A Chain of Vertex-Sharing {Co^III₂Co^II₂}_n Squares with Single-Ion Magnet Behavior

Abstract

A new mixed-valence one-dimensional coordination polymer of formula {[Co^II(MeOH)₂][(μ-NC)₂Co^III(dmphen)(CN)₂]₂}_n·2nH₂O (1) was obtained by reacting the Ph₄P[Co^II(dmphen)(CN)₃] metalloligand (dmphen = 2,9-dimethyl-1,10-phenanthroline and Ph₄P⁺ = tetraphenylphosphonium ion) with cobalt(II) acetate tetrahydrate. The structural analysis shows the formation of a neutral 4,2-ribbon-like chain of vertex-sharing cyanido-bridged {Co^III₂Co^II₂} squares in which the metalloligand underwent an oxidation process and a reorganization to form {Co^III(dmphen)(CN)₄}⁻ linkers that coordinate to the [Co^II(MeOH)₂]²⁺ units through single cyanido ligands. Both cobalt(II) and Co(III) cations are six-coordinated in distorted octahedral environments. The shortest intrachain distance between the paramagnetic cobalt(II) ions is 7.36 Å, a value which is shorter than the shortest interchain one (10.36 Å). Variable-temperature (1.9–300 K) static (dc) magnetic measurements for 1 indicate the occurrence of magnetically isolated high-spin cobalt(II) ions with a D value of +67.0 cm⁻¹. Dynamic alternating current (ac) magnetic measurements between 2.0–13 K reveal that 1 exhibits slow magnetic relaxation under non-zero applied dc fields, being thus a new example of field-induced SIM with easy-plane magnetic anisotropy. Theoretical calculations by CASSCF/NEVPT2 on 1 support the results from magnetometry. The relaxation of the magnetization occurs in the ground state under external dc fields through a two-phonon Raman process and one intra-Kramers mechanism.

1. Introduction

Cyanido spacers represent a prolific platform in metal assembling for magnetic molecule-based materials such as single-molecule magnets (SMMs), single-ion magnets (SIMs) or single-chain magnets (SCMs) which are very appealing systems considering their potential use in molecular electronics [1,2]. We focused on cyanido-bridged heterometallic complexes which exhibit slow relaxation of the magnetization, and which were successfully obtained through the rational bottom-up approach involving the use of cyanido-bearing metalloligands against highly anisotropic species [3,4,5,6,7,8]. Complex cations of 3d (Mn^III, Co^II) and 4f (Dy^III, Yb^III, Tb^III) metal centers or heterometallic phenoxo-bridged d-f units ({Ni^IILn^III} and {Cu^IILn^III}) behave as SIMs or SMMs fragments, with four-, six- or eight-coordinate homo- and heteroleptic cyanide-containing complex anions such as [Co^III(CN)₆]³⁻, [Co^III(AA)(CN)₄]⁻, [Fe^II(AA)₂(CN)₂], [Co₂^III(2,5-dpp)(CN)₈]²⁻, [Ni^II(CN)₄]²⁻, [Pt^IVBr₂(CN)₄]²⁻, [M^IV(CN)₈]⁴⁻ and [M^IV(AA)CN)₆]²⁻, being used as diamagnetic linkers (M = Mo, W; AA = bidentate ligand; 2,5-dpp = 2,5-bis(2-pyridyl)pyrazine) [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. Most of the heterometallic compounds reported are of the mixed d-f type, where a cyanido building block of a diamagnetic transition metal ion (S = 0) coordinates through the cyanide bridges to an anisotropic Ln^III complex cation: (i) a 3D network of SMMs, {[Dy^III(H₂O)₂][Co^III(CN)₆]}_n · 2.2nH₂O [13]; (ii) several one-dimensional (1D) coordination polymers of SMMs whose general formula is {[Dy^III(MeOH)₄][Fe^II(AA)(CN)₂]}(CF₃SO₃)₃ · nMeOH [16]; (iii) and discrete complexes, such as a pentanuclear emissive SMM, {[Dy^III(H₂O)₃(tmpo)₃]₂[Pt^IVBr₂(CN)₄]₃} · 2H₂O [20], a heterobinuclear field-induced SMM, [Yb^IIICo^III(CN)₆(bpyO₂)₂(H₂O)₃] · 4H₂O [15], a heterotrimetallic decanuclear square showing SMM behavior, [(Mo^IV(CN)₈)₂(Cu^IILTb^III)₄]⁴⁺ [21], and a metallocyclic molecular nanomagnet, {[Ni^II(Me₂valpn)]₂Dy^III(H₂O)Co(CN)₆}₂⋅ 8H₂O⋅2DMF⋅6CH₃CN [12] [tmpo = trimethylphosphine oxide, bpyO₂ = 2,2′-bipyridine-N,N’-dioxide; H₂L = N,N’-bis(3-methoxysalicylidene)ethylenediamine and H₂Me₂valpn = N,N’-bis(3-methoxysalicylidene)-2,2-dimethyl-1,3-diaminopropane]. Fewer examples of d nodes acting as SIMs or SMMs within heterometallic coordination compounds are known: the honeycomb structure {[Co^II(TODA)₃][Co^III(CN)₆]₂ · 9H₂O}_n [10], the tubular 1D motif [Co^II(L_N3O2)]₆[Co^III(CN)₆]₄ · 26H₂O [11], the chain of SIMs with seven-coordinate iron(II) ions {[Fe^II(H₂DAPBH)][Ni^II(CN)₄]}_n [19], and 1D compounds behaving as SMMs with formulas {[Co^II(bpp)(H₂O)][W^IV(CN)₈]}_n·6nH₂O [24] and [Co^II(CH₃OH)₂(DMSO)₂(μ-NC)₂Co₂^III(μ-2,5-dpp)(CN)₆]_n·4nCH₃OH [17] {TODA = 1,4,10-trioxa-7,13-diazacyclopentadecane; L_N3O2 = 2,13-dimethyl-3,12,18-triaza-6,9-dioxabicyclo-[12.3.1]octadeca-1(18),2,12,14,16-pentaene, H₂DAPBH = 2,6-diacetylpyridine bis-benzoylhydrazone and bpp = 2,6-di(1-pyrazolyl)pyridine}.

