Novel polynuclear architectures incorporating Co 2+ and K + ions bound by dimethylmalonate anions: Synthesis, structure, and magnetic properties

Inorganica Chimica Acta 396 (2013) 108–118 Contents lists available at SciVerse ScienceDirect Inorganica Chimica Acta journal homepage: www.elsevier.com/locate/ica Novel polynuclear architectures incorporating Co2+ and K+ ions bound by dimethylmalonate anions: Synthesis, structure, and magnetic properties Ekaterina N. Zorina a,⇑, Natalya V. Zauzolkova a, Aleksei A. Sidorov a, Grigory G. Aleksandrov a, Anatoly S. Lermontov a, Mikhail A. Kiskin a, Artem S. Bogomyakov b, Vladimir S. Mironov c, Vladimir M. Novotortsev a, Igor L. Eremenko a a b c N.S. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninsky Prosp. 31, 119991 Moscow, Russian Federation International Tomography Center, Siberian Branch of the Russian Academy of Sciences, Institutskaya Str. 3a, 630090 Novosibirsk, Russian Federation A.V. Schubnikov Institute of Crystallography, Russian Academy of Sciences, Leninsky Prosp. 59, 119333 Moscow, Russian Federation a r t i c l e i n f o Article history: Received 31 May 2012 Received in revised form 28 September 2012 Accepted 5 October 2012 Available online 5 November 2012 Keywords: Polymeric cobalt(II) complex Dimethylmalonate ligands X-ray diffraction analysis Magnetic properties a b s t r a c t The reaction of potassium dimethylmalonate (K2Me2Mal) and cobalt(II) pivalate [Co(Piv)2]n under various conditions resulted in {[K2Co(H2O-jO)(l-H2O)(l6-Me2Mal)(l5-Me2Mal)]2H2O}n (1) and {[K6Co36(H2O-jO)22(l-H2O)6(l3-OH)20(l4-HMe2Mal-j2O,O0 )2(l6-Me2Mal-j2O,O0 )2(l5-Me2Mal-j2O,O0 )8 (l4-Me2Mal-j2O,O0 )12(l4-Me2Mal)6]58H2O}n (2) (where Me2Mal2 is the dimethylmalonate dianion). Coordination polymers 1 and 2 were characterized by X-ray diffraction and magnetochemical studies. Analysis of the magnetic behavior indicates that 1 is characterized by an extremely high anisotropy of magnetic susceptibility and very weak spin coupling between CoII centers through malonate groups; compound 2 contains a highly symmetric, spherical-like Co36 metal core that exhibits low magnetic anisotropy and antiferromagnetic interactions between CoII centers. Theoretical aspects of anisotropic magnetic properties of orbitally-degenerate CoII ions in polynuclear cobalt(II) complexes are discussed. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction 2. Experimental It is well known that, when polynuclear carboxylate complexes are constructed from malonate anions and transition metal ions, crystallization from water or water–alcohol solutions mainly gives coordination polymers with chain, layer, or frame molecular structures build of the bis-chelating dianion [MII(Mal)2]2 (MII = Co, Ni, Cu, Zn) (see, for example, [1–7]). No polymeric metal-containing malonate systems incorporating large 3d metal containing fragment as structural units are known to date. A promising synthetic strategy to prepare such coordination compounds is based on the ligand-deficient approach that enforces malonate anions to carry out the bridging functions. In this work, we report the preparation of two novel polymeric malonate cobalt(II) complexes with potassium ions, one of which contains an unusual highly symmetric, spherical-like Co36 hexanegative anion that functions as a structure-forming molecular building block. These CoII complexes are structurally and magnetically characterized. We also provide some theoretical analysis of a complicated magnetic behavior of these complexes containing orbitally-degenerate six-coordinate CoII ions with an unquenched orbital momentum. 2.1. Synthesis ⇑ Corresponding author. Tel.: +7 495 955 4817; fax: +7 495 952 1279. E-mail addresses: kamphor@mail.ru (E.N. Zorina), bus@tomo.nsc.ru (A.S. Bogomyakov), mirsa@list.ru (V.S. Mironov). 0020-1693/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ica.2012.10.016 Reagents and solvents were commercial available (Aldrich) and used without further purification. Distilled water was used for the synthesis of new compounds. Polymeric cobalt pivalate [Co(Piv)2]n was synthesized according to a known procedure [8]. The K2Me2Mal salt was prepared by the neutralization of KOH with H2Me2Mal. 2.1.1. {[K2Co(H2O-jO)(l-H2O)(l6-Me2Mal)(l5-Me2Mal)]2H2O}n (1) [Co(Piv)2]n (0.49 g, 1.89 mmol) was added to a solution of K2Me2Mal (obtained from potassium hydroxide (0.42 g, 7.58 mmol) and dimethylmalonic acid (0.5 g, 3.78 mmol)) in EtOH (20 ml). The reaction mixture was stirred with weak heating (t = 50 °C) for 10 min to produce a thick violet precipitate. The precipitate was filtered off, washed with EtOH, and dissolved in H2O (30 ml). The resulting crimson solution was kept for two weeks under air at room temperature. The resulting violet crystals are suitable for X-ray diffraction analysis. The yield of 1 is 0.64 g (71%). Anal. Calc. for C10H20CoK2O12: C, 25.59; H, 4.29. Found: C, 25.71; H, 4.38%. IR spectra, m/cm1: 3495 s, 2983 m, 2941 m, 2878 m, 2103 w, 1637 s, 1607 s, 1549 s, 1478 s, 1464 m, 1441 s, 1384 m, 1357 m, 1343 s, 1207 m, 1184 m, 109 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 1173 m, 1017 w, 966 w, 892 m, 844 m, 798 w, 782 w, 702 m, 580 m, 533 m, 476 m. 2.1.2. {[K6Co36(H2O-jO)22(l-H2O)6(l3-OH)20(l4-HMe2Malj2O,O0 )2(l6-Me2Mal-j2O,O0 )2(l5-Me2Mal-j2O,O0 )8(l4-Me2Malj2O,O0 )12(l4-Me2Mal)6]58H2O}n (2) [Co(Piv)2]n (0.2 g, 0.77 mmol) was added to a solution of K2Me2Mal (obtained from potassium hydroxide (0.17 g, 3.04 mmol) and dimethylmalonic acid (0.5 g, 1.52 mmol)) in EtOH (20 ml). The reaction mixture was stirred with weak heating (t = 50 °C) for 10 min to produce a thick violet precipitate. The resulting suspension was refluxed for 90 min in a water bath. The precipitate was filtered