Pivalate Clusters - ACS Publications - American Chemical Society

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Tetranuclear {CoII2CoIII2}, Octanuclear {CoII4CoIII4}, and Hexanuclear {CoIII3DyIII3} Pivalate Clusters: Synthesis, Magnetic Characterization, and Theoretical Modeling Ioana Radu,† Victor Ch. Kravtsov,† Serghei M. Ostrovsky,† Oleg S. Reu,† Karl Kram ̈ er,‡ Silvio Decurtins,‡ ,‡ ,† ,† Shi-Xia Liu,* Sophia I. Klokishner,* and Svetlana G. Baca* †

Institute of Applied Physics, Academy of Sciences of Moldova, Academiei 5, MD-2028 Chisinau, Republic of Moldova Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, 3012 Bern, Switzerland

‡

S Supporting Information *

ABSTRACT: New tetranuclear and octanuclear mixed-valent cobalt(II/III) pivalate clusters, namely, [NaCo4(O2CCMe3)6(HO2CCMe3)2(teaH)2(N3)]· 2H 2 O ( in tw o p o ly m or ph i c mo d ifications, 1 a nd 1a ) an d [Co8(O2CCMe3)10(teaH)4(N3)](Me3CCO2)·MeCN·H2O (2) have been synthesized by ultrasonic treatment of a dinuclear cobalt(II) pivalate precursor with sodium azide and triethanolamine (teaH3) ligand in acetonitrile. The use of Dy(NO3)3·6H2O in a similar reaction led to the precipitation of a tetranuclear [NaCo4(O2CCMe3)4(teaH)2(N3)(NO3)2(H2O)2]·H2O (3) cluster and a heterometallic hexanuclear [Co3Dy3(OH)4(O2CCMe3)6(teaH)3(H2O)3](NO3)2·H2O (4) cluster. Single-crystal X-ray analysis showed that 1 (1a) and 3 consist of a tetranuclear pivalate/teaH3 mixed-ligand cluster [CoII2CoIII2(O2CCMe3)4(teaH)2(N3)]+ decorated with sodium pivalates [Na(O2CCMe3)2(HO2CCMe3)2]− (1 or 1a) or sodium nitrates [Na(NO3)2]− (3) to form a square-pyramidal assembly. In 2, the cationic [Co8(O2CCMe3)10(teaH)4(N3)]+ cluster comprises a mixed-valent {CoII4CoIII4} core encapsulated by an azide, 4 teaH2− alcoholamine ligands, and 10 bridging pivalates. Remarkably, in this core, the μ4-N3− ligand joins all four CoII atoms. The heterometallic hexanuclear compound 4 consists of a cationic [CoIII3DyIII3(OH)4(O2CCMe3)6(teaH)3(H2O)3]2+ cluster, two NO3− anions, and a crystallization water molecule. The arrangement of metal atoms in 4 can be approximated as the assembly of a smaller equilateral triangle defined by three Dy sites with a Dy···Dy distance of 3.9 Å and a larger triangle formed by Co sites [Co···Co, 6.1−6.2 Å]. The interpretation of the magnetic properties of clusters 2−4 was performed in the framework of theoretical models, taking into account the structural peculiarities of clusters and their energy spectra. The behavior of clusters 2 and 3 containing CoII ions with orbitally nondegenerate ground states is determined by the zero-field splitting of these states and Heisenberg exchange interaction between the ions. To get a good understanding of the observed magnetic behavior of cluster 4, we take into consideration the crystal fields acting on the DyIII ions, the ferromagnetic coupling of neighboring DyIII ions, and the intercluster antiferromagnetic exchange. For all examined clusters, the developed models describe well the observed temperature dependence of the magnetic susceptibility and the field dependence of magnetization. The computational results apparently show that in cluster 4 two DyIII ions with similar nearest surroundings demonstrate single-molecule-magnet (SMM) behavior, while the strong rhombicity of the ligand surrounding hinders the SMM behavior of the third DyIII ion.

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INTRODUCTION Over the last decades, the preparation and investigation of highnuclear 3d and 3d−4f cluster compounds have attracted much interest because they represent perspective magnetic materials for diverse applications ranging from high-density information storage devices to molecular electronics.1 A huge number of transition-metal complexes showing interesting magnetic properties, in particular single-molecule magnets (SMMs), the development of which was started with the discovery and investigation of the first “Mn12 acetate” SMM, have been reported so far, and mostly studied metal complexes were Mn-, Fe-, Ni-, or Co-based clusters. For excellent reviews covering recent progress in this area, see ref 2 and references cited © XXXX American Chemical Society

therein. Lately, researchers have turned their attention to exploration of the magnetic properties of 4f ions3 and their incorporation into transition-metal clusters; a number of heterometallic 3d-Ln polynuclear clusters having diverse structures and nuclearities with exceptional SMM properties have been revealed.4 Among all of these varieties of Co-based polynuclear clusters,5 their Co/Ln analogues represent a special case because interpretation of the magnetic data for polynuclear clusters containing high-spin CoII d7 ions in an octahedral Received: November 26, 2016

A

DOI: 10.1021/acs.inorgchem.6b02827 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Table 1. Crystal Data and Details of Structural Determinations for 1−4 1 formula cryst syst space group a, Å b, Å c, Å β, deg V, Å3 Z final R indices [I > 2σ(I)] largest diff peak and hole, e Å−3

C52H104Co4N5NaO24 monoclinic P21/c 25.3033(7) 46.0939(11) 28.2463(10) 99.911(3) 32452.8(2) 16 R1 = 0.0914, wR2 = 0.1616 1.202 and −0.535

1a

2

C52H112Co4N5NaO28 orthorhombic Cmcm 17.9330(6) 26.3905(8) 16.6146(5) 90 7863.0(4) 4 R1 = 0.0482, wR2 = 0.1394 0.483 and −0.357

C80.5H155.25Co8N7.75O35 monoclinic P21/c 20.8200(6) 18.8098(4) 30.8575(9) 98.669(3) 11946.4(6) 4 R1 = 0.0704, wR2 = 0.1799 0.667 and −0.753

environment with their first-order orbital contribution is often quite difficult, and each additional case gives more understanding to this field. Note that the first Co4-based SMM with (hydroxymethyl)pyridine was developed by Christou et al.6 in 2002, while the first phosphorus−supported CoII/GdIII SMM was reported by Clerac et al.7 in 2007 and then extended to a family of heterometallic trinuclear CoII/LnIII (Ln = Tb, Dy, Ho) SMMs.8 Considering that DyIII (6H15/2) ions have large spin ground states with large total angular momenta and strong intrinsic magnetic anisotropies, several mixed-valent CoII,III/ DyIII-containing SMMs with original topologies and diverse nuclearities have also been reported. The structures encompass {CoDy 2 }, 9 {Co 2 Dy 2 }, 10 {Co 2 Dy 4 }, 11 {Co 2 Dy 10 },12 and {Co 3 Dy 4 } 1 3 clusters and the largest 52-metal ion {Co10Dy42}14 cluster as well as a 2D Co/Dy network constructed of rare {Co4Dy2} clusters with a planar core.15 In this respect, the development of new synthetic pathways to assemble novel polynuclear homo- and heterometallic Cobased complexes is a considerable challenge. In continuing our research on the design and investigation of polynuclear carboxylate complexes with alcoholamine ligands,16 we report herein the simple route to the preparation of new mixed-valent Co clusters, namely, tetranuclear [NaCo4(O2CCMe3)6(HO2CCMe3)2(teaH)2(N3)]·2H2O (1 and 1a) and [NaCo4(O2CCMe3)4(teaH)2(N3)(NO3)2(H2O)2]· H 2 O (3), octanuclear [Co 8 (O 2 CCMe 3 ) 10 (teaH) 4 (N 3 )](Me3CCO2)·MeCN·H2O (2), and hexanuclear heterometallic cobalt/dysprosium pivalate [Co3Dy3(OH)4(O2CCMe3)6(teaH)3(H2O)3](NO3)2·H2O (4) clusters from dinuclear cobalt(II) pivalate precursor [Co2(H2O)(O2CCMe3)4(HO2CCMe3)4] and triethanolamine (teaH3) ligand. The crystal structures and magnetic properties of these complexes as well as the theoretical models for an explanation of these properties are discussed.

