www.elsevier.nl/locate/poly

Polyhedron 19 (2000) 2483–2491

A theoretical analysis of how geometrical distortions onCu(m-Cl)2Cu dimers influence their electronic and magnetic

properties

Montserrat Rodrıguez a, Antoni Llobet a,*, Montserrat Corbella b

a Departament de Quımica, Uni6ersitat de Girona, Campus de Montili6i, E-17071 Girona, Spainb Departament de Quımica Inorganica, Uni6ersitat de Barcelona, Martı i Franques, 1-11, 08028 Barcelona, Spain

Abstract

A structural classification of dimers, containing the Cu(m-Cl)2Cu core, based on data obtained from X-ray diffraction analysisreported in the literature has been performed. In these complexes, the local geometry around the copper metal center is generallya square pyramid, with a different degree of distortion towards a trigonal bipyramid. The global geometry of the dinuclearcomplex can be described in terms of the relative arrangement of the two square pyramids, giving rise to three types of geometries,termed: coplanar bases, parallel bases and perpendicular bases. Ideal models representing these geometries were defined and EHcalculations were performed in each case, showing the different molecular orbitals involved in their corresponding frontierorbitals, together with their energy. EH calculations were also carried out for dimers embodying different type of structuraldistortions from the ideal models. The results obtained from those EH calculations have proven to be extremely useful for theproper interpretation and correlation of the magnetic data and dimer structure for those Cu(m-Cl)2Cu complexes reported in theliterature. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Magnetic properties; Dimers; Geometrical distortions; Magnetostructural correlations

1. Introduction

The magnetic properties of transition metal com-plexes are of tremendous importance both from a basicresearch point of view and also because of their multi-ple technological applications [1–3]. As a consequence,there has been substantial interest, over the years, incorrelating magnetic properties and molecular struc-ture. On the other hand, the propagation of magneticinformation over large distances is a topic that hasattracted considerable interest in recent years [4–10].

For dihydroxo bridged dinuclear copper complexes[11–24], a good degree of success has been accom-plished in correlating structure and magnetic properties.In sharp contrast, no unique magneto-structural corre-lation has been found for dichloro bridged dinuclearcopper complexes. Furthermore, a recent report haspresented a new compound that constitutes the first

example of a ferromagnetic dinuclear copper with aspin-ladder disposition and moderate interactions [25].

Given the current interest in dinuclear dichlorobridged copper complexes, we have undertaken a theo-retical analysis on the different geometrical factors thatinfluence their electronic and magnetic properties, inorder to offer a framework for future reference.

2. Experimental

Molecular orbital calculations have been carried outusing CACAO 4.0 (computer-aided composition ofatomic orbitals) [26], which is a program based onextended Huckel (EH) type of analysis.

Ideal models were used as the starting point of ouranalysis. In the models, the N atoms of the ligands weresubstituted for simple amino groups. EH calculationsfor complex [Cu2(dpt)2Cl2]Cl2 (34) (see Table 1) [25],showed that there is no significant difference for bothenergies and frontier orbital topologies between the realcomplex and the model.

* Corresponding author. Tel.: +34-972-418262; fax: +34-972-418150.

E-mail address: llobet@fc.udg.es (A. Llobet).

0277-5387/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.PII: S 0277 -5387 (00 )00548 -9

M. Rodrıguez et al. / Polyhedron 19 (2000) 2483–24912484

For each model, all bonding angles between Cu andthe bonded ligand atoms, arranged in a cis fashion,were taken as 90°. All Cu�N bond distances were takenas 2.0 A, , while we distinguished between basal andapical Cu�Cl bond distances. The former was taken as2.51 A, , whereas we used 2.70 A, for the latter. In theperpendicular bases case, we took both Cu�Cl bonddistances as 2.51 A, .

The three models used, together with the drawing oftheir corresponding HOMO and LUMO frontier or-bitals, are depicted in Fig. 1.

Throughout the present paper, the description ofatomic orbital participation is only considered if it hasa contribution of more than 1% to the correspondingmolecular orbital.

