One-Dimensional Chains of Paddlewheel-Type Dichromium(II,II

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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One-Dimensional Chains of Paddlewheel-Type Dichromium(II,II) Tetraacetate Complexes: Study of Electronic Structure Influenced by σ- and π‑Donation of Axial Linkers Po-Jung Huang,† Yoshiki Natori,‡ Yasutaka Kitagawa,‡ Yoshihiro Sekine,†,§ Wataru Kosaka,†,§ and Hitoshi Miyasaka*,†,§ †

Department of Chemistry, Graduate School of Science, Tohoku University, 6-3 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan Department of Materials Engineering Science, Osaka University, 1-3 Machikaneyama-chou, Toyonaka, Osaka 560-0043, Japan § Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan ‡

S Supporting Information *

ABSTRACT: Paddlewheel-type carboxylate-bridged dichromium(II,II) complexes possess intriguing properties such as high redox activity and thermally assisted paramagnetism. However, the relationship of their structures with electronic states and physical properties has not been extensively studied. In this work, we investigated a series of one-dimensional chain complexes based on the paddlewheel-type dichromium(II,II) tetraacetate complex ([Cr2II,II(OAc)4] = [Cr2II,II]) with pyridine/pyrazine-type organic linkers (μ2-Lax) having different σand π-donating abilities to clarify the electronic structure of [Cr2II,II] assemblies. The chain compounds are stable in air, probably owing to their robust polymerized forms. X-ray crystallographic studies and magnetic measurements revealed that the basicity (pKb) of Lax, which quantitatively correlates with the σdonor strength of Lax, modulates the Cr−Cr and Cr−Lax distances and the energy separation (ES−T) between the diamagnetic (singlet) and thermally populated paramagnetic (triplet) states. The Cr−Cr and Cr−Lax distances are strongly influenced by σ- and π-donation from Lax, while the frontier δ orbital makes only a small contribution to the structural features. Density functional theory calculations were conducted to clarify this issue. The calculations produced the following unanticipated results against the long-known model: (i) the σ bonding orbital is the HOMO and dominates bonding in the [Cr2II,II] unit, (ii) the total Cr−Cr bond order is less than 1.0, and (iii) the δ orbital electron density is almost completely localized on the chromium sites. The computational results accurately predict the magnetic behavior and provide evidence for a new configuration of frontier orbitals in [Cr2II,II(RCO2)4(Lax)2].

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INTRODUCTION Over 100 paddlewheel-type carboxylate-bridged dichromium(II,II) complexes [Cr2II,II(RCO2)4(Lax)2] (abbreviated as [Cr2], Scheme 1), where R and Lax represent carboxylate substituents and axial ligands, respectively, have been structurally characterized,1−3 although they were still unstable in air comparable to mononuclear CrII complexes.4−7 In these works, the dichromium compounds have been assumed to possess a diamagnetic electronic structure with a quadruple Cr−Cr bond based on a σ22π4δ2δ*02π*0σ*0 frontier orbital set (Scheme 1a),8,9 but the weak paramagnetism arising from thermally populated excited states was seldom discussed.10,11 Hence, the correlation between structural and magnetic properties is yet to be fully explored.12 A critical shortcoming in comprehensively comparing [Cr2] compounds is the large variety of structural variables employed without systematically fixing either R or Lax.13 Therefore, the approach of maintaining a single carboxylate bridge (RCO2− in Scheme 1) and different Lax linkers is introduced to clarify the axial ligand contribution to the electronic structure of the Cr− © XXXX American Chemical Society

Cr core and the temperature-dependent paramagnetism. In this paper, we report an unambiguous electronic structure of [Cr2] complexes, based on electron localization at each Cr site without assuming a quadruple Cr−Cr bond, for a series of onedimensional [Cr2(OAc)4(μ2-Lax)]n chains with organic linkers (μ2-Lax) of 2-aminopyrazine (amp), 1,5-naphthyridine (nap), 4,4′-bipyridine (bpy), and pyrazine (pyz): [Cr2(OAc)4(amp)]n (1), [Cr2(OAc)4(nap)]n (2), {[Cr2(OAc)4(bpy)]·xMeCN}n (3), and [Cr2(OAc)4(pyz)]n (4)14(OAc− = acetate), respectively. The organic linkers are pyridine or pyrazine derivatives having different degrees of σ-donating ability and somewhat dissimilar π contributions, although they possess similar conjugated π-systems. Chain formation rendered these compounds with higher air stability than other discrete [Cr2] complexes.12 The Cr−Cr and Cr−Lax distances vary as a function of the σ/π electronic effects of Lax. The Cr−Cr length also strongly correlates with the energy separation (ES−T) Received: February 7, 2018

