Inorganica Chimica Acta 396 (2013) 108–118

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Inorganica Chimica Acta

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Novel polynuclear architectures incorporating Co2+ and K+ ions boundby dimethylmalonate anions: Synthesis, structure, and magnetic properties

Ekaterina N. Zorina a,⇑, Natalya V. Zauzolkova a, Aleksei A. Sidorov a, Grigory G. Aleksandrov a,Anatoly S. Lermontov a, Mikhail A. Kiskin a, Artem S. Bogomyakov b, Vladimir S. Mironov c,Vladimir M. Novotortsev a, Igor L. Eremenko a

a N.S. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninsky Prosp. 31, 119991 Moscow, Russian Federationb International Tomography Center, Siberian Branch of the Russian Academy of Sciences, Institutskaya Str. 3a, 630090 Novosibirsk, Russian Federationc A.V. Schubnikov Institute of Crystallography, Russian Academy of Sciences, Leninsky Prosp. 59, 119333 Moscow, Russian Federation

a r t i c l e i n f o

Article history:Received 31 May 2012Received in revised form 28 September 2012Accepted 5 October 2012Available online 5 November 2012

Keywords:Polymeric cobalt(II) complexDimethylmalonate ligandsX-ray diffraction analysisMagnetic properties

0020-1693/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.ica.2012.10.016

⇑ Corresponding author. Tel.: +7 495 955 4817; faxE-mail addresses: kamphor@mail.ru (E.N. Zor

Bogomyakov), mirsa@list.ru (V.S. Mironov).

a b s t r a c t

The reaction of potassium dimethylmalonate (K2Me2Mal) and cobalt(II) pivalate [Co(Piv)2]n undervarious conditions resulted in {[K2Co(H2O-jO)(l-H2O)(l6-Me2Mal)(l5-Me2Mal)]�2H2O}n (1) and{[K6Co36(H2O-jO)22(l-H2O)6(l3-OH)20(l4-HMe2Mal-j2O,O0)2(l6-Me2Mal-j2O,O0)2(l5-Me2Mal-j2O,O0)8

(l4-Me2Mal-j2O,O0)12(l4-Me2Mal)6]�58H2O}n (2) (where Me2Mal2� is the dimethylmalonate dianion).Coordination polymers 1 and 2 were characterized by X-ray diffraction and magnetochemical studies.Analysis of the magnetic behavior indicates that 1 is characterized by an extremely high anisotropy ofmagnetic susceptibility and very weak spin coupling between CoII centers through malonate groups; com-pound 2 contains a highly symmetric, spherical-like Co36 metal core that exhibits low magnetic anisotropyand antiferromagnetic interactions between CoII centers. Theoretical aspects of anisotropic magneticproperties of orbitally-degenerate CoII ions in polynuclear cobalt(II) complexes are discussed.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

It is well known that, when polynuclear carboxylate complexesare constructed from malonate anions and transition metal ions,crystallization from water or water–alcohol solutions mainly givescoordination polymers with chain, layer, or frame molecular struc-tures build of the bis-chelating dianion [MII(Mal)2]2� (MII = Co, Ni,Cu, Zn) (see, for example, [1–7]). No polymeric metal-containingmalonate systems incorporating large 3d metal containing frag-ment as structural units are known to date. A promising syntheticstrategy to prepare such coordination compounds is based on theligand-deficient approach that enforces malonate anions to carryout the bridging functions. In this work, we report the preparationof two novel polymeric malonate cobalt(II) complexes with potas-sium ions, one of which contains an unusual highly symmetric,spherical-like Co36 hexanegative anion that functions as a struc-ture-forming molecular building block. These CoII complexes arestructurally and magnetically characterized. We also provide sometheoretical analysis of a complicated magnetic behavior of thesecomplexes containing orbitally-degenerate six-coordinate CoII ionswith an unquenched orbital momentum.

ll rights reserved.

: +7 495 952 1279.ina), bus@tomo.nsc.ru (A.S.

2. Experimental

2.1. Synthesis

Reagents and solvents were commercial available (Aldrich) andused without further purification. Distilled water was used forthe synthesis of new compounds. Polymeric cobalt pivalate[Co(Piv)2]n was synthesized according to a known procedure [8].The K2Me2Mal salt was prepared by the neutralization of KOH withH2Me2Mal.

2.1.1. {[K2Co(H2O-jO)(l-H2O)(l6-Me2Mal)(l5-Me2Mal)]�2H2O}n (1)[Co(Piv)2]n (0.49 g, 1.89 mmol) was added to a solution of K2Me2-

Mal (obtained from potassium hydroxide (0.42 g, 7.58 mmol) anddimethylmalonic acid (0.5 g, 3.78 mmol)) in EtOH (20 ml). The reac-tion mixture was stirred with weak heating (t = 50 �C) for 10 min toproduce a thick violet precipitate. The precipitate was filtered off,washed with EtOH, and dissolved in H2O (30 ml). The resulting crim-son solution was kept for two weeks under air at room temperature.The resulting violet crystals are suitable for X-ray diffraction analy-sis. The yield of 1 is 0.64 g (71%). Anal. Calc. for C10H20CoK2O12: C,25.59; H, 4.29. Found: C, 25.71; H, 4.38%. IR spectra, m/cm�1: 3495s, 2983 m, 2941 m, 2878 m, 2103 w, 1637 s, 1607 s, 1549 s, 1478s, 1464 m, 1441 s, 1384 m, 1357 m, 1343 s, 1207 m, 1184 m,

Table 1Crystal data and structure refinement for 1 and 2.

Compound 1 2

Formula C10H20CoK2O12 C150H374Co36K6O226

Formula weight (g mol�1) 469.39 8150.67Crystal system triclinic monoclinicSpace group P�1 P21/na (Å) 8.486(3) 22.053(1)b (Å) 10.694(4) 28.8254(14)c (Å) 11.541(4) 24.7174(12)a (�) 74.122(5) 90.00b (�) 68.625(5) 90.0248(8)c (�) 68.974(5) 90.00V (Å3) 898.0(6) 15712.5(13)Z 2 2Absorption coefficient (mm�1) 1.479 2.04Maximum and minimum

transmission0.866/0.930 0.553/0.822

Dcalc (mg/m3) 1.784 1.733Crystal size (mm) 0.10 � 0.05 � 0.05 0.33 � 0.14 � 0.10h (�) 2.58–30.34 2.3–25.5Reflection measured 9332 144142Reflection unique 3715 26388Rint 0.0252 0.0634Goodness-of-fit (GOF) on F2 1.053 0.998Final R indices [I > 2r(I)] R1 = 0.0302,

wR2 = 0.0735R1 = 0.0683,wR2 = 0.1887

R indices (all data) R1 = 0.0361,wR2 = 0.0760

R1 = 0.0884,wR2 = 0.2121

E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 109

1173 m, 1017 w, 966 w, 892 m, 844 m, 798 w, 782 w, 702 m, 580 m,533 m, 476 m.

