DALTON FULL PAPER J. Chem. Soc., Dalton Trans., 1998, 3905–3909 3905 Structure and magnetic behaviour of the one-dimensional [{Ni2(Medien)2(Ï1,1-N3)2(Ï1,3-N3)}n][ClO4]n compound with unusually strong ferro-antiferromagnetic alternating interactions Albert Escuer,*a Ramon Vicente,a M. Salah El Fallah,a Sujit B. Kumar,a Franz A. Mautner b and Dante Gatteschi c a Departament de Química Inorgànica, Universitat de Barcelona, Diagonal, 647, 08028-Barcelona, Spain. E-mail: http:www.ub.es/inorgani/molmag.htm b Institut für Physikalische und Theorestische Chemie, Technische Universität Graz, A-8010 Graz, Austria c Dipartimento di Chimica, Universitá degli Studi di Firenze, Via Maragliano 75-77, 50144 Firenze, Italy Received 7th July 1998, Accepted 29th September 1998 A new monodimensional m-azido-nickel(II) complex of formula [{Ni2(Medien)2(m1,1-N3)2(m1,3-N3)}n][ClO4]n 1 [Medien = bis(2-aminoethyl)methylamine] has been synthesized and crystallographically characterised.The nickel atom is placed in an octahedral environment bridged by two end-on azido ligands and one end-to-end azido bridge to the neighbouring nickel atoms, giving an alternated 1-D system. The magnetic behaviour corresponds to an alternating ferro-antiferromagnetic chain. The superexchange parameters have been calculated as JAF = 234.7 cm21 and JFM = 138.2 cm21, a = 1.10, by means of an improved analytical expression for the magnetic susceptibility of the isotropic ferro-antiferromagnetic S = 1 Heisenberg chain in terms of the alternation parameter a = JFM/|JAF|.Magnetic properties have been correlated to the structural data. Introduction One-dimensional magnetic materials have attracted increasing interest, and have been thoroughly studied from both experimental and theoretical points of view mostly due to their position between high nuclearity clusters and extended 3-D lattices, which opens up new possibilities for understanding phenomena that cannot be explained in a higher dimension.1–4 In recent years the azide bridge has been shown to be able to generate systems from discrete molecules 5 with diVerent nuclearity to 3-D compounds,6 and specifically for nickel(II) a large number of one-dimensional systems have been reported.7 The most common topologies for the 1-D nickel–azide system consist of homogeneous chains with a single end-to-end bridge, with four co-ordination sites of the nickel environment occupied by four polyamine ligands or the double end-to-end bridge with the two remaining co-ordination sites occupied by two diamine blocking ligands.7 The end-to-end kind of compound has been extensively studied from synthetic and magnetic points of view and suitable models were proposed to explain and predict the magnitude of the antiferromagnetic coupling as a function of the bond parameters in the bridge region.5c,8 Less common are the examples of end-on ferromagnetic chains and the alternating systems.9 This latter kind of unusual system may be classified in several types: alternating end-to-end systems, alternating end-to-end/end-on systems and complex alternance of bridges, for which the magnetic analysis becomes more complicated or impossible in some cases.Continuing with our work in this field we report the syntheses and magnetic behaviour of the compound [{Ni2(Medien)2(m1,1-N3)2- (m1,3-N3)}n][ClO4]n [Medien = bis(2-aminoethyl)methylamine] which shows the single end-to-end/double end-on alternance, giving a ferro-antiferromagnetic alternating system.To fit our experimental data an improved expression built on the basis of the increasing ring system calculations has been developed and checked. Experimental Synthesis