3. Results and discussion

A number of dichloro bridged dicopper complexeshave been reported in the literature so far [25,27–53].At first glance their molecular structure shows thatthere is a whole variety of bond distances and angles, insharp contrast with dihydroxo bridged dicopper com-plexes, that display a more homogeneous behaviorfrom this perspective. Moreover, a closer examinationof their structural parameters shows that, in dihydroxobridged copper complexes, the geometry around thecopper metal center is basically a square pyramid. Thetwo pyramids are spatially arranged so that they sharea basal edge, which contains the two OH− bridgingligands, and the corresponding apical positions are

Table 1DES-T and Magnetostructural correlation parameters for selected binuclear copper complexes containing the Cu(m-Cl)2Cu core

Geometry type b a a/R DES-T (cm−1)Compound a Reference

29.388.5 [27]PAR(1) [Cu(Cl)2(TMSO)]2 −17.012 [28](2) [Cu2(baamo)2Cl2] PAR 82.9 29.52

PAR 29.9 −7.4 [29](3) [Cu(2-pic)2Cl2]2 100.63PAR 30.7 −5.6 [30](4) [Cu(tmen)Cl2]2 96.8

[31]−2.131.4(5) [Cu(Me3en)Cl2]2 84.84PARPAR 32.18 −4.6 [32](6) [Cu(Pypep)Cl]2·2H2O 91.1PAR 86.87(7) [CuCl2(TTPP1)]2 32.15 −7.4 [33]

[34]6.332.6(8) [Cu(dmg)Cl2]2 88PARPAR 89.9(9) [Cu2(terpy)2Cl2][PF6]2 33.02 −5.9 [35]

0.4 [36](10) [Cu(dien)Cl]2(ClO4)2 PAR 92.05 33.5PAR 96.68(11) [Cu(bpdio)Cl2]2 33.99 4.87 [37]PAR 89.1(12) [Cu2Cl3(C7H6N2)5]Cl·4H2O 34.01 5.6 [38]PAR 90.94(13) [CuCl2(TTPP2)]2 34.18 −20.8 [33]

(14) [Cu(4-Meox)2Cl2]2 [36]−2.634.4PAR0.1 [51]34.894.84PAR(15) [Cu(Et3en)Cl2]2

(16) [Rh(en)3]2[Cu2Cl8]Cl2·2H2O −13.8PAR 94.58 34.96 [39]95.3 [51]PAR(17) [Cu(4-Metz)(DMF)Cl2]2 −3.435.0

PAR 94.83(18) [Ir(en)3]2[Cu2Cl8]Cl2·2H2O 35.06 −13.0 [39]−14.6(19) [Co(en)3]2[Cu2Cl8]Cl2·2H2O [38]PAR 95.2 35.2

COP 95.7(20) [Cu2Cl4(2pyq)2] 38.7 −10 [40][53]−82.640.0(21) [Cu(Guan)Cl3]2·2H2O 97.9COP

COP 94.9(22) [(C5H5N)NH2]2Cu2Cl6 40.73 42 [41]41.795.3 [42](23) (4-BzpipdH)2[Cu2Cl6] COP 41.6233.7 [52]40.76(24) [Cu2Cl2(HB(1-pz)3)2] COP 94.4

(25) (Me2NH2)2[Cu2Cl6] :20COP 95.6 41.57 [43]95.5 [44]COP(26) (i-PrNH3)2[Cu2Cl6] −19.4641.34

COP 97.5(27) (paraquat)[Cu2Cl6] 42.61 −26.41 [42]−37.53 [45](28) (melH2)[Cu2Cl6] COP 95.8 40.82

41.30COP −38.23 [46]95.9(29) K2[Cu2Cl6]41.82COP −61.16 [47]95.8(30) (morphH)2[Cu2Cl6]

[48]−93.1241.88(31) (DBTTF)[Cu2Cl6] 96.2COP45.1 [49](32) (Ph4As)2[Cu2Cl6] COP 93.8

COP 93.2(33) (Ph4P)2[Cu2Cl6] 53.4 [50](34) [Cu2(dpt)2Cl2]Cl2 [25]42.9435.91PER 91.4

a Ligand abbreviations: baamo: 8-amino-5-aza-4-methyl-3-octene-2-onate; bpdio: 2,2-bis-(2-pyridyl)-1,3-dioxolane; 4-BzpipdH: 4-benzilpyperi-dinic cation; DBTTF: dibenzotetratiafulvalenic cation; dien: diethylenetriamine; dmg: dimethylglioxime; en: ethylendiamine; Et3en: N,N,N %-tri-ethylethylendiamine; Guan: guaninic cation (2-aminohypoxantinic, C5H5N5O); HB(1-pz)3: hydrotris(1-pirazolyl)borate; i-Pr: isopropyl; Me3en:N,N,N %-trimethylethylendiamine; melH2: melaminic cation, C3H2N3(NH2)3