Redox labile cyanido building blocks have been described in the literature [25,26,27,28,29]. In this respect, we reported several heterometallic complexes which were obtained by using the heteroleptic cyanide-bearing [W^V(bpy)(CN)₆]⁻ or [Co^II(dmphen)(CN)₃]⁻ complexes as building blocks for metal assembling, processes that were accompanied by a reduction from W^V to W^IV or an oxidation from Co^II to Co^III to form more stable species as nodes within the {Ni^IIDy^IIIW^IV} [22] and {Co^IIIMn^III} [9] coordination polymers, respectively. The [W^V(bpy)(CN)₆]⁻ species underwent reduction to form a 2D network of SMMs in which diamagnetic W(IV) spacers connected the {Ni^IIDy^III} nodes, whereas the Co(II) ion within the [Co^II(dmphen)(CN)₃]⁻ complex anion was oxidized, turning into the [Co^III(dmphen)(CN)₄]⁻ linker in the resulting {Co^IIIMn^III} chain of SIMs.

Herein, we describe the preparation and magneto-structural study of a 4,2-ribbon-like chain of the formula {[Co^II(MeOH)₂][(μ-NC)₂Co^III(dmphen)(CN)₂]₂}_n·2nH₂O (1) where vertex-sharing {Co^III₂Co^II₂}_n squares and field-induced slow relaxation of the magnetization occur. Remarkably, the low-spin [Co^II(dmphen)(CN)₃]⁻ species which is used as a metalloligand for fully solvated cobalt(II) ions undergoes an oxidation process and a reorganization into the more stable diamagnetic [Co^III(dmphen)(CN)₄]⁻ unit in 1.

2. Results and Discussion

2.1. Synthesis, IR Spectroscopy and Powder X-ray Diffraction

In previous works, we explored the use of the low-spin [Co^II(dmphen)(CN)₃]⁻ complex anion as a metalloligand for the [Mn^III(salen)(H₂O)]⁺ complex cation [9,30]. This complex-as-ligand strategy afforded two heterobimetallic chains of formulas {[Mn^III(salen)(μ-NC)₂Co^III(dmphen)(CN)₂]}_n [9] and {[Mn^III(salen)(μ-NC)₂Co^II(dmphen)(CN)]·2H₂O}_n [30]. The oxidation of the Co(II) ion to Co(III) occurred in the formation of the first one, a process that could be explained by taking into account the oxidizing activity of the [Mn^III(salen)(H₂O)]⁺ complex cation. Single crystals of the neutral {Mn^IIICo^III} chain were grown in a test tube by slow diffusion, after a few weeks. As far as the second chain is concerned, the kinetic factor was most likely determinant in its formation because single crystals formed within a day. In the present report, the reaction between [Co^II(dmphen)(CN)₃]⁻ and Co(CH₃COO)₂·4H₂O in the methanol afforded orange crystals of 1 by slow evaporation of the resulting solution in the open air after five days. The oxidation of the cobalt(II) ion from the cyanide-bearing metalloligand to cobalt(III) in 1 is favored by the strong ligand field character of the dmphen and cyanide ligands that would stabilize the [Co^III(dmphen)(CN)₄]⁻ unit in this 1D compound.