The complex [{Ni2(Medien)2(m1,1-N3)2(m1,3-N3)}n][ClO4]n was synthesized by the addition of 15 ml of an aqueous solution of sodium azide (0.23 g, 4 mmol) to an aqueous solution obtained by mixing 0.73 g (2 mmol) of nickel perchlorate and 0.24 g (2 mmol) of the Medien ligand.Slow evaporation of the blue resulting solution provided blue crystals suitable for X-ray determination. Yield 60%. [Calc. (Found) for C10H30ClN15- Ni2O4: C, 20.8 (20.8); H, 5.2 (5.3); N, 36.4 (36.4)%]. The IR spectrum shows the typical absorptions corresponding to the Medien ligand, the perchlorate counter anion and the characteristic n(N3) at 2090, 2028 and 2055 (sh) cm21. Spectral and magnetic measurements Infrared spectra (4000–400 cm21) were recorded from KBr pellets on a Nicolet 520 FTIR spectrophotometer. Magnetic measurements were carried out with a DSM8 pendulum susceptometer, working in the temperature range 300–4 K.The applied external magnetic field was 1.5 T. Diamagnetic corrections were estimated from Pascal tables. Crystallographic data collection and refinement The single crystal data were collected on a modified STOE fourcircle diVractometer (crystal size 0.55 × 0.35 × 0.30 mm). The crystallographic data, conditions retained for the intensity data collection, and some features of the structure refinement are listed in Table 1.The accurate unit-cell parameters were determined from automatic centring of 25 reflections (12 < q < 188) and refined by least-squares methods. Intensities were collected with graphite-monochromated Mo-Ka radiation, using the w-scan technique. 5462 Reflections were collected in the range 2.90 < 2q < 27.408 (4917 independent reflections, Rint 0.0242).3906 J.Chem. Soc., Dalton Trans., 1998, 3905–3909 No intensity decay of 3 control reflections (21 3 21; 21 4 23; 0 22 24), collected every hour, was observed. Corrections were applied for Lorentz-polarisation eVects but not for absorption (range of transmission: 0.650–1.000). The structure was solved by direct methods using the SHELXS 86 10 computer program, and refined by full-matrix least-squares methods on F2 using SHELXL 9311 incorporated in the SHELXTL/PC V 5.03 program package.12 Fourier-diVerence maps indicated two split orientations of one partially disordered Medien ligand and the perchlorate counter anion.Refinement of the corresponding population parameters gave values of 0.60(1) and 0.40(1) for the Medien ligand and 0.67(1) and 0.33(1) for the perchlorate. All non-hydrogen atoms were refined anisotropically. Hydrogen atoms were located on calculated positions and assigned six common isotropic displacement factors (one for each type of parent C and N atom in each Medien ligand).The final R factor was 0.0398 (wR2 = 0.0999). The number of parameters refined was 378. Goodness of fit 1.048. Maximum shift/e.s.d. = 0.05. Maximum and minimum peaks in the final diVerence synthesis were 0.614 and 20.546 e Å23, respectively. Significant bond parameters are given in Table 2. CCDC reference number 186/1180. Results and discussion Crystal structure The labelled diagram for complex 1 together with a chain perspective are shown in Fig. 1. The structure consists of Ni(Medien) units bridged by azido ligands, giving a monodimensional compound and perchlorate counter anions. Two azide co-ordination modes are present in an alternating form along the chain: each nickel atom has a double end-on bridge with one of the neighbouring nickel atoms whereas the bridge with a second nickel atom consists of a single end-to-end azido linkage. Each Ni(1)–Ni(1A) and Ni(2)–Ni(2B) subunit has an inversion centre, and the structure may thus be envisaged