Synthesis, Characterization, and Modeling of Magnetic Properties of a

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Synthesis, Characterization and Modeling of Magnetic Properties of a Hexanuclear Aminoalcohol-Supported {Co Co Dy } Pivalate Cluster II2

III2

III2

Ioana Radu, Victor Ch. Kravtsov, Karl W. Krämer, Silvio Decurtins, Shi-Xia Liu, Oleg Reu, Serghei Ostrovsky, Sophia Klokishner, and Svetlana G. Baca J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b01378 • Publication Date (Web): 21 Mar 2016 Downloaded from http://pubs.acs.org on March 22, 2016

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The Journal of Physical Chemistry

Synthesis, Characterization and Modeling of Magnetic Properties of a Hexanuclear Aminoalcohol-Supported {CoII2CoIII2DyIII2} Pivalate Cluster Ioana Radu,† Victor Ch. Kravtsov,† Karl Krämer,‡ Silvio Decurtins,‡ Shi-Xia Liu,‡ Oleg S. Reu,† Serghei M. Ostrovsky,† Sophia I. Klokishner,†,* and Svetlana G. Baca†,* †

Institute of Applied Physics, Academy of Sciences of Moldova, Academiei 5, MD2028

Chişinau, R. Moldova ‡

Departement für Chemie und Biochemie, Universität Bern, Freiestrasse 3, 3012-Bern,

Switzerland

ABSTRACT:

A

heterometallic

hexanuclear

mixed-valence

Co-Dy

cluster

[Co4Dy2(OH)2(O2CCMe3)8(HO2CCMe3)2(teaH)2(N3)2]·2(EtOH) (1) has been prepared from the reaction of dinuclear Co(II) pivalate with triethanolamine and azide ligands and characterized by elemental analysis, IR spectroscopy and X-ray crystallography. The metal atoms in the {CoII2CoIII2DyIII2} cluster core are bridged by two µ3-hydroxy groups, two azide N3− anions, six pivalate residues and two doubly deprotonated teaH2− ligands. A theoretical model has been developed to explain the magnetic behavior of 1. The model takes into account the crystal fields

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acting on the DyIII ions and the anti- and ferromagnetic exchange interactions in the pairs Co-Dy and Co-Co, respectively. The Stark structure for the DyIII ions is calculated with due account of the covalence effects within the frames of the exchange charge model of the crystal field. It is demonstrated that at low temperatures the magnetic properties of the cluster are determined by the interaction of the ground state Kramers doublet of the CoII ion with those Stark levels of the DyIII ions, for which the energies are smaller than the spin-orbital coupling parameter. At higher temperatures, the population of the CoII ion multiplets with the angular momentum values 3/2 and 5/2 leads to the increase of the magnetic susceptibility. The observed temperature dependence of the χMT product and field dependence of the magnetization are satisfactorily explained within the framework of the suggested model.

1. INTRODUCTION The study of the magnetic behavior of 3d metals combined with lanthanides was pioneered by the Gatteschi group in the 1980s1-3 and then continued in the 1990s by the group of Winpenny4 and others.5,6 Recently the design and construction of 3d-4f compounds has attracted a new wave of interest not only due to their potential applications in the field of magnetism,7-10 luminescence,11-15 gas adsorption and bimetallic catalysis16-18 but also due to their fascinating architectures and topologies.19-28 Heteronuclear and luminescent lanthanide compounds have also been extensively employed as phosphors, representing a new class of luminescent probes for biological applications,29-31 whereas heteronuclear endohedral lanthanide clusters within C80 exhibit a variety of magnetic phenomena.32,33 The first example of a series of custom-designed, catalytically active 3d/DyIII coordination clusters, has been reported by Kostakis et al.34 A


2

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careful choice of the organic ligand has allowed the synthesis of coordination clusters that remain intact in solution and display a remarkable catalytic activity. From another perspective, the interest in 3d-4f complexes has received the greatest impetus since single-molecule magnets (SMMs) of this type demonstrate large angular momentum, considerable single ion anisotropy and much stronger exchange interactions as compared with those between 4f-ions. SMMs of 3d-4f type are potential candidates for molecular spintronic devices and quantum computing in the future.35-42 Thus, many interesting 3d-4f compounds have been obtained and examined. However, just a few studies on the interaction between lanthanides and transition metal ions have been reported so far.43-48 It is well known that in heterometallic clusters magnetic interactions between 3d and 4f ions are considerably stronger than 4f-4f interactions and rather complicated, and the combination of these two types of metal ions into a single material may produce unexpected properties. To better understand the origin of the 3d-4f interactions and their effect on the magnetic behavior, the construction of small complexes with a limited number and accurately chosen composition of 3d and 4f metal ions is essential. The exchange interaction manifests itself more pronounced when the metal ions comprising the cluster possess ground states with large angular momenta. From this point of view the combination, for instance of CoII ions in an octahedral arrangement and lanthanide ions such as DyIII (6H15/2), TbIII (7F6) and HoIII (5I8) is promising.49-60 With the aim to elucidate the magneto-structural correlations in 3d-4f clusters and to evaluate the effect of magnetic interactions between 3d and 4f ions, we herein report the synthesis, structural characterization and magnetic behavior of a novel hexanuclear mixed-valence heterometallic aminoalcohol supported {CoII2CoIII2DyIII2} pivalate cluster, formulated as