A

DOI: 10.1021/acs.inorgchem.8b00352 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Scheme 1. Structures and Frontier Orbital Energy Diagrams of [Cr2II,II(RCO2)4(Lax)2]a

a

(a) Model assuming a quadruple Cr−Cr bond and (b) current model with quasi-localized electron densities. 44.70 (45.20), H 4.31 (4.41), N 7.82 (8.01)%. Selected IR data (KBr, cm−1): 3060 (m), 2995 (m), 2933 (m), 1587 (s), 1445 (s), 1345 (m), 1217 (m), 1073 (m), 1045 (m), 1025 (m), 1005 (m), 817 (m), 678 (s), 626 (s). X-ray Crystallography. Suitable single crystals of all complexes were selected for single-crystal X-ray diffraction analysis. Data were collected at temperatures ranging from 103 to 293 K on a CCD diffractometer (Rigaku Saturn 724) with a multilayer mirror and monochromated Mo Kα radiation (λ = 0.71075 Å). Heavy Nujol and thin Kapton films were used for the measurements. Refinement of cell parameters and data reduction were performed with the CrystalClear software package.18 Crystal structures were solved by direct methods (SHELXT19 for 1 and 2 at 293 K and 3 at 103−199 K and SHELXD20 and SIR201121 for 1 and 2 at 103 K, respectively) and refined using the CrystalStructure crystallographic software package with full-matrix least-squares F2 values.22 All non-hydrogen atoms were refined anisotropically. Organic hydrogen atoms were placed in ideal, calculated positions with isotropic thermal parameters located on the respective carbon atoms that are not partially occupied. Crystallographic data for 1 (at 103 K; CCDC-1822493 and 293 K; CCDC1822494), 2 (at 103 K; CCDC-1822495 and 293 K; CCDC1822496), 3 (at 103 K; CCDC-1822497 and 169 K; CCDC1822498), and 4 (at 103 K; CCDC-1822499) are summarized in Table S1. Selected bond distances and angles are listed in Tables S2− S4. Physical Measurements. Infrared (IR) spectra were recorded as KBr pellets with a JASCO FT/IR-4200 spectrometer. Thermogravimetric analyses (TGA) were recorded on a Shimadzu DTG-60H apparatus under a nitrogen atmosphere at temperatures of 298−573 K at a heating rate of 5 K min−1. X-ray powder diffraction (XRPD) patterns were recorded using a Rigaku Ultima IV diffractometer with Cu Kα radiation (λ = 1.5418 Å) at room temperature to confirm the bulk sample purity of all compounds (Figure S3). Magnetic susceptibility measurements were conducted with a Quantum Design SQUID magnetometer (MPMS-XL) at temperatures of 1.8−300 K with an applied magnetic field of 0.1 T. Diamagnetic corrections were estimated from Pascal’s constants and subtracted from the experimental susceptibility data to determine the molar paramagnetic susceptibility of each compound.23 An Andeen−Hagerling 2700A capacitance bridge with an input voltage of 0.2−15 V (the suitable voltage was automatically selected by the instrument) was employed for measurement of dielectric constants at 68.1−20 000 Hz on a powder sample (∼5 mg) compressed into a 10 mm diameter, ∼0.1 mm thick pellet, which was placed between two stainless steel plates to create a parallel-plate capacitor. Au wires were attached using Au paste. The capacitor was placed in a cryostatic system equipped with coaxial cables for dielectric constant measurement. Computational Details. Density functional theory (DFT) calculations with a Gaussian basis set were performed by reducing the real complexes into two types of model structures consisting of one and two Cr2 units, i.e., [Lax−{Cr2}−Lax] and [Lax−{Cr2}−Lax− {Cr2}−Lax], as illustrated in Scheme 2. The models were identified by the abbreviations o and t for the one- and two-unit models, respectively, as in xo and xt, where x = 1−4. All structures were