off, washed with EtOH, and dissolved in H2O (30 ml). The resulting crimson solution was kept for 4 weeks under air at room temperature. The resulting violet crystals are suitable for X-ray diffraction analysis. The yield of 2 is 0.034 g (19%). Anal. Calc. for C150H374Co36K6O226: C, 22.10; H, 4.62. Found: C, 21.9; H, 4.5%. IR spectra, m/cm1: 3535 s, 3444 m.w, 2982 m, 2203 w, 1599 s, 1541 s, 1464 s, 1433 s, 1351 s, 1190 m, 935 w, 891 m, 834 m, 790 m, 729 m, 652 m, 610 m, 557 m, 482 w. 2.2. Methods Elemental analysis of the resulting compounds was carried out with a ‘‘Carlo Erba’’ automatic C,H,N,S-analyzer. IR spectra of the complexes were recorded using a ‘‘Perkin Elmer Spectrum 65’’ instrument in KBr pellets in the frequency range of 4000– 400 cm1. The magnetochemical measurements were performed on a Quantum Design MPMSXL SQUID magnetometer in the temperature range of 5–300 K in a magnetic field of up to 5 kOe. The calculated molar magnetic susceptibility vM was corrected for the diamagnetic contribution. The effective magnetic moment was calculated by the formula leff = (8vT)1/2. 2.3. X-ray analysis X-ray diffraction studies were carried out on a Bruker SMART APEX II diffractometer equipped with a CCD detector (graphite monochromator, k = 0.71073 Å). The experimental set of reflections for complexes 1 and 2 was obtained using the standard method [9]. Semi-empirical absorption corrections for both complexes were applied [10]. The structures of the complexes of interest were solved by direct methods using and refined by the least squares method in anisotropic full-matrix approximation (the positions of hydrogen atoms were fixed with UH = 0.082). Hydrogen atoms were generated geometrically and refined in the ‘‘riding’’ model. All calculations were carried out with the use of the SHELX97 program package [11]. The crystallographic data and the refinement procedure details are given in Table 1. The structure of complex 1 was determined without applying any additional restrictions, except above mentioned restrictions on hydrogens. Some of dimethylmalonate groups in structure 2 are particular unordered, and as result the lengths of similar bond C–O were essentially different. Therefore some of distances in the C–O groups of some dimethylmalonate groups are restrained to a target value d (‘free variable’). Additionally also position multiplicity of some atom O of some molecules water were not equal 1.0. And its sites occupation factors reastrained to be constant (usually 5). 3. Results and discussion 3.1. Synthesis and structure of 1 We have found that the reaction of polymeric cobalt(II) pivalate [Co(Piv)2]n with potassium dimethylmalonate K2Me2Mal (where Table 1 Crystal data and structure refinement for 1 and 2. Compound 1 2 Formula Formula weight (g mol1) Crystal system Space group a (Å) b (Å) c (Å) a (°) b (°) c (°) V (Å3) Z Absorption coefficient (mm1) Maximum and minimum transmission Dcalc (mg/m3) Crystal size (mm) h (°) Reflection measured Reflection unique Rint Goodness-of-fit (GOF) on F2 Final R indices [I > 2r(I)] C10H20CoK2O12 469.39 triclinic  P1 8.486(3) 10.694(4) 11.541(4) 74.122(5) 68.625(5) 68.974(5) 898.0(6) 2 1.479 0.866/0.930 C150H374Co36K6O226 8150.67 monoclinic P21/n 22.053(1) 28.8254(14) 24.7174(12) 90.00 90.0248(8) 90.00 15712.5(13) 2 2.04 0.553/0.822 1.784 0.10  0.05  0.05 2.58–30.34 9332 3715 0.0252 1.053 R1 = 0.0302, wR2 = 0.0735 R1 = 0.0361, wR2 = 0.0760 1.733 0.33  0.14  0.10 2.3–25.5 144142 26388 0.0634 0.998 R1 = 0.0683, wR2 = 0.1887 R1 = 0.0884, wR2 = 0.2121 R indices (all data) Me2Mal is the dimethylmalonate dianion) in EtOH (t = 50 °C) gives a 2D-polymer {[K2Co(H2O-jO)(l-H2O)(l6-Me2Mal)(l5-Me2Mal)]2H2O}n (1), which was isolated as violet crystals. According to X-ray diffraction data (Table 1), polymer 1 does not incorporate the well-known six-membered chelate rings with metal centers (Fig. S1) typical of structural units in this kind of systems, which is unusual for polymeric coordination malonates with transition metal atoms in the absence of additional N-donor ligands [12,13]. The octahedral environment of cobalt(II) ions in structure 1 (Fig. 1) formally consists of O atoms of four carboxylate groups, two of which belong to different dianions from two fourmembered chelate fragments CoO2C, whereas the two remaining O atoms belong to two other dianions (Table 2). 3.2. Synthesis and structure of 2 It has been found that prolonged refluxing of a suspension of compound 1 in EtOH (90 min) gives a new coordination polymer {[K6Co36(H2O-jO)22(l-H2O)6(l3-OH)20(l4-HMe2Mal-j2O,O0 )2(l6-Me2Mal-j2O,O0 )2(l5-Me2Mal-j2O,O0 )8(l4-Me2Mal-j2O,O0 )12(l4-Me2Mal)6] 58H2O}n (2), in which the {[Co36(H2O-jO)12(l3-OH)20(l4-HMe2Malj2O,O0 )2(l4-Me2Mal-j2O,O0 )22(l4-DMM)6]}n6 36-nuclear hexanegative anion interlinked by potassium cations are the main structural units (Fig. 2). The {Co36}6 hexanegative anion is located in the crystallographic center of symmetry. It should be noted that one of the three independent potassium cations in the unit cell is disordered and occupies two positions with 1/2 population. A fraction of the malonate ligands are also disordered; the O atoms in some of them occupy two equivalent positions. All the metal atoms in {Co36}6, which has a Ci symmetry, have a distorted octahedral coordination comprising O atoms of malonate groups, OH-groups, or water molecules. Some O atoms of the malonate groups serve as bridges between cobalt(II) ions. Formally, {Co36}6 incorporates only 12 water molecules, 16 water molecules are coordinated to the K ions, while the remaining 58 ones are crystallization water molecules that are bound via hydrogen bonds. 