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[Co4Dy2(OH)2(O2CCMe3)8(HO2CCMe3)2(teaH)2(N3)2]·2(EtOH) (1). A theoretical model for the description of the magnetic properties of the obtained cluster is also presented in detail.

2. EXPERIMENTAL DETAILS Materials and methods. All reactions were carried out under aerobic conditions using commercial grade solvents. [Co2(µ-OH2)(O2CCMe3)4(HO2CCMe3)4] was prepared as reported elsewhere.61 Commercially available ligands were used without further purification. Infrared spectra were recorded on a Perkin-Elmer Spectrum One spectrometer using KBr pellets in the region 4000 - 400 cm–1. Magnetic susceptibility data for 1 were obtained using a Quantum Design MPMS-5XL SQUID magnetometer. The data were acquired in the temperature range 1.9 - 300 K and at a field of 1 kG. All data were corrected for the contribution of the sample holder and the diamagnetic contributions of compound 1 (-0.45 × molecular weight × 10−6 cm3 mol−1). X-ray crystallography. Diffraction datasets for 1 were collected on an Oxford Xcalibur CCD diffractometer with graphite-monochromatized Mo-Kα radiation. The summary of the data collection and the crystallographic parameters of compound 1 is listed in Table 1. After collection and integration, the data were corrected for Lorentz and polarization effects and absorption. 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.62 All non-hydrogen atoms in cluster 1 were refined with anisotropic displacement parameters. Hydrogen atoms were placed in fixed, idealized positions and refined as rigidly bonded to the corresponding atom. Some methyl groups of carboxylate ligands in 1 were found to be disordered; application of restraints provided reasonable geometrical parameters and thermal displacement coefficients. The selected bond distances are given in Table 2 and angles in Table S1. The asymmetric unit of


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1 with the numbering scheme is presented in Figure S1 and a packing diagram in Figure S3. The Figures were prepared with DIAMOND 3.2k software package63 and Mercury SCD 3.6 program. Crystallographic data for the structure 1 has been deposited with the Cambridge Crystallographic Data Centre under CCDC 1451999.

Table 1. Crystal Data and Structure Refinement for 1 Empirical formula

C66H132Co4Dy2N8O30

M

2078.51

T/K

293(2)

λ/Å

0.71073

Crystal system

tetragonal

Space group

I41/a

a/Å

36.1167(8)

b/Å

36.1167(8)

c/Å

14.5070(4)

V/Å3

18923.1(10)

Z

8

Dc /g cm−3

1.459

µ/ mm−1

2.317

F(000)

8512

θ range for data collection/°

2.919 to 25.049

Index ranges

−42 ≤ h ≤ 42; −37 ≤ k ≤ 42; −10 ≤ l ≤ 17

Reflections collections

21332

Number of unique refls. (Rint)

8337 (0.056)

R1, wR2,

0.0502, 0.1039

Largest diff. hole and peak / e Å−3

0.976, −0.565


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Table 2. Selected Bond Distances (Å) for 1 Dy1−O5

2.273(4)

Co1−O12

2.104(4)

Dy1−O13

2.289(4)

Co1−O2

2.147(2)

Dy1−O8

2.328(4)

Co1−N2

2.065(5)

Dy1−O1

2.343(4)

Co1−O12_a

2.246(4)

Dy1−O3

2.394(4)

Co2−O13

1.887(4)

Dy1−O6

2.395(4)

Co2−O12

1.908(4)

Dy1−O10

2.422(5)

Co2−O9

1.913(4)

Dy1−O7

2.477(5)

Co2−O1

1.925(4)

Co1−O4

2.064(4)

Co2−N2_a

1.952(5)

Co1−O1

2.099(4)

Co2−N1

1.985(5)