between the diamagnetic (singlet) ground state and paramagnetic (triplet) first excited state. The strong σ- and πdependences can be rationalized only by considering two localized antiferromagnetically coupled CrII spin carriers (S = 2) rather than a quadruply bonded Cr−Cr system (Scheme 1).15 On the basis of unrestricted DFT calculations, the σ orbital is the highest occupied molecular orbital (HOMO) and dominates the [Cr2] bonding motif. The δ orbital makes a much smaller contribution to the Cr−Cr bond, because occupation numbers generated from natural orbital calculations indicate that only the σ and π orbitals of each Cr site overlap efficiently. This resulting Cr−Cr bond order is actually much less than that of a formal quadruple bond. The correlation between ES−T and pKb also suggests that the magnetism of [Cr2] is controlled predictably by changes in Lax.

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EXPERIMENTAL SECTION

Materials. All reagents were commercially available and were used as received without further purification. Acetonitrile solvent for compound synthesis was distilled under an anaerobic condition before use. Anhydrous chromous acetate was prepared following the method described in the literature.16,17 New compounds 1−3 were synthesized in a commercial glovebox under a nitrogen atmosphere. Compound 4 was synthesized following a method described elsewhere.14 Synthesis of [Cr2(OAc)4(amp)]n (1). Chromous acetate (0.136 g, 0.4 mmol) and 2-aminopyrazine (0.076 g, 0.8 mmol) were each dissolved in 0.1 L of dry acetonitrile. Each solution was divided into 50 2 mL portions after filtration. Narrow tubes (8 mm i.d.) were used to allow slow interdiffusion of the 2 mL chromous acetate and aminopyrazine solutions as lower and upper layers, respectively, which were separated by ca. 1 mL of MeCN. Red block crystals were isolated after a few days and collected by filtration. Yield 67%. Anal. Calcd (found) for C12H17Cr2N3O8 (1): C 33.11 (33.19), H 3.94 (3.94), N 9.65 (9.79)%. Selected IR data (KBr, cm−1): 3399 (m), 3341 (m), 3229 (m), 1652 (m), 1592 (s), 1535 (m), 1447 (s), 1214 (m), 1011 (m), 678 (m). Synthesis of [Cr2(OAc)4(nap)]n (2). Compound 2 was synthesized in a manner similar to that for 1, but with 1,5-naphthyridine (0.104 g, 0.8 mmol) instead of 2-aminopyrazine. Red block crystals were obtained after about 1 week with a yield of 42%. Anal. Calcd (found) for C16H18Cr2N2O8 (2): C 40.86 (40.85), H 3.86 (3.91), N 5.96 (6.13)%. Selected IR data (KBr, cm−1): 3074 (m), 1599 (s), 1505 (s), 1450 (s), 1415 (s), 1350 (m), 1228 (m), 1026 (m), 831 (m), 676 (s), 621 (m). Synthesis of {[Cr2(OAc)4(bpy)]·CH3CN}n (3). Compound 3 was synthesized in a manner similar to that for 1, but with 4,4′-bipyridine (0.094 g, 0.6 mmol) instead of 2-aminopyrazine. Red block crystals precipitated within a few days after complete interdiffusion of the two phases and gave a yield of ca. 40%. 0.6 molecules of CH3CN were lost after exposure to air (Figure S1), but it was impossible to remove all CH3CN lattice molecules even after heating at 85 °C for 3 days as shown in Figure S2. Anal. Calcd (found) for C20H23Cr2N3O8 (3): C B


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Inorganic Chemistry

constructed from experimental X-ray crystallographic results determined at several temperatures. We use the 103 K structure unless otherwise noted. The Cartesian coordinates of the models are summarized in Table S5. A spin-unrestricted (U) DFT method was applied to these models, because they are open-shell systems that involve localized spins on the Cr(II) ions. Conventional hybrid DFT functionals such as B3LYP reportedly overestimate antiferromagnetic interactions.24 Therefore, we used the BHandHLYP/6-31G* level of theory, which reproduces the experimental magnetic interactions of similar [Cr2] complexes.15,25 All calculations were performed using Gaussian 09.26

Scheme 2. Illustrations of (a) One-[Cr2]- and (b) Two[Cr2]-Unit Models for DFT Calculations