110 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 Fig. 1. Structure of a fragment of the polymeric chain of cobalt(II) atoms in 1 and its bonding with potassium atoms (hydrogen atoms are omitted). Table 2 Selected bond lengths (Å) and angles (°) for 1 and 2. Bond 1 2 Co. . .Co 5.586(2) Co–O(Me2Mal) Co–O(l-H2O) Co–O(H2O-jO) Co–O(l3-O) K–O(Me2Mal) K–O(l-H2O) K–O(H2O-jO) 2.0039(15)–2.2767(16) – – – 2.6601(16)–2.7862(18) 2.896(2)–2.8998(19) 2.877(2) Co(i). . .Co(i) in Aa 3.11(2)–3.17(2)Co(i). . .Co(i) in Ba 3.56(2)–3.59(2) Co(e). . .Co(i) in B 2.99(2)–3.05(2) 2.018(6)–2.186(5) 2.069(6)–2.082(7) 2.056(6)–2.066(7) 2.019(5)–2.075(6) 2.652(8)–2.914(10) 2.811(8)–3.088(12) 2.692(11)–2.935(18) 1 O1–Co1–O2 O7–Co1–O8 O3–Co1–O5 2 O(Me2Mal-j2O,O0 )–Co(i)–O(Me2Malj2O,O0 ) O(OHA)–Co(i)–O0 (OHB) O(Me2Mal)–Co(e)–O(Me2Mal) O(OHB)–Co(e)–O(Me2Mal) Co(i)–O(OHA)–Co(i) Co(i)–O(OHB)–Co(i) Co(i)–O(OHA)–Co(e) a 60.26(5) 60.27(6) 99.28(6) 84.2(2)–86.3(2) 105.7(2)–108.1(2) 86.9(2)–93.4(2) 81.8(2)–83.9(2) 94.2(2)–96.2(2) 99.2(2)–101.6(2) 121.5(2)–123.7(3) 94.0(2)–96.3(2) See the text and Fig. 4. The coordination number of independent K cations in structure 2 is 6; they are bound to O atoms of malonate anions and water molecules (Fig. 2). Cations K1 and K3 are bound to the O atoms of only one 36-nuclear complex hexaanion, whereas the K2 cation is coordinated to O atoms of dimethylmalonate dianions belonging to two different {Co36} anions, which results in zig-zag polymeric chains. The cobalt atoms in {Co36}6 form a complex architecture that formally consists of an external cuboctahedron (12 atoms (Co(e)) marked pink in Fig. 3) and an internal truncated cube (24 atoms (Co(i)) marked blue in Fig. 3). The distance from the geometric center to each Co(e) atoms is 7.7 Å, whereas the distance from the geometric center to each Co(i) atom is 5.7 Å. The structure involves an uncommon (O,O0 ,O00 ,O000 )-l4 bonding type of dimethylmalonate dianions (six dianions), where all the four O atoms of each dianion are bound to separate CoII ions (Fig. S2). The internal CoII ions are bound to the external ones via chelate bridging O atoms of the acid dianions and via hydroxo bridges. All the 24 cobalt atoms of the internal frame have the same ligand environment. The environment of the external atoms is formed by acid anions and by bridging and monodentate-bound water molecules. Cobalt atoms in compound 2 are grouped into triangular fragments of two types (A and B, blue and pink triangles in Fig. 3b) forming the frame of the Co36 spherical-like metal core (Fig. 3b). Eight nearly isosceles triangles of type A (blue) consist of Co(i) atoms only (with the Co(i). . .Co(i) distances of 3.11(2)–3.17(2) Å and \Co(i)–Co(i)–Co(i) angles of 59.1–60.8°). Twelve triangles of type B (pink) consist of one Co(e) atom and two Co(i) atoms (with Co(i). . .Co(i) = 3.56(2)–3.59(2) Å, Co(e). . .Co(i) = 2.99(2)–3.05(2) Å, \Co(i)–Co(i)–Co(e) = 52.9–54.2°, and \Co(i)–Co(e)–Co(i) = 71.7– 73.1°) (Fig. 3b). In each triangle A, all three cobalt atoms are the vertices of conjugate triangles B (the dihedral angle between the two planes of the neighboring triangles A and B ranges from 107° to 110°, Fig. 3b). Triangles B have only two common vertices with triangles A, the third cobalt atom is a vertex of the cuboctahedron (Fig. 3). Each triangle A is capped by a l3-OH bridging group, whose oxygen atom (O3M, O4M, O5M, O7M, or symmetry related atoms) locates at 0.92–0.95 Å out of the Co3 plane inside the cavity of a spherical Co36 frame. Distance analysis indicates that H atoms do not form H-bonds with oxygen atoms located inside the cavity of the molecule. The hydrogen atoms of the OH-groups in the triangles B form bifurcated H-bonds with two oxygen atoms of the l4-bridging dicarboxylic anions (with the O(OHB). . .O(Me2Mal) distance of 3.20–3.32 Å, Fig. S3, Table S1); the oxygen atom of the hydroxyl group (O1M, O2M, O6M, O8M, O9M, O10M, or symmetry related atoms) locates at 0.79–0.81 Å out of the Co3 plane. 3.3. Magnetic properties of 1 and 2 According to magnetic measurements, the vMT product of compound 1 decreases with the lowering temperature to reach a minimum of 2.24 cm3 mol1 K at 17 K (vM being the molar magnetic susceptibility per formula unit) (Fig. S4); below this temperature vMT shows some increase (see Fig. 4a). In the temperature range of 20–300 K, the plot of inverse susceptibility versus temperature obeys the Curie–Weiss law with C and h parameters of 2.921 ± 0.006 cm3 mol1 K and 8.7 ± 0.3 K (R2 = 0.99984) (Fig. S4), respectively. The value C = 2.921 cm3 mol1 K is considerably larger than the expected spin-only value (C = 1.875 cm3 mol1 K for S = 3/2 and g = 2) due to orbital contribution to the magnetic susceptibility for octahedrally coordinated CoII ions [14,15]. At room temperature, the effective magnetic moment of 1 is 4.83 lB per cobalt atom, which is consistent with the experimental values observed for numerous cobalt complexes with high-spin (S = 3/2) octahedral CoII centers (4.4–5.2 lB) [16,17]. The vMT product of compound 2 steadily decreases upon cooling from 300 to 5 K; however, in contrast to compound 1, at low E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 111 Fig. 2. Structure of a fragment of 2 (hydrogen atoms are omitted). temperature the vMT curve of 2 shows no kink-like feature (Fig. 5a). In the temperature range of 16–300 K, the vM1 versus T plot follows the Curie–Weiss law with C and h parameters of 113.1 ± 0.2 cm3 K/mol (3.14 cm3 mol1 K per CoII ion) and – 13.5 ± 0.3 K (R2 = 0.99993), respectively (Fig. S5). Again, C = 3.14 cm3 mol1 K is larger than the spin-only value for three unpaired electrons (C = 1.875 cm3 mol1 K). For compound 2, the effective magnetic moment at room temperature is 29.41 lB per {Co36} molecule or 4.90 lB per cobalt atom (Fig. S5). In the both