Symmetry transformations used to generate equivalent atoms: a = 1-x,-y,-z

Synthesis of [Co4Dy2(OH)2(O2CCMe3)8(HO2CCMe3)2(teaH)2(N3)2]·2(EtOH) (1). [Co2(µOH2)(O2CCMe3)4(HO2CCMe3)4] (0.18 g, 0.19 mmol), [Dy(NO3)3]·6H2O (0.06 g, 0.13 mmol), H3tea (0.03 g, 0.2 mmol), and NaN3 (0.006 g, 0.09 mmol) were stirred in a mixture of MeCN and EtOH (1:1, 6 ml) for 30 min at room temperature and then the mixture was filtered. The filtrate was kept in a closed vial with small holes for slow evaporation of solvent for 3 months. Then a white precipitate was filtered off and the filtrate was left for further evaporation. Green crystals suitable for X-ray analysis were isolated after 3 months, washed with ethanol, and air dried. Yield: 0.005 g, 2.6% (based on Co pivalate). Elemental analysis calcd. for C66H132Co4Dy2N8O30 (2078.52 g mol–1): C, 38.06; H, 6.39; N, 5.38%. Found: C, 37.69; H, 6.45; N, 4.96%. IR (KBr pellet): ν = 3397 (br. m), 2959 (m), 2927 (m), 2870 (sh), 2083 (vs), 1687 (m), 1596 (vs), 1543 (sh), 1484 (s), 1459 (sh), 1423 (s), 1375 (sh), 1361 (s), 1291 (m), 1228 (m), 1208 (sh), 1103 (m),


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1051 (w), 954 (w), 934 (sh), 905 (m), 811 (w), 789 (w), 757 (w), 714 (w), 607 (m), 538 (sh), 510 (w), 486 (m) cm−1.

3. RESULTS AND DISCUSSION 3.1. Synthesis and characterization. The reaction of dinuclear cobalt(II) pivalate [Co2(µOH2)(O2CCMe3)4(HO2CCMe3)4] with dysprosium(III) nitrate hexahydrate, triethanolamine (teaH3) and sodium azide in a mixture of MeCN/EtOH (1:1) at ambient temperature resulted in a new heterometallic hexanuclear mixed-valence {CoII2CoIII2DyIII2} cluster with composition [Co4Dy2(OH)2(O2CCMe3)8(HO2CCMe3)2(teaH)2(N3)2]·2(EtOH) (1). Green crystals of 1 were obtained after 6 months with a small yield of ∼3%. In the IR spectrum, the characteristic strong bands related to asymmetric and symmetric stretching vibrations of the coordinated carboxylate groups were observed at 1596−1543 and 1423 cm−1. In addition, the band corresponding to the −CO2H stretching vibration of monodentate pivalic acids is located at 1687 cm−1. Multiple bands in the range of 2959−2870 cm−1 originate from the asymmetric and symmetric C−H stretching vibrations of the methyl groups in the pivalates. These are accompanied by a strong band at 1484 cm−1 arising from the asymmetric bending vibration of the methyl groups and a typical doublet at 1375−1361cm−1 from the symmetric bending vibrations in tert-butyl groups. The strong band at 2083 cm−1 can be assigned to the bridging azide ligands. The presence of solvate EtOH molecules as well as OH− groups and the monodentate pivalic acids causes the appearance of a strong OH absorption band around 3397 cm−1. 3.2. X-ray diffraction study. A single-crystal X-ray diffraction analysis showed that compound 1 crystallizes in the centrosymmetric tetragonal space group I41/a (No. 88). The asymmetric unit contains half of the cluster (two cobalt atoms, one dysprosium atom, one


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hydroxy anion, four pivalate anions, one pivalic acid molecule, one doubly protonated aminoalcohol ligand, one azide anion) and one solvent ethanol molecule (Fig. S1 in Supplementary Information). The cluster resides on a center of symmetry, therefore having Ci molecular symmetry. Charge consideration and atomic distances (BVS: bond valence sum analysis)64-66 indicate that two of four Co centers are in the 2+ oxidation state (Co1, BVS: 2.08), whereas the remaining two are in the 3+ oxidation state (Co2, BVS: 3.52). Thus, the cluster core is composed of two CoII, two CoIII, and two DyIII ions bridged by two µ3-hydroxy groups, two azide N3− anions, six bridging pivalate residues and additionally linked by two doubly deprotonated teaH2− ligands (Fig. 1a). The neutral monodentate pivalic acid and a chelating pivalate ion cup each of the DyIII centers completing the coordination sphere of the metal ions. This results in a distorted octahedral surrounding for all cobalt atoms: a NO5 donor set for CoII centers by a µ3-hydroxo atom, two O atoms from two bridging pivalates, two O atoms from different teaH2− ligands and a N atom from bridging azide; and a N2O4 donor set for CoIII centers by a µ3-hydroxo atom, an O atom from bridging carboxylate, two O atoms and a N atom from a teaH2− ligand and a N atom from bridging azide. The CoII−O bond distances are in the range of 2.064(4) – 2.246(4) Å and the CoII−N bond distance is 2.065(5) Å (see Table 2). The CoIII−ligand bond distances are shorter compared to the above mentioned CoII−ligand bond distances and are in the range of 1.887(4) – 1.925(4) Å (CoIII−O) and 1.952(5) and 1.985(5) Å (CoIII−N). The Dy atoms have an approximately square-antiprismatic O8 coordination by a µ3-hydroxo atom, an O atom from teaH2− ligand, three O atoms from three bridging carboxylates, two O atoms from chelating pivalate and an O atom from monodentate pivalic acid molecule. The Dy−O bond distances range from 2.273(4) to 2.477(5) Å. The heterometallic hexanuclear cluster can also be viewed as two {CoIICoIIIDyIII(µ3-O} triangles bridged by two azide ligands, as shown in Figure 1b, and two