2.1.2. {[K6Co36(H2O-jO)22(l-H2O)6(l3-OH)20(l4-HMe2Mal-j2O,O0)2(l6-Me2Mal-j2O,O0)2(l5-Me2Mal-j2O,O0)8(l4-Me2Mal-j2O,O0)12(l4-Me2Mal)6]�58H2O}n (2)

[Co(Piv)2]n (0.2 g, 0.77 mmol) was added to a solution of K2-

Me2Mal (obtained from potassium hydroxide (0.17 g, 3.04 mmol)and dimethylmalonic acid (0.5 g, 1.52 mmol)) in EtOH (20 ml).The reaction mixture was stirred with weak heating (t = 50 �C)for 10 min to produce a thick violet precipitate. The resulting sus-pension was refluxed for 90 min in a water bath. The precipitatewas filtered off, washed with EtOH, and dissolved in H2O (30 ml).The resulting crimson solution was kept for 4 weeks under air atroom temperature. The resulting violet crystals are suitable forX-ray diffraction analysis. The yield of 2 is 0.034 g (19%). Anal. Calc.for C150H374Co36K6O226: C, 22.10; H, 4.62. Found: C, 21.9; H, 4.5%. IRspectra, m/cm�1: 3535 s, 3444 m.w, 2982 m, 2203 w, 1599 s, 1541 s,1464 s, 1433 s, 1351 s, 1190 m, 935 w, 891 m, 834 m, 790 m,729 m, 652 m, 610 m, 557 m, 482 w.

2.2. Methods

Elemental analysis of the resulting compounds was carried outwith a ‘‘Carlo Erba’’ automatic C,H,N,S-analyzer. IR spectra of thecomplexes were recorded using a ‘‘Perkin Elmer Spectrum 65’’instrument in KBr pellets in the frequency range of 4000–400 cm�1. The magnetochemical measurements were performedon a Quantum Design MPMSXL SQUID magnetometer in the tem-perature range of 5–300 K in a magnetic field of up to 5 kOe. Thecalculated molar magnetic susceptibility vM was corrected forthe diamagnetic contribution. The effective magnetic momentwas calculated by the formula leff = (8vT)1/2.

2.3. X-ray analysis

X-ray diffraction studies were carried out on a Bruker SMARTAPEX II diffractometer equipped with a CCD detector (graphitemonochromator, k = 0.71073 Å). The experimental set of reflec-tions for complexes 1 and 2 was obtained using the standard meth-od [9]. Semi-empirical absorption corrections for both complexeswere applied [10]. The structures of the complexes of interest weresolved by direct methods using and refined by the least squaresmethod in anisotropic full-matrix approximation (the positionsof hydrogen atoms were fixed with UH = 0.082). Hydrogen atomswere generated geometrically and refined in the ‘‘riding’’ model.All calculations were carried out with the use of the SHELX97 pro-gram package [11]. The crystallographic data and the refinementprocedure details are given in Table 1. The structure of complex1 was determined without applying any additional restrictions, ex-cept above mentioned restrictions on hydrogens. Some of dimeth-ylmalonate groups in structure 2 are particular unordered, and asresult the lengths of similar bond C–O were essentially different.Therefore some of distances in the C–O groups of some dimethyl-malonate groups are restrained to a target value d (‘free variable’).Additionally also position multiplicity of some atom O of somemolecules water were not equal 1.0. And its sites occupation fac-tors reastrained to be constant (usually �5).

3. Results and discussion

3.1. Synthesis and structure of 1

We have found that the reaction of polymeric cobalt(II) pivalate[Co(Piv)2]n with potassium dimethylmalonate K2Me2Mal (where

Me2Mal is the dimethylmalonate dianion) in EtOH (t = 50 �C)gives a 2D-polymer {[K2Co(H2O-jO)(l-H2O)(l6-Me2Mal)(l5-Me2-

Mal)]�2H2O}n (1), which was isolated as violet crystals. Accordingto X-ray diffraction data (Table 1), polymer 1 does not incorporatethe well-known six-membered chelate rings with metal centers(Fig. S1) typical of structural units in this kind of systems, whichis unusual for polymeric coordination malonates with transitionmetal atoms in the absence of additional N-donor ligands [12,13].

The octahedral environment of cobalt(II) ions in structure 1(Fig. 1) formally consists of O atoms of four carboxylate groups,two of which belong to different dianions from two four-membered chelate fragments CoO2C, whereas the two remainingO atoms belong to two other dianions (Table 2).

3.2. Synthesis and structure of 2

It has been found that prolonged refluxing of a suspension ofcompound 1 in EtOH (90 min) gives a new coordination polymer{[K6Co36(H2O-jO)22(l-H2O)6(l3-OH)20(l4-HMe2Mal-j2O,O0)2(l6-Me2-Mal-j2O,O0)2(l5-Me2Mal-j2O,O0)8(l4-Me2Mal-j2O,O0)12(l4-Me2Mal)6]�58H2O}n (2), in which the {[Co36(H2O-jO)12(l3-OH)20(l4-HMe2Mal-j2O,O0)2(l4-Me2Mal-j2O,O0)22(l4-DMM)6]}n

6� 36-nuclear hexanega-tive anion interlinked by potassium cations are the main structuralunits (Fig. 2).