compounds h is negative. Although a negative Weiss temperature h is often regarded as being indicative of antiferromagnetic spin coupling, the situation with six-coordinate (quasioctahedral) CoII centers in 1 and 2 is more complicated due to the presence of an unquenched (first-order) orbital momentum L = 1 associated with the orbital degeneracy of the ground state. The total spin S = 3/2 of CoII is coupled with the orbital angular momentum L = 1 to form several energy levels. Therefore, the total spin S = 3/2 of CoII is not a good quantum number; this fact leads to a peculiar magnetic behavior of CoII ions, which differs considerably from that of ordinary (spin-only) S = 3/2 ions (such as Cr3+ or Mn4+). In the regular octahedral Oh symmetry, the ground 4 T1g(3d7) orbital level splits into the ground Kramers doublet U7, two excited quartet levels U8 and U08 , and the upper Kramers doublet U6 (Fig. 6a). In distorted octahedral CoII centers, the 4T1g(3d7) manifold splits into six Kramers doublets U(n) (n = 0–5) (Fig. 6b). The ground Kramers doublet U(0) is characterized by a highly anisotropic g-tensor. It is important to note that the energy separation between the U(0) ground state and the excited states U(n) is normally much larger (>100 cm1) than the exchange parameters J of the spin coupling between CoII centers (in most cases, J  10 cm1 or less) [15– 27,29–36]. Therefore, only the ground Kramers doublet U(0) is involved in the exchange spin coupling between CoII magnetic centers. This implies that at low temperature CoII ion behaves as an anisotropic magnetic center with a fiction spin s = 1/2, whose ±1/2 projections correspond to the two components of the ground Kramers doublet U(0). Exchange interactions of the U(0) Kramers doublet with neighboring magnetic centers are also anisotropic: the experimental data [20–27] and theory [28] indicate that exchange interactions between octahedral CoII centers are described by a highly anisotropic spin Hamiltonian siJsj for a fiction spin s = 1/2 (J being a 3  3 matrix composed of anisotropic exchange parameters Jab, a,b = x, y, z), not by the conventional S = 3/2 isotropic spin Hamiltonian JSiSj. This fact complicates considerably theoretical analysis of magnetic behavior of cobalt(II) compounds, especially for polynuclear CoII complexes. Now we turn to the modeling of the magnetic behavior of 1 and 2. For a consistent analysis of magnetic properties of CoII compounds, it is crucially important to provide a proper description of single-center electronic and magnetic characteristics of CoII ions in a distorted octahedral environment. In fact, the wave function of the U(0) ground state and energy positions of excited U(n) states are very sensitive to distortions in the local geometry of the CoII center. In many works on the molecular magnetism of CoII compounds, this analysis is based on a conventional approach, in which the low-symmetry splitting of the ground 4T1 energy level of CoII is described by the bL2z  2=3c þ EbL2x  L2y c term, where Lx,y,z are the projection operators of the effective orbital momentum L = 1 (associated with the lowest 4T1 orbital triplet) and D and E are the axial and rhombic energy splitting parameters, respectively. Here D and E are adjustable parameters, which are obtained from the fitting to the experimental vMT curve. In fact, the rhombic term EbL2x  L2y c is often omitted due to overparameterization of the fitting procedure. [16,17,29–36]; as will be shown below (Fig. 7 and Table 3), this approximation is generally invalid for 1 and 2. Although this approach provides reasonable results for selected dinuclear cobalt(II) complexes [29–36], its application for strongly distorted low-symmetry six-coordinate CoII centers may generally 112 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 Fig. 3. Structure of the metal frame in 2: (a) – cuboctahedron formed by external Co(e) atoms (pink) and a rhombic cuboctahedron formed by the internal Co(i) atoms (blue), (b) – the core formed by triangles A and B (see text). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) be unreliable. In fact, inspection of the local structure of CoII centers in 1 and 2 reveals an irregular character of distortions in the CoO6 octahedra, which show no distinct tetragonal elongation/compression axes and exhibit a considerable scatter in the O–Co–O bonds angles. This is especially true for the CoII centers in 1, in which the O–Co–O bonds angles deviate strongly from 90° (Fig. 7). In this situation, we use a more realistic single-center model Hamiltonian for the CoII centers H¼ X i>j X e2 þ f3d li si þ V LF þ lB ðkL þ 2SÞH; jr i  rj j i ð1Þ where the first term represents Coulomb repulsion between 3d electron of CoII (where i and j runs over 3d electrons), the second term is the spin–orbit coupling, VLF is the ligand-field Hamiltonian, and the last term represents the Zeeman interaction with the external magnetic field H. In these calculations we use B = 750 and C = 3500 cm1 Racah parameters for the Coulomb term in Eq. (1), the spin–orbit coupling constant f3d = 480 cm1, and the k = 0.85 orbital reduction factor in the Zeeman term. The ligand-field Hamiltonian VLF is calculated in terms of the angular overlap model Fig. 4. (a) Comparison of the experimental and calculated vMT product of compound 1, (b) calculated anisotropy of magnetic susceptibility of 1 (at 5 kOe). Black circles refer to the measured magnetic susceptibility; open circles correspond to the experimental data scaled by a factor of 1.025 to take into account uncontrolled solvent losses and/or a diamagnetic contaminant (see text for detail). Magnetic susceptibility of 1 is highly anisotropic, especially at low temperature. This results in