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3 C32H68Co4N7NaO23 monoclinic C2/c 35.6257(16) 14.1944(6) 20.3710(7) 98.007(4) 10200.9(7) 8 R1 = 0.0560, wR2 = 0.1361 0.680 and −0.470

4 C48H105Co3Dy3N5O35 monoclinic P21/n 16.1980(3) 19.1136(3) 26.0111(4) 91.6717(15) 8049.7(2) 4 R1 = 0.0494, wR2 = 0.1207 1.102 and −0.852

X-ray Crystallography. Diffraction data set for 1−4 were collected on a Xcalibur CCD diffractometer equipped with graphitemonochromatized Mo Kα radiation. After collection and integration, data were corrected for Lorentz and polarization effects. The structure was solved by direct methods and refined by full-matrix least squares on weighted F2 values for all reflections using the SHELX suite of programs.18 All non-H atoms in clusters were refined with anisotropic displacement parameters. H atoms were placed in fixed, idealized positions and refined as rigidly bonded to the corresponding atom. The H atoms in the disordered solvent water (H2O) molecules were not localized. The tert-butyl groups of pivalate ligands in 1−4 and the branches of teaH ligands in 1 and 1a were found to be disordered over two positions; therefore, various restraints were applied to obtain reasonable geometrical parameters and thermal displacement coefficients. Details for the crystallographic data and refinement are summarized in Table 1 (Table S1), and selected geometric parameters for 1−4 are given in Table 2. The figures were prepared with the DIAMOND 3.2k software package19 and Mercury 3.8. CCDC 1518223 (1), 1518220 (1a), 1518222 (2), 1518219 (3), and 1518221 (4) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. Magnetic Measurements. The magnetic susceptibility data of 1− 4 were obtained using a Quantum Design MPMS-5XL SQUID magnetometer. The polycrystalline sample was compacted and immobilized into a cylindrical poly(tetrafluoroethylene) (PTFE) capsule. The data were acquired as a function of the field and temperature. All data were corrected for the contribution of the sample holder (PTFE capsule) and the diamagnetic contribution of compounds 1−4: −0.45 × molecular weight × 10−6 cm3 mol−1. Syntheses of [NaCo4(O2CCMe3)6(HO2CCMe3)2(teaH)2(N3)]·2H2O (1) and [Co8(O2CCMe3)10(teaH)4(N3)](Me3CCO2)·MeCN·H2O (2). [Co2(H2O)(O2CCMe3)4(HO2CCMe3)4] (0.18 g, 0.2 mmol), teaH3 (0.03 g, 0.2 mmol), and NaN3 (0.006 g, 0.1 mmol) were dissolved in acetonitrile (MeCN; 6 mL). The reaction mixture was treated in an ultrasonic bath for 30 min. The dark-brown solution was filtered and allowed to evaporate slowly at room temperature. Green needlelike crystals of 1 and dark-green prismatic crystals of 2 suitable for X-ray measurements were obtained after 1 month, washed with cold MeCN, and dried in air. Then, clusters 1 and 2 were manually separated. Polymorphic modification 1a and an additional amount of 2 were precipitated from the filtrate and manually separated. Yield: 0.05 g (1), 0.078 g (1a), and 0.01 g (2). Elem anal. Calcd for 1, C52H104Co4N5NaO24 (1442.11 g mol−1): C, 43.31; H, 7.27; N, 4.86. Found: C, 43.57; H, 7.06; N, 4.69. Found for 1a: C, 44.18; H, 7.30; N, 4.65. FT-IR: ν 3365 (br m), 2957 (m), 2925 (sh), 2900 (sh), 2867 (m), 2092 (s), 2068 (s), 1702 (m), 1585 (vs), 1565 (sh), 1556 (vs), 1481 (s), 1458 (sh), 1408 (vs), 1370 (sh), 1360 (s), 1299 (m), 1223 (m), 1195 (m), 1093 (sh), 1069 (m), 1033 (w), 1005 (w), 922 (m), 893 (m), 868 (w), 802 (w), 786 (w), 761 (w), 745 (w), 693 (w), 669 (sh), 622 (m), 606 (sh), 590 (m), 539 (m), 513 (m) cm−1. Elem anal. Calcd for 2, C80.5H155.25Co8N7.75O35 (2263.31 g mol−1): C, 42.72; H,

EXPERIMENTAL SECTION

Materials and General Procedures. All reactions were carried out under aerobic conditions using commercial-grade solvents. [Co2(H2O)(O2CCMe3)4(HO2CCMe3)4] was prepared as reported elsewhere.17 Commercially available ligands were used without further purification. Caution! Care should be taken when using the potentially explosive sodium azide. IR spectra were recorded on a FT/IR-4700 type A spectrometer in the region 4000−500 cm−1. Thermogravimetric analysis (TGA) measurements were carried out with a Mettler Toledo TGA/SDTA 851 analyzer in dry N2 (60 mL min−1) at a heating rate of 5 K min−1. A WiseClean WUC-A02H ultrasonic bath operating at 40 kHz with a maximum power output of 140 W was used for ultrasonic irradiation. B


Article

Inorganic Chemistry Table 2. Selected Bond Distances (Å) in 1−4

a

1, CoII Co2A−O17A Co2A−O20A Co2A−O2A Co2A−O9A Co2A−O3A Co4A−O21A Co4A−O18A Co4A−O6A Co4A−O11A Co4A−O7A Co2B−O17B Co2B−O20B Co2B−O9B Co2B−O3B

2.010(6) 2.013(6) 2.054(8) 2.057(6) 2.087(7) 1.997(6) 2.009(6) 2.041(7) 2.057(6) 2.073(7) 2.000(6) 2.014(6) 2.039(6) 2.051(7)

Co2B−O2B Co4B−O21B Co4B−O18B Co4B−O11B Co4B−O7B Co4B−O6B Co2C−O20C Co2C−O17C Co2C−O2C Co2C−O3C Co2C−O9C Co4C−O11C Co4C−O18C

2.078(7) 1.995(5) 2.005(5) 2.054(6) 2.069(7) 2.077(6) 1.982(6) 1.998(5) 2.049(7) 2.071(6) 2.084(7) 1.985(8) 2.009(5)

Co4C−O6C Co4C−O21C Co4C−O7C Co2D−O9D Co2D−O17D Co2D−O3D Co2D−O20D Co2D−O2D Co4D−O21D Co4D−O18D Co4D−O7D Co4D−O6D Co4D−O11D

2.011(6) 2.032(6) 2.069(7) 1.977(7) 1.992(6) 2.004(7) 2.032(6) 2.071(8) 1.978(6) 1.995(6) 2.059(8) 2.067(7) 2.097(7)

1.982(7) 2.064(7) 1.870(5) 1.871(6) 1.918(6) 1.922(6) 1.973(7) 2.052(7) 1.864(5) 1.875(6) 1.923(6) 1.930(6) 1.985(6) 2.075(6) 1.874(6) 1.875(5)

Co3C−O4C Co3C−O5C Co3C−N2C Co3C−N3C Co1D−O18D Co1D−O17D Co1D−O8D Co1D−O1D Co1D−N1D Co1D−N3D Co3D−O21D Co3D−O20D Co3D−O4D Co3D−O5D Co3D−N2D Co3D−N3D

1.919(6) 1.924(6) 1.962(7) 2.052(7) 1.853(6) 1.887(6) 1.907(6) 1.922(7) 1.972(7) 2.058(6) 1.858(6) 1.882(6) 1.917(6) 1.924(6) 1.985(7) 2.054(7)

2.050(3) 2.060(3)

Co2−O2

2.060(3)

1.926(2) 1.926(2)

Co1−N1 Co1−N2

1.976(4) 2.0629(17)

2.024(5) 2.065(4) 2.178(6) 1.971(4) 1.987(5) 2.027(5) 2.031(5)

Co7−N7 Co8−O22 Co8−O18 Co8−O16 Co8−O19 Co8−N7

2.171(6) 1.958(4) 2.000(5) 2.032(5) 2.047(4) 2.174(6)

1.897(4) 1.924(4) 1.930(4) 1.979(6) 1.841(4) 1.891(4) 1.904(5) 1.909(5)

Co5−O27 Co5−N4 Co6−O28 Co6−O27 Co6−O13 Co6−O12 Co6−O31 Co6−N3

1.922(4) 1.964(6) 1.846(4) 1.898(4) 1.911(5) 1.913(5) 1.916(4) 1.978(6)

3.169(1) 2.812(1) 3.221(1)

Co7···Co8 Co1···Co8

3.479(1) 3.173(1)

2.133(4) 2.014(3)

Co4−O6 Co4−O7

2.026(4) 2.037(4)

1, CoIII Co1A−O17A Co1A−O18A Co1A−O1A Co1A−O8A Co1A−N1A Co1A−N3A Co3A−O21A Co3A−O20A Co3A−O4A Co3A−O5A Co3A−N2A Co3A−N3A Co1B−O18B Co1B−O17B Co1B−O1B Co1B−O8B

1.854(6) 1.869(6) 1.924(7) 1.926(6) 1.992(7) 2.053(7) 1.857(6) 1.873(5) 1.920(6) 1.926(6) 1.979(8) 2.054(7) 1.861(6) 1.863(5) 1.935(6) 1.937(5)

Co1B−N1B Co1B−N3B Co3B−O20B Co3B−O21B Co3B−O4B Co3B−O5B Co3B−N2B Co3B−N3B Co1C−O18C Co1C−O17C Co1C−O8C Co1C−O1C Co1C−N1C Co1C−N3C Co3C−O20C Co3C−O21C