The {Co36}6� hexanegative anion is located in the crystallo-graphic center of symmetry. It should be noted that one of thethree independent potassium cations in the unit cell is disorderedand occupies two positions with �1/2 population. A fraction of themalonate ligands are also disordered; the O atoms in some of themoccupy two equivalent positions. All the metal atoms in {Co36}6�,which has a Ci symmetry, have a distorted octahedral coordinationcomprising O atoms of malonate groups, OH-groups, or water mol-ecules. Some O atoms of the malonate groups serve as bridges be-tween cobalt(II) ions. Formally, {Co36}6� incorporates only 12water molecules, 16 water molecules are coordinated to the K ions,while the remaining 58 ones are crystallization water moleculesthat are bound via hydrogen bonds.

Fig. 1. Structure of a fragment of the polymeric chain of cobalt(II) atoms in 1 and itsbonding with potassium atoms (hydrogen atoms are omitted).

Table 2Selected bond lengths (Å) and angles (�) for 1 and 2.

Bond 1 2

Co. . .Co 5.586(2) Co(i). . .Co(i) in Aa

3.11(2)–3.17(2)Co(i). . .Co(i) in Ba

3.56(2)–3.59(2)Co(e). . .Co(i) in B2.99(2)–3.05(2)

Co–O(Me2Mal) 2.0039(15)–2.2767(16) 2.018(6)–2.186(5)Co–O(l-H2O) – 2.069(6)–2.082(7)Co–O(H2O-jO) – 2.056(6)–2.066(7)Co–O(l3-O) – 2.019(5)–2.075(6)K–O(Me2Mal) 2.6601(16)–2.7862(18) 2.652(8)–2.914(10)K–O(l-H2O) 2.896(2)–2.8998(19) 2.811(8)–3.088(12)K–O(H2O-jO) 2.877(2) 2.692(11)–2.935(18)

1O1–Co1–O2 60.26(5)O7–Co1–O8 60.27(6)O3–Co1–O5 99.28(6)

2O(Me2Mal-j2O,O0)–Co(i)–O(Me2Mal-

j2O,O0)84.2(2)–86.3(2)

O(OHA)–Co(i)–O0(OHB) 105.7(2)–108.1(2)O(Me2Mal)–Co(e)–O(Me2Mal) 86.9(2)–93.4(2)O(OHB)–Co(e)–O(Me2Mal) 81.8(2)–83.9(2)

94.2(2)–96.2(2)Co(i)–O(OHA)–Co(i) 99.2(2)–101.6(2)Co(i)–O(OHB)–Co(i) 121.5(2)–123.7(3)Co(i)–O(OHA)–Co(e) 94.0(2)–96.3(2)

a See the text and Fig. 4.

110 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118

The coordination number of independent K cations in structure2 is 6; they are bound to O atoms of malonate anions and watermolecules (Fig. 2). Cations K1 and K3 are bound to the O atoms

of only one 36-nuclear complex hexaanion, whereas the K2 cationis coordinated to O atoms of dimethylmalonate dianions belongingto two different {Co36} anions, which results in zig-zag polymericchains.

The cobalt atoms in {Co36}6� form a complex architecture thatformally consists of an external cuboctahedron (12 atoms (Co(e))marked pink in Fig. 3) and an internal truncated cube (24 atoms(Co(i)) marked blue in Fig. 3). The distance from the geometric cen-ter to each Co(e) atoms is 7.7 Å, whereas the distance from the geo-metric center to each Co(i) atom is 5.7 Å.

The structure involves an uncommon (O,O0,O00,O000)-l4 bondingtype of dimethylmalonate dianions (six dianions), where all thefour O atoms of each dianion are bound to separate CoII ions(Fig. S2).

The internal CoII ions are bound to the external ones via chelatebridging O atoms of the acid dianions and via hydroxo bridges. Allthe 24 cobalt atoms of the internal frame have the same ligandenvironment. The environment of the external atoms is formedby acid anions and by bridging and monodentate-bound watermolecules.

Cobalt atoms in compound 2 are grouped into triangular frag-ments of two types (A and B, blue and pink triangles in Fig. 3b)forming the frame of the Co36 spherical-like metal core (Fig. 3b).Eight nearly isosceles triangles of type A (blue) consist of Co(i)atoms only (with the Co(i). . .Co(i) distances of 3.11(2)–3.17(2) Åand \Co(i)–Co(i)–Co(i) angles of 59.1–60.8�). Twelve triangles oftype B (pink) consist of one Co(e) atom and two Co(i) atoms (withCo(i). . .Co(i) = 3.56(2)–3.59(2) Å, Co(e). . .Co(i) = 2.99(2)–3.05(2) Å,\Co(i)–Co(i)–Co(e) = 52.9–54.2�, and \Co(i)–Co(e)–Co(i) = 71.7–73.1�) (Fig. 3b). In each triangle A, all three cobalt atoms are thevertices of conjugate triangles B (the dihedral angle between thetwo planes of the neighboring triangles A and B ranges from 107�to 110�, Fig. 3b). Triangles B have only two common vertices withtriangles A, the third cobalt atom is a vertex of the cuboctahedron(Fig. 3). Each triangle A is capped by a l3-OH bridging group,whose oxygen atom (O3M, O4M, O5M, O7M, or symmetry relatedatoms) locates at 0.92–0.95 Å out of the Co3 plane inside the cavityof a spherical Co36 frame. Distance analysis indicates that H atomsdo not form H-bonds with oxygen atoms located inside the cavityof the molecule. The hydrogen atoms of the OH-groups in the tri-angles B form bifurcated H-bonds with two oxygen atoms of thel4-bridging dicarboxylic anions (with the O(OHB). . .O(Me2Mal)distance of 3.20–3.32 Å, Fig. S3, Table S1); the oxygen atom ofthe hydroxyl group (O1M, O2M, O6M, O8M, O9M, O10M, or sym-metry related atoms) locates at 0.79–0.81 Å out of the Co3 plane.

3.3. Magnetic properties of 1 and 2

According to magnetic measurements, the vMT product of com-pound 1 decreases with the lowering temperature to reach a min-imum of 2.24 cm3 mol�1 K at 17 K (vM being the molar magneticsusceptibility per formula unit) (Fig. S4); below this temperaturevMT shows some increase (see Fig. 4a). In the temperaturerange of 20–300 K, the plot of inverse susceptibility versus temper-ature obeys the Curie–Weiss law with C and h parametersof 2.921 ± 0.006 cm3 mol�1 K and �8.7 ± 0.3 K (R2 = 0.99984)(Fig. S4), respectively. The value C = 2.921 cm3 mol�1 K is consider-ably larger than the expected spin-only value (C = 1.875 cm3 mol�1 Kfor S = 3/2 and g = 2) due to orbital contribution to the magneticsusceptibility for octahedrally coordinated CoII ions [14,15]. Atroom temperature, the effective magnetic moment of 1 is 4.83 lB

per cobalt atom, which is consistent with the experimental valuesobserved for numerous cobalt complexes with high-spin (S = 3/2)octahedral CoII centers (4.4–5.2 lB) [16,17].