Figure 1. ORTEP diagrams of (a) 1, (b) 2, and (c) 3 at 103 K drawn with ellipsoids of 50% probability. C, N, O, and Cr are shown in gray, blue, red, and pink, respectively. The solvent of crystallization in 3 and the H atoms in all complexes are omitted for clarity. N2 in 1 experiences positional disorder with half occupancy at each position. Symmetry operation codes of #: 1 + x, 1 + y, 1 + z; those of * are listed in the Supporting Information. C


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Inorganic Chemistry

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RESULTS AND DISCUSSION

Synthetic Procedure. One-dimensional chain compounds 1−3 containing a [Cr2] unit were synthesized by liquid−liquid interdiffusion in acetonitrile with a layer of pure CH3CN separating the two phases in a narrow glass tube. Acetonitrile was the chosen solvent, because its modest coordinating ability allowed polymerization to proceed slowly. This inhibited lability at the dichromium(II,II) axial ligand sites and produced well-shaped crystalline samples in good yield. Solid samples of 1, 2, and 4 are stable in air, whereas 3 contains a solvent of crystallization (CH3CN; see the Experimental Section and Figure S1) and is air-stable for only 1 day. Compound 4, which was the only [Cr2] coordination polymer known previously, was prepared and characterized as described in the literature.14 Structure Description. The compounds in this work are alternating molecular strings comprising a [Cr2(OAc)4] unit and an organic Lax linker. The structures of 1−3 plus that of 4 at 103 K were measured at several temperatures in the range of 103−293 K. Crystallographic parameters are summarized in Table S1. Compounds 1 and 2 crystallize in the triclinic space group P1̅ with an inversion center lying at the midpoint of [Cr2] and Lax (Z = 1) at all temperatures (Figure 1a,b). Two structurally independent units are characterized in 3, which displays a non-centrosymmetric form with monoclinic space group Cc at 103−132 K and a 2-fold symmetric form with C2/c at 141−169 K (Z = 8) (Figure 1c). The temperature-induced structural transition results from twisting of the bpy fragment in one of the two chain units (Figure S4). The structural transition was confirmed by the temperature dependence of the dielectric properties (Figure S5). The chains in 1 and 2 align parallel to one another along the [111] direction. No obvious interchain interaction is found in 1 (Figure S6), but one methyl group of the acetate bridges in 2 lies in the vicinity of the nap fragment from a neighboring chain with a CH3···aromatic distance of about 3.7 Å (Figure S7). Two structurally independent chains of 3 propagate adjacently along the b-axis with an acetonitrile of crystallization located between the chains (Figure S8). The Cr−Cr distance is the most puzzling parameter in the work on [Cr2] complexes. In this work, it depends on Lax and equals 2.3452(8), 2.381(1), 2.323, and 2.2705(9) Å at 103 K in 1, 2, 3, and 4, respectively, where the value for 3 is the average of the two chains. A plot of the Cr−Cr distance at 103 K versus the pKb of Lax reveals a roughly linear relationship between the Cr−Cr bond distance and ligand basicity (i.e., σ-donation) (Figure 2). The large deviation in 2 may result from π backdonation by Lax, which cannot be ignored in pyridine/pyrazinetype ligands. The π* orbital of nap lies at a lower energy (−2.133 eV) in 2 compared with that of amp (−1.448 eV in 1), bpy (−2.018 eV in 3), and pyz (−1.829 eV in 4). The Cr−N axial bond distances of 2.357(2), 2.415(2), 2.325, and 2.310(2) Å at 103 K in 1, 2, 3, and 4, respectively, also are proportional to the Cr−Cr distance (Figure 3). The relationship, however, is the inverse of that found in previous studies of [Cr2(RCO2)4(Lax)2] complexes with σ-type axial ligands.3,4,13 However, the result should be interpreted cautiously, because multiple factors may contribute to the observation including (i) the antibonding contribution of π-orbitals between Cr and Lax and (ii) π backdonation from Cr to the π* orbital of π-conjugated Lax (Cr→ Lax) in competition with the σ-donation of Lax (Cr←Lax). Steric effects introduced by coordination of Lax also must be considered in discussing the impact of axial ligation. Compound

Figure 2. Plot of Cr−Cr distance at 103 K versus pKb for 1 (blue square), 2 (brown square), 3 (purple square), and 4 (red square). The solid line represents the least-squares linear fit for 1, 3, and 4 (data point for 2 is omitted; see text).