Co2−O7#2 Co2−O7#1

1.999(2) 1.999(2)

Co2−O3 Co2−O2#3

Co1−O7 Co1−O7#1

1.873(2) 1.873(2)

Co1−O1#1 Co1−O1

Co3−O25 Co3−O5 Co3−O7 Co3−O4 Co3−N5 Co4−O30 Co4−O8

1.963(4) 1.981(5) 2.025(5) 2.029(5) 2.196(6) 1.967(4) 1.993(5)

Co4−O6 Co4−O9 Co4−N5 Co7−O28 Co7−O15 Co7−O14 Co7−O17

Co1−O22 Co1−O21 Co1−O20 Co1−O1 Co1−O24 Co1−N1 Co2−O25 Co2−O3

1.862(4) 1.891(4) 1.910(4) 1.917(4) 1.921(4) 1.982(5) 1.864(4) 1.891(5)

Co2−O24 Co2−O21 Co2−O2 Co2−N2 Co5−O30 Co5−O31 Co5−O10 Co5−O11

Co1···Co2 Co2···Co3 Co3···Co4

2.812(1) 3.228(1) 3.534(1)

Co4···Co5 Co5···Co6 Co6···Co7

1a, CoII

1a, CoIII

2, CoII

2, CoIII

2, Metal···Metal

3, CoII Co2−O2 Co2−O12

2.014(4) 2.016(3)

Co2−O15W Co4−O10 C


Article

Inorganic Chemistry Table 2. continued 3, CoII Co2−O9 Co2−O3

2.018(3) 2.032(4)

Co4−O13

2.024(3)

Co4−O16W

2.065(4)

1.983(4) 2.073(4) 1.883(3) 1.887(3)

Co3−O5 Co3−O4 Co3−N2 Co3−N5

1.926(3) 1.926(3) 1.980(4) 2.065(4)

3.1028(9)

Co1···Co4

3.0791(9)

1.875(6) 1.887(5) 1.888(5) 1.901(6) 1.905(6) 1.983(7) 2.280(5) 2.291(6) 2.327(6) 2.345(6) 2.367(5) 2.382(5) 2.404(5) 2.410(6)

Co3−O23 Co3−O24 Co3−O14 Co3−O3 Co3−O15 Co3−N3 Dy3−O23 Dy3−O13 Dy3−O21 Dy3−O12 Dy3−O2 Dy3−O3 Dy3−O4 Dy3−O3W

1.876(6) 1.885(6) 1.892(6) 1.906(5) 1.915(6) 1.972(7) 2.314(6) 2.320(6) 2.334(6) 2.347(6) 2.368(5) 2.379(5) 2.386(5) 2.404(6)

3.9151(6) 3.2824(12) 3.2933(12)

Dy2···Dy3 Dy3···Co3 Dy3···Co2

3.9230(5) 3.2877(12) 3.3042(11)

3, CoIII Co1−O10 Co1−O9 Co1−O8 Co1−O1

1.874(3) 1.883(3) 1.915(3) 1.919(3)

Co1−N1 Co1−N5 Co3−O13 Co3−O12

Co1···Co2 Co2···Co3

3.0826(9) 3.0704(9)

Co3···Co4

3, Metal···Metal

4, CoIII Co1−O18 Co1−O17 Co1−O1 Co1−O7 Co1−O6 Co1−N1 Dy1−O24 Dy1−O17 Dy1−O16 Dy1−O5 Dy1−O1 Dy1−O3 Dy1−O4 Dy1−O1W

1.874(6) 1.878(6) 1.905(5) 1.911(6) 1.922(6) 1.976(8) 2.292(5) 2.309(6) 2.312(6) 2.343(6) 2.377(5) 2.381(5) 2.386(5) 2.471(6)

Co2−O20 Co2−O2 Co2−O21 Co2−O10 Co2−O11 Co2−N2 Dy2−O20 Dy2−O18 Dy2−O9 Dy2−O8 Dy2−O4 Dy2−O1 Dy2−O2 Dy2−O2W

Dy1···Co3 Dy1···Co1 Dy1···Dy2

3.2714(12) 3.2908(12) 3.9054(5)

Dy1···Dy3 Dy2···Co2 Dy2···Co1

4, Metal···Metal

a

Symmetry codes: #1, x, y, −z + 1/2; #2, −x + 1, y, −z + 1/2.

Scheme 1. Synthesis of Clusters 1−4

6.91; N, 4.79. Found: C, 41.79; H, 6.41; N, 4.05. FT-IR: ν 3471 (br m), 2959 (m), 2928 (sh), 2867 (m), 2118 (s), 1685 (w), 1600 (sh), 1549 (vs), 1481 (s), 1458 (sh), 1414 (vs), 1374 (sh), 1359 (s), 1286 (w), 1225 (s), 1189 (w), 1088 (m), 1055 (m), 1032 (m), 1009 (m), 936 (m), 923 (sh), 900 (m), 865 (w), 787 (w), 745 (w), 656 (m), 626 (sh), 604 (m), 581 (sh), 528 (m), 509 (m) cm−1.

Syntheses of [NaCo4(O2CCMe3)4(teaH)2(N3)(NO3)2(H2O)2]·H2O (3) and [Co 3 Dy 3 (OH) 4 (O 2 CCMe 3 ) 6 (teaH) 3 (H 2 O) 3 ](NO 3 ) 2 ·H 2 O (4). [Co2(H2O)(O2CCMe3)4(HO2CCMe3)4] (0.18 g, 0.2 mmol), Dy(NO3)3·6H2O (0.06 g, 0.2 mmol), teaH3 (0.03 g, 0.2 mmol), and NaN3 (0.006 g, 0.1 mmol) were dissolved in MeCN (6 mL). The reaction mixture was treated with ultrasonic waves for 30 min. The D


Article

Inorganic Chemistry

N3− in 2, the corresponding peak appears at 2118 cm−1. The stretching vibrations of the coordinated NO3− anions appear at 1099 cm−1 as a medium-intensity band. The medium-intensity peaks at 622−596 and 539−512 cm−1 are regarded as characteristic vibrations of the Co−O and Co−N bonds. TGA for 1−4 was performed under a nitrogen atmosphere in the temperature range of 25−800 °C. The TGA data show that thermal decomposition of the clusters proceeds through several weakly resolved steps to the final metal oxides. For cluster 1, the decomposition starts at 50 °C with the removal of one coordinated pivalic acid and azide ligand up to 210 °C with a weight loss of 10.65% (calcd, 10.25%) followed by complete removal of the remaining ligands until approximately 590 °C (total weight loss of 78.95%). In the temperature range of 25− 150 °C, cluster 2 loses the solvent (MeCN and H2O) molecules (found, 2.22%; calcd, 2.58%). Upon further heating, the remaining ligands completely decompose up to 430 °C with a total weight loss of 71.04%. Up to 160 °C, cluster 3 exhibits a weight loss of 4.60%, which indicates the removal of two coordinated and one solvate H2O molecules (calcd, 4.67%) followed by complete decomposition of the ligands in three weakly resolved steps until 500 °C to a final product with a total weight loss of 88.83%. Similar to 3, cluster 4 loses two coordinated and one solvate H2O molecules (found, 2.12%; calcd, 2.73%) before 180 °C and then completely decomposes in four weakly resolved steps until 600 °C to a final product with a total weight loss of 70.4%. Structural Description. Compounds 1, 1a, and 3 crystallize in the space groups P21/c, Cmcm, and C2/c, respectively. The asymmetric unit of 1 contains four neutral [NaCo4(O2CCMe3)6(HO2CCMe3)2(teaH)2(N3)] clusters and eight disordered H2O molecules. In 1a, a neutral [NaCo4(O2CCMe3)6(HO2CCMe3)2(teaH)2(N3)] cluster resides on a special position (Wyckoff letter 4c), thus emulating the C2v symmetry. The asymmetric unit consists of one-quarter of the cluster and 1.5 crystallization H2O molecule (Figure S1). Because the individual cluster does not possess C2v molecular symmetry, the structure of 1a reveals a disorder of teaH ligands in accordance with the mirror plane symmetry. A similar disorder of the teaH ligand was found in 1, where clusters reside in general positions. The asymmetric unit of 3 consists of a neutral [NaCo4(O2CCMe3)4(teaH)2(N3)(NO3)2(H2O)2] cluster and one crystallization H2O molecule (Figure S3). The molecular structures of 1 (1a) and 3 are shown in Figure 1, and selected bond distances are listed in Table 2. The clusters consist of four Co atoms bridged by four pivalates, two bridging teaH2− ethanolamine ligands, and one N3− azide ligand to form a calix-like tetranuclear unit (Figure 1d) capped with a sodium cation and two pivalic acid molecules in 1 (1a) or two NO3− ions in 3. In 1 (1a), two pivalate ligands additionally bridge CoII atoms and a Na+ cation. The Co atoms in the vertexes of the rhombus are close to a common plane within ±0.14 Å. In both clusters, two CoIII ions [supported by bond-valence summation (BVS),20 3.38−3.54] are six-coordinated and adopt distorted octahedral N2O4 geometries with two carboxylate O atoms from two bridging pivalates [Co−O distances range from 1.915(3) to 1.926(3) Å] and two O atoms from a doubly deprotonated teaH2− ligand [Co−O, 1.874(3)−1.887(3) Å]. The coordination spheres of these atoms are completed by the amine N atom of the teaH2− ligand [Co−N, 1.983(4) and 1.980(4) Å] and the N atom of a bridging azide ion [Co−N, 2.073(4) and 2.065(4) Å].