The FTIR spectrum of 1 shows two strong bands at 2172 and 2128 cm⁻¹ which are attributed to the stretching vibrations of the bridging and terminal cyanido ligands, respectively (Figure S1). The fact that these peaks are observed at 2171 and 2140 cm⁻¹ in the infrared spectra of the related {Co^IIIMn^III} and [Mn^II(MAC)(μ-NC)₂Co₂^III(μ-2,5-dpp)(CN)₆]_n·7nH₂O chains [9,31] and that the stretching vibration of the terminal cyanide for PPh₄[Co^III(4,4′-dmbipy)(CN)₄] (4,4′dmbipy = 4,4′-dimethyl-2,2′-bipyridine) occurs at 2130 cm⁻¹ [9], supports the coexistence of the bridging cyanide between Co(II) and Co(III) and terminal cyanide ligands at Co(III) in 1. The peaks at 1627, 1598 and 1562 cm⁻¹ would correspond to the C=N_dmphen bond vibration and the ring-stretching modes of the dmphen ligand. Finally, the strong intensity peak at 442 cm^–1 is most likely due to the vibrations of the Co^II-O bond. All these spectroscopic features are sustained by the X-ray crystal structure of 1. Additionally, the purity of the bulk sample is confirmed by the agreement between its PXRD pattern and the calculated one from the single crystal X-ray diffraction (Figure S2). The powder XRD was performed on a fresh sample, the compound losing crystallinity over time.

2.2. Description of the Structure

Compound 1 crystallizes in the triclinic system, spatial group P-1 and its structure consists of neutral chains of vertex-sharing squares of formula {[Co^II(MeOH)₂][(μ-NC)₂Co^III(dmphen)(CN)₂]₂}_n·2nH₂O (1). The asymmetric unit is made up by a cyanido-bridged {Co^IIICo^II} unit, where the [Co^III(dmphen)(CN)₄]⁻ metalloligand coordinates to a diaquacobalt(II) ion through a single cyanido group (Figure 1, left).

Further, each metalloligand connects to another Co^II ion to give {Co^III₂Co^II₂} squares, sharing the Co^II ions as vertices. In such a way, a neutral, 4,2-ribbon-like chain, running parallel to the crystallographic b axis, results (Figure 1, right). This type of topology was observed in previously reported heterobimetallic chains obtained by using [M^III(L’)(CN)₄]⁻ (M = Cr and Fe; L’ = bipy and phen) [32,33,34,35,36,37], [Cr(ampy)(CN)₄]⁻ (ampy = 2-aminomethylpyridine) [33], [Fe^III(bpym)(CN)₄]⁻ (bpym = 2,2′-bipyrimidine) [38], [Fe^III(4,4′-dmbpy)(CN)₄]⁻ [39,40,41] and [Fe^III(dbphen)(CN)₄]⁻ (dbphen = 5,6-dibromo-1,10-phenanthroline) [42] as building blocks towards fully solvated transition metal ions.

Selected bond lengths and angles for 1 are listed in

Table 1. Main bond lengths (Å) and angles (deg) for 1 *.

Co1-O1	2.125(5)	O1-Co1-O1 c	180.0
Co1-O1 e	2.125(5)	N5-Co1-O1	89.6(2)
Co1-N4 a	2.129(6)	N4-Co1-O1	90.7(2)
Co1-N4 f	2.129(6)	N1-Co2-N2	82.7(2)
Co1-N5	2.102(5)	Co2-C15-N3	178.8(6)
Co2-N1	2.011(5)	Co2-C16-N4	174.4(6)
Co2-N2	2.034(5)	Co2-C17-N5	176.3(6)
Co2-C15	1.898(6)	Co2-C18-N6	176.4(8)
Co2-C16	1.872(7)	Co1-N5-C17	169.5(5)
Co2-C17	1.922(7)	Co1 b-N4-C16	176.5(6)
Co2-C18	1.875(8)

* Symmetry code: (a) = 1 − x, 1 − y, −z; (b) = −1 + x, y, z; (c) = 1 − x, 2 − y, −z; (e) = 2 − x, 1 − y, −z; (f) = 1 + x, y, z.