a rise of the experimental vMT curve below 17 K due to a magnetic field-driven orientation of microcrystals along the magnetic easy axis in powdered samples of 1. (AOM) [37,38] with the AOM parameters er = 4000 cm1 for the O ligands (at R0(Co–O) = 2.10 Å) and with the fixed ratio of er/ep = 4; the radial dependence of the AOM parameters is approximated by er;p ðRÞ ¼ er;p ðR0 ÞðR0 =RÞn with n = 4 and R0 = 2.10 Å. A similar model was used to analyze magnetic properties of FeII-based single-molecule magnets [39]; simplified AOM calculations were performed for CoII complexes to interpret their optical spectra [33]. Energy levels of the U(n) Kramers doublets and the anisotropic g-tensor of the U(0) ground state are obtained by a numerical diagonalization of the model Hamiltonian (1) in the full set of 3d7 wave functions involving 120 |LMLSMSi microstates. The results of calculations for the only distinct CoII center in the cobalt chains in 1 are shown in Fig. 7; results for selected CoII centers in the Co36 cluster in 2 (Figs. 2, 3, S2, and S3) are presented in Table 3. These results reveal an important difference between compounds 1 and 2 in the electronic structure and magnetic characteristics of CoII centers. In compound 1, the low-symmetry splitting of E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 113 Fig. 6. Spin–orbit splitting of the ground 4T1(3d7) orbital triplet state of CoII ions in (a) regular octahedral coordination (Oh symmetry) and in (b) distorted octahedral coordination. Fig. 5. (a) Comparison of the experimental and calculated vMT product of the Co36 molecular cluster in 2, (b) calculated anisotropy of magnetic susceptibility of 2 (at 5 kOe). The drop of the experimental vMT curve below 20 K is due to Co–Co antiferromagnetic exchange interactions with the exchange parameter J  3 cm1. the ground 4T1 orbital triplet is considerably larger (1800 cm1) than that in all CoII centers in the Co36 core in 2 (360–800 cm1, Table 3) due to a larger distortion of the CoO6 octahedron, Fig. 7. These energies should be compared with the total spin–orbit splitting energy of the ground 4T1g orbital triplet in a regular CoO6 octahedron, which is about 900 cm1 (at f3d = 480 cm1; see Fig. 6a): in 2 the orbital splitting energy is less than the spin–orbit splitting energy, while in 1 their ratio is opposite. Therefore, the orbital momentum of CoII centers remains unquenched in 2, but it is partially quenched in 1. The latter fact can be clearly seen from the energy level structure of the spin–orbit states U(n) in 1: six spin–orbit levels are grouped into three close pairs (U(0) + U(1), U(2) + U(3), and U(4) + U(5)), which can be regarded as a result of a second-order zero-field splitting (ZFS) of the three split components 4T1(1), 4 T1(2), and 4T1(3) of the 4T1 orbital triplet, lying at 0, 788, and 1797 cm1, respectively. (Fig. 7). As a result, the energy of the first excited Kramers doublet U(1) in 1 is lower (120 cm1) than in 2 (140–235 cm1), Table 3; this can manifest in the overall behavior of the vMT curve due to the difference in the thermal population of the first excited U(1) level. Calculated g-tensors of the ground Kramers doublet U(1) also show considerable difference. In compound 1, the g-tensor of the ground state has an extremely high Ising-type anisotropy with the principal components g1 = 0.83, g2 = 0.93, and g3 = 8.03. By contrast, all of the CoII centers in 2 have a rhombic anisotropic g-tensor with essentially different g-components, typically, g1  2.5, g2  4 and g3  6 (Table 3). These values are within the range expected for rhombically distorted six-coordinate CoII centers [39,40]; in fact, they are close to the experimental data on CoII complexes obtained from EPR measurements [26]). These features have a strong impact on the anisotropy of magnetic susceptibility of 1 and 2 (see below). Based on these results, we calculate magnetic susceptibility of 1 and 2 with taking into account the one-center contributions only; the role of exchange interactions is discussed below. The components Ma (a = x, y, z) of the magnetic moment M of the sample in an external magnetic field H are obtained from the conventional equation Ma ¼ NkB T @ ln ZðHÞ ; @Ha ð2Þ where kB and N are the Boltzmann’s constant and Avogadro’s number, respectively; Z(H) is the partition function ZðHÞ ¼ XX n ðnÞ expðEi ðHÞ=kB TÞ; ð3Þ i with Ei ðHÞ being the energy of the i-th electronic state of the CoII center number n involved in the cobalt cluster in the magnetic field H (for instance, in 2 n runs from 1 to 36). Then the diagonal components vaa of the tensor of magnetic susceptibility {vab } is written as vaa ¼ Ma =Ha ; magnetic susceptibility of a powder sample is given by v ¼ vxx þ vyy þ vzz =3. Calculated magnetic susceptibility for 1 and 2 (at the experimental magnetic field of H = 5 kOe) is shown in Figs. 4 and 5, respectively. In the both compounds, at T > 20 K the calculated vMT curve agrees reasonably with the experimental data. However, in 1 the calculated vMT value is somewhat larger than the experimental one in the whole temperature range (20–300 K). The reasons for the discrepancy in 1 probably include the sampling/solvent loss aspects, perhaps with some diamagnetic contaminant following ðnÞ 114 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 Fig. 7. Calculated energy positions (in cm1) of the split orbital components (4T1(1), 4T1(2), and 4T1(3)) of the ground 4T1 orbital triplet, those of the Kramers doublets U(n) (n = 0–5), and the principal components (g1, g2, and g3) of the anisotropic g-tensor of the ground Kramers doublet U(0) of the CoII center in the chain compound 1. The local structure of the CoII center is shown; selected bond angles and