8

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µ3-O atoms from one of the ethanol arm of the different teaH2− ligands. The metal-metal separations within the triangle are unequivalent and range from 3.070(1) to 3.576(1) Å. The CoII…CoIII distance between the triangles in 1 is 3.204(1) Å and the CoII…CoII distance is 3.335(1) Å (Fig. 1b).

a


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b Figure 1. (a) Structure of 1 with a partial labeling scheme. Hydrogen atoms (except µ3-hydroxo atom) and solvate EtOH molecules are omitted for clarity. Color scheme: Dy atoms, green; CoII atoms, pink; CoIII atoms, light blue spheres; N atoms, blue; O atoms, red; C atoms, grey sticks. Intramolecular hydrogen O…O bonds are shown as dotted yellow lines. (b) Highlighting the {CoIICoIIIDyIII(µ3-O)} scalene triangles bridged by azide ligands and the magnetic exchange parameters in the neighboring CoII-DyIII (J1) and CoII-CoII (J2) pairs within the hexanuclear cluster in 1. It is noteworthy that there are strong intracluster O−H…O hydrogen bonds of 2.596(7) Å between uncoordinated (O11) and bridging (O3) carboxylates (Fig. 1a). Further, hydroxyl ions (O1) are hydrogen bonded to solvate EtOH molecules (O15) with O1−H…O15 = 2.850(8) Å and the solvate EtOH molecules also form strong O15−H…O7 hydrogen bonds of 2.671(8) Å with one oxygen atom from the chelating pivalates, as shown in Figure S2. Finally, strong


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O14−H…O6 [1/4+y,1/4-x,1/4+z] hydrogen bonds of 2.781(8) Å between one uncoordinated arm of teaH2- ligands and one of the carboxylate oxygen belonging to chelating pivalates from neighboring clusters generate a three-dimensional assembly (Fig. S3).

3.3. Magnetic properties of the {CoII2CoIII2Dy2} cluster 3.3.1. Observed magnetic susceptibility. The magnetic susceptibility and magnetization measurements of 1 have been performed (Fig. 2). The χMT plot exhibits a RT value of 35.4 cm3 K mol−1, in good agreement with the sum of the theoretical value of 28.3 cm3 K mol−1 for two uncoupled DyIII ions (g = 4/3 and population of all sub-levels of the ground term at RT ) and the experimental value for two CoII ions of about 6.8 cm3 K mol−1 (includes orbital contributions). This value decreases gradually with lowering the temperature and more rapidly below 50 K to reach 23 cm3 K mol−1 at 1.9 K. The field dependence of the magnetization, measured at 1.9 K, is shown in Figure 2. The magnetization reaches a value of 16 µB at a field of 5 Tesla while approaching a slightly higher saturation value (5.3 µB are typically observed per DyIII and 3 µB count per CoII).67 35 30 -1

16

25

M/µBNA

12

20

3

χT, cm K mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


15

8 4

10 0

5

0

1

2

3

4

5

Magnetic Field / Tesla

0 0

50

100

150

200

250

300

T,K


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Figure 2. χT vs. T and magnetization vs. external magnetic field (T = 1.9 K) for the {CoII2CoIII2DyIII2} cluster 1 (circles); solid lines calculated with the set of the best fit parameters: G = 1, ZO = 0.3, J1 = - 0.25 cm−1, J2 = 0.45 cm−1 (see 3.3.3).