The vMT product of compound 2 steadily decreases upon cool-ing from 300 to 5 K; however, in contrast to compound 1, at low

Fig. 2. Structure of a fragment of 2 (hydrogen atoms are omitted).

E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 111

temperature the vMT curve of 2 shows no kink-like feature(Fig. 5a). In the temperature range of 16–300 K, the vM

�1 versusT plot follows the Curie–Weiss law with C and h parameters of113.1 ± 0.2 cm3 K/mol (3.14 cm3 mol�1 K per CoII ion) and –13.5 ± 0.3 K (R2 = 0.99993), respectively (Fig. S5). Again,C = 3.14 cm3 mol�1 K is larger than the spin-only value for threeunpaired electrons (C = 1.875 cm3 mol�1 K). For compound 2, theeffective magnetic moment at room temperature is 29.41 lB per{Co36} molecule or 4.90 lB per cobalt atom (Fig. S5).

In the both compounds h is negative. Although a negative Weisstemperature h is often regarded as being indicative of antiferro-magnetic spin coupling, the situation with six-coordinate (quasi-octahedral) CoII centers in 1 and 2 is more complicated due tothe presence of an unquenched (first-order) orbital momentumL = 1 associated with the orbital degeneracy of the ground state.The total spin S = 3/2 of CoII is coupled with the orbital angularmomentum L = 1 to form several energy levels. Therefore, the totalspin S = 3/2 of CoII is not a good quantum number; this fact leads toa peculiar magnetic behavior of CoII ions, which differs consider-ably from that of ordinary (spin-only) S = 3/2 ions (such as Cr3+

or Mn4+). In the regular octahedral Oh symmetry, the ground4T1g(3d7) orbital level splits into the ground Kramers doublet U7,two excited quartet levels U8 and U08, and the upper Kramers dou-blet U6 (Fig. 6a).

In distorted octahedral CoII centers, the 4T1g(3d7) manifold splitsinto six Kramers doublets U(n) (n = 0–5) (Fig. 6b). The ground Kra-mers doublet U(0) is characterized by a highly anisotropic g-tensor.It is important to note that the energy separation between the U(0)

ground state and the excited states U(n) is normally much larger(>100 cm�1) than the exchange parameters J of the spin couplingbetween CoII centers (in most cases, J � 10 cm�1 or less) [15–27,29–36]. Therefore, only the ground Kramers doublet U(0) isinvolved in the exchange spin coupling between CoII magneticcenters. This implies that at low temperature CoII ion behaves as

an anisotropic magnetic center with a fiction spin s = 1/2, whose±1/2 projections correspond to the two components of the groundKramers doublet U(0). Exchange interactions of the U(0) Kramersdoublet with neighboring magnetic centers are also anisotropic:the experimental data [20–27] and theory [28] indicate that ex-change interactions between octahedral CoII centers are describedby a highly anisotropic spin Hamiltonian siJsj for a fiction spins = 1/2 (J being a 3 � 3 matrix composed of anisotropic exchangeparameters Jab, a,b = x, y, z), not by the conventional S = 3/2 isotro-pic spin Hamiltonian JSiSj. This fact complicates considerably theo-retical analysis of magnetic behavior of cobalt(II) compounds,especially for polynuclear CoII complexes.

Now we turn to the modeling of the magnetic behavior of 1 and2. For a consistent analysis of magnetic properties of CoII com-pounds, it is crucially important to provide a proper descriptionof single-center electronic and magnetic characteristics of CoII ionsin a distorted octahedral environment. In fact, the wave function ofthe U(0) ground state and energy positions of excited U(n) states arevery sensitive to distortions in the local geometry of the CoII center.In many works on the molecular magnetism of CoII compounds,this analysis is based on a conventional approach, in which thelow-symmetry splitting of the ground 4T1 energy level of CoII is de-scribed by the bL2

z � 2=3c þ EbL2x � L2

yc term, where Lx,y,z are the pro-jection operators of the effective orbital momentum L = 1(associated with the lowest 4T1 orbital triplet) and D and E arethe axial and rhombic energy splitting parameters, respectively.Here D and E are adjustable parameters, which are obtained fromthe fitting to the experimental vMT curve. In fact, the rhombic termEbL2

x � L2yc is often omitted due to overparameterization of the fit-

ting procedure. [16,17,29–36]; as will be shown below (Fig. 7and Table 3), this approximation is generally invalid for 1 and 2.Although this approach provides reasonable results for selecteddinuclear cobalt(II) complexes [29–36], its application for stronglydistorted low-symmetry six-coordinate CoII centers may generally

Fig. 3. Structure of the metal frame in 2: (a) – cuboctahedron formed by externalCo(e) atoms (pink) and a rhombic cuboctahedron formed by the internal Co(i)atoms (blue), (b) – the core formed by triangles A and B (see text). (Forinterpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)

Fig. 4. (a) Comparison of the experimental and calculated vMT product ofcompound 1, (b) calculated anisotropy of magnetic susceptibility of 1 (at 5 kOe).Black circles refer to the measured magnetic susceptibility; open circles correspondto the experimental data scaled by a factor of 1.025 to take into accountuncontrolled solvent losses and/or a diamagnetic contaminant (see text for detail).Magnetic susceptibility of 1 is highly anisotropic, especially at low temperature.This results in a rise of the experimental vMT curve below 17 K due to a magneticfield-driven orientation of microcrystals along the magnetic easy axis in powderedsamples of 1.