. The cobalt(II) ion in 1 (Co1) is surrounded by four cyanide-nitrogen atoms building the equatorial plane and two trans-positioned methanol molecules in the axial positions, the whole set of donor atoms defining a slightly distorted octahedral geometry. In this respect, the estimated ChSM value for the environment of the Co1 atom is 0.016 (a zero value corresponds to the ideal octahedron as predicted by the SHAPE program; see Table S1 and Figure S3) [43,44]. The values of the equatorial Co1-N_cyanide bond lengths are 2.102(5) and 2.129(6) Å for Co1-N5 and Co1-N4a, respectively, while those of the axial Co1-O_MeOH bond distances are of 2.125(5) Å (Co1-O1), these structural features accounting for the octahedral distortion. The values of the Co1-N-C bond angles cover the wide range between 169.5(5) and 176.5(6)° for C16-N4-Co1b and C17-N5-Co1, respectively.

The Co(III) ions from the crystallographically independent [Co^III(dmphen)(CN)₄]⁻ metalloligand (Co2) is also six-coordinated by a didentate dmphen molecule and four cyanide-carbon atoms in a somewhat more distorted octahedral environment than the cobalt(II) ion [estimated ChSM values through the SHAPE program of 0.459 (Co2); see Table S1 and Figure S3]. The main source of this distortion is the reduced value of the bite angle of the chelating dmphen, of 82.7(2)°. The Co2-C_cyanide bond distances cover the range 1.872(7)–1.922(7) Å, values that agree with those previously reported for other cyanido-based cobalt(III) complexes [9,17,31,45,46]. The Co2-N_dmphen bond lengths [2.034(5), 2.011(5) Å, are longer than those of the Co2-C_cyanide, as expected. The Co2-C-N_cyanide bond angles are close to linearity, their values varying in the range between 174.4(6) (Co2-C16-N4) and 178.8(6)° (Co2-C15-N3).

The cobalt atoms within each square unit of 1 form angles at the corners which deviate slightly from the ideal value of 90° (ca. 91.93 and 88.04° for Co1b-Co2a-Co1 and Co2a-Co1b-Co2, respectively). Very close intermetallic distances are found along the edges of the {Co^III₂Co^II₂} squares, ca. 5.13 Å both for Co1···Co2 and Co1···Co2a [symmetry code: (a) = 1 − x, 1− y, −z; (b) = −1 + x, y, z]. The values of the shortest intra- and interchain distances between the paramagnetic cobalt(II) ions are 7.38 (Co1^…Co1b) and 10.92 Å (Co1^…Co1d), respectively [symmetry code: (d) = x, 1 + y, z].

The neutral chains in 1 are further interconnected through hydrogen bonds involving the coordinated methanol molecules, two peripheral cyanide ligands and the water molecules of crystallization leading to a supramolecular 2D network that grows in the crystallographic ac plane (Figure 2 and Table S2). Supramolecular π-π stacking interactions between dmphen ligands from adjacent chains (value of the centroid···centroid distance of ca. 3.59 Å) contribute to the stabilization of this supramolecular network (Figure S4).

2.3. Static (dc) Magnetic Properties

The dc magnetic properties of compound 1, as the χ_MT against T plot (χ_M being the magnetic susceptibility per Co^III₂Co^II unit), are shown in Figure 3. At room temperature, χ_MT is equal to 2.81 cm³ mol⁻¹ K, a value which is as expected for a magnetically diluted high-spin cobalt(II) ion with a significant orbital angular momentum [47]. The cobalt(III) ions in 1 are diamagnetic. Upon cooling, χ_MT continuously decreases to reach a value of 1.62 cm³ mol⁻¹ K at 1.9 K. There is no maximum of the magnetic susceptibility in the χ_M vs. T plot. The observed decrease in χ_MT could be due to the thermal depopulation of the higher Kramer doublets of the high-spin cobalt(II) ion and/or to antiferromagnetic interactions between the paramagnetic cobalt(II) ions. This last possibility is to be ruled out because of the large cobalt(II)···cobalt(II) distance (shortest intra- and interchain values of ca. 7.36 and 10.36 Å, respectively).