3.3.2. Hamiltonian of the {CoII2CoIII2DyIII2} cluster. The X-ray analysis of the compound under study shows that the two CoIII ions are diamagnetic. From this it follows that the magnetic properties of the {CoII2CoIII2Dy2} cluster are entirely determined by the paramagnetic CoII and DyIII ions. The contribution from these metal ions to the observed magnetic properties is determined by two factors and, namely, by the individual energy spectrum of each magnetic ion and their exchange interactions. Therefore, the total Hamiltonian of the cluster is represented as follows: H =

∑ (H

i =1, 2

Dy i

)

ex + H iCo + H iex + H CoCo

(1)

where the H iDy and H iCo are the Hamiltonians of single DyIII and CoII ions, H iex describes the ex exchange interaction in the pairs of neighboring Dy and Co ions (see Fig. 1) and, finally, H CoCo

is the exchange interaction of the CoII ions. The exchange interaction between the distant DyIII and CoII ions as well as the exchange interaction between the DyIII ions is not included in consideration due to its smallness as compared with other relevant interactions. The Hamiltonian of a single DyIII ion looks as follows H iDy = H cDy (i ) + H ZDy (i )

(2)

with H cDy (i ) being the interaction of the its DyIII ion with the nearest ligand surrounding comprising eight oxygen ions and H ZDy (i ) representing the Zeeman interaction Dy H ZDy (i ) = µB H ( LDy i + 2Si ) ,

(3)


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III Dy where LDy i and Si are the operators of the orbital angular momentum and the spin of the Dy

ion, respectively, and µB is the Bohr magneton. Since the energy gaps between the terms of the free DyIII ion significantly exceed the crystal field splitting of the 6H15/2 ground state multiplet, the following approximation is used Dy J , mJ LDy J , mJ = g J J , mJ JiDy J , mJ , i + 2 Si

(4)

Dy here J iDy = LDy is the operator of the total angular momentum of the DyIII ion and i + Si

g j = 4 / 3 is the Lande factor for the ground 6H15/2 multiplet of the DyIII ion. Then the operator of Zeeman interaction for this ion can be presented in the following form: Dy ( i ) H Zeem = g J µ B HJ iDy

(5)

In the model suggested herein, the symmetry of the ligand environment of each CoII ion is assumed to be approximately cubic. The proofs for this approximation will be given below in section 3.3.3. Under this assumption the Hamiltonian of a single CoII ion has the form Co H iCo = − 32 κλ Li Si µ B + H (− 32 κ LCo i + g e Si ) ,

(6)

where the first term describes the spin-orbital interaction, while the second one represents the Zeeman interaction. The factor -3/2 comes from the fact that the real angular momentum for the T1 state is equal to the angular momentum of the 4P free-ion state multiplied by -3/2, κ is the

4

orbital reduction factor. Finally, the exchange interaction in the pairs Co-Dy and Co-Co is assumed to be of Heisenberg type

2 ex H iex = − J1 SiCo J iDy , H CoCo = −2 J 2 S1Co S 2Co 3

(7)

The crystal field Hamiltonian acting within the space of the 4f orbitals of the i-th DyIII ion can be written in the following form:


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H cDy ( i ) =

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 0 0 m −m m m m −m m m   Al Cl + ∑ Al (Cl + ( −1) Cl ) + Bl (Cl − ( −1) Cl )  , l = 2,4,6  m =1,l 

∑

(8)

where Clm (ϑ , φ ) = 4π ( 2l + 1) Yl m (ϑ , φ ) are the tensor spherical operators and ( Yl m (ϑ, φ ) are 12

the normalized spherical harmonics). Since the Dy-ions in the complex have completely identical ligand surroundings, the crystal field potentials for these ions include the same spherical harmonics, and the numerical values of the parameters Alm and Blm for both ions coincide. Therefore and further on, the evaluation of the crystal field parameters Alm and Blm is described for one of the Dy ions. This evaluation has been performed in the framework of the exchangecharge model of the crystal field68-70 taking into account the effects of covalence. In this model each parameter Al|m | and Bl|m | was presented in the following form Al|m| = Al|m|( pc ) + Al|m|( ec ) , Bl|m| = Bl|m|( pc ) + Al|m|( ec ) ,

(9)

where the components Al|m|( pc ) and Bl|m|( pc ) describe the interaction of the 4f electrons with the point charges (pc) of the surrounding ligands, while the parameters Al|m|( ec ) and Bl|m|( ec ) describe the contribution of exchange charges coming from the overlap of the 4f orbitals of the DyIII ions with the ligand orbitals. The expressions for the parameters Al|m|( pc ) , Bl|m|( pc ) , Al|m|( ec ) and Bl|m|( ec ) look as follows

Al|m|( pc ) = (−1)m ∑ α

|m|( pc ) l

B

Z e 2 < r l > (1 − σ l ) 1 m Cl (ϑα , ϕα ) + Clm* (ϑα , ϕα )  , l +1 ( Rα ) 2

Z e 2 < r l > (1 − σ l ) 1 Clm (ϑα , ϕα ) − Clm* (ϑα , ϕα )  , = ( −1) ∑ l +1 ( Rα ) 2 α m