as two non-equivalent Ni(m1,1-N3)2Ni planar units bridged by one m1,3-N3 ligand.The environments of Ni(1) and Ni(2) are quite similar, with the tridentate Medien ligand in fac co-ordination. Bond distances to the N atoms of the end-on bridge [Ni(1)– N(11) 2.110(2), Ni(1)–N(11A) 2.116(3), Ni(2)–N(31) 2.113(3) and Ni(2)–N(31B) 2.112(3) Å] are very similar, and slightly shorter than the bond distances to the N atoms of the end-toend azido bridge [Ni(1)–N(21) 2.159(3) and Ni(2)–N(23) 2.142(3) Å].The Ni(1)–N(11)–Ni(1A) 100.8(1) and Ni(2)– N(31)–Ni(2B) 98.9(1)8 bond angles are smaller than the common bond angles found in previous dimeric Ni(m1,1-N3)2Ni entities, which show values between 101 and 1048.14–17 The endto- end bridge shows asymmetric co-ordination as is normal for this ligand, Ni(1)–N(21)–N(22) 138.1(2) and N(22)–N(23)– Ni(2) 125.7(2)8. The t torsion angle, defined as the dihedral between Ni(1)–N(21)–N(22)–N(23) and N(21)–N(22)–N(23)– Fig. 1 An ORTEP13 drawing of [{Ni2(Medien)2(m1,1-N3)2(m1,3-N3)}n]- [ClO4]n with the atom-labelling scheme. Thermal ellipsoids are at the 50% probability level. Ni(2) mean planes is 162.8(4)8. The Ni ? ? ? Ni distance in the end-on units is 3.257(1) Å for Ni(1)–Ni(1A) and 3.203(1) Å for Ni(2)–Ni(2B), whereas the Ni(1) ? ? ? Ni(2) distance is greater, 6.060(2) Å, due to the end-to-end co-ordination of the bridge.The structure of the [{Ni2(Medien)2(m1,1-N3)2(m1,3-N3)}n][ClO4]n compound shows the same double/single bridge alternance as the previously reported 9b [{Ni2(dpt)2(m1,3-N3)2(m1,3-N3)}n]- [ClO4]n, dpt = bis(3-aminopropyl)amine, Fig. 2. The diVerence between the two systems lies in the kind of bridge, alternating double end-on/single end-to-end for the present compound and only end-to-end bridges for the previous complex. From the synthetic and magnetic points of view, these compounds are a nice example of the extreme versatility of the azido ligand in providing uncommon magnetic systems on the basis of simple synthetic procedures.The model and calculation Ferro-antiferromagnetic systems have attracted much attention in the past few years, mainly focused on their complicated magnetic behaviour derived from the simultaneous exchange coupling interactions. One of the consequences has been the development of suitable models to explain their magnetic properties.For the S = 5/2 system, which permits the treatment as a classical vector, appropriate equations have been proposed,18 whereas for lower S values several authors have solved numerically the magnetic exchange expressions for the alternating anti- Fig. 2 Perspective view of [{Ni2(Medien)2(m1,1-N3)2(m1,3-N3)}n][ClO4]n and comparison with the related [{Ni2(dpt)2(m1,3-N3)2(m1,3-N3)}n][ClO4]n compound. Table 1 Crystal data and structure refinement for [{Ni2(Medien)2- (m1,1-N3)2(m1,3-N3)}n][ClO4]n Formula Formula weight Crystal system Space group a/Å b/Å c/Å a/8 b/8 g/8 V/Å3 ZT /8C l(Mo-Ka)/Å Dc, Dm/g cm23 m(Mo-Ka)/mm21 R wR2 C10H30ClN15Ni2O4 577.36 Triclinic P1� (no. 2) 7.421(1) 12.339(3) 14.171(5) 113.35(2) 100.80(3) 96.45(2) 1144.9(6) 2 25(2) 0.71069 1.675, 1.66(3) 1.813 0.0398 0.0999J. Chem. Soc., Dalton Trans., 1998, 3905–3909 3907 Fig. 3 Temperature dependence of cr versus Tr for N = 2, 3, 4, 5 rings (solid lines) and N = infinite (dashed line) for the alternating parameter a = 0. 