Figure 3. Plot of Cr−Cr distance versus Cr−N distance for 1 (blue square), 2 (brown square), 3 (purple square), and 4 (red square). The measurement temperatures for each compound are indicated, and the solid line represents the least-squares linear fit for all data.

2 stands out in this regard as evidenced by the Cr−Cr−N angles of 178.57(5), 174.76(5), 177.0, and 177.36(6)° in 1, 2, 3, and 4, respectively. Elongation of the Cr−Cr bond also leads to a weakening of the intraunit Cr−Cr interaction, which stabilizes the paramagnetic excited state (vide inf ra). Magnetic Properties. Direct current (dc) magnetic susceptibility measurements were performed on polycrystalline samples of 1−4 and [Cr2II,II(OAc)4] (Cr-OAc) under a 1 kOe external field at temperatures of 1.8−300 K (Figure 4). χMT values of 0.108, 0.138, 0.161, 0.160, and 0.103 cm3 K mol−1 at 300 K for 1, 2, 3, 4, and Cr-OAc, respectively, decrease almost monotonically upon cooling and reach values of 0.01−0.02 cm3 K mol−1 at 1.8 K. The non-negligible values at high temperatures suggest the presence of a finite spin gap and paramagnetic excited states, although the singlet state is the ground state. The magnetic properties of discrete [Cr2] complexes have been studied by Drago and O’Connor et al.12 The paramagnetic contribution was treated as a simple singlet/ triplet Boltzmann distribution based on the van Vleck model in eq 1. All experimental data were treated for the presence of a mononuclear CrII impurity by use of eq 2.12 χCr = 2

Ng 2μB 2 kT

2e−ES−T / kT + TIP 1 + 3e−ES−T / kT

χ = (1 − P)χCr + 2Pχp 2

D

(1) (2)


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Inorganic Chemistry

Table 1. Fitted Parameters for Magnetic Data of Cr-OAc and 1−4 with Fixed g = 2 compound

ES−T (cm−1)

TIP (× 10−4 cm3 mol−1)

P × 10−4

θ (K)

Cr-OAc 1 2 3 4

1713(34) 1603(40) 1583(7) 1644(22) 1693(5)

1.68(6) 2.42(5) 3.57(2) 2.95(4) 3.68(1)

7.78(3) 2.72(7) 2.98(9) 10.37(9) 7.17(4)

−16(2) −4.7(3) −30(2) −17.2(3) −37.5(3)

Figure 5. Plot of ES−T versus pKb for 1 (blue square), 2 (brown square), 3 (purple square), and 4 (red square), where the solid line represents the least-squares linear fit including only the data of 1, 3, and 4 (point 2 is neglected; see text).

(Figure 5). In other words, ES−T depends on both the Cr−Cr and Cr−Lax bond distances and is relatively small for complexes with a long Cr−Cr bond distance. To clarify this correlation, a theoretical investigation including DFT calculations on a small chain fragment (Lax−[Cr2]−Lax−[Cr2]−Lax) was conducted. Theoretical Calculations. The intraunit magnetic interaction between CrII ions was first examined by calculating effective exchange integral (J) values of the Heisenberg Hamiltonian (Ĥ Heisenberg) with the one-unit models (1o−4o, Scheme 2a). For these two-spin state models the Hamiltonian becomes ĤHeisenberg = −2J12 S1̂ ·S2̂

Figure 4. Temperature dependence of direct current (dc) magnetic susceptibilities of 1−4 and Cr-OAc under a 1 kOe transverse field. Solid black lines represent the best fits assuming that only the singlet ground and first paramagnetic excited states are occupied in the dichromium subunit. The resulting parameters are summarized in Table 1.