Al|m|( ec ) = (−1)m

Sl ( Rα ) e2 (2l + 1) Clm (ϑα , ϕα ) + Clm* (ϑα , ϕα )  , ∑ 7 Rα α


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Bl|m|( ec ) = (−1)m

e2 (2l + 1) Sl ( Rα ) m Cl (ϑα , ϕα ) − Clm* (ϑα , ϕα )  , ∑ 7 R α α

(10)

here Rα ,ϑα ,ϕα are the spherical coordinates of the α -th oxygen ligand with the effective charge Ze . Their numerical values for the complex under examination are given in Table S2. In our calculations the following values of the radial integrals r l been used

r 2 = 0.849

a.u.,

r 4 = 1.977

a.u.,

and shielding factors σ l have

r 6 = 10.44

a.u. and σ 2 = 0.527 ,

σ 4 = −0.0199 , σ 6 = − 0.0316 ,71 the values Sl ( Rα ) are given by the relation68,69 Sl ( Rα ) = G ( S s2 ( Rα ) + Sσ2 ( Rα ) + γ l Sπ2 ( Rα )),

γ 2 = 3 / 2, γ 4 = 1/ 3, γ 6 = −3 / 2,

where

S s ( Rα ) = 4 f , m = 0 2 s , Sσ ( Rα ) = 4 f , m = 0 2 p, m = 0 , Sπ ( Rα ) = 4 f , m = 1 2 p, m = 1

are

the overlap integrals of the 4f wave functions of the DyIII ion and 2s, 2p wave functions of the oxygen ions, the value G represents the dimensionless phenomenological parameter of the model. Numerical values of the overlap integrals used in this work have been computed with the aid of the radial 4f wave functions of DyIII and 2s, 2p functions of the O2− given in ref. 72,73 Then the crystal field potential (8) was written down in terms of equivalent operators74:

H cDy ( i ) =

 0 0 m m m m   al Ol + ∑ ( al Ol + bl Ql )  , l = 2,4,6  m =1,l 

∑

(11)

where the parameters alm and blm are connected with the parameters Alm and Blm of the Hamiltonian H cf (1) by the relations

al0 = Al0 γ l 0 J ξl J

4π , alm = Alm γ lm J ξ l J 2l + 1

4π , blm = Blm γ lm J ξl J 2l + 1

4π , (12) 2l + 1


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

here the parameters J ξl J

Page 16 of 34

(l=2,4,6) are the so called Stevens constants α , β , γ which

3 2 2 take on the values α = −2 /(9 ⋅ 5 ⋅ 7) , β = −8 /(11 ⋅ 45 ⋅ 273) and γ = 4 /(3 ⋅ 7 ⋅11 ⋅13 ) 75 for the DyIII

ion. For a single DyIII ion the crystal field parameters alm and blm expressed as functions of the parameter G are given in Table S3. The full matrix of Hamiltonian (1) including the interactions between four angular momenta as well as the interactions with the crystal and magnetic fields is rather large (the dimension of the space is 36864). To simplify the time-consuming procedure of diagonalization we assume that the nearest surrounding of the CoII ion is almost cubic and first take into account only the contribution to the magnetic properties of the ground CoII Kramers doublet with total fictitious angular momentum j = 1 / 2 . We also suppose that the energy levels of the whole cluster associated with the highest group of levels of the CoII ions with j = 3 / 2, 5 / 2 do not contribute significantly to the magnetic properties of the {CoII2CoIII2DyIII2} cluster for temperatures

kT < λ . For the indicated temperature range this approximation seems to be reasonable since for the CoII ion the parameter λ is approximately equal to −180 cm−1 and large as compared with the exchange interactions in the Co-Dy and Co-Co pairs. Actually, in the Co-Dy pairs the parameter J1 is of the order of several wavenumbers or even less due to the small overlap of the 3d and 4f orbitals. The smallness of the parameter J 2 is also expected because its value for the angle ∠ Co−O−Co = 100° is of the order of several wavenumbers.76 As to the DyIII ion for

kT < λ , only those Stark levels of the ground 6H15/2 multiplet are taken into account which energies are smaller than λ . Under the accepted approximation the exchange interactions in the pairs Co-Dy and Co-Co can be projected onto the restricted space representing the direct product


16

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of the ground Kramers doublet for the Co-ion and Stark levels arising from the splitting of the 6