2+; 4-Meox: 4-methyloxazole; 4-Metz: 4-methyltriazole; morphH:morpholinic cation (tetrahydro-1,4-oxazinic); paraquat: 1,1%-dimethil-4,4%-bipyridinic cation; 2-pic: 2-methylpyridine; Pypep: pyperidinic cation,N-(2-(4-imidazolyl)ethyl)-2-pyridine-2-carboxamidic; 2pyq: 2-(2%-pyridyl)quinoxaline; tmen: N,N,N %,N %-tetramethylethylendiamine; TMSO: tetra-methylsulfoxide; trpy: 2,2%:6%,2%%-terpyridine; TTPP1: 2,5,8-trithia [9](2,5)thiophenophane; TTPP2: 2,5,9,12-tetrathia [13](2,5)thiophenophane.

b COP stands for coplanar bases, PAR for parallel bases and PER for perpendicular bases.

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Fig. 1. Polygon arrangements found for N3Cu(m-Cl)2CuN3 type of dimers together with their EH calculated HOMO and LUMO frontier orbitalsfor ideal models (see Section 2 for details): (A) coplanar bases; (B) parallel bases; (C) perpendicular bases.

situated in opposite directions. This geometry, termedcoplanar bases, is shown in Fig. 1(A) for the ho-mologous Cu2Cl2 complexes, and it is invariably thetype of structural arrangement observed for most ofdihydroxo bridged complexes reported to date.

For dinuclear dichlorobridged pentacoordinatedcopper complexes, the local geometry around the cop-per metal center is also generally a square pyramid,although the degree of distortion is somewhat greaterthan in the hydroxo case. In sharp contrast, and dueto the relatively larger bond distances and anglespresented, dichloro bridged complexes exhibit twomore different geometries with regard to the rela-tive arrangement of squared pyramids, besides tothe coplanar bases case. Those two new geo-metries are termed parallel bases and perpendicular

bases, and are represented in Fig. 1(B and C), respec-tively.

3.1. Ideal models

In the parallel bases case, the two square pyramidsshare a base-to-apex edge so that the Cl atom situ-ated at the vertex of one base becomes the apicalvertex of the other square pyramid, and just the op-posite happens for the other Cl bridging ligand. Inthe perpendicular bases case, the two square pyra-mids share a base to apex edge, but now the apicalchloro ligand of one pyramid is also the apical ofthe other one, and the same happens for the otherchloro ligand: in both pyramids it lies on the base.

Fig. 1 presents, for the three possible geometriesadopted by dinuclear dichloro bridging copper com-

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plexes, the schematic structural drawings, idealizedpolygon arrangements and the drawings and energies ofEH calculated frontier orbitals based on ideal models.EH analysis for the ideal coplanar bases case gives anenergy gap of 0.036 eV between HOMO and LUMOorbitals (see Fig. 1(A)) which, in turn, are about 0.8 eVabove occupied orbitals. The calculations indicate, forthe HOMO orbital, the following orbital participation:Cu d orbitals, 42%; N p orbitals, 32%; basal Cl porbitals, 24%. For LUMO orbital: Cu d orbitals, 44%;N p orbitals, 32%; basal Cl p orbitals 24%. The contri-bution from the apical N ligand to both frontier or-bitals is less than 1%. A summary of the resultsobtained from EH analysis performed for the threedifferent arrangements is shown in Table 2.

As it can be observed in Fig. 1, the Cu metal centersuse dx 2−y 2 type orbitals for a s* interaction with pN

and pCl orbitals, for any of the structural arrangements.For the coplanar bases case, the LUMO orbital is anantisymmetric dCu–dCu orbital combination, whereasthe HOMO orbital is a dCu–dCu symmetric combina-tion. For both parallel and perpendicular bases cases,the LUMO orbital is the symmetric combination ofthese dCu–dCu orbitals, and the HOMO corresponds tothe antisymmetric one.