dark-brown solution was filtered and allowed to evaporate slowly at room temperature. Green prismatic crystals of 3 suitable for X-ray measurements were obtained after 3 days, filtered and washed with cold MeCN, and dried in air. Yield: 0.009 g. Keeping the filtrate over 1 month in the fridge at 5 °C gave purple crystals of 4, which have been filtered, washed with cold MeCN, H2O, and ethanol (EtOH), and airdried. Yield: 0.04 g. Elem anal. Calcd for 3, C32H68Co4N7NaO23 (1177.64 g mol−1): C, 32.64; H, 5.82; N, 8.33. Found: C, 32.74; H, 5.85; N, 7.33. IR (KBr pellet): ν 3423 (br m), 2959 (m), 2927 (m), 2868 (m), 2078 (m), 1567 (vs), 1483 (s), 1458 (sh), 1414 (vs), 1384 (vs), 1227 (s), 1099 (m), 1041 (sh), 1016 (sh), 933 (m), 899 (sh), 826 (sh), 787 (w), 631 (m), 603 (sh), 515 (m) cm−1. Elem anal. Calcd for 4, C48H105Co3Dy3N5O35 (1976.65 g mol−1): C, 29.17; H, 5.35; N, 3.54. Found: C, 29.02; H, 5.22; N, 3.81. FT-IR: ν 3417 (br m), 2956 (m), 2925 (m), 2871 (m), 1555 (vs), 1481 (s), 1458 (sh), 1409 (vs), 1371 (s), 1359 (s), 1329 (sh), 1226 (s), 1088 (m), 1057 (sh), 1041 (sh), 1014 (sh), 928 (m), 809 (m), 825 (w), 744 (w), 622 (sh), 596 (m), 537 (sh), 512 (m) cm−1.

■

RESULTS AND DISCUSSION

Synthesis and Characterization. Ultrasonic treatment of the MeCN solution containing a preformed dinuclear cobalt(I I ) p iv a la t e p r e cu rs o r [ Co 2 ( H 2 O ) ( O 2 C CM e 3 ) 4 (HO2CCMe3)4] with sodium azide and teaH3 led to the precipitation in 1 month of three kinds of crystals: green needle crystals of [NaCo4(O2CCMe3)6(HO2CCMe3)2(teaH)2(N3)]· 2H2O (1), green prismatic crystals of its polymorphic modification (1a), and dark-green prismatic crystals of [Co8(O2CCMe3)10(teaH)4(N3)](Me3CCO2)·MeCN·H2O (2), which can be separated only by hand with yields of approximately 15%, 35%, and 30%, respectively (Scheme 1). Then, we used dysprosium(III) nitrate hexahydrate in a similar reaction to generate heterometallic Co/Dy complexes. First, the green prismatic crystals of [NaCo4(O2CCMe3)4(teaH)2(N3)(NO3)2(H2O)2]·H2O (3) were precipitated in low 8% yield at room temperature in 3 days, followed by the formation of purple hexanuclear heterometallic cobalt/dysprosium pivalate crystals of [Co 3 Dy 3 (OH) 4 (O 2 CCMe 3 ) 6 (teaH) 3 (H 2 O) 3 ](NO3)2·H2O (4) under low temperature over 1 month in 39% yield (Scheme 1). Keeping the reaction mixture after ultrasonic irradiation at a low temperature of 5 °C gave a mixture of green and purple crystals. Clusters 1−4 were further characterized by IR and TGA. The IR spectra of 1−4 display very strong and broad bands in the regions of 1582−1549 and 1414−1408 cm −1 corresponding to the asymmetric and symmetric vibrations of the coordinated bridging carboxylate groups, respectively. The vibrations of carboxylate groups for two coordinated pivalic acids in 1 and a pivalate anion in 2 are detected at 1702 and 1685 cm−1, respectively. In the range of 2959−2868 cm−1, the asymmetric and symmetric C−H stretching vibrations for methyl groups of pivalates and methylene −(CH2)− groups of teaH2− ligands are observed. A strong single band at 1481 cm−1 and a shoulder at 1458 cm−1 are ascribed to the C−H asymmetric bending vibrations for alkyl groups, whereas their symmetric bending vibrations appear as a doublet at 1374− 1358 cm−1, which overlaps with strong vibrations of the coordinated NO3− anions at 1326 cm−1 (in 3 and 4). The presence of solvate and coordinated H2O molecules, as well as OH groups of doubly deprotonated teaH2− ligands caused the appearance of broad absorption bands in the range of 3471− 3365 cm−1. A medium-intensity peak at 2095−2092 cm−1 corresponds to the NN stretching vibrations of one-end bridging azide ligand in 1 and 3, whereas for the μ4-bridging E


Article

Inorganic Chemistry

hydrogen-bonded framework in 3. The coordinated H2O molecule (O15W; Figure S4) forms an intracluster O−H···O hydrogen bond of 2.826(6) Å with the O17 atom of the coordinated NO3− anion. Further, the H2O molecule O15W participates in the formation of two intermolecular hydrogen bonds with a nitrate anion [O15W−H···O21 (−x + 1/2, y − 1/2, −z + 1/2) = 2.788(6) Å] and the uncoordinated O atom from the EtOH part of the teaH2− ligand [O11−H···O15W (x, −y, z − 1/2) = 2.692(6) Å] from the neighboring clusters. The second coordinated H2O molecule O16W is also involved in an intermolecular O−H···O hydrogen bond of 2.696(6) Å with the uncoordinated O14 atom (−y + 1, z − 1/2) from the neighboring cluster. Thus, through the hydrogen bonds formed by crystalline H2O molecules, 2D hydrogen-bonded layers are formed (Table S2). Compound 2 crystallizes in the monoclinic space group P21/c and consists of a cationic [Co8(O2CCMe3)10(teaH)4(N3)]+ cluster (Figure S2), a pivalic anion, and crystallization MeCN and H2O molecules. As shown in Figure 2, [Co8(O2CCMe3)10(teaH)4(N3)]+ comprises a

Figure 1. Molecular structure of clusters 1 (a) and 3 (b). Color code: CoIII, purple spheres; CoII, pink spheres, NaI, yellow spheres; C, gray sticks; O, red sticks; N, blue sticks. The azide is highlighted as blue balls. Solvent H2O molecules and H atoms are omitted for clarity. (c) View of a {Co4} core highlighting the CoII ions with pink polyhedra and CoIII ions with purple polyhedra. (d) Side views of 1 and 3 showing the crownlike formation of a {Co4} core.

The two CoII ions (supported by BVS,20 1.93−2.09) are fivecoordinated by two carboxylate O atoms from two bridging pivalates [Co−O distances range from 2.014(4) to 2.037(4) Å], two O atoms from two doubly deprotonated teaH2− molecules [Co−O, 2.016(3)−2.024(3) Å], and an O atom from the coordinated H2O molecule to complete a square-pyramidal O5 geometry [Co−O, 2.133(4) and 2.065(4) Å]. As expected from oxidation states, the CoIII centers have shorter metal−ligand bond distances compared to longer ones for the CoII centers (Table 2). The CoII···CoIII separations are in the narrow range of 3.070(1)−3.103(1) Å, and the CoIII···CoIII distance equals 3.881(2) Å through the azide bridge. A Na+ ion that decorates the {CoII2CoIII2} cluster is eight-coordinated by eight O atoms from carboxylate ligands in 1 [Na−O, 2.319(4)−2.729(4) Å] and four O atoms from two nitrates [Na−O, 2.459(5)− 2.631(6) Å] and four O atoms from two alcoholamines [Na− O, 2.450(4)−2.537(4) Å] in 3. The square-pyramidal arrangement of the NaCo4 centers in the cores 1 and 3 resembles that of the square-pyramidal Co5 clusters reported by Powell et al.,21 although in Powell’s clusters, all metal centers are CoII atoms. In 1 and 1a, pivalic acids coordinated to the Na+ ion form intramolecular O−H···O hydrogen bonds of 2.565(15)− 2.684(7) Å with O atoms from bridging pivalates. Two coordinated and one crystalline H2O molecules together with one uncoordinated EtOH group of a doubly deprotonated teaH2− as well as the nitrate anions are all involved in a set of intra- and intermolecular hydrogen bonds, giving an extensive