Co–O distances (in Å, blue numbers) are indicated. The CoO6 polyhedron is a strongly distorted octahedron with no symmetry elements (C1 point symmetry) having no distinct elongation/compression axes. Despite this fact, the calculated g-tensor of the ground U(0) Kramers doublet has a nearly uniaxial Ising-like character, g1 = 0.83, g2 = 0.93, and g3 = 8.03. Note that energy splitting pattern of the 4T1(1), 4T1(2), and 4T1(3) orbital components is incompatible with the tetragonal-symmetry approach (D – 0, E = 0) for the ligand-field splitting Hamiltonian D[Lz2  2/3] + E[Lx2  Ly2] used in Ref. [16,17,27,29–36]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 3 Energy positions (in cm1) of the split orbital components (4T1(1), 4T1(2), and 4T1(3)) of the ground 4T1 orbital tripleta and Kramers doublets U(n) (n = 0–5), and the principal components (g1, g2, and g3) of the anisotropic g-tensor of the ground Kramers doublet U(0) calculated for selected crystallographically independent CoII centers in the Co36 cluster in 2. 4 T1(1) 4 T1(2) 4 T1(3) U(0) U(1) U(2) U(3) U(4) U(5) g1 g2 g3 Co(1) Co(2) Co(3) Co(5) Co(7) Co(10) Co(12) Co(15) Co(18) 0 201 360 0 235 439 826 919 1000 2.87 3.79 5.92 0 618 807 0 140 701 987 1140 1266 2.24 4.10 5.88 0 582 748 0 149 667 964 1103 1227 2.28 4.13 5.85 0 617 758 0 143 684 982 1107 1240 2.30 4.39 5.60 0 563 712 0 154 646 952 1080 1208 2.32 4.24 5.75 0 592 805 0 146 684 973 1140 1264 2.20 3.80 6.16 0 644 753 0 144 694 997 1108 1245 2.28 4.32 5.67 0 522 750 0 157 645 939 1108 1219 2.24 3.82 6.18 0 202 359 0 237 438 827 920 1001 2.86 3.81 5.93 a The energies of the 4T1(1), 4T1(2), and 4T1(3) orbital components are essentially different pointing to the fact that the rhombic term E[Lx2  Ly2] of the low-symmetry ligand-field Hamiltonian D[Lz2  2/3] + E[Lx2  Ly2] is not small. This implies that the commonly used tetragonal-symmetry approach (D – 0, E = 0) [16,17,27,29–36] is rather unrealistic for compound 2. E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 drying off the solvent, because the crystals tend to lose solvent molecules rather readily. This effect can be taken into account empirically by applying a scaling factor to the experimental vMT data. A good correspondence between the experimental and calculated vMT curves is obtained with a scaling factor of 1.025 (Fig. 4b). Below 20 K, the calculated and experimental curves show some deviation in the both compounds; we show that its origin in compound 1 and 2 is different. In compound 1, upon cooling the experimental vMT curve exhibits a minimum at ca. 17 K and then increases. Formally, this can be attributed to a ferromagnetic spin coupling between CoII ions in the cobalt chain of 1. However, this type of scenario is probably rather unlikely for several reasons. First, exchange interactions between CoII ions mediated by a long malonate group are expected to be too weak to match the minimum at 17 K in the vMT curve of 1, Fig. 4a. Secondly, a low symmetry of CoII centers in 1 is generally unfavorable for ferromagnetism, which requires simultaneous orthogonally of all pairwise combinations of magnetic orbitals involved in two magnetically coupled CoII centers; in fact, ferromagnetic spin coupling is rather uncommon in CoII dinuclear complexes [16,17,29–36]. These arguments are supported by direct microscopic calculations of the exchange parameter in the Co–Co pair in 1, which is slightly antiferromagnetic (J = 0.6 cm1, see Fig. 8 below). The rise of the vMT curve below 17 K is more likely due to a magnetic field-driven orientation of microcrystals along the magnetic easy axis at low temperature in powdered samples of 1. Indeed, calculations indicate an extremely strong anisotropy of the magnetic susceptibility of 1 at low temperature; in fact, below 20 K vyy is about ten times larger than vxx and vzz, Fig. 4b. This is well consistent with an Ising-like anisotropy of the ground-state g-tensor of 1 discussed above (see Fig. 7). By contrast, in compound 2 the decrease in vMT below 20 K can safely be related to an antiferromagnetic spin coupling (Fig. 5a). Indeed, at 5 K the vMT value per CoII ion is about 1.3 cm3 mol1 K, which is well below the expected one for a magnetically isolated CoII ion (vMT  1.75 cm3 mol1 K) [14–17]. A more detailed information on exchange interactions in 2 is provided below. It is noteworthy that, in contrast to compound 1, the anisotropy of magnetic susceptibility in 2 is very weak, Fig. 5b. This is well consistent with a spherical-like character of the high-symmetry Co36 metal core (Figs. 2 and 3, S2, S3). Albeit magnetic anisotropy of individual CoII centers in Co36 is rather pronounced (as is evidenced by a high anisotropy of the ground-state g-tensor, g1  2.5, g2  4 and g3  6, Table 3), the total magnetic anisotropy of the Co36 molecular cluster drops due to different orientations of the local magnetic axes of CoII centers. Therefore, the low-temperature magnetic measurements for 2 are probably free of the torquing (crystallite-orientation) effects observed in 1. Besides, because of a low overall magnetic anisotropy (Fig. 5b), the Co36 molecular cluster is seemingly not promising as a potential single-molecule magnet (SMM) [41]; several CoII-based SMM complexes were reported in the literature [42–44]. Now we discuss the Co–Co spin coupling and estimate exchange parameters in 1 and 2. Some theoretical approaches have been developed in the literature to calculate the spin Hamiltonian for describing the spin coupling between orbitally-degenerated CoII ions [14–36]). For dinuclear CoII complexes, exchange parameters can be derived from the fitting to the experimental vMT curves in terms of a model parametric Hamiltonian, involving isotropic spin coupling