Having in mind these features, we treated the magnetic data of 1 through the Hamiltonian Equation (1):

H = −αλL_CoS_Co + ∆[L_z,CoS_Co − L(L + 1)/3] + βH(g_eS_Co − αL_Co)

(1)

The first term in this Hamiltonian describes the spin-orbit coupling (SOC) where λ is the spin-orbit coupling parameter and α is an orbital reduction factor defined as α = Aκ. κ represents the reduction in the orbital momentum caused by the delocalization of the unpaired electrons on the ligands covalency. The A parameter takes values of 3/2 and 1 in the weak and strong crystal field limits, respectively, and it considers the admixture of the upper ⁴T_1g(⁴P) state into the ⁴T_1g(⁴F) ground state. The second term models the axial splitting of the ⁴T_1g ground state of the ideal O_h symmetry of the cobalt(II) ion into singlet ⁴A₂ and doublet ⁴E levels, ∆ being the energy gap between these levels. The ⁴A₂ and ⁴E levels split in turn by second-order SOC, leading to two and four Kramers doublets. Finally, the third term corresponds to the Zeeman interaction, which includes both spin and orbital contributions. The best-fit parameters of the magnetic data of 1 from the whole temperature range explored through the VPMAG program [48] are α = 1.24, λ = −163 cm⁻¹ and ∆ = +553 cm⁻¹ with F = 8.0 × 10⁻⁶ (F is the agreement factor defined as ∑[P_exp–P_calcd]²/∑[P_exp]², where P is the physical property under study). The obtained values of α, λ and ∆ for 1 are in the range of those previously reported for other six-coordinate high-spin cobalt(II) complexes [17,49,50,51,52,53,54,55,56,57].

Due to the strong axial distortion of the cobalt(II) ion, both structurally (see Table 1) and magnetically (∆ = +553 cm⁻¹), an important reduction in the orbital momentum is expected. Therefore, a spin Hamiltonian currently used to simultaneously fit the χ_MT vs. T and M against T plots, which is based on the assumption that the zero-field splitting (zfs) of S = 3/2 is dominant, can be applied. The corresponding Hamiltonian is expressed by Equation (2)

H_zfs+Zeeman = D[S_z² − S(S + 1)] + E(S_x² − S_y²) + βH[g_//S_z + g_⊥(S_x + S_y)]

(2)

where S, D, and E are the ground spin state and axial and transverse anisotropies, respectively, β is the Bohr magneton and H is the applied dc field. If E = 0 (a case where the rhombic distortion is neglected), 2D for 1 corresponds to the energy gap between the ±1/2 and ±3/2 doublets arising from the second order SOC of the quartet ground state of the axially distorted octahedral cobalt(II) ion. As the M vs. H/T curves for 1 in the temperature range from 2.0 to 9 K quasi collapse (see inset of Figure 3), a large value of D is predicted. The simultaneous analysis of the variable-temperature magnetic susceptibility and magnetization data under different applied dc fields and temperatures of 1 through the VPMAG package [48] led to the following best-fit parameters: D = +67.0 cm⁻¹, E/D = 0.13, g_// = 2.44, g_⊥ = 2.51 and TIP = 930 × 10⁻⁶ cm³ mol⁻¹ with F = 7.6 × 10⁻⁶. The simulated curves with these values match well the experimental data in the temperature ranges explored. When we started with a negative value of D, no reasonable results were obtained. Consequently, this system can be considered as a doublet at low temperatures. The positive sign of the zfs parameter arises from the interaction between the ground and excited electronic states coupled through the SOC and illustrates the strong easy-plane anisotropy of the high-spin cobalt(II) in 1. The value of D for 1 lies within the range of those reported for other examples of SIMs with six-coordinate cobalt(II) ions [17,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70].

2.4. Theoretical Calculations

To confirm the validity of the results from magnetometry for 1, theoretical CASSCF/NEVPT2 calculations were carried out. Owing to the high disorder observed in 1, two different geometries for the Co^II coordination sphere can be extracted (Table S3). Given that each Co^II ion is surrounded by four Co^III ions, the model that introduces all electronic effects on the cobalt(II) center is too large to be calculated at a moderate computational cost. Therefore, a simpler model was built by substituting the Co^III ions and their surroundings with a simple proton, which simulates the presence of a positively charged entity bound to the cyanide bridging ligands that decrease the magnitude of its ligand field (just as the Co^III ion does in the actual system). The sign and magnitude of the computed value of D for the two mononuclear models (+42.9 and +62.7 cm^–1 for A and B, respectively) agree with the one from magnetometry. To be more precise, the result extracted from experimental data is close to the calculated ones. A similar case occurs with the calculated E/D ratio, which takes high (0.179) and low (0.050) values for the first high- and second low-rhombic distorted models. Consequently, from magnetometry where only a single geometry for the Co^II coordination sphere is considered, an intermediate value (that is 0.13) very close to the theoretical mean one (0.115) is found for the E/D ratio. The calculated components for the g-tensor show an axial magnetic anisotropy in both models with a parallel contribution lower than the perpendicular one (g_z = 2.057, g_y = 2.418, g_x = 2.524, g_⊥ = 2.471, and g_z = 2.062, g_y = 2.505, g_x = 2.610, g_⊥ = 2.560 for the A and B models, respectively), whereas A points to a smaller value of D (|g_z − g_⊥| (0.414 and 0.498) and a larger rhombicity (|g_x − g_y|/|g_z − g_⊥| = 0.256 and 0.211). ⁴T_1g is the ground term for a high-spin d⁷ configuration of a Co^II ion in an octahedral environment. Due to geometric or ligand-field distortions, it splits into three states; one of them is the ground state and the other two are the closest excited states (ca. 1490 and 990 cm^–1 for A and B). For this type of compound, the interaction between these excited states and the ground one contributes mainly to the zfs, which is also observed for the A and B models with estimated contributions to D [+42.1 (A) and +56.0 cm^–1 (B)], which are somewhat above 90% of the calculated total value.