112 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118

be unreliable. In fact, inspection of the local structure of CoII cen-ters in 1 and 2 reveals an irregular character of distortions inthe CoO6 octahedra, which show no distinct tetragonal elonga-tion/compression axes and exhibit a considerable scatter in theO–Co–O bonds angles. This is especially true for the CoII centersin 1, in which the O–Co–O bonds angles deviate strongly from90� (Fig. 7). In this situation, we use a more realistic single-centermodel Hamiltonian for the CoII centers

H ¼Xi>j

e2

jri � rjjþ f3d

Xi

lisi þ VLF þ lBðkLþ 2SÞH; ð1Þ

where the first term represents Coulomb repulsion between 3delectron of CoII (where i and j runs over 3d electrons), the secondterm is the spin–orbit coupling, VLF is the ligand-field Hamiltonian,and the last term represents the Zeeman interaction with the exter-nal magnetic field H. In these calculations we use B = 750 andC = 3500 cm�1 Racah parameters for the Coulomb term in Eq. (1),the spin–orbit coupling constant f3d = 480 cm�1, and the k = 0.85orbital reduction factor in the Zeeman term. The ligand-field Ham-iltonian VLF is calculated in terms of the angular overlap model

(AOM) [37,38] with the AOM parameters er = 4000 cm�1 for the Oligands (at R0(Co–O) = 2.10 Å) and with the fixed ratio of er/ep =4; the radial dependence of the AOM parameters is approximatedby er;pðRÞ ¼ er;pðR0ÞðR0=RÞn with n = 4 and R0 = 2.10 Å. A similarmodel was used to analyze magnetic properties of FeII-based sin-gle-molecule magnets [39]; simplified AOM calculations were per-formed for CoII complexes to interpret their optical spectra [33].Energy levels of the U(n) Kramers doublets and the anisotropic g-ten-sor of the U(0) ground state are obtained by a numerical diagonaliza-tion of the model Hamiltonian (1) in the full set of 3d7 wavefunctions involving 120 |LMLSMSi microstates. The results of calcu-lations for the only distinct CoII center in the cobalt chains in 1 areshown in Fig. 7; results for selected CoII centers in the Co36 cluster in2 (Figs. 2, 3, S2, and S3) are presented in Table 3.

These results reveal an important difference between com-pounds 1 and 2 in the electronic structure and magnetic character-istics of CoII centers. In compound 1, the low-symmetry splitting of

Fig. 5. (a) Comparison of the experimental and calculated vMT product of the Co36

molecular cluster in 2, (b) calculated anisotropy of magnetic susceptibility of 2 (at5 kOe). The drop of the experimental vMT curve below �20 K is due to Co–Coantiferromagnetic exchange interactions with the exchange parameter J � 3 cm�1.

Fig. 6. Spin–orbit splitting of the ground 4T1(3d7) orbital triplet state of CoII ions in(a) regular octahedral coordination (Oh symmetry) and in (b) distorted octahedralcoordination.

E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 113

the ground 4T1 orbital triplet is considerably larger (�1800 cm�1)than that in all CoII centers in the Co36 core in 2 (360–800 cm�1, Ta-ble 3) due to a larger distortion of the CoO6 octahedron, Fig. 7.These energies should be compared with the total spin–orbit split-ting energy of the ground 4T1g orbital triplet in a regular CoO6 octa-hedron, which is about 900 cm�1 (at f3d = 480 cm�1; see Fig. 6a): in2 the orbital splitting energy is less than the spin–orbit splittingenergy, while in 1 their ratio is opposite. Therefore, the orbitalmomentum of CoII centers remains unquenched in 2, but it is par-tially quenched in 1. The latter fact can be clearly seen from the en-ergy level structure of the spin–orbit states U(n) in 1: six spin–orbitlevels are grouped into three close pairs (U(0) + U(1), U(2) + U(3), andU(4) + U(5)), which can be regarded as a result of a second-orderzero-field splitting (ZFS) of the three split components 4T1(1),4T1(2), and 4T1(3) of the 4T1 orbital triplet, lying at 0, 788, and1797 cm�1, respectively. (Fig. 7). As a result, the energy of the firstexcited Kramers doublet U(1) in 1 is lower (120 cm�1) than in 2(140–235 cm�1), Table 3; this can manifest in the overall behaviorof the vMT curve due to the difference in the thermal population ofthe first excited U(1) level. Calculated g-tensors of the ground Kra-mers doublet U(1) also show considerable difference. In compound1, the g-tensor of the ground state has an extremely high Ising-typeanisotropy with the principal components g1 = 0.83, g2 = 0.93, and

g3 = 8.03. By contrast, all of the CoII centers in 2 have a rhombicanisotropic g-tensor with essentially different g-components, typ-ically, g1 � 2.5, g2 � 4 and g3 � 6 (Table 3). These values are withinthe range expected for rhombically distorted six-coordinate CoII

centers [39,40]; in fact, they are close to the experimental dataon CoII complexes obtained from EPR measurements [26]). Thesefeatures have a strong impact on the anisotropy of magnetic sus-ceptibility of 1 and 2 (see below).

Based on these results, we calculate magnetic susceptibility of 1and 2 with taking into account the one-center contributions only;the role of exchange interactions is discussed below. The compo-nents Ma (a = x, y, z) of the magnetic moment M of the sample inan external magnetic field H are obtained from the conventionalequation

Ma ¼ NkBT@ ln ZðHÞ@Ha

; ð2Þ

where kB and N are the Boltzmann’s constant and Avogadro’s num-ber, respectively; Z(H) is the partition function

ZðHÞ ¼X

n

Xi

expð�EðnÞi ðHÞ=kBTÞ; ð3Þ

with EðnÞi ðHÞ being the energy of the i-th electronic state of the CoII

center number n involved in the cobalt cluster in the magnetic fieldH (for instance, in 2 n runs from 1 to 36). Then the diagonal compo-nents vaa of the tensor of magnetic susceptibility {vab} is written asvaa ¼ Ma=Ha; magnetic susceptibility of a powder sample is givenby v ¼ vxx þ vyy þ vzz

� �=3. Calculated magnetic susceptibility for 1

and 2 (at the experimental magnetic field of H = 5 kOe) is shownin Figs. 4 and 5, respectively.