JS1S2 between the true S1 = S2 = 3/2 spins on the two CoII centers, effective spin–orbit coupling akLS within the ground 4T1 term, and the low-symmetry splitting DbL2z  2=3c þ EbL2x  L2y c of the 4T1g term; examples are described in [16,17,27,29–36]). For some particular cases, analytical expressions for the magnetic susceptibility were derived [34]. However, in our case the use of such approaches is hardly possible due to severe complications discussed above (especially for a giant Co36 molecular cluster). Here 115 we use an alternative approach based on microscopic calculations of exchange parameters in terms of a many-electron superexchange model described in [45]. In these calculations, the set of electron transfer parameters tij (which are one-electron matrix elements connecting magnetic 3d orbitals (3di(A) and 3dj(B); i and j are orbital indexes, i, j = xy, yz, zx, x2  y2, and z2) on two CoII ions in the exchange-coupled pair CoII(A)–CoII(B), tij = hdi(A)|h|dj(B)i) are obtained from extended Huckel calculations (using standard atomic parameterization [46]) for the actual exchange-coupled cobalt pairs in 1 and 2 (see Fig. 9 below). Electron transfer parameters are derived by projection of 3d-rich molecular orbitals of the CoII(A)–CoII(B) pair onto pure 3d atomic orbitals of two metal atoms, as described in [47]. The Co(A)MCo(B) charge-transfer energy is set to 65 000 cm1 (8 eV); this approach has been previously used to analyze magnetic properties of NiII compound [48]. More details of these calculations are reported in the Supplementary data. Herein our calculations are limited to the isotropic spin Hamiltonian only for the true spin S = 3/2 of CoII, that describes exchange interaction between two orbitally degenerate CoII ions (A and B) with the spin–orbit coupling switched off. Generally, this Hamiltonian is written as H = JSASB + TSASB, where J is a constant and T is an orbital operator (represented by a 9  9 traceless matrix, see Supplementary data) acting on the orbital part of wave functions in the space 4T1g (A)  4T1g(B) of the dimension 12  12 = 144. The aim of this work is to estimate the exchange parameter J for the cobalt pair in 1 (Fig. 8) and for selected representative exchange-coupled CoII pairs in 2 (Fig. 9); in addition, we examine so-called Lines’ approach, in which the orbitally-dependent term TSASB is omitted [49]. First we calculate the exchange parameter J in the isotropic spin Hamiltonian JSASB (for SA = SB = 3/2) that acts in the truncated space of wave functions 4T1(1A)  4T1(1B) of the dimension 4  4 = 16; here 4T1(1A) and 4T1(1B) are the lowest states (orbital singlets) resulting from the orbital splitting of the 4T1 orbital triplet in distorted CoII(A) and CoII(B) centers (see Fig. 7 and Table 3). This approach is based on the fact that on each CoII center the energy separation between the 4T1(1) and 4T1(2) orbital components is much larger than the exchange parameter (J  10 cm1 or less) (Fig. 7). Calculations show that the spin coupling in 1 is weakly antiferromagneic, J = 0.6 cm1 (Fig. 8). This result is consistent with the experimental data on CoII malonate complexes indicating weak antiferromagnetic interactions between CoII ions mediated by malonate groups [50]. We can therefore conclude that weak exchange interactions have virtually no effect on the magnetic susceptibility of 1 in the temperature range of 5–300 K; the increase of vMT below 17 K is caused by the effect of strong anisotropy of the magnetic susceptibility, as discussed above. For the two main types of cobalt pairs in 2 we obtain J = 2.2 and 3.5 cm1, respectively, Fig. 9. Qualitatively, these values are reasonably consistent with the onset point (20–25 K) of the drop of the vMT curve of 2 at low temperature. Approximately, the onset temperature is estimated by T0  6J/kB, where 6J is the total spin energy splitting in exchange-coupled CoII-CoII pairs resulted from an isotropic spin coupling JSASB (SA = SB = 3/2, with the spin–orbit coupling switched off, see Figs. 8 and 9). Below this point antiferromagnetic exchange interactions are well seen in the vMT curve (Fig. 5); thus, with J  3 cm1 we obtain T0  25 K in 2. It is important to note that calculated exchange parameters in 1 and 2 are within the range of J values observed in small CoII carboxylate clusters, in which exchange interactions are mostly antiferromagnetic; representative examples were recently reviewed in [34]. In conclusion, we examine the applicability of the Lines’ approach [49] to the CoII complexes 1 and 2. For this, we repeat superexchange calculations for the aforementioned Co pairs shown in Figs. 8 and 9 applying projection of the charge-transfer states of the CoII(A)–CoII(B) pair onto the extended (12  12) space of wave 116 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 Fig. 8. The structure of the CoII(A)-CoII(B) exchange-coupled pair in 1 and the calculated exchange parameter (antiferromagnetic, J = –0.6 cm1) in the isotropic spin Hamiltonian H = JSASB (SA = SB = 3/2) describing spin coupling between the two lowest orbital components 4T1(1A) and 4T1(1B) of the CoII(A) and CoII(B) centers. Energy positions of excited orbital components are indicated in cm1. Exchange parameters Jmn for the spin coupling between various combinations (m, n) = 4T1(mA)  4T1(nB) of the ground and excited orbital components are also calculated, J12 = J21 = 0.98, J13 = J31 = 0.65, J23 = J32 = 0.83, J22 = 0.39, and J33 = 0.30 cm1. These exchange parameters correspond to the diagonal matrix elements of the (JI + T) orbital matrix of the extended spin Hamiltonian H = JSASB + TSASB; there are also some off-diagonal matrix elements connecting the (m, n) and (m0 , n0 ) pair states. Fig. 9. The