According to the geometry of the Co^II coordination sphere in 1, with four bridged cyanide ligands building a plane and two O-donor solvent molecules on the axial sites, the z-axis of the zfs tensor is placed on this O-Co-O vector and the four cyanide-nitrogen atoms form the equatorial plane (Figure S5). It is worth noting that some deviations from the axial axis occur due to several distortions of the octahedral coordination sphere.

2.5. Dynamic (ac) Magnetic Properties

Alternating current (ac) magnetic susceptibility measurements for 1 were carried out in the temperature range from 2.0 to 10 K to investigate its magnetization dynamics. No frequency dependence was observed for the ac components in the absence of a magnetic field (H_dc), a feature which is usually attributed to a fast relaxation by quantum tunneling of magnetization (QTM). However, for easy-plane magnetic anisotropy (D > 0) as in 1, no energy barrier arises from the zfs to govern the magnetic relaxation. Instead, the swift spin reversal in the absence of H_dc is associated with the enabled direct pass between the two M_S components of the ground ±1/2 Kramers doublet. Such a mechanism is known as an intra-Kramer (IK) relaxation [71]. Although an IK can suppress the occurrence of the slow magnetic relaxation phenomenon, it becomes less efficient when applying an external dc magnetic field. Therefore, frequency-dependent χ_M′ and χ_M″ signals are observed under H_dc of 2.5 and 5.0 kOe (Figure 4 and Figure S6), in agreement with a slow magnetic relaxation process typical of high-spin cobalt(II) SIMs.

Two relaxation processes can be distinguished from the χ_M″ vs. T curves (Figure 4). They occur at blocking temperatures (T_B) close enough to superimpose and, consequently, no clear maxima are appreciated. It is possible to identify one process being predominant at higher temperatures (T_B > 5.0 K) that shifts towards lower T_B values by decreasing the frequency of the oscillating magnetic field (ν) and another process which seems to be temperature-independent occurring at lower temperatures (T_B < 4.0 K). In these cases, where no maxima can be discerned, the approximation to calculate the magnetic relaxation times (τ) of τ = 1/2πν at T = T_max cannot be applied. Therefore, the best way to extract this parameter is the joint analysis of the χ_M′ and χ_M″ vs. ν curves (Figure S7a,b) through the generalized Debye model [Equations (3) and (4)], which also takes into account the static and infinite magnetic susceptibilities (χ_S and χ_T) as well as the exponential factor that describes the broadness of the spectra (α) [72]:

$${\chi }^{\prime }={\chi }_s+\left({\chi }_t-{\chi }_s\right)\frac{1+{\left(\omega \tau \right)}^{1-\alpha }sin\left(\alpha \pi /2\right)}{1+2{\left(\omega \tau \right)}^{1-\alpha }sin\left(\alpha \pi /2\right)+{\left(\omega \tau \right)}^{2-2\alpha }}$$

(3)

$${\chi }^{″}=\left({\chi }_t-{\chi }_s\right)\frac{{\left(\omega \tau \right)}^{1-\alpha }cos\left(\alpha \pi /2\right)}{1+2{\left(\omega \tau \right)}^{1-\alpha }sin\left(\alpha \pi /2\right)+{\left(\omega \tau \right)}^{2-2\alpha }}$$

(4)

We tried to use a double relaxation model to analyze both the aforementioned lower- and higher-temperature distinct processes, where each process was considered additive and independent. However, it resulted in overparameterization, and no reliable data could be extracted from this approach. Alternatively, the contribution of the temperature-independent process was omitted because of a lack of accuracy derived from its very low T_B values (below 2.0 K). This method allowed us to obtain a good set of magnetic parameters for the higher-temperature process that reproduces well the χ_M′ and χ_M″ vs. ν curves (Figure S7a,b), as well as the Argand plots (Figure S7c). For that, the data of temperatures below 3.5 (H_dc = 5.0 kOe) or 4.5 K (H_dc = 2.5 kOe) were discarded in the analysis. The relatively high values of α at these temperatures (0.26 and 0.40 for H_dc = 2.5 and 5.0 kOe, respectively) and how they continuously decrease down to 0.13 at 7.0 K, support the occurrence of additional relaxation processes that become less relevant when the temperature increases, as predicted from a qualitative analysis of the χ_M′ and χ_M″ against T plots.