Figure 2. Molecular structure of cluster 2. Inset: Simplified {CoII4CoIII4} metallic core. Color code: CoIII, purple spheres; CoII, pink spheres; C, gray sticks; O, red sticks; N, blue sticks. H atoms, a pivalic anion, and solvate molecules are omitted for clarity.

central Co4 core in which metal ions reside in the vertexes of a flattend tetrahedron and are joined by a μ4-azide and four bridging pivalate residues. BVS20 calculations (with a value of 2.06−2.08) suggest that all of these Co atoms are in the 2+ oxidation state. Four pivalate ligands are μ-bridging the central CoII4 atoms to four outer CoIII centers (supported by BVS, 3.51−3.60), together with four teaH2− alcoholamine ligands. Finally, two bridging pivalates complete the coordination sphere of CoIII atoms. All central CoII atoms are fivecoordinated and have a NO4 environment by one N atom from an azide, three O atoms from three pivalates, and one O atom of the teaH2− ligand, with CoII−O distances in the range of 1.958(4)−2.065(4) Å and the CoII−N distance being of 2.171(6)−2.196(6) Å. The coordination polyhedron of CoII atoms is intermediate between a square-planar pyramid and a trigonal bipyramid. Four outer CoIII centers are all sixcoordinated, and their octahedral geometry involving a NO5 donor set is completed by two O atoms of two carboxylate moieties and three O atoms and one N atom coming from two teaH2− ligands. F


Article

Inorganic Chemistry The CoIII−O distances are in the range 1.841(4)−1.930(4) Å, and the CoIII−N distances are 1.964(6)−1.982(5) Å, which are shorter compared to the CoII−O and CoII−N distances (Table 2). The metal···metal separations CoII···CoIII within the cluster range from 3.169(1) to 3.228(1) Å, the CoII···CoII distances are 3.534(1) and 3.479(1) Å, and the shortest metal··· metal distance of 2.812(1) Å is found between CoIII atoms (Table 2). Compound 4 crystallizes in the monoclinic space group P21/n and consists of a cationic [Co3Dy3(OH)4(O2CCMe3)6(teaH)3(H2O)3]2+ cluster, two NO3− anions, and a crystallization H2O molecule. The cluster (Figure 3) is composed of

magnetic behavior that cannot be described within the framework of a unified theoretical approach. Therefore, the magnetic characteristics of each cluster are examined separately, taking into account the structural peculiarities of the cluster, the individual magnetic properties of each ion, and the specifics of the interion magnetic interaction. Note that two polymorphic modifications of 1 and 1a show similar magnetic behavior. Cluster 3. The schematic structure of this tetranuclear Co complex is shown in Figure 1c. The cluster consists of two CoII and two CoIII ions. Each CoIII is surrounded by four O atoms and two N atoms. The corresponding metal−ligand distances are typical for the low-spin CoIII electronic configuration (spin S = 0). So, the system under examination can be regarded as two high-spin CoII ions coupled through the superexchange interaction mediated by the diamagnetic low-spin CoIII ions acting as bridges. Each CoII ion is in a square-pyramidal arrangement of five O atoms and is regarded as a S = 3/2 system with the axial zero-field splitting (ZFS).22,23 The Hamiltonian for analysis of the magnetic behavior of the complex under study is H=

∑

Si Di Si − 2Jex S1S2 + μB

i = 1,2

∑ i = 1,2

Si giH

(1)

where the first part is the ZFS term, the second one is the isotropic exchange interaction between the CoII ions, and the last one is the Zeeman perturbation. In eq 1, Jex and μB are the isotropic exchange parameter and Bohr magneton, respectively. In the local coordinate systems (with the zi axes coinciding with local C4 axes), the Di tensors are diagonal ⎛−D/3 0 0 ⎞ ⎜ ⎟ Di = ⎜ 0 −D/3 0 ⎟ ⎜ ⎟ ⎝ 0 0 2D/3⎠

Figure 3. Molecular structure of cluster 4. Inset: View of the arrangement of atoms in the {Co3Dy3} core. Color code: CoIII, purple spheres; DyIII, light-blue spheres; C, gray sticks; O, red sticks; N, blue sticks. H atoms, nitrate anions, and a solvate H2O molecule are omitted for clarity.

(2)

where D is the axial ZFS parameter. For metal ions with squarepyramidal coordination, the Zeeman part of the Hamiltonian (1) is characterized by two different principal values of the g tensor (parallel and perpendicular to the local C4 axes). However, to avoid overparameterization, we introduced an average value of the Lande factor gav. In order to properly describe the magnetic anisotropy of the complex, we have taken into account the noncolinearity of the anisotropy axes of the mononuclear CoII moieties. For the examined complex, the corresponding angle is α = 103°. For calculation of the matrix elements of the Hamiltonian (1), we introduce the molecular coordinate system (XYZ), as shown in Figure 4. The local Di tensors in the molecular coordinate system are obtained by unitary transformation (clockwise rotation for one

three CoIII and three DyIII atoms bridged by four μ3-hydroxy groups and six pivalate residues and additionally linked by three partly deprotonated teaH2− ligands. Thus, the arrangement of CoIII and DyIII atoms in 4 can be viewed as an intersection of a smaller equilateral triangle defined by three Dy sites with a Dy···Dy distance of 3.9 Å and a larger triangle formed by Co sites [Co···Co, 6.1−6.2 Å] (Figure 3, inset). The dihedral angle between the Dy3 and Co3 triangular planes is equal to 37.2°. Each of the CoIII atoms in 4 is six-coordinated, adopting an octahedral NO5 geometry by an O atom from the μ3-OH group, two O atoms from two carboxylates, two O atoms and a N atom of the teaH2− ligand with Co−N distances of 1.972(7)−1.983(7) Å and Co−O distances being in the range 1.874(6)−1.922(6) Å. All DyIII atoms are eightcoordinated, having a distorted square-antiprismatic O8 environment with Dy−O distances of 2.280(5)−2.471(6) Å through three μ3-OH groups, two O atoms of the different carboxylate moieties, two O atoms from two amino alcohol ligands, and a H2O molecule completing the coordination sphere of DyIII atoms. The hydroxyl groups, protonated ethanolic groups of teaH2− ligands, and coordinated and crystallization H2O molecules as well as NO3− anions form an extended hydrogen-bonded network in 4 (Table S3 and Figures S5 and S6). Modeling of the Magnetic Properties of Clusters 2−4. The different geometrical structures and magnetic composition of the clusters under examination result in their different

Figure 4. Molecular (XYZ) and local (XiYiZi) coordinate systems (the Y and Yi axes are perpendicular to the figure surface). G


Article

Inorganic Chemistry ion and counterclockwise for another ion around the Y axis by the angle α/2). After this transformation, the local ZFS tensors acquire the form ⎞ ⎛ 1 2 0 ± D sin α ⎟ ⎜−D/3 + D sin (α /2) 2 ⎟ ⎜ ⎟ Di = ⎜ 0 −D/3 0 ⎟ ⎜ 1 ⎜⎜ ± D sin α 0 2D/3 − D sin 2(α /2)⎟⎟ ⎠ ⎝ 2

(3)

The high-temperature magnetic behavior of the compound under study indicates the presence of a temperatureindependent paramagnetic (χTIP) contribution to the magnetic susceptibility. This contribution is also accounted for in analysis of the magnetic behavior. The values of the magnetization and magnetic susceptibility for an arbitrary direction of the applied magnetic field are calculated as M(θ , φ) = NAkBT

∂ {ln Z[H(θ , φ)]} ∂H(θ , φ)

χ (θ , φ) = M(θ , φ)/H(θ , φ)

Figure 6. Magnetization versus external magnetic field for cluster 3: symbols, experimental data measured at 1.9 K; solid line, theoretical curve calculated with D = −3.8 cm−1, gav = 2.455, and Jex = −1.36 cm−1.