structure of the two main types of CoII(A)–CoII(B) exchange-coupled pairs in the Co36 cluster in 2 and calculated exchange parameters. functions 4T1(A)  4T1(B). In this way, we obtain a 9  9 matrix (JI + T) (I being the unit matrix) of the orbital operator involved in the spin Hamiltonian H = JSASB + TSASB; details of these calculations are presented in the Supplementary data. Then the (JI + T) matrix is diagonalized. The set of the eigenvalues {ti} of the (JI + T) matrix provides a quantitative criterion for the correctness of the Lines’ approach, which predicts ti  J (because of T = 0). Therefore, the scatter in the ti values measures the degree of the validity of the Lines’ approach. Our calculations indicate that for the CoII pairs in 1 and 2 the ti eigenvalues vary considerably: in some cases they can even reverse the sign from antiferromagmanetic to ferromagnetic (Table 4). Exchange parameters Jmn for the spin coupling between various combinations (m, n) = 4T1 (mA)  4T1(nB) of the ground and excited orbital components are 117 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 Table 4 Eigenvalues ti (in cm1) of the (JI + T) orbital matrix involved in the orbitally-dependent spin Hamiltonian H = JSASB + TSASB for the cobalt exchange pairs in 1 and 2 (see Figs. 8 and 9). No. of the pair t1 t2 t3 t4 t5 t6 t7 t8 t9 1 (Fig. 11) 2 (Fig. 12a) 3 (Fig. 12b) 1.49 6.38 4.32 1.16 5.54 3.65 1.03 4.97 3.32 0.85 4.00 3.03 0.77 3.82 2.75 0.51 1.84 2.48 0.46 1.44 2.13 0.30 0.88 1.88 +0.34 +1.27 1.11 also different. Thus, for the CoII(A)–CoII(B) pair in 1 (Fig. 8) they are J12 = J21 = 0.98, J13 = J31 = 0.65, J23 = J32 = 0.83, J22 = 0.39, and J33 = 0.30 cm1 (see Fig. 9 and captions). Note that these exchange parameters are the diagonal matrix elements of the (JI + T) orbital matrix; there are also some off-diagonal matrix elements connecting the (m, n) and (m0 , n0 ) pairs states, see Fig. 8. These results indicate that the Lines’ approach is generally invalid for the CoII complexes 1 and 2. This fact may be very important in calculations of the effective (s = 1/2) anisotropic spin Hamiltonian sAJsB, which is obtained by the first-order projection of the JSASB + TSASB; Hamiltonian onto the subspace of the ground-state wave functions U(0)(A)  U(0)(B). The key point here is that the spin–orbit coupling strongly mixes the split 4T1(1), 4T1(2) and 4T1(3) orbital components (see Fig. 6), which enter the ground-state U(0) wave functions with comparable weights (unless the orbital splitting of the 4T1 state due to distortions is not too large, less than or comparable to the spin–orbit splitting, see Fig. 6). Therefore, the result of calculations of the anisotropic exchange Hamiltonian sAJsB based on the true orbitally-dependent spin Hamiltonian JSASB + TSASB may differ considerably from that of the Lines’ approach (JSASB only) because the three orbital component 4T1(k) (k = 1–3) have essentially different exchange parameters (Table 4) and they are further mixed by the off-diagonal exchange parameters of the orbital T matrix. However, a more detailed analysis of the anisotropic s = 1/2 spin Hamiltonian sAJsB related to the ground U(0) Kramers doublet of CoII is out of the scope of this paper because it is too lengthy and sophisticated; besides, its results cannot unambiguously be corroborated by limited experimental magnetic data on 1 and 2. 4. Conclusion Using a ligand-deficient synthetic approach, we were successful in obtaining two novel polynuclear CoII malonate complexes with bridging malonate groups. Compound 1 has a chain-type structure which is stabilized by large potassium cations. Compound 2 contains a novel hexanegative anion [Co36(H2O)12(OH)20(HMe2Mal)2 (Me2Mal)28]6 with a fascinating, highly symmetric, spherical-like Co36 metal core that serves as a structural building block. Theoretical analysis of the magnetic susceptibility of 1 and 2 reveal an important difference in the origin of their magnetic behavior. Compound 1 is characterized by an extremely high anisotropy of magnetic susceptibility originating from an uniaxial Ising-like anisotropy of the ground-state g-tensor of strongly distorted sixcoordinate CoII centers. At low temperature this results in crystallite-orientation effects in an external magnetic field giving rise to some increase of the vMT curve; formally, this mimics ferromagnetism of 1. Microscopic calculations indicate that long malonate bridging groups are poor mediators of exchange interactions between CoII ions (J = 0.6 cm1). By contrast, compound 2 has a low magnetic anisotropy due to a spherical-like character of the Co36 metal core, but exhibits more pronounced antiferromagnetic exchange interactions between carboxylate-bridged CoII ions (with J  3 cm1). Because of general weakness of Co-Co exchange interactions, above 25 K the magnetic susceptibility of 1 and 2 is well described by one-center contributions only due to thermal population of excited states of individual CoII ions. Our results indicate that the commonly used Lines’ approach is very limitedly applicable to calculations of the anisotropic exchange spin Hamiltonian for CoII compounds 1 and 2. Acknowledgments This study was supported by the Russian Foundation for Basic Research (project nos. 11-03-00556, 11-03-00735, 11-03-12109), the Council on Grants of the President of the Russian Federation (grant NSh-2357.2012.3), the Ministry of Education and Science of the Russian Federation (SC-14.740.11.0363), the Russian Academy of Sciences, and the Siberian Branch of the Russian Academy of Sciences. Appendix A. Supplementary material CCDC 884787 and 884788 contain the supplementary crystallographic data for compounds 1 and 2. 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