The values of τ are displayed in the form of ln τ vs. ln T plots in Figure 5. Satisfactory least-squares fits of the experimental data were obtained through Equation (5)

τ^–1 = τ_IK^–1 + τ_RAMAN^–1 = τ_IK^–1 + CTⁿ

(5)

which expresses a double spin reversal mechanism involving a two-phonon Raman and an IK relaxation prevailing at higher and lower temperatures, respectively. As expected, the values of the C and n Raman coefficients are very similar regardless of H_dc (Table S4). Moreover, the values of n between 6 and 7 (6.7 and 6.5 under H_dc fields of 2.5 and 5.0 kOe, respectively) indicate that acoustic phonons are involved in the Raman spin-lattice relaxation. Even though the τ_IK values are close, a slight decrease was observed when we increased H_dc, revealing that the spin reversal through this mechanism becomes faster. This is the opposite trend which should be expected for the greater splitting of the ground ±1/2 Kramers doublet promoted by a higher H_dc. Several circumstances may explain this feature, but the limited precision in determining τ (as denoted by the standard deviations in Figure 5), the influence of the low-temperature parallel process or even the arising of faster secondary mechanisms of relaxation that depend differently on H_dc, such as the one-phonon direct mechanism (τ^–1 = AT), are most likely the main sources of this deviation.

3. Materials and Methods

3.1. Materials and General Methods

The chemicals used as well as the solvents were of reagent grade and were purchased from commercial sources. Ph₄P[Co(dmphen)(CN)₃]·4H₂O was prepared as described in the literature [45]. Elemental analyses (C, H, N) were performed on a Perkin Elmer 2400 analyzer. IR spectra were carried out on a FTIR Bruker Tensor V-37 spectrophotometer using KBr pellets in the range from 4000 to 400 cm⁻¹.

Caution! The high toxicity of the cyanides means that great caution is required in their use. The syntheses were carried out at a mmol scale, in a well-ventilated hood. The waste was treated with solutions of NaClO and NaOH to transform the cyanide into cyanate.

3.2. Preparation of {[Co^II(MeOH)₂][(μ-NC)₂Co^III(dmphen)(CN)₂]₂}_n·2nH₂O (1)

A solution of 0.082 g (0.11 mmol) of Ph₄P[Co(dmphen)(CN)₃]·4H₂O in 15 mL methanol was poured into a methanolic solution (20 mL) of 0.04 g (0.22 mmol) Co(CH₃COO)₂·4H₂O, with a few drops of acetic acid. The orange solution formed was left undisturbed for five days. X-ray quality orange prism-like crystals were obtained. Yield: ca. 55% (1). Anal. Calcd for C₃₈H₃₆N₁₂Co₃O₄ (1): C, 26.82; H, 1.06; N, 21.40. Found: C, 26.87; H, 1.02; N, 21.32%. IR (KBr/cm⁻¹): 3438s, 2172vs and 2128s [ν_CNcyanide], 1627s [ν_C=N], 1429vs, 1378s, 1159m, 863vs, 729s, 442s.

3.3. Physical Measurements

Direct current (dc) magnetic susceptibility measurements (1.9–300 K) under applied dc magnetic fields of 5000 G (T ≥ 50 K) and 100 G (1.9 ≤ T ≤ 50 K) and variable-field (0–5 T) magnetization measurements (2.0–10 K) on crushed crystals of 1 (mixed with grease to avoid the crystallite orientation) were carried out with a Quantum Design SQUID magnetometer. Variable-temperature (2.0–12 K) alternating current (ac) magnetic susceptibility measurements under different applied dc magnetic fields in the range 0 to 2500 G were performed for 1 by using a Quantum Design Physical Property Measurement System (PPMS). The magnetic susceptibility data of both compounds were corrected for the diamagnetism of the constituent atoms and the sample holder (a plastic bag). Powder X-ray diffraction (XPRD) measurements were done on a PANalytical Empyrean X-ray diffractometer using Cu-Kα radiation (α = 1.5418 Å), in which the X-ray tube was operated at 40 kV and 30 mA ranging from 5 to 30°.