4, 1.5, 3.0 and 6.0. ferromagnetic chain and alternating ferro-antiferromagnetic systems of spins S = 1/2.19 Recently, an expression to fit ferroantiferromagnetic S = 1 chains was proposed by Borras- Table 2 Selected bond lengths (Å) and angles (8) for [{Ni2(Medien)2- (m1,1-N3)2(m1,3-N3)}n][ClO4]n Ni(1)–N(1) Ni(1)–N(2) Ni(1)–N(3) Ni(1)–N(11) Ni(1)–N(11A) Ni(1)–N(21) N(11)–N(12) N(12)–N(13) N(21)–N(22) N(1)–Ni(1)–N(2) N(1)–Ni(1)–N(3) N(1)–Ni(1)–N(11) N(1)–Ni(1)–N(11A) N(1)–Ni(1)–N(21) N(2)–Ni(1)–N(3) N(2)–Ni(1)–N(11) N(2)–Ni(1)–N(11A) N(2)–Ni(1)–N(21) N(3)–Ni(1)–N(11) N(3)–Ni(1)–N(11A) N(3)–Ni(1)–N(21) N(11)–Ni(1)–N(11A) N(11)–Ni(1)–N(21) N(11A)–Ni(1)–N(21) N(12)–N(11)–Ni(1) N(12)–N(11)–Ni(1A) Ni(1)–N(11)–Ni(1A) N(22)–N(21)–Ni(1) N(11)–N(12)–N(13) N(21)–N(22)–N(23) 2.065(3) 2.145(3) 2.076(3) 2.110(2) 2.116(3) 2.159(3) 1.179(3) 1.152(4) 1.163(4) 82.7(1) 98.0(1) 91.8(1) 86.8(1) 174.0(1) 83.7(1) 174.1(1) 102.5(1) 96.0(1) 95.0(1) 172.6(1) 87.7(1) 79.2(1) 89.7(1) 87.8(1) 124.8(2) 134.3(2) 100.8(1) 138.1(2) 179.7(3) 178.1(3) Ni(2)–N(4) Ni(2)–N(5) Ni(2)–N(6) Ni(2)–N(23) Ni(2)–N(31) Ni(2)–N(31B) N(22)–N(23) N(31)–N(32) N(32)–N(33) N(4)–Ni(2)–N(5) N(4)–Ni(2)–N(6) N(4)–Ni(2)–N(31) N(4)–Ni(2)–N(31B) N(4)–Ni(2)–N(23) N(5)–Ni(2)–N(6) N(5)–Ni(2)–N(31) N(5)–Ni(2)–N(31B) N(5)–Ni(2)–N(23) N(6)–Ni(2)–N(31) N(6)–Ni(2)–N(31B) N(6)–Ni(2)–N(23) N(31)–Ni(2)–N(31B) N(23)–Ni(2)–N(31) N(23)–Ni(2)–N(31B) N(32)–N(31)–Ni(2) N(32)–N(31)–Ni(2B) Ni(2)–N(31)–Ni(2B) N(22)–N(23)–Ni(2) N(31)–N(32)–N(33) 2.081(3) 2.118(3) 2.081(3) 2.142(3) 2.113(3) 2.112(3) 1.165(4) 1.194(3) 1.149(4) 82.9(1) 96.1(1) 86.5(1) 91.6(1) 172.8(1) 83.4(1) 100.4(1) 174.1(1) 94.3(1) 175.6(1) 95.0(1) 90.1(1) 81.4(1) 87.5(1) 91.4(1) 125.8(2) 121.0(2) 98.9(1) 125.7(2) 177.8(3) Almenar et al.,20 assuming that the ring of N = 5 pairs of S = 1 spins describes the chain behaviour satisfactorily.In this section, therefore, we felt it appropriate to extend those calculations and attempt to develop such an expression for the N = infinite extrapolation, in order to improve the expression for large a = JFM/|JAF| values.The Hamiltonian for the Heisenberg alternating ferroantiferromagnetic chain can be written as in eqn. (1) where N is H = 2 N21 S i = 1 JAFS2iS2i 1 1 1 JFMS2iS2i 2 1 (1) the number of spin pairs, JAF and JFM are the nearest neighbour antiferro- and ferro-magnetic exchange interactions. By using the usual computational technique, based on the calculation of the properties of finite rings of increasing size, we have determined the magnetic susceptibility of alternating ferro-antiferromagnetic chains for various a values.The series of calculations were made using the computer program CLUMAG, which uses the irreducible tensor operator (ITO) formalism.21 Owing to the diYculties associated with the large dimensions of the calculations and the required computing times, our calculations were only achieved up to 10 spins (N = 5), and by the same reason the influence in the low temperature region of the zero field splitting parameter D has not been considered.Fig. 3 reports the reduced magnetic susceptibility curves of the chains N = 2, 3, 4 and 5 for a = 0.4, 1.5, 3 and 6. Closer examination shows that when a is low (0.4) the two curves N = 4 and 5 are indistinguishable throughout the temperature range, whereas significant diVerences become observable when a increases especially at low temperature (below the reduced temperature, Tr = 1.3 for a = 1.5, 1.6 for 3 and 1.8 for 6), and the maximum deviation becames 2.9% for a = 6.Nevertheless, it seems clear that the unique sequence (N = infinite) will appear in the intermediate region bracketed by the curves for odd N and those for even N, exactly between N = 5 and 4, which led us to assume that the curves of half of the sum between N = 5 and 4,3908 J.Chem. Soc., Dalton Trans., 1998, 3905–3909 Table 3 CoeYcients for the polynominals for 0 £ a £ 2 and 2 £ a < 6 A B C D E 0£a£2 a0 0.610392 a1 22.56528 a2 3.3881 a321.68187 