(3)

where Ŝx (x = 1, 2) is the spin operator for each CrII ion, and J12 is the effective exchange integral between them. The J12 values are calculated by use of the Yamaguchi equation27−29 J12 =

In eqs 1 and 2, ES−T is the energy separation between the singlet and triplet states, TIP is the temperature-independent paramagnetism, and χ is the overall susceptibility. χCr2 and χp represent the respective contributions of the target [Cr2] complex and the impurity. The fraction of the impurity is P, and its susceptibility is given by the Curie−Weiss value of χp = 2Ng2μB2/k(T − θ). The paramagnetic parameters for 1−4 and Cr-OAc are summarized in Table 1. It should be noted that zero-field splitting of the paramagnetic CrII impurity contributes to the decrease of χMT upon cooling. Thus, the fitting range was restricted to values above a certain temperature of ca. 30−50 K, which differed for each compound. Although the χT−T plots include contributions from TIP and a paramagnetic impurity, thermal population of the excited state as defined by ES−T is influenced by the axial linker. The ES−T versus pKb plot indicates a general decrease in ES−T with increasing Lax basicity

EAFM − E FM 2 ⟨S ̂ ⟩FM − ⟨S ̂ ⟩AFM 2

(4)

2

where Ex and ⟨S ̂ ⟩x (x = AFM, FM) represent the total energies 2 and ⟨S ̂ ⟩ values, respectively. AFM and FM signify antiferromagnetic and ferromagnetic states, respectively. Calculated J12 values are listed in Table S6 together with the 2 total energies and ⟨S ̂ ⟩ values. All calculated J12 values are negative and equal −500 to −700 cm−1, which indicates an antiferromagnetic interaction between adjacent CrII ions. As depicted in Figure 6, there is a strong correlation between the Cr−Cr distance and J12 values (R2 > 0.99). This suggests that the strength of the antiferromagnetic interaction is directly related to the Cr−Cr separation in the unit. The observed orbital overlap tendency between CrII ions was further examined by calculating natural orbitals (NOs), which were obtained by diagonalizing the first-order density matrices.30,31 From the occupation number of the ith NO (ni), the overlap E


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Inorganic Chemistry

experimental results in Figures 2 and 3, indicating that the Cr− Cr distance is quite sensitive to Lax and is affected greatly by σ and π contributions from Cr−Lax bonding. Features from a molecular orbital viewpoint were investigated as well. The calculated molecular orbitals of 3o are depicted in Figure 8. Frontier orbital energies of all models are

Figure 6. Plot of coupling constant J12 versus Cr−Cr distance for 1 (blue square), 2 (brown square), 3 (purple square), and 4 (red square). The solid black line is the result of a least-squares linear fit for all four compounds at various temperatures.

between spin-polarized α and β orbital pairs of the orbital (Ti) was estimated as Ti = ni − 1

(5)

The calculated NOs of all models are similar to one another. The NOs of 3o depicted in Figure S9 emphasize the Cr−Cr interaction, where the NOs of valence electrons clearly show σ-, π⊥-, π//-, and δ-type bonding features. The ni values of these NOs are summarized in Table S7. The occupation numbers of the σ- and π-bonding orbitals are ca. 1.50 and 1.18, but equal only 1.07 for the δ-type orbital. The result clearly indicates that the α and β electrons in the δ orbital are fully spin-polarized and are localized on each chromium site. Moreover, the occupation numbers of the σ- and π-type orbitals decrease with increasing Cr−Cr bond length, whereas values for the δ-type orbital scarcely change as shown in Figure 7b. The overlaps between the α and β electrons in σ- and π-type orbitals evaluated from eq 5 are less than 1.0. However, there are significant interactions involving adjacent CrII ions. As illustrated in Figure 7, the overlaps of σ- and π-type orbitals correlate with both the Cr−Cr distance and J12 value. Consequently, [Cr2(RCO2)4(Lax)2] complexes should not be described as covalent species containing a quadruple bond, but rather as dinuclear Cr units strongly coupled through σ- and πtype orbitals. These facts also provide direct evidence for the

Figure 8. Calculated frontier orbital energies of 3o and corresponding visualized orbitals.

summarized in Tables S8 and S9. The outputs indicate that the σ orbital, which lies at about −6.9 to −6.5 eV, is the HOMO, followed by the degenerate π orbitals, HOMO-1 and HOMO2. The δ orbital lies just below the π orbitals, except in 1o, wherein HOMO-1 and HOMO-2 consist of Lax orbitals. This result contrasts with the widely held understanding of a “covalent-type quadruple bond,” in which δ and δ* orbitals are the HOMO and LUMO, respectively, as illustrated in Scheme 1a.32 The phenomenon occurs only in cases involving axial ligand orbitals in addition to the spin-polarized Cr2 electronic structure (Scheme 1b). However, the σ and π orbitals become stable when the axial ligands are removed from the model, which suggests that the σ and π orbitals interact significantly