H15/2 multiplet of the DyIII ion. In this approximation the Hamiltonians of exchange and Zeeman

interactions look as follows 10 50 Co ( i ) Co ex H% iex = − J1 siCo J iDy , H% CoCo = − J 2 s1Co s2Co , H% Z = geff µB Hsi 9 9

(13)

5 g eff = κ + g e Co 3 and si (i = 1, 2) represents the pseudo-spin ½ operator for the CoII ions. where 3.3.3. Calculation of the magnetic characteristics. The eigenvalues Ei (H ,θ , ϕ ) (H is the

magnitude of the external magnetic field, 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 axes) of Hamiltonian (13) are further used for the calculation of the magnetization M (T , H ,θ , ϕ ) and magnetic susceptibility χ (T ,θ ,ϕ ) : ∂ { ln[Z (T , H ,θ ,ϕ )] }, ∂H

M (T , H ,θ , ϕ ) = N A k BT

χ (T , θ , ϕ ) = M (T , H ,θ , ϕ ) H ,

(14) (15)

where Z (T , H , θ , ϕ ) = ∑ exp[− E i (H , θ , ϕ ) k B T ]

(16)

i

is the partition function. The definition of the magnetic susceptibility in Eq. (15) assumes that this value is measured in a weak magnetic field, that is, in a linear regime. The magnetization

M (T , H ) for a powder sample in the general case is then obtained by averaging over the field directions

M (T , H ) = (4π )

−1

2π

π

∫ dϕ ∫ dθ M (T , H ,θ , ϕ ) sin(θ ) dθ dϕ , 0

(17)

0


17


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Page 18 of 34

while the magnetic susceptibility χ (T ) of the powder sample in a linear regime can be approximated by

χ (T ) = (1 3)

∑

χαα (T ) ,

(18)

α = x, y , z

where χαα are the components of the magnetic susceptibility tensor. When calculating the magnetic susceptibility of the {CoII2CoIII2DyIII2} cluster for temperatures kT < λ the TIP contribution77 Co = N A µ B2 χTIP

40( g e + 32 k ) 2 81κ λ

(19)

arising from the mixing of the ground Kramers doublets of the CoII ion with its excited multiplets by the external magnetic field was taken into account as well. At this stage the time has come to explain why in the accepted model the ligand surroundings of the CoII ions in the {CoII2CoIII2Dy2} cluster are supposed to be of cubic symmetry (see Eq. (6)). With this aim a

1   single CoII ion in the axial surrounding is examined, the term ∆  L2Z − L( L + 1)  ( ∆ is the axial 3   crystal field parameter) is added to Hamilltonian (6) and the χ T product is calculated as a function of ∆ at 300 K. The results of this simulation are presented in Fig. 3. From Figure 3 it follows that at T = 300 K for a single CoII ion in the cubic surrounding ( ∆ = 0 )

χ T = 3.38cm3 K mol-1 and even small axial distortions of both signs reduce this value. At the same time, for a single DyII ion the room temperature χ T value is 14.17 cm3 K mol−1. This means that for non-interacting two DyIII and two CoII ions in cubic surrounding the χ T value at T = 300 K should be 35.10 cm3 K mol−1. Since the observed room temperature χ T value for the whole complex is 35.4 cm3 K mol−1 and the exchange interaction in the Co-Dy pair is negligibly


18

Page 19 of 34

small as compared with the thermal energy one can confirm that the consideration of the CoII ions in the cubic crystal field model is a reasonable approximation.

3.5

-1

T=300K 3.0

3

χT, cm K mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.5

2.0 -10000

-5000

0

5000

10000

-1

∆, cm

Figure 3. The χ T product for a single CoII ion at T = 300 K calculated as a function of the axial

distortion ∆ for κ = 1. The further procedure of calculation of the magnetic characteristics for temperatures kT < λ consists in the following. First, with the aid of Eq. (10) the parameters of the crystal field acting on the DyIII ion are obtained as functions of the effective charge Z of the oxygen ligand and the parameter G of the exchange charge model, then the eigenvalues Ei ( H ,θ ,φ ) of the total Dy ex Hamiltonian including the Hamiltonians H i , H% iex , H% CoCo , H% ZCo (i ) are calculated. Further on, for

the description of the magnetic properties of the complex under examination the best fit procedure is applied and the parameters G , J1 , J 2 and Z are considered as the fitting ones keeping in mind that the parameter G satisfies the condition G > 0. The procedure of calculation of χ T and magnetization M (T , H ) is repeated until for certain values of G , J1 ,