ions are in the low-spin configuration and possess a diamagnetic ground state. In contrast, the CoII ions are in the high-spin configuration and determine the magnetic behavior of the studied complex. Each CoII ion is in a mixed-ligand environment formed by four O ions and one N ion. The nearest surroundings of the CoII ions are intermediate between a square pyramid and a trigonal bipyramid. As a result, the orbital angular momentum of the Co ion is quenched, and each Co ion can be treated as S = 3/2 with strong local anisotropy described by the ZFS tensor. To avoid overparameterization, we assume that only the axial ZFS parameter is nonzero. The presence of N atoms in the mixed nearest surroundings of the Co ions allows one to describe the system as trigonalbipyramidal with the anisotropy axis directed toward the N atom. Structural analysis demonstrates that from the magnetic point of view the studied complex can be regarded as two CoII dimers. The exchange interaction within each of these dimers takes place via the bridging N atom and is relatively strong. The exchange interaction between Co ions from different dimers takes place through the long bridge consisting of three N ions and is expected to be much weaker than that within the CoII dimers. So, we neglect this weak exchange and regard the studied complex as two noninteracting Co dimers. As a consequence, the magnetic behavior of cluster 2 can be calculated similarly to the case of cluster 3 with the use of eqs 1−5. For the local zi axes directed toward the N ions, the angle α is about 108°. During calculation of the magnetic susceptibility, the contribution of χTIP has been taken into account as well. The results of the theoretical simulation of the magnetic behavior are presented in Figures 7 and 8 as solid lines. The best-fit parameters are parts of the figure captions. The exchange interaction was found to be antiferromagnetic, which explains the decrease of the χT product with a lowering of the temperature. The obtained value of the axial ZFS parameter is in the range of these values for five-coordinated Co ions.24 The presented model describes well the experimental observations. Cluster 4. The average bond distances Co−O and Co−N are 1.894 and 1.977 Å, respectively, and testify to the presence of the magnetically silent low-spin CoIII ions in the complex under examination. Therefore, the magnetic properties of the complex are only determined by its three DyIII ions. For strongly screened 4f electrons of Ln ions, a sufficiently adequate approximation is the allowance for the interaction of these ions with the ligands of the first coordination sphere. The

(4) (5)

where Z is the partition function and kB and NA are the Boltzmann constant and Avogadro number, respectively. Angles θ and φ describe the orientation of the magnetic field with respect to the molecular coordinate system. The powderaveraged magnetic susceptibility is determined as χav = (χx + χy + χz)/3, whereas for calculation of the magnetization, the averaging over all possible orientations of the external magnetic field is performed. The proposed model satisfactorily explains the observed direct-current (dc) magnetic behavior (χT vs temperature and magnetization vs magnetic field) of the studied complex (Figures 5 and 6).

Figure 5. Temperature dependence of χT for cluster 3: symbols, experimental data; solid line, theoretical curve calculated with D = −3.8 cm−1, gav = 2.455, Jex = −1.36 cm−1, and χTIP = 0.003 cm3 mol−1 (for each ion).

The best-fit parameters are parts of the figure captions. The obtained values of the local parameters (D and gav) are typical for CoII ions in the square-pyramidal environment. The small value of the superexchange parameter Jex agrees with the fact that the exchange interaction takes place through long bridges including diamagnetic CoIII ions. Cluster 2. The complex under study consists of four CoIII and four CoII ions. The structure of this complex is presented in Figure 2. Analysis of the bond lengths indicates that all CoIII H


Article

Inorganic Chemistry A p|m| (pc)

m

= ( −1)

Zαe 2⟨r p⟩(1 − σp) 1

∑

(R α ) p + 1

α

2

[Cpm(ϑα , φα)

+ Cpm *(ϑα , φα)]

Bp|m| (pc) = ( −1)m ∑

Zαe 2⟨r p⟩(1 − σp) 1 (R α ) p + 1

α

−

Cpm *(ϑα ,

2

[Cpm(ϑα , φα)

φα)]

(8)

Rα, ϑα, and φα are the spherical coordinates of the αth ligand with the effective charge Zαe. In the calculations, the following values of the radial integrals ⟨rp⟩ and shielding factors σp for the DyIII ion have been used: ⟨r2⟩ = 0.849 au, ⟨r4⟩ = 1.977 au, ⟨r6⟩ = 10.44 au, σ2 = 0.527, σ4 = −0.0199, and σ6 = −0.0316.36 The numerical values of the charges of O atoms have been identified with their formal charges ZO = −0.5. The contribution of exchange charges (ec) arising from overlap of the 4f orbitals of the DyIII ion with the ligand orbitals is described by the following expression:26,28,35

Figure 7. Temperature dependence of χT for cluster 2: symbols, experimental data; solid line, theoretical curve calculated with D = −35 cm−1, Jex = −10.4 cm−1, gav = 2.0, and χTIP = 2.2 × 10−3 cm3 mol−1 (per Co ion).

A p|m| (ec) = ( −1)m +

Cpm *(ϑα ,

Bp|m| (ec) = ( −1)m −

e 2(2p + 1) 7

α

Sp(R α) Rα

[Cpm(ϑα , φα)

φα)]

e 2(2p + 1) 7

Cpm *(ϑα ,

∑

∑ α

Sp(R α) Rα

[Cpm(ϑα , φα)

φα)]

(9)

Sp(R α) = G[Ss 2(R α) + Sσ 2(R α) + γpSπ 2(R α)]

(10)

where Figure 8. Magnetic-field dependence of magnetization for cluster 2: symbols, experimental data measured at 1.9 K; solid line, theoretical curve calculated with D = −35 cm−1, Jex= −10.4 cm−1, and gav = 2.0.

γ2 =

III

nearest ligand surroundings of each Dy ion in the {CoIII3DyIII3} complex consists of eight O atoms. To describe the magnetic properties of the cluster, first we introduce the molecular coordinate system {X, Y, Z} and three local frames of reference for the DyIII ions. The local axes {xi, yi, zi} (i = 1−3) for each DyIII ion are parallel to the molecular ones, with the DyIII ion placed in the origin of the local coordinate system. The spherical coordinates of the O ligands for each DyIII ion are given in Tables S4−S6. The crystal-field Hamiltonian acting within the space of the 4f orbitals of the DyIII ion is written in the following form: Hcf =

∑ l = 2,4,6

{Al0Cl0 +

∑

3 1 3 , γ = , γ6 = − 2 4 3 2

Sσ(Rα) = ⟨4f, m = 0|2s⟩, Ss(Rα) = ⟨4f, m = 0|2p, m = 0⟩, and Sπ(Rα) = ⟨4f, m = 1|2p, m = 1⟩ are the overlap integrals of the 4f wave functions of the DyIII ion and 2s and 2p wave functions of the oxygen ions and G is the dimensionless phenomenological parameter of the model. Numerical values of the overlap integrals used in this work have been computed with the aid of radial 4f wave functions of DyIII and 2s and 2p functions of OII given in refs 37 and 38. The crystal-field potential (11) in terms of equivalent operators39 has the form Hcf =

Alm(Cl−m + ( −1)m Clm)

∑

{al0Ol0 +

l = 2,4,6

m = 1, l

+ Blm(Cl−m − ( −1)m Clm)}

A|m|(pc) p

(11)

bml

where the parameters and are connected with the parameters Aml and Bml of the Hamiltonian Hcf (6) as follows:35

(6)

Bp|m| = Bp|m| (pc) + A p|m| (ec)

(almOlm + blmQ lm)}

m = 1, l

aml

where Cmp (ϑ,φ) = [4π/(2p + 1)]1/2Ypm(ϑ,φ) are the tensor spherical operators [Ypm(ϑ,φ) are the normalized spherical harmonics]. The crystal-field parameters Amp and Bmp in eq 6 are evaluated in the framework of the exchange-charge model of the crystal field25−35 and represented as A p|m| = A p|m| (pc) + A p|m| (ec) ,

∑

4π , 2l + 1 4π alm = Almγlm⟨J ||ξl||J ⟩ , 2l + 1 4π blm = Blmγlm⟨J ||ξl||J ⟩ 2l + 1

al0 = Al0γl 0⟨J ||ξl||J ⟩

(7)

B|m|(pc) p

where the components and originate from the interaction of the 4f electrons with the point charges (pc) of the surrounding ligands and appear as follows:

(12)

Here the parameters ⟨J∥ξ∥J⟩ (l = 2, 4, 6) represent the socalled Stevens constants α, β, and γ, which take on the values α I


Article

Inorganic Chemistry

field and the exchange interaction between the clusters of sublattices A and B taken within the mean-field approximation:

= −2/(9 × 5 × 7), β = −8/(11 × 45 × 273), and γ = 4/(33 × 7 × 112 × 132)40 for DyIII ions. Hamiltonian of Cluster 4. The molecule under examination contains three DyIII and three diamagnetic CoIII ions. The total Hamiltonian of the molecule appears as follows: H = Hclust + HIC

HA = Hclust −

A

ex where Hclust = ∑i = 1,2,3 HiDy + HDyDy is the Hamiltonian of an Dy isolated cluster, in which Hi describes the ith DyIII ion in the ex cluster and HDyDy stands for the Heisenberg exchange interaction that couples the three DyIII ions in the cluster, while the second term in eq 13, HIC, accounts for the intercluster interaction taken within the mean-field approximation. Because the CoIII ions are diamagnetic, they do not contribute to the magnetic properties. The Hamiltonian for a single DyIII ion appears as follows:

B

∑ i = 1,2,3

{JXDy(i)⟨JXDy ⟩ + JYDy(i)⟨JYDy ⟩ B

A

B

A

(19)

A

n

(m = X , Y , Z ; n = A, B)

(20)