In the both compounds, at T > 20 K the calculated vMT curveagrees reasonably with the experimental data. However, in 1 thecalculated vMT value is somewhat larger than the experimentalone in the whole temperature range (20–300 K). The reasons forthe discrepancy in 1 probably include the sampling/solvent lossaspects, perhaps with some diamagnetic contaminant following

Fig. 7. Calculated energy positions (in cm�1) of the split orbital components (4T1(1), 4T1(2), and 4T1(3)) of the ground 4T1 orbital triplet, those of the Kramers doublets U(n)

(n = 0–5), and the principal components (g1, g2, and g3) of the anisotropic g-tensor of the ground Kramers doublet U(0) of the CoII center in the chain compound 1. The localstructure of the CoII center is shown; selected bond angles and Co–O distances (in Å, blue numbers) are indicated. The CoO6 polyhedron is a strongly distorted octahedronwith no symmetry elements (C1 point symmetry) having no distinct elongation/compression axes. Despite this fact, the calculated g-tensor of the ground U(0) Kramers doublethas a nearly uniaxial Ising-like character, g1 = 0.83, g2 = 0.93, and g3 = 8.03. Note that energy splitting pattern of the 4T1(1), 4T1(2), and 4T1(3) orbital components isincompatible with the tetragonal-symmetry approach (D – 0, E = 0) for the ligand-field splitting Hamiltonian D[Lz

2 � 2/3] + E[Lx2 � Ly

2] used in Ref. [16,17,27,29–36]. (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 3Energy positions (in cm�1) of the split orbital components (4T1(1), 4T1(2), and 4T1(3)) of the ground 4T1 orbital tripleta and Kramers doublets U(n) (n = 0–5), and the principalcomponents (g1, g2, and g3) of the anisotropic g-tensor of the ground Kramers doublet U(0) calculated for selected crystallographically independent CoII centers in the Co36 clusterin 2.

Co(1) Co(2) Co(3) Co(5) Co(7) Co(10) Co(12) Co(15) Co(18)

4T1(1) 0 0 0 0 0 0 0 0 04T1(2) 201 618 582 617 563 592 644 522 2024T1(3) 360 807 748 758 712 805 753 750 359U(0) 0 0 0 0 0 0 0 0 0U(1) 235 140 149 143 154 146 144 157 237U(2) 439 701 667 684 646 684 694 645 438U(3) 826 987 964 982 952 973 997 939 827U(4) 919 1140 1103 1107 1080 1140 1108 1108 920U(5) 1000 1266 1227 1240 1208 1264 1245 1219 1001g1 2.87 2.24 2.28 2.30 2.32 2.20 2.28 2.24 2.86g2 3.79 4.10 4.13 4.39 4.24 3.80 4.32 3.82 3.81g3 5.92 5.88 5.85 5.60 5.75 6.16 5.67 6.18 5.93

a The energies of the 4T1(1), 4T1(2), and 4T1(3) orbital components are essentially different pointing to the fact that the rhombic term E[Lx2 � Ly

2] of the low-symmetryligand-field Hamiltonian D[Lz

2 � 2/3] + E[Lx2 � Ly

2] is not small. This implies that the commonly used tetragonal-symmetry approach (D – 0, E = 0) [16,17,27,29–36] is ratherunrealistic for compound 2.

114 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118

E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 115

drying off the solvent, because the crystals tend to lose solventmolecules rather readily. This effect can be taken into accountempirically by applying a scaling factor to the experimental vMTdata. A good correspondence between the experimental and calcu-lated vMT curves is obtained with a scaling factor of 1.025 (Fig. 4b).Below �20 K, the calculated and experimental curves show somedeviation in the both compounds; we show that its origin in com-pound 1 and 2 is different. In compound 1, upon cooling the exper-imental vMT curve exhibits a minimum at ca. 17 K and thenincreases. Formally, this can be attributed to a ferromagnetic spincoupling between CoII ions in the cobalt chain of 1. However, thistype of scenario is probably rather unlikely for several reasons.First, exchange interactions between CoII ions mediated by a longmalonate group are expected to be too weak to match the mini-mum at 17 K in the vMT curve of 1, Fig. 4a. Secondly, a low symme-try of CoII centers in 1 is generally unfavorable for ferromagnetism,which requires simultaneous orthogonally of all pairwise combina-tions of magnetic orbitals involved in two magnetically coupledCoII centers; in fact, ferromagnetic spin coupling is rather uncom-mon in CoII dinuclear complexes [16,17,29–36]. These argumentsare supported by direct microscopic calculations of the exchangeparameter in the Co–Co pair in 1, which is slightly antiferromag-netic (J = �0.6 cm�1, see Fig. 8 below). The rise of the vMT curve be-low 17 K is more likely due to a magnetic field-driven orientationof microcrystals along the magnetic easy axis at low temperaturein powdered samples of 1. Indeed, calculations indicate an extre-mely strong anisotropy of the magnetic susceptibility of 1 at lowtemperature; in fact, below 20 K vyy is about ten times larger thanvxx and vzz, Fig. 4b. This is well consistent with an Ising-like anisot-ropy of the ground-state g-tensor of 1 discussed above (see Fig. 7).

By contrast, in compound 2 the decrease in vMT below 20 K cansafely be related to an antiferromagnetic spin coupling (Fig. 5a). In-deed, at 5 K the vMT value per CoII ion is about 1.3 cm3 mol�1 K,which is well below the expected one for a magnetically isolatedCoII ion (vMT � 1.75 cm3 mol�1 K) [14–17]. A more detailed infor-mation on exchange interactions in 2 is provided below. It is note-worthy that, in contrast to compound 1, the anisotropy of magneticsusceptibility in 2 is very weak, Fig. 5b. This is well consistent witha spherical-like character of the high-symmetry Co36 metal core(Figs. 2 and 3, S2, S3). Albeit magnetic anisotropy of individual CoII

centers in Co36 is rather pronounced (as is evidenced by a highanisotropy of the ground-state g-tensor, g1 � 2.5, g2 � 4 andg3 � 6, Table 3), the total magnetic anisotropy of the Co36 molecu-lar cluster drops due to different orientations of the local magneticaxes of CoII centers. Therefore, the low-temperature magnetic mea-surements for 2 are probably free of the torquing (crystallite-orien-tation) effects observed in 1. Besides, because of a low overallmagnetic anisotropy (Fig. 5b), the Co36 molecular cluster is seem-ingly not promising as a potential single-molecule magnet(SMM) [41]; several CoII-based SMM complexes were reported inthe literature [42–44].