Figure 7. (a) Correlation between J12 values and occupation numbers, and (b) change in occupation numbers as a function of Cr−Cr distance for 1 (blue, square), 2 (brown, square), 3 (purple, square), and 4 (red, square). F


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Inorganic Chemistry with Lax and the CrII ion. Thus, the out-of-phase interactions between the [Cr2]-based bonding orbitals and the Lax lone pair are destabilizing and form the HOMO−HOMO-2 pair, whereas the δ orbital does not participate in this process. Therefore, it is important to consider the interaction between the [Cr2] unit and Lax in understanding the electronic structure of [Cr2]. Details of the α and β frontier orbitals with atomic coordinates obtained from crystallographic data at several temperatures are listed in Tables S8 and S9. The molecular orbitals of 3t are portrayed in Figure S10. We also examined interunit magnetic interactions between neighboring [Cr2] centers units in the chain using the two-unit models (1t−4t) shown in Scheme 2b. Because eq 4 for a Heisenberg model is not applicable to four-spin systems, we adopted an Ising Hamiltonian (Ĥ Ising), which considers only the Sz component 4

(6)

Jz12

where are the Ising model J values. Because it has been reported that the Ising model applies to fully spin-polarized systems, we confirmed its reliability with the one-unit model (Scheme 2a) before considering the two-unit model (Scheme 2b).33 For two spin sites, the Ising Hamiltonian becomes z z ĤIsing = −2J12z S1̂ ·S2̂

(9b)

⟨Ĥ udud⟩ = 16J12 + 8J23 + 8J13

(9c)

⟨Ĥ uuud⟩ = −8J23 + 8J13

(9d)

where ⟨Ĥ state⟩ is the total energy of each spin state. Results are summarized in Table S10. The Jz12 values of 1t−4t are consistent with the values for a single [Cr2] unit model, whereas Jz23 and Jz13 are negligible relative to Jz12. The results indicate that spins are localized on the dichromium core and that intraunit exchange is dominant in the chains. Magnetostructural Correlation and Electronic Structure of the [Cr2] unit. Previous work on carboxylate-bridged paddlewheel-type dichromium complexes ([Cr2(RCO2)4(Lax)2]) has emphasized the important role of carboxylate bridges and axial ligation on Cr−Cr bond character, but most proposed correlations and conclusions were imprecise and therefore ambiguous, because of the variety of structural variables.3,4,13 No obvious correlation was found in the present work between orbital energies and ES−T or J12 values (Figure S11). This means that orbital energies are not needed to rationalize the population of paramagnetic states, but that the Cr−Cr distance, which affects orbital overlap, should be considered instead. The experimental energy separations (ES−T) of 1−4 correlate closely with the theoretically estimated J12 values (Figure 9a) and Cr−Cr distances (Figure 9b). The theoretically estimated 2J12 values are slightly underestimated compared with the experimental ones (ES−T), because the BHandHLYP functional has a tendency to underestimate J12 due to increased overlap between the α and β orbital pair.34,35

z z ĤIsing = −2 ∑ Jijz Sî ·Sĵ i>j

⟨Ĥ uudd⟩ = −16J12 + 8J23 + 8J13

(7)

Jz12

values are obtained from energies of the AFM and FM states as follows

EAFM − E FM (8) 16 z The calculated J12 values are summarized in Table S10. The results indicate that the Ising model accurately reproduces the results of the Heisenberg Hamiltonian, which is in line with the applicability of the Ising model to fully spin-polarized electronic structures. For a four-site system, we assume the exchange interactions illustrated in Scheme 3, where Jz12 (= Jz34) and Jz23 are J12z =

Scheme 3. Spin−Spin Interactions in the Two-[Cr2]-Unit Model

the coupling constants between neighboring Cr ions in the [Cr2] subunit and between Cr ions bridged by Lax, respectively. Jz13 (= Jz24) is the coupling constant between next neighbor Cr ions. The coupling constant between terminal Cr ions, Jz14, is ignored. The total energies of the four spin states in which each Cr(II) ion has spin are calculated as follows (Cr1 Cr2 Cr3 Cr4) = (u u u u), (u u d d), (u d u d), (u u u d)

where u and d represent s = 4/2 and −4/2 Cr(II) ions, respectively. J values are obtained by solving the simultaneous equations ⟨Ĥ uuuu⟩ = −16J12 − 8J23 − 8J13

Figure 9. Plots of (a) J12 and (b) Cr−Cr distance versus ES−T for 1 (blue square), 2 (brown square), 3 (purple square), and 4 (red square). The solid lines represent the least-squares linear fits.