The averaged values of the components of the total angular momentum for subsystem n (n = A, B) are

⟨JmDy ⟩ =

∑

n

⟨JmDy(i) ⟩ n

(21)

i = 1,2,3

The values ⟨JDy(i) mn ⟩ are calculated for a given magnitude and direction of the external magnetic field H(θ,φ), where the angles θ and φ describe the orientation of the applied external magnetic field with respect to the local coordinate axes of the ith Dy ion. Further eqs 19−21 are solved using a self-consistent procedure. Calculation of the Magnetic Properties of Cluster 4. With the aid of eqs 6−10 for each DyIII ion in the cluster, the crystal-field parameters (Tables S7−S9) have been obtained as functions of the only parameter G of the exchange-charge model. In fact, this model allowed a significant reduction of the number of fitting parameters: for three Dy ions instead of 27 × 3 parameters Aml and Bml in the calculations, there appears only one fitting parameter G, which characterizes the exchangecharge contribution. The eigenvalues Ei(H,θ,φ) of the cluster Hamiltonian described by the first term in eq 13 (here H is the magnitude of the external magnetic field and θ and φ are the angles of the spherical coordinate system characterizing the orientation of this field with respect to the molecular X, Y, Z frame of reference) are used for calculation of the components of the molar magnetic susceptibility

In the derivation of eq 16, the expression gJ − gL 1 SDy(i) = JDy(i) = JDy(i) gS − gL 3 (17) III

valid within the ground-state H15/2 term of the Dy ion was used. Finally, the intercluster interaction HIC in the mean-field approximation is described as i = 1,2,3

zJ ′ 9

n

(16)

∑

B

⟨JmDy(i) ⟩ = Tr{exp[−H n/kT ]JmDy(i) }/Tr{exp[−H n/kT ]}

2 ex HDyDy = − Jex (JDy(1) JDy(2) + JDy(1) JDy(3) + JDy(2) JDy(3) ) 9

HIC = −zJ ′⟨S⟩

A

where i = 1, 2, and 3 numbers the Dy ions within the Dy3Co3 complex. For both types of clusters, the mean values of the components of the total angular momentum operator are calculated as

where JDy(i) = LDy(i) + SDy(i) is the operator of the total angular momentum of the DyIII ion, gJ = 4/3 is the Lande factor for the ground-state 6H15/2 multiplet of the DyIII ion, LDy(i) and SDy(i) are the operators of the orbital angular momentum and the spin of the DyIII ion, respectively, and μB is the Bohr magneton. The exchange interaction in the Dy−Dy pairs is assumed to be of the Heisenberg type and appears as follows:

6

B

III

(15)

4 , g = 1, gS = 2) 3 L

A

+ JZDy(i)⟨JZDy ⟩}

with HDy(i) being the interaction of the ith DyIII ion with the cr nearest ligand surroundings comprising eight O ions and HDy(i) Z representing the Zeeman interaction:26,35

(gJ =

i = 1,2,3

{JXDy(i)⟨JXDy ⟩ + JYDy(i)⟨JYDy ⟩

B

HB = Hclust −

(14)

HZDy(i) = μB g JHJDy(i)

∑

+ JZDy(i)⟨JZDy ⟩}

(13)

HiDy = HcrDy(i) + HZDy(i)

zJ ′ 9

SDy(i) (18)

mol χαα = NAkT

where ⟨S⟩ is the mean value of the total spin of the cluster, J′ is the parameter of intercluster interaction, and z is the number of nearest neighbors of a given {CoIII3DyIII3} cluster. The meanfield approximation is employed to reduce the problem of interacting clusters to the problem of a single {CoIII3DyIII3} cluster in the molecular field. The low-temperature behavior of the magnetic susceptibility of the compound under examination indicates that the intercluster exchange interaction is antiferromagnetic. Therefore, further on, we subdivide the crystal into two sublattices, A and B, in such a way that clusters A have as neighbors clusters B and vice versa. For both sublattices, the Hamiltonian contains two parts and, namely, the Hamiltonian Hclust of the isolated cluster in the magnetic

∂2 ln[Z(Hα)]Hα → 0 ∂Hα2

(α = x , y , z ) (22)

where Z(Hα) =

∑ exp[−Ei(Hα)/kT ] i

(23)

is the partition function and Ei(Hα) (α = x, y, z) are the energies of the {Dy3Co3} complex in the external magnetic field. Because the total angular momentum of the ground state of a Dy ion is 15/2, the dimension of the total matrix of the cluster Hamiltonian is 16 × 16 × 16 = 4096. Besides this, the treatment of the intercluster interaction in the mean-field J


Article

Inorganic Chemistry approximation makes the fitting procedure with three parameters (G, Jex, and zJ′) even more time-consuming. To simplify this procedure and to describe properly the magnetic behavior of the {Dy3Co3} complex in the whole temperature range, first we calculate the components of the magnetic susceptibility tensor χmol αα for a single cluster with the aid of the eigenvalues Ei(H,θ,φ) of the Hamiltonian Hclust. The influence of the intercluster interaction on the principal components of the magnetic susceptibility tensor is included in the model with the aid of the following relationship:41 mol −1 (χαα )−1 = (χαα ) −λ

(α = x , y , z )

these two different ways, the correspondence between the parameters λ and zJ′ is obtained, and at the second stage of the best-fit procedure, the magnetization as a function of the external magnetic field at 1.9 K is calculated with the account of the low-lying Stark levels of each Dy ion. The procedure is repeated until the optimum coincidence between the calculated magnetic susceptibility and magnetization and the observed ones is achieved. Magnetic Properties of Cluster 4. The static dc magnetic properties of the {CoIII3DyIII3} cluster were measured in the temperature range 1.9−300 K at 1000 Oe dc field. The temperature dependence of the χT product for the powder sample for the {CoIII3DyIII3} complex calculated with the set of best-fit parameters is shown in Figure 9. The inset represents

(24)

Here λ is the molecular-field parameter that accounts for the intercluster interaction. This approximation is successfully applied42 and is nearly equivalent to the more rigorous selfconsistent-field method.43,44 Finally, the powder-averaged magnetic susceptibility is obtained as 1 χ = (χxx + χyy + χzz ) (25) 3 To calculate the magnetization versus magnetic field, we use the procedure suggested in ref 44. The calculation is performed by taking into account the whole Hamiltonian of the system (13) including the intercluster interaction (18), and it is accompanied by the self-consistent procedure described by eqs 19−21. The molar magnetization of subsystem n (n = A, B) along the given direction of the external magnetic field is calculated as44 M n = NA

∑

Figure 9. Temperature dependence of the χT product of the {CoIII3DyIII3} complex 4 calculated with the set of best-fit parameters G = 1, Jex = 0.8 cm−1, and λ = −0.027 cm−3 mol: circles, experimental data; solid lines, calculations. Inset: Magnetization versus magnetic field measured at 1.9 K and calculated at G = 1, Jex = 0.8 cm−1, and zJ′ = −0.075 cm−1.

(μ X(i) sin θ cos φ + μY(i)sin θ sin φ n

i = 1,2,3

n

+ μZ(i) cos θ )

(26)

n

where the angles θ and φ determine the field direction, NA is the Avogadro number, and μm(i) = −gJ μ ⟨JmDy(i) ⟩ n

B

(27)

n

the magnetization versus magnetic field measured at 1.9 K in the range 0−5 T. The χT plot exhibits a room temperature value of 42.6 cm3 K mol−1, which is in good agreement with the theoretical value of 42.5 cm3 K mol−1 representing the sum of the contributions from three uncoupled DyIII ions (gJ = 4/3 and JDy = 15/2). With a drop in the temperature, the χT product slightly increases and reaches a maximal value of 48.9 cm3 K mol−1 at 30 K. Upon a further decrease of the temperature, the χT product decreases rapidly to a value of 18.5 cm3 K mol−1 at 1.9 K. From Figure 9, it is seen that the magnetic susceptibility of the {CoIII3DyIII3} cluster is quite well described with the set of best-fit parameters G = 1, Jex = 0.8 cm−1, and λ = −0.027 cm−3 mol. The corresponding value of parameter zJ′ = −0.075 cm−1 was calculated as described above. The exchange interaction between the DyIII ions turns out to be a ferromagnetic one of small magnitude, which is quite common for trinuclear DyIII compounds.45−49 At the same time, our calculations reveal that even a very small intercluster interaction (λ = −0.027 cm−3 mol) plays a significant role in the behavior of the magnetic susceptibility below 70 K. When λ = 0 (Figure 9), the calculated χT product increases gradually with a decrease of the temperature and reaches a maximal value of 59.5 cm3 K mol−1 at T = 5.5 K. With a further decrease of the temperature, the χT product diminishes to 54.2 cm3 K mol−1 at T = 1.9 K. Thus, for λ = 0, the model does not reproduce the χT values at temperatures up to 50 K.

