1426 vs, 1313 m, 1261 w, 1200 vw, 1172 vw, 1102 vw, 889 w, 798 w, 729 w, 677 w, 628 w, and 461 m.

3.2.2. Synthesis of [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ (3)

A suspension of [Ru₂(O₂CC₃H₇)₄Cl]_n (90.9 mg, 0.15 mmol (based on Ru₂ dinuclear unit)) was stirred with AgBF₄ (31.1 mg, 0.16 mmol) in THF (20 mL) for 24 h at room temperature, and the reaction vessel was covered with aluminum foil to shield against the light. The precipitate of AgCl was removed by filtration through celite. The filtrate solution was concentrated to a small portion by evaporating under reduced pressure and stood overnight to give a brown microcrsytalline solid, which was separated by filtration, washed with hexane, and dried under vacuum overnight. The yield was 71.8 mg (69% based on [Ru₂(O₂CC₃H₇)₄Cl] unit). Anal. Found: C, 28.33; H, 4.41%. Cacld. for C₁₆H₃₂BF₄O₁₀Ru₂, C, 28.54, H, 4.79%. IR (KBr disk, cm⁻¹): 2965 s, 2932 m, 2878 m, 1455 vs, 1428 vs, 1320 m, 1266 w, 1213 w, 1090 vs, 801 w, 739 m, 673 m, 525 vw, and 465 m.

3.3. Crystal Structure Determination

Single crystals of 2 and 3 suitable for X-ray crystal structure analysis were obtained by the recrystallization from dichloromethane–diethyl ether and dichloromethane–benzene mixed solvents, respectively. X-ray crystallographic data (

Table 1. Crystallographic data of ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] (2) and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ (3) ^a.

	2	3
Empirical formula	C32H64Cl2NO8Ru2	C16H32BF4O10Ru2
Formula mass	863.88	673.37
Temperature	90 K	90 K
Crystal system	Triclinic	Monoclinic
Space group	$P\overline{1}$	P 2/c
a	16.0297(11) Å	12.600(4) Å
b	16.0936(11) Å	8.808(3) Å
c	18.6813(13) Å	13.968(4) Å
α	68.4640(10)°	90°
β	68.5090(10)°	106.581(4)°
γ	64.3420(10)°	90°
Unit-cell volume, V	3915.3(5) Å3	1485.7(8) Å3
Formula per unit cell, Z	4	2
Density, Dcalcd	1.466 g cm−3	1.505 g cm−3
Crystal size	0.330 × 0.300 × 0.200 mm3	0.300 × 0.160 × 0.060 mm3
Absorption coefficient, µ	0.953 mm−1	1.080 mm−1
θ range for data collection	1.641–28.500°	2.768–24.496°
Reflections collected/unique	25828/18244	8821/2430
R indices [I > 2σ(I)] b	R1 = 0.0348, wR2 = 0.0867	R1 = 0.0265, wR2 = 0.0783
Goodness-of-fit on F2	1.072	1.164

^a Standard deviations in parentheses; ^b R₁ = ∑||F_o| − |F_c||/∑|F_o|; wR₂ = [∑w(F_o² − F_c²)²/∑(F_o²)²]^1/2.

) were collected for a single crystal at 90 K on a Bruker CCD X-ray diffractometer (SMART APEX) using graphite-monochromated Mo Kα radiation (λ = 0.71073 Å) for 2 and a RIGAKU Saturn 724 CCD system equipped with a Mo rotating-anode X-ray generator with monochromated Mo Kα radiation (λ = 0.71075 Å) for 3. Diffraction data of 2 and 3 were processed using APEX2 (Bruker) and CrystalClear-SM (RIGAKU), respectively. The structures of 2 and 3 were solved by intrinsic phasing methods (SHELEX) and direct methods (SIR-2011), respectively and refined using the full-matrix least-squares technique (F²) with SHELXL-2014 as part of the SAINT (Bruker) (Billerica, MS, USA) and CrystalStructure 4.2.5 (RIGAKU) (Tokyo, Japan) software, respectively. Non-hydrogen atoms were refined with anisotropic displacement parameters, and all hydrogen atoms were refined with a riding model. Selected bond distances and angles for 2 and 3 are given in Tables S1 and S2, respectively.

CCDC-1887475 and 1887753 contain the supplementary crystallographic data for ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] (2) and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ (3), respectively. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre [22].

3.4. Computational Details

The unrestricted density functional theory (uDFT) calculations applied in this study were performed with the long-range and dispersion correlated hybrid DFT functional method, ωB97XD, on the Gaussian 09 program [23]. The Los Alamos effective core potential LANL08(f) and Pople’s 6-311 + G* basis sets were applied for the Ru and other atoms, respectively. All molecular geometries were fully optimized and checked by the vibrational frequency analyses. The solvent effect of CH₂Cl₂ was considered by the polarizable continuum model (PCM). The redox potentials were estimated by using the standard method with the Born–Harbor cycle and Gibbs free energy changes, which was defined by Noodleman [24]. In order to estimate the redox potentials (E^calc_1/2) for the Ru₂⁵⁺ → Ru₂⁴⁺ and Ru₂⁶⁺ → Ru₂⁵⁺ processes, the atomic coordinates of optimized geometries for Ru₂⁴⁺, Ru₂⁵⁺, and Ru₂⁶⁺ species are needed for [Ru₂(O₂CC₃H₇)₄Cl] (model compound of 1), [Ru₂(O₂CC₃H₇)₄Cl₂]⁻ (model compound of 2), and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]⁺ (model compound of 3), respectively. All of the coordinates used for the estimations are given in Tables S3–S11. We subtracted 4.68 V (IUPAC value) [25] from the calculated absolute potentials of the Ru₂ complexes to make a direct comparison to the experimental CV data referenced to the SCE.

4. Conclusions

By using [Ru₂(O₂CC₃H₇)₄Cl]_n as a starting material, ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂] and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄ were prepared. Their lantern-type dinuclear structures with axial ligands of Cl⁻ or H₂O were confirmed by X-ray crystal structure analyses. Temperature dependent magnetic susceptibility measurements were performed to show that all of the complexes ([Ru₂(O₂CC₃H₇)₄Cl]_n, ⁿBu₄N[Ru₂(O₂CC₃H₇)₄Cl₂], and [Ru₂(O₂CC₃H₇)₄(H₂O)₂]BF₄) had an S = 3/2 ground state, with a large zero-field splitting (D = 60–80 cm⁻¹). No important magnetic interaction was observed between the dinuclear units for the complexes. Cyclic voltammograms (measured in CH₂Cl₂ with an electrolyte of ⁿBu₄N(BF₄)) showed the Ru₂⁵⁺/Ru₂⁴⁺ process at −0.2–−0.4 V (vs. SCE) and the Ru₂⁶⁺/Ru₂⁵⁺ one at 1.3–1.4 V (vs. SCE), where the potentials were confirmed by the DFT calculation for [Ru₂(O₂CC₃H₇)₄Cl₂]⁻.