a4 0.310599 b0 0.141083 b1 0.503112 b2 20.687456 b3 0.331817 b4 20.0547117 c0 1.17598 c1 23.14941 c2 3.18665 c3 21.49803 c4 0.269656 d0 1.26115 d1 21.584444 d2 3.30872 d3 1.86917 d4 0.369253 e0 0.282429 e1 21.15824 e2 0.896513 e3 20.383948 e4 0.0743106 2 £ a £ 6 a0 38.728 a1 251.9772 a2 25.4004 a3 25.38647 a4 0.454228 b0 16.4703 b1221.8691 b2 10.4464 b3 22.1991 b4 0.185766 c0 32.1303 c1 242.9283 c2 20.6105 c 24.3098 c4 0.357483 d0 18.3973 d1 223.3778 d2 12.0541 d3 22.66954 d4 0.236077 e0 57.5268 e1 276.6243 e2 36.553 e3 27.6135 e4 0.630971 N• = [(N = 4 1 N = 5)/2], should describe the behaviour of the infinite chain with negligible uncertainty (dashed curves on Fig. 3). Based on this proposition, and applying the same strategy reported in the literature, is possible to generate an expression of cr, which depends on Tr and a, by fitting all the infinite theoretical susceptibility curves, eqn.(2) where cr = 3cm|JAF|/ cr = Tr 2 1 ATr 1 B Tr 3 1 CTr 2 1 DTr 1 E (2) 2Ng2mB 2 and the reduced temperature Tr is given by kT/|JAF|; A–E are the fitting coeYcients, which depend on a, and such dependence can be described by the use of a polynomial expression (3) to the fourth degree in a. (In eqn. (3) x0 etc. corre- X = x0 1 x1a 1 x2a2 1 x3a3 1 x4a4 (3) spond to a0–e0 from Table 3.) Two sets of coeYcients have been proposed according to the value of a, Table 3.The reduced susceptibility expression can be converted into magnetic susceptibility in the habitual form to give eqn. (4) where cm = 2Ng2mB 2 3kT 1 1 Ax 1 Bx2 1 1 Cx 1 Dx2 1 Ex3 (4) x = |JAF|/kT. The expression with the two sets of A–E coef- ficients is valid for kT/|JAF| > 0.22, as shown in Fig. 4, which gives the calculated magnetic susceptibility of the infinite chain with good approximation (R = 1.5 × 1025), even for high values of a.Fig. 4 Temperature dependence of cm (theoretical) versus T for N = infinite. The solid lines are the best fits calculated for diVerent values of the alternating parameter a = 0.2, 0.6, 1.2, 2.0, 3, 4, 5 and 6 (JAF = 250 cm21 and g = 2.35). Magnetic properties and magneto-structural correlations The cmT product and the molar magnetic susceptibilities vs. T in the 300–4 K range for [{Ni2(Medien)2(m1,1-N3)2(m1,3-N3)}n]- [ClO4]n 1 are plotted in Fig. 5, which shows an overall antiferromagnetic behaviour: cmT decreases on cooling from 1.34 cm3 K mol21 at 292 K and tends to zero at low temperature, showing a maximum of susceptibility at 50 K (1.30 × 1022 cm3 mol21). The fit of the experimental data with the above equation gave the best parameters JAF = 234.7, JFM = 138.2 cm21, a = 1.10, g = 2.34 and R = 4.2 × 1025. The strong ferromagnetic contribution of JFM to the global magnetic behaviour is reflected in the very slow decrease of cmT in the high temperature range 300– 150 K.Despite the mathematic quality of the fit, the sign and magnitude of the calculated coupling constants should be chemically reasonable in comparison with those for ferro- or anti-ferromagnetic models or well established experimental data. The best known interaction is the antiferromagnetic superexchange through the single end-to-end azido bridge, which has been modelled as a function of the two Ni–N–N bond angles and the t torsion angle defined as the angle between the mean planes Ni–N–N–N and N–N–N–Ni9.8 Analysis of published data indicates that the best fit JAF value of 234.7 cm21, the Ni–N–N bond angles 138.1/125.78 and the t torsion angle of 162.88 are consistent with the J value expected for a compound with a medium t angle.A useful comparison is oVered by the [{Ni(cyclam)(m1,3-N3)}n][ClO4]n homogeneous chain, which shows practically