Now we discuss the Co–Co spin coupling and estimate exchangeparameters in 1 and 2. Some theoretical approaches have beendeveloped in the literature to calculate the spin Hamiltonian fordescribing the spin coupling between orbitally-degenerated CoII

ions [14–36]). For dinuclear CoII complexes, exchange parameterscan be derived from the fitting to the experimental vMT curves interms of a model parametric Hamiltonian, involving isotropic spincoupling �JS1S2 between the true S1 = S2 = 3/2 spins on the two CoII

centers, effective spin–orbit coupling akLS within the ground 4T1

term, and the low-symmetry splitting DbL2z � 2=3c þ EbL2

x � L2yc of

the 4T1g term; examples are described in [16,17,27,29–36]). Forsome particular cases, analytical expressions for the magnetic sus-ceptibility were derived [34]. However, in our case the use of suchapproaches is hardly possible due to severe complications dis-cussed above (especially for a giant Co36 molecular cluster). Here

we use an alternative approach based on microscopic calculationsof exchange parameters in terms of a many-electron superex-change model described in [45].

In these calculations, the set of electron transfer parameters tij

(which are one-electron matrix elements connecting magnetic 3dorbitals (3di(A) and 3dj(B); i and j are orbital indexes, i, j = xy, yz,zx, x2 � y2, and z2) on two CoII ions in the exchange-coupled pairCoII(A)–CoII(B), tij = hdi(A)|h|dj(B)i) are obtained from extendedHuckel calculations (using standard atomic parameterization[46]) for the actual exchange-coupled cobalt pairs in 1 and 2 (seeFig. 9 below). Electron transfer parameters are derived by projec-tion of 3d-rich molecular orbitals of the CoII(A)–CoII(B) pair ontopure 3d atomic orbitals of two metal atoms, as described in [47].The Co(A)MCo(B) charge-transfer energy is set to 65 000 cm�1

(8 eV); this approach has been previously used to analyze magneticproperties of NiII compound [48]. More details of these calculationsare reported in the Supplementary data. Herein our calculationsare limited to the isotropic spin Hamiltonian only for the true spinS = 3/2 of CoII, that describes exchange interaction between twoorbitally degenerate CoII ions (A and B) with the spin–orbit cou-pling switched off. Generally, this Hamiltonian is written asH = �JSASB + TSASB, where J is a constant and T is an orbital operator(represented by a 9 � 9 traceless matrix, see Supplementary data)acting on the orbital part of wave functions in the space 4T1g

(A) � 4T1g(B) of the dimension 12 � 12 = 144. The aim of this workis to estimate the exchange parameter J for the cobalt pair in 1(Fig. 8) and for selected representative exchange-coupled CoII pairsin 2 (Fig. 9); in addition, we examine so-called Lines’ approach, inwhich the orbitally-dependent term TSASB is omitted [49].

First we calculate the exchange parameter J in the isotropic spinHamiltonian �JSASB (for SA = SB = 3/2) that acts in the truncatedspace of wave functions 4T1(1A) � 4T1(1B) of the dimension4 � 4 = 16; here 4T1(1A) and 4T1(1B) are the lowest states (orbitalsinglets) resulting from the orbital splitting of the 4T1 orbital tripletin distorted CoII(A) and CoII(B) centers (see Fig. 7 and Table 3). Thisapproach is based on the fact that on each CoII center the energyseparation between the 4T1(1) and 4T1(2) orbital components ismuch larger than the exchange parameter (J � 10 cm�1 or less)(Fig. 7). Calculations show that the spin coupling in 1 is weaklyantiferromagneic, J = �0.6 cm�1 (Fig. 8). This result is consistentwith the experimental data on CoII malonate complexes indicatingweak antiferromagnetic interactions between CoII ions mediatedby malonate groups [50]. We can therefore conclude that weak ex-change interactions have virtually no effect on the magnetic sus-ceptibility of 1 in the temperature range of 5–300 K; the increaseof vMT below 17 K is caused by the effect of strong anisotropy ofthe magnetic susceptibility, as discussed above. For the two maintypes of cobalt pairs in 2 we obtain J = �2.2 and �3.5 cm�1, respec-tively, Fig. 9. Qualitatively, these values are reasonably consistentwith the onset point (�20–25 K) of the drop of the vMT curve of2 at low temperature. Approximately, the onset temperature isestimated by T0 � 6J/kB, where 6J is the total spin energy splittingin exchange-coupled CoII-CoII pairs resulted from an isotropic spincoupling �JSASB (SA = SB = 3/2, with the spin–orbit couplingswitched off, see Figs. 8 and 9). Below this point antiferromagneticexchange interactions are well seen in the vMT curve (Fig. 5); thus,with J � �3 cm�1 we obtain T0 � 25 K in 2. It is important to notethat calculated exchange parameters in 1 and 2 are within therange of J values observed in small CoII carboxylate clusters, inwhich exchange interactions are mostly antiferromagnetic; repre-sentative examples were recently reviewed in [34].

In conclusion, we examine the applicability of the Lines’ ap-proach [49] to the CoII complexes 1 and 2. For this, we repeatsuperexchange calculations for the aforementioned Co pairs shownin Figs. 8 and 9 applying projection of the charge-transfer states ofthe CoII(A)–CoII(B) pair onto the extended (12 � 12) space of wave

Fig. 8. The structure of the CoII(A)-CoII(B) exchange-coupled pair in 1 and the calculated exchange parameter (antiferromagnetic, J = –0.6 cm�1) in the isotropic spinHamiltonian H = �JSASB (SA = SB = 3/2) describing spin coupling between the two lowest orbital components 4T1(1A) and 4T1(1B) of the CoII(A) and CoII(B) centers. Energypositions of excited orbital components are indicated in cm�1. Exchange parameters Jmn for the spin coupling between various combinations (m, n) = 4T1(mA) � 4T1(nB) of theground and excited orbital components are also calculated, J12 = J21 = �0.98, J13 = J31 = �0.65, J23 = J32 = �0.83, J22 = �0.39, and J33 = �0.30 cm�1. These exchange parameterscorrespond to the diagonal matrix elements of the (�JI + T) orbital matrix of the extended spin Hamiltonian H = �JSASB + TSASB; there are also some off-diagonal matrixelements connecting the (m, n) and (m0 , n0) pair states.

Fig. 9. The structure of the two main types of CoII(A)–CoII(B) exchange-coupled pairs in the Co36 cluster in 2 and calculated exchange parameters.