III

is the magnetic moment of the ith Dy ion in subsystem n along the direction m (m = X, Y, Z). The molar magnetization of the whole sample along the direction of the external magnetic field is given by the relationship 1 M(H , θ , φ) = [MA (H , θ , φ) + MB(H , θ , φ)] (28) 2 The magnetization of the powder sample is obtained by averaging over the field direction: M=

1 4π

∫0

π

sin θ dθ

∫0

2π

d φ M (H , θ , φ )

(29)

Further on, we apply the best-fit procedure for the description of the magnetic susceptibility and field dependence of the magnetization for the {CoIII3DyIII3} complex. This procedure is performed as follows. At the first stage, the magnetic susceptibility χT is calculated for a given set of parameters G, Jex, and λ with the aid of eqs 22−25. At temperature T = 1.9 K, at which the field dependence of magnetization is measured, only the low-lying Stark levels of the Dy ions are populated. As a result, at this temperature, the principal values of the magnetic susceptibility for a given set of parameters G, Jex, and zJ′ can be calculated as χα = Mα/H (α = x, y, z), where the magnetization is calculated with the aid of eqs 26−28. By a comparison of the susceptibilities calculated in K


Article

Inorganic Chemistry In order to reveal the individual contributions of the DyIII ions comprising the {CoIII3DyIII3} cluster to its magnetic behavior, further on we calculate the χiααT (α = X, Y, Z; i = 1, 2, 3) components for each ion. It goes without saying that in these calculations we use the parameter G = 1 obtained from the best-fit procedure and, of course, neglect the intra- and intercluster exchange. Then, for each Dy ion, we pass from the molecular frame (X, Y, Z) to the local frames (Xi, Yi, Zi) (i = 1, 2, 3; Figure 10) in which the χiαβT

Figure 12. Temperature dependence of χT for the Dy2 ion in 4 calculated with G = 1 and ZO = 0.5.

Figure 10. Mutual orientation of the molecular frame (X, Y, Z) and the local frames (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3) in which the components χzzT(Dy1), χzzT(Dy2), and χzzT(Dy3) for the Dy ions in cluster 4 take on their maximum values.

tensor takes on the diagonal form and the χiZZT (i = 1, 2, 3) components take on their maximum values. For the Dy(i) complexes, the parts of the rotated (local) frames e′αi (α = X, Y, Z) have the following components in the molecular frame of reference: e′X1 = {0.1599, 0.9803, 0.1162}, e′Y1 = {−0.2823, 0.1582, −0.9462}, e′Z1 = {−0.9459, 0.1185, 0.3020}, e′X2 = {0.1795, −0.9633, −0.1996}, e′Y2 = {0.7942, 0.26163, −0.5484}, e′Z2 = {0.5805, −0.0601, 0.8120}, e′X3 = {0.8803, 0.4741, 0.0166}, e′Y3 = {0.4700, −0.8764, 0.1049}, and e′Z3 = {0.0643, −0.0845, −0.9943}; here the indices 1, 2, and 3 relate to the Dy1, Dy2, and Dy3 ions, respectively. The calculated temperature dependence of the χiααT (α = Xi, Yi, Zi) components for each DyIII ion in its local frame is presented in Figures 11−13. At temperature T = 1.9 K, for all DyIII ions, the χiXXT and χiYYT components are close to zero, while the χiZZT components attain values of 35.3 cm3 K mol−1 (Dy1), 35.4 cm3 K mol−1 (Dy2), and 35.7 cm3 K mol−1 (Dy3). With the temperature increase, the χiZZT components reach

Figure 13. Temperature dependence of χT for the Dy3 ion in 4 calculated with G = 1 and ZO = 0.5.

their maximal values of 36.6 cm3 K mol−1 (Dy1), 36.7 cm3 K mol−1 (Dy2), and 37.1 cm3 K mol−1 (Dy3) at T = 9 K. A further increase of the temperature reveals a significant difference between the transverse components of χiXXT and χiYYT for the Dy1 ion, testifying thus that this ion does not manifest SMM behavior. Another picture is obtained for Dy2 and Dy3 ions (Figures 12 and 13). For these ions in the whole temperature range, the χiXXT and χiYYT components are almost equal, while χiZZT is much higher. However, this difference decreases with increasing temperature. The Stark structures of the Dy2 and Dy3 ions obtained with the optimal set of best-fit parameters (Figures 14a and 15a), which fit the magnetic susceptibility and magnetization of the {CoIII3DyIII3} complex, principally evidence the negative axial anisotropy for these ions and their potential SMM behavior. For all Stark levels of these two ions, the mean value JkZ̅ = ⟨ψκ|JẐ |ψκ⟩ of the projection of the total angular momentum was calculated with the aid of the wave function ψκ = ΣJZ CJkZ|JZ⟩ obtained from diagonalization of the crystal field. It was obtained that JkZ̅ decreases with an increase of the level energy; thus, a barrier for the reversal of magnetization is formed. At the same time, for each level in Figures 14a and 15a, the mean value of the total angular momentum generally differs from half-integers, thus testifying to the presence of the rhombic component in the crystal fields acting on the Dy2 and Dy3 ions. Namely, this fact leads to the appearance of the maximum in the ac magnetic susceptibility in the presence of constant magnetic field, which suppresses tunneling. The low-temperature spatial distributions of the magnetization for Dy2 and Dy3 ions in the {CoIII3DyIII3} cluster are

Figure 11. Temperature dependence of the χT product of the Dy1 ion in 4 calculated with the set of best-fit parameters G = 1 and ZO = 0.5. L


Article

Inorganic Chemistry

Figure 14. (a) Scheme of the energy levels of the Dy2 ion in 4 calculated with G = 1 and ZO = 0.5. For each level, the mean value of the operator JZ is indicated. (b) Spatial distribution of the magnetization at T = 1 K for the Dy2 ion calculated with the set of best-fit parameters at the fixed magnitude H = 0.1 T of the external magnetic field. (c) Cross section (θ = π/2) of the magnetization M(θ,φ) surface at H = 0.1 T.

Figure 15. (a) Scheme of the energy levels of the Dy3 ion in 4 calculated with G = 1 and ZO = 0.5. For each level, the mean value of the operator JZ is indicated. (b) Spatial distribution of the magnetization at T = 1 K for the Dy3 ion calculated with the set of best-fit parameters at the fixed magnitude H = 0.1 T of the external magnetic field. (c) Cross section (θ = π/2) of the magnetization M(θ,φ) surface at H = 0.1 T.

similar (Figures 14b and 15b) and have dumbbell shape. The corresponding cross sections (θ = π/2) of the magnetization M(θ,φ) surface (Figures 14c and 15c) at 1 K reveal the small difference between the Mx and My components, in agreement with the temperature dependence of χiXXT and χiYYT given in Figures 12 and 13.

antiferromagnetic exchange. It has been demonstrated that two of the DyIII ions in 4 manifest SMM behavior. The strong rhombic component of the crystal field acting on the third DyIII ion damps its SMM behavior.

CONCLUSION A facile synthetic pathway to the preparation of novel polynuclear homo- and heterometallic Co-based clusters, [NaCo4(O2CCMe3)6(HO2CCMe3)2(teaH)2(N3)] (in two polymorphic modifications 1 and 1a), [Co8(O2CCMe3)10(teaH)4(N3)](Me3CCO2)·MeCN·H2O (2), [NaCo4(O2CCMe3)4(teaH)2(N3)(NO3)2(H2O)2]·H2O (3), and [Co3Dy3(OH)4(O2CCMe3)6(teaH)3(H2O)3](NO3)2·H2O (4) clusters has been developed. All of them have been characterized by single-crystal X-ray diffraction analysis. Their magnetic properties have been fully studied both experimentally and theoretically. Different theoretical models have been applied to gain insight into the observed magnetic behavior. The model for heterometallic Co/Dy cluster 4 takes into account the crystal fields acting on the DyIII ions, the ferromagnetic coupling of the DyIII ions in the cluster, and the intercluster

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b02827. Asymmetric units with atom-numbering schemes for 1− 4, tables of hydrogen bonds, tables of spherical coordinates of the ligands, and crystal-field parameters of the Dy ions in 4 (PDF) X-ray crystallographic data in CIF format (CIF) X-ray crystallographic data in CIF format (CIF) X-ray crystallographic data in CIF format (CIF) X-ray crystallographic data in CIF format (CIF) X-ray crystallographic data in CIF format (CIF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel: +41 31 6314296 (S.-X.L.). M


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Inorganic Chemistry *E-mail: [email protected]. Tel: +373 22 738604 (S.I.K.). *E-mail: [email protected]. Tel: +373 22 738154 (S.G.B).

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ORCID

Shi-Xia Liu: 0000-0001-6104-4320 Svetlana G. Baca: 0000-0002-2121-2091 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Swiss National Science Foundation (Grant SCOPES IZ73ZO_152404/1). REFERENCES

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