the same structural and magnetic parameters: Ni–N–N bond angles 140.7/128.28, t = 166.98 and J = 239.2 cm21.22 Less systematized data are available for the double end-on kind of bridge, but the best fit JFM lies in the typical range of J values for this kind of compound, for which J close to 140 Fig. 5 Molar magnetic susceptibility and the cmT product vs. temperature for [{Ni2(Medien)2(m1,1-N3)2(m1,3-N3)}n][ClO4]n. Solid lines show the best fit obtained by applying eqn. (3) (see text).J. Chem.Soc., Dalton Trans., 1998, 3905–3909 3909 cm21 is a normal value. The slightly lower Ni–N–Ni9 bond angle is not expected to be relevant in the light of the data summarized in Table 4, which show a similar J value for all the reported compounds with Ni–N–Ni9 bond angles between 100.8 and 104.98. This result is also consistent with the calculations performed by Ruiz et al.23 by means of density functional methods, which predict a maximum ferromagnetic coupling around the bond angle Ni–N–Ni9 = 1048 and a narrow range of this bond parameter (±88 approximately), in which minor J diVerences should be expected. Concluding remarks A new structurally and magnetically alternating 1-D nickel(II)– azido system has been fully characterized and its superexchange coupling constants have been determined as JAF = 234.7 and JFM = 138.2 cm21, a = 1.1.These results have been calculated by extrapolation of the expected properties for rings of increasing size up to N = 5 pairs of S =1.The best fit parameters are consistent with the values that may be expected on the basis of the structural bond parameters in the bridging region, which confirm the validity of the sign and magnitude of the J values found. One of the most interesting aspects of the present work is the application for the first time of the theoretical expressions to a system in which the two superexchange interactions are strong, the results lying in the optimum range of a, which permits an accurate determination of the J values.Acknowledgements A. E. and R. V. thank the Comisión Interministerial de Ciencia y Tecnologia (Grant PB096/0163) for support of this research. F. A. M. thanks Professor C. Kratky (University of Graz) for use of experimental equipment and the Osterreichische Nationalbank (Jubilaeumsfondsproject 6630) for financial support. References 1 W. E. Hatfield, in Extended Linear Chain Compounds, ed. J. S. Miller, Plenum, New York, 1983, vol. 3. 2 J. C. Bonner, in Magneto-Structural Correlations in Exchange Coupled Systems, eds. R. D. Willet, D. Gatteschi and O. Kahn, NATO ASI Series, Reidel, Dordrecht, 1984. Table 4 Bond angles and J superexchange parameters for the ferromagnetic [NiNi] pairs with a double end-on azido bridge and aliphatic blocking ligands {en = ethane-1,2-diamine, Medt = bis(3-aminopropyl)- methylamine, 232-tet = N,N9-bis(2-aminoethyl)propane-1,3-diamine, Me3[12]N3 = 2,4,4-trimethyl-1,5,9-triazacyclododec-1-ene} Compound [Ni2(en)4(m-N3)2][ClO4]2 [Ni2(Medpt)2(N3)2(m-N3)2](ClO4)2 [Ni2(232-tet)2(m-N3)2][ClO4]2 [Ni2(232-tet)2(m-N3)2][PF6]2 [Ni2(Me3[12]N3)(m-N3)2] Ni2(Medien)2(m-N3)2 fragment Ni–N–Ni/8 104.3 104.0 104.9 104.6 103.8 100.8 98.9 J/cm21 43.4 46.7 33.8 34.3 43.9 38.2 Ref. 14 15 16 17 16 This work 3 Physics in One Dimension, eds. J. Bernasconi and T. Schneider, Springer, Berlin, 1981. 4 Organic and Inorganic Low-Dimensional Crystalline Materials, eds.P. Delhaes and M. Drillon, Plenum, New York, 1987, vol. B, p. 168. 5 (a) M. I. Arriortua, R. Cortés, L. Lezama, T. Rojo and X. Solans, Inorg. Chim. Acta, 1990, 174, 263; (b) R. Cortés, J. I. Ruiz de Larramendi, L. 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