3.4. Computational Details

The parameters that determine the axial (D) and rhombic (E) components of the local zero-field splitting (zfs) of 1 were estimated from theoretical calculations based on a second-order N-electron valence state perturbation theory (CASSCF/NEVPT2) [73,74,75], which often provides accurate values of the nearby excited states energies and for the zfs tensor of mononuclear first-row transition metal complexes. As a starting wavefunction, one found from a previous complete active space (CAS) calculation was used. Calculations were carried out on the experimental geometries with version 4.0.1 of the ORCA programme [76], using the def2-TZVP basis set proposed by Ahlrichs [77,78] and the auxiliary TZV/C Coulomb fitting basis sets [79,80,81]. The contributions to zfs from 10 quartet and 20 doublet excited states generated from an active space with seven electrons in five d orbitals were included using an effective Hamiltonian. The RIJCOSX method was used combining resolution of the identity (RI) and “chain of spheres” COSX approximations for the Coulomb and exchange terms, respectively [82,83,84].

3.5. X-ray Data Collection and Structure Refinement

X-ray quality single crystals of 1 were measured on an Oxford Diffraction XCALIBUR Eos CCD diffractometer equipped with graphite-monochromated Mo-Kα radiation (λ = 0.71073 Å). The crystals were positioned 40 mm from the CCD detector and 248 frames were measured each for 125 s over a 1° scan width. The determination of the unit cell and data integration was established by using the CrysAlis package of Oxford Diffraction [85]. Multi-scan correction for absorption was applied. The structure was solved with the program SHELXT using the intrinsic phasing method and refined by the full-matrix least-squares method on F² with SHELXL [86,87]. Olex2 was used as an interface to the SHELX programs [88]. All hydrogen atoms attached were introduced in idealized positions and refined using a riding model. The structural images were obtained with a Diamond 4 program [89]. The unit cell parameters and refinement conditions for 1 are given in

Table 2. Crystal data and structure refinement for 1.

Empirical Formula	C38H36Co3N12O4
Formula weight	901.58
T/K	200
Crystal system	Triclinic
Space group	P-1
a/Å	7.3830(6)
b/Å	10.9266(12)
c/Å	12.9259(13)
α/°	80.056(9)
β/°	74.231(8)
γ/°	77.893(9)
Volume/Å3	973.74(18)
Z	1
ρcalcg/cm3	1.537
μ/mm−1	1.320
F(000)	461.0
Crystal size/mm3	0.06 × 0.06 × 0.06
Radiation	Mo Kα (λ = 0.71073 Å)
2θ range for data collection/°	3.842 to 49.798
Index ranges	−8 ≤ h ≤ 8, −12 ≤ k ≤ 12, −15 ≤ l ≤ 15
Reflections collected	9083
Independent reflections	3385 [Rint = 0.0609]
Data/restraints/parameters	3385/4/270
Goodness-of-fit on F2	1.093
Final R indexes [I ≥ 2σ(I)]	R1 = 0.0793, wR2 = 0.1612
Final R indexes [all data]	R1 = 0.1196, wR2 = 0.1787
Largest diff. peak/hole (e Å−3)	1.66/−0.63

. The supplementary crystallographic data can be obtained free of charge via www.ccdc.cam.ac.uk/conts/retrieving.html or [email protected] accessed on 25 March 2023, CCDC-2252204 (1)

4. Conclusions

Our attempts to explore the coordination ability of the low-spin [Co^II(dmphen)(CN)₃]⁻ complex anion to fully solvated metal cations provided the 4,2-ribbon-like chain of formula {[Co^II(MeOH)₂][(μ-NC)₂Co^III(dmphen)(CN)₂]₂}_n·2nH₂O (1) where the low-spin cobalt(II) ion from the starting metalloligand underwent oxidation to diamagnetic cobalt(III) together with a reorganization of its environment. This phenomenon was observed previously in the reaction of the same low-spin cobalt(II) building block with the preformed [Mn^III(salen)(H₂O)]⁺ complex cation. In contrast to what occurs in 1, a heterobimetallic zigzag chain of formula {[Mn^III(salen)(μ-NC)Co^III(dmphen)(CN)₃]}_n resulted in this last case, the oxidant being the manganese(III) from the complex cation. Static (dc) and dynamic (ac) magnetic measurements reveal that 1 is a new example of a field-induced SIM with an easy-plane anisotropy, the positive sign and size of D from magnetometry being substantiated by theoretical calculations. The analysis of the relaxation of the magnetization at low temperatures of 1 obeys a combination of an intra-Kramers mechanism and a Raman process.