19


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Page 20 of 34

J 2 and Z the optimal coincidence between the calculated and experimental χ T and M (T , H ) curves is achieved. For temperatures kT > λ the magnetic characteristics can be simply obtained since they represent a sum of contributions coming from non-interacting CoII and DyIII ions. The calculated temperature dependence of the magnetic susceptibility and field dependence of magnetization with the parameters G = 1, ZO = 0.3, J1 = - 0.25cm−1, J2 = 0.45 cm−1 are shown in Fig. 2, ibidem the experimental data are given. The magnetic susceptibility and magnetization are well reproduced in the low temperature range T < 100 K, projecting the exchange interaction between the CoII and DyIII ions onto the basis representing the direct product of the ground Kramers doublet for the CoII ions and all Stark levels of the DyIII ions. At higher temperatures the magnetic susceptibility is not affected by the exchange interaction in the CoII-DyIII and CoIICoII pairs due to its smallness as compared with kT, and good coincidence between the calculated and experimental χT data is achieved taking into account the population of all Stark levels of the DyIII ions and all spin-orbital multiplets for the CoII ions. Within the accepted approach the agreement 1 N

∑ (( χT ) i

criteria exp i

for

the

magnetic

− ( χT )icalc ) /(( χT )iexp ) 2 = 2

4%

susceptibility

and

δM =

and 1 N

magnetization

∑(M

exp i

− M icalc

)

2

are

δ χT =

/ ( M iexp ) 2 = 4% .

i

Thus, the developed model describes quite well the magnetic characteristics of the examined cluster. The obtained signs and the values of the best fit exchange parameters are reasonable. The weak exchange interaction in the Co-Co pair is caused by the fact that the bridging group does not provide a good pathway for this interaction. The obtained positive value of the exchange parameter for the observed angle of 100° is in quite a good agreement with the dependence of this parameter on the Co-bridge-Co angle analyzed in Ref.76 As to the Dy-Co pair a wide range


20

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of ferro- and antiferromagnetic interactions was observed between the LnIII and the CoII cations.78 This justifies the possibility of existence of antiferromagnetic type exchange interaction in the Co-Dy pair revealed for the complex under examination. As to the effective charge of the oxygen ligand the best fit value is close to the formal charge of this ligand. However, a special consideration of the exchange parameters as well as of the ligand charge supported by DFT calculations is necessary to be performed.

4. SUMMARY

A new heterometallic hexanuclear mixed-valence {CoII2CoIII2DyIII2} cluster with the composition [Co4Dy2(OH)2(O2CCMe3)8(HO2CCMe3)2(teaH)2(N3)2]·2(EtOH) (1) has been prepared and characterized. A single-crystal X-ray diffraction analysis showed that compound 1 comprises neutral centrosymmetric clusters and crystallization ethanol molecules. The cluster is composed of two {CoIICoIIIDyIII(µ3-O)} triangles bridged by two azide ligands and two µ3-O atoms from two teaH2− ligands. A model for description of the magnetic properties of the exchange coupled cluster has been developed. The model takes into account the crystal fields acting on the DyIII ions and the exchange interaction in the pairs CoII-DyIII and CoII-CoII. The Stark structure of the 6H15/2 ground state multiplet of the DyIII ions is calculated in the exchange charge model of the crystal field with allowance for covalence effects. The magnetic susceptibility and magnetization data are well reproduced in the low temperature range T < 100 K, projecting the exchange interaction between the CoII and DyIII ions onto the basis representing the direct product of the ground Kramers doublet for the CoII ions and all Stark levels of the DyIII ions. At higher temperatures the magnetic susceptibility is not affected by the exchange interaction in the CoII-DyIII and CoII-CoII pairs due to its smallness as compared with kT, and


21


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Page 22 of 34

good agreement between the calculated and experimental χT data is achieved taking into account the population of the Stark levels of the DyIII ions and all spin-orbital multiplets for the CoII ions.

ASSOCIATED CONTENT Supporting Information. CIF file giving X-ray crystallographic data for 1, asymmetric unit

with atom numbering scheme and packing diagram, tables. This information is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors

Sophia I. Klokishner * - Institute of Applied Physics, Academy of Sciences of Moldova, Academiei

5,

MD2028

Chişinau,

R.

Moldova;

Tel:

+373

22

738604;

E-mail:

[email protected] Svetlana G. Baca* - Institute of Applied Physics, Academy of Sciences of Moldova, Academiei 5, MD2028 Chişinau, R. Moldova; Tel: +373 22 738154; E-mail: [email protected] Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors express their gratitude for financial support to the Swiss National Science Foundation (SCOPES project IZ73ZO_152404/1). The financial support of the Supreme


22

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Council for Science and Technological Development of the Republic of Moldova (Project No. 15.817.02.06F) is also highly appreciated.

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Synthesis, Characterization, and Modeling of Magnetic Properties of a

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