116 E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118

functions 4T1(A) � 4T1(B). In this way, we obtain a 9 � 9 matrix(�JI + T) (I being the unit matrix) of the orbital operator involvedin the spin Hamiltonian H = �JSASB + TSASB; details of these calcula-tions are presented in the Supplementary data. Then the (�JI + T)matrix is diagonalized. The set of the eigenvalues {ti} of the(�JI + T) matrix provides a quantitative criterion for the correct-ness of the Lines’ approach, which predicts ti � �J (because of

T = 0). Therefore, the scatter in the ti values measures the degreeof the validity of the Lines’ approach. Our calculations indicate thatfor the CoII pairs in 1 and 2 the ti eigenvalues vary considerably: insome cases they can even reverse the sign from antiferromagma-netic to ferromagnetic (Table 4). Exchange parameters Jmn for thespin coupling between various combinations (m, n) = 4T1

(mA) � 4T1(nB) of the ground and excited orbital components are

Table 4Eigenvalues ti (in cm�1) of the (�JI + T) orbital matrix involved in the orbitally-dependent spin Hamiltonian H = �JSASB + TSASB for the cobalt exchange pairs in 1 and 2 (see Figs. 8and 9).

No. of the pair t1 t2 t3 t4 t5 t6 t7 t8 t9

1 (Fig. 11) �1.49 �1.16 �1.03 �0.85 �0.77 �0.51 �0.46 �0.30 +0.342 (Fig. 12a) �6.38 �5.54 �4.97 �4.00 �3.82 �1.84 �1.44 �0.88 +1.273 (Fig. 12b) �4.32 �3.65 �3.32 �3.03 �2.75 �2.48 �2.13 �1.88 �1.11

E.N. Zorina et al. / Inorganica Chimica Acta 396 (2013) 108–118 117

also different. Thus, for the CoII(A)–CoII(B) pair in 1 (Fig. 8) they areJ12 = J21 = �0.98, J13 = J31 = �0.65, J23 = J32 = �0.83, J22 = �0.39, andJ33 = �0.30 cm�1 (see Fig. 9 and captions). Note that these ex-change parameters are the diagonal matrix elements of the(�JI + T) orbital matrix; there are also some off-diagonal matrixelements connecting the (m, n) and (m0, n0) pairs states, seeFig. 8. These results indicate that the Lines’ approach is generallyinvalid for the CoII complexes 1 and 2.

This fact may be very important in calculations of the effective(s = 1/2) anisotropic spin Hamiltonian sAJsB, which is obtained bythe first-order projection of the �JSASB + TSASB; Hamiltonian ontothe subspace of the ground-state wave functions U(0)(A) � U(0)(B).The key point here is that the spin–orbit coupling strongly mixesthe split 4T1(1), 4T1(2) and 4T1(3) orbital components (see Fig. 6),which enter the ground-state U(0) wave functions with comparableweights (unless the orbital splitting of the 4T1 state due to distor-tions is not too large, less than or comparable to the spin–orbitsplitting, see Fig. 6). Therefore, the result of calculations of theanisotropic exchange Hamiltonian sAJsB based on the true orbital-ly-dependent spin Hamiltonian �JSASB + TSASB may differ consider-ably from that of the Lines’ approach (�JSASB only) because thethree orbital component 4T1(k) (k = 1–3) have essentially differentexchange parameters (Table 4) and they are further mixed by theoff-diagonal exchange parameters of the orbital T matrix. However,a more detailed analysis of the anisotropic s = 1/2 spin Hamilto-nian sAJsB related to the ground U(0) Kramers doublet of CoII isout of the scope of this paper because it is too lengthy and sophis-ticated; besides, its results cannot unambiguously be corroboratedby limited experimental magnetic data on 1 and 2.

4. Conclusion

Using a ligand-deficient synthetic approach, we were successfulin obtaining two novel polynuclear CoII malonate complexes withbridging malonate groups. Compound 1 has a chain-type structurewhich is stabilized by large potassium cations. Compound 2 con-tains a novel hexanegative anion [Co36(H2O)12(OH)20(HMe2Mal)2

(Me2Mal)28]6� with a fascinating, highly symmetric, spherical-likeCo36 metal core that serves as a structural building block. Theoret-ical analysis of the magnetic susceptibility of 1 and 2 reveal animportant difference in the origin of their magnetic behavior. Com-pound 1 is characterized by an extremely high anisotropy of mag-netic susceptibility originating from an uniaxial Ising-likeanisotropy of the ground-state g-tensor of strongly distorted six-coordinate CoII centers. At low temperature this results in crystal-lite-orientation effects in an external magnetic field giving rise tosome increase of the vMT curve; formally, this mimics ferromagne-tism of 1. Microscopic calculations indicate that long malonatebridging groups are poor mediators of exchange interactionsbetween CoII ions (J = �0.6 cm�1). By contrast, compound 2 has alow magnetic anisotropy due to a spherical-like character of theCo36 metal core, but exhibits more pronounced antiferromagneticexchange interactions between carboxylate-bridged CoII ions (withJ � �3 cm�1). Because of general weakness of Co-Co exchangeinteractions, above 25 K the magnetic susceptibility of 1 and 2 iswell described by one-center contributions only due to thermal

population of excited states of individual CoII ions. Our results indi-cate that the commonly used Lines’ approach is very limitedlyapplicable to calculations of the anisotropic exchange spin Hamil-tonian for CoII compounds 1 and 2.

Acknowledgments

This study was supported by the Russian Foundation for BasicResearch (project nos. 11-03-00556, 11-03-00735, 11-03-12109),the Council on Grants of the President of the Russian Federation(grant NSh-2357.2012.3), the Ministry of Education and Scienceof the Russian Federation (SC-14.740.11.0363), the Russian Acad-emy of Sciences, and the Siberian Branch of the Russian Academyof Sciences.

Appendix A. Supplementary material

CCDC 884787 and 884788 contain the supplementary crystallo-graphic data for compounds 1 and 2. These data can be obtainedfree of charge from The Cambridge Crystallographic Data Centrevia www.ccdc.cam.ac.uk/data_request/cif. Supplementary dataassociated with this article can be found, in the online version, athttp://dx.doi.org/10.1016/j.ica.2012.10.016.

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