(9a) G


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Inorganic Chemistry Therefore, the experimental data relevant to Cr−Cr and Cr− Lax distances and ES−T values are consistent with the theoretical results. However, the σ-orbital contribution to HOMO is crucial in considering the effect of axial ligation on paramagnetic behavior for axially bonded [Cr2] complexes. The contribution of π orbitals, which is influenced by the πconjugation of Lax, also cannot be ignored. Indeed, the occupation numbers of the σ and π orbitals contribute to the Cr−Cr bond. The proportional relationship between the Cr− Cr distance and Cr−Lax (Figure 2) is best understood from the antibonding interaction between the lobes of Lax and [Cr2] in the HOMO (σ), HOMO-1 (π), and HOMO-2 (π) orbitals. The specific behavior of 2, which is evident in Figures 2 and 5, deserves comment. The LUMO energy of 2, which comprises the π orbital of the axial nap ligand, is significantly lower than that of the other complexes as summarized in Tables S8 and S9. Therefore, the π effect should be considered in addition to that of pKb, which leads to enhanced π backdonation, a lower LUMO energy, and an elongated Cr−Cr bond. Thus, π back-donation makes an important contribution to the Cr−Cr distance and the strength of the magnetic coupling (J12).

plots of J12 vs HOMO/LUMO, crystallographic data of 1−4, selected bond lengths and angles for 1−3, Cartesian coordinates of 1o−4o and 1t−4t, calculated total energies and coupling constants of 1o−4o, calclated occupation numbers of frontiers orbitals of 1−4, orbital energies in α/β spin of AFM system for 1−4, calclated total energies and coupling constants of 1t−4t (PDF) Accession Codes

CCDC 1822493−1822499 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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Corresponding Author

*Tel: +81-22-215-2030. Fax: +81-22-215-2031. E-mail: [email protected]. ORCID

Hitoshi Miyasaka: 0000-0001-9897-0782

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Notes

CONCLUSIONS Paddlewheel-type dichromium(II,II) complexes, which are a stable form of CrII-containing complexes, have been characterized and discussed in terms of the Cr−Cr bond for decades. However, comprehensive study of the connection between their temperature dependent magnetic behavior and the Cr−Cr distance, ligand electron-donating ability, and other structural parameters has been lacking. Despite difficulties in handling CrII complexes and synthesizing their polymeric compounds,36 and in mind of only a few CrII-based metal−organic frameworks being reported recently,37−40 we have successfully prepared four one-dimensional chain compounds comprising the [CrII2] subunit and different axial organic linkers (Lax). A paradox arises upon interpreting the influence of the σ and π character of Lax on [Cr2] in terms of a well-known model that assumes a quadruple bond between Cr sites. Therefore, unrestricted DFT calculations were conducted under the condition of localized electron density at each metal center, where a strong antiferromagnetic interaction imposed by broken symmetry prevails. The results reveal the unprecedented discovery that the metal-based σ orbitals and ligandbased π orbitals form the HOMO and LUMO, respectively. The δ-type orbitals make almost no contribution to the metal− metal interaction, and the properties of the [Cr2] unit are greatly influenced by the σ and π character of axially coordinated Lax. The singlet/triplet energy gap (ES−T) is an important property of [Cr2] units, because thermally activated paramagnetism, which may be employed in magnetic or electronic materials, can be controlled by simple adjustment of Lax.

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AUTHOR INFORMATION

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a Grant-in-Aid for Scientific Research (Grant No. 15K13652 and 26810029) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, a Grand-in-Aid for Scientific Research on Innovative Areas (“π-System Figuration” Area 2601, no. 15H00983) from JSPS, the E-IMR project, and IMR collaborative research program.

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REFERENCES

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00352. TG data for 3, PXRD for 1−4, packing structures of 1−3, temperature dependence of dielectric constants for 3, natural orbitals of 3o, frontier molecular orbitals of 3t, H


Article

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One-Dimensional Chains of Paddlewheel-Type Dichromium(II,II

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