In the frontier orbitals, for the parallel bases case,each bridging Cl ligand interacts, in a sigma fashion,only with one of the Cu metals. It is interesting to notethat, for perpendicular bases case, the contribution tofrontier orbitals of the apical Cl ligand is less than 1%in both HOMO and LUMO orbitals.

3.2. Distortions from ideal models

In this section we described how frontier orbitalstopology and energy were affected by structural distor-tions. The distortions chosen are those that lead to thetype of distorted structures found for real complexes, orthose that help to understand the magnetic behavior ofcopper dimers reported in the literature.

3.2.1. Coplanar basesThe first distortion considered in this case consists on

an elongation of the Cu�Cl bond distances, maintainingbond angles intact, therefore producing a symmetricenlargement of the squared core. As the Cu�Cl distanceis progressively enlarged from 2.2 to 2.8 A, , the energygap between frontier orbitals is gradually decreased. Atthis point the two orbitals are nearly degenerate. This isdue to the fact that, as the Cu�Cl bond distance isincreased, the effective bonding decreases and thereforethe two Cu centers become basically independent.

The second distortion considered was a symmetricincrease and decrease of the Cu�Cl�Cu bond anglesthat produces, as a consequence, a decrease and in-crease of the Cu�Cl bond distances, respectively. In thiscase, the frontier orbitals energy gap reaches a mini-mum at CuClCu bond angle equal to 90°; for thisangle, the overlap between the pCl orbitals and the dCu

orbitals is practically identical in both HOMO andLUMO orbitals, due to the orthogonality of pCl or-bitals involved (see Fig. 1(A)). As the angle is increased,both orbitals increase in energy, but the LUMO in-creases at a faster pace. On the other hand, when theangle decreases, both frontier orbitals do stabilize, butnow the HOMO does it faster.

The third distortion considered was the Cu geometri-cal transformation from a square pyramid (sqp) to atrigonal bipyramid (tbp)(see Fig. 2). In this case, thefrontier orbitals energy and the gap remain practicallyconstant over the exerted distortion. However, orbitalcomposition and shape are substantially different. Thefrontier orbitals involved in the tbp geometry resemblenow a orbital (Fig. 2(C)), and some degree of participa-tion from the apical ligand orbitals was found.

3.2.2. Parallel basesFor this geometry we have considered two different

distortions. The first distortion, represented in Fig. 3,consisted on the transformation of a sqp to tbp geome-

Table 2Energies and participation of atomic orbitals to HOMO and LUMO orbitals calculated for ideal models

Geometry type Coplanar bases Parallel bases Perpendicular bases

Energy GAP between HOMO and LUMO orbitals (eV) 0.036 0.0960.065Energy above occupied orbitals (eV) 1.50.8 1.3HOMO Cu d orbitals participation (%) 4242 44

32HOMO N p orbitals participation (%) 44 4212HOMO basal Cl p orbitals participation (%) 24 12

44LUMO Cu d orbitals participation (%) 42 44444432LUMO N p orbitals participation (%)

24LUMO basal Cl p orbitals participation (%) 10 10

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Fig. 2. Distortion from the coplanar bases ideal model. (A) Schematic diagram showing the applied distortion from sqp to tbp through amodification of the indicated angles sa (apical) and sb (basal). (B) Walsh diagram showing the energy as function of synchronized variations ofsa and sb (step 1: initial idealized coplanar bases; step 2: sa=5°, sb=10°; step 3: sa=10°, sb=20°; step 4: sa=15°, sb=30°). (C) Drawing ofHOMO and LUMO frontier orbitals obtained in step 4.

Fig. 3. Distortion from the parallel bases ideal model I. (A) Schematic diagram showing the applied distortion from sqp to tbp through amodification of the indicated bond angles and distances. (B) Walsh diagram showing the energy as function of angle (step 2–4) and bond (step5–6) variations (step 1: initial idealized parallel bases; step 2, 3 and 4, aa=15, 30 and 45°, respectively; step 4, 5 and 6 Cu�Cl bond distance 2.7,2.5 and 2.3 respectively). (C) Drawing of HOMO and LUMO frontier orbitals obtained in step 6.

try for the Cu metal center. As in the previous case,the dCu metal orbitals involved change from type to,and some overlap between each bridging Cl and bothCu metal centers is observed. In sharp contrast with

the previous case, an important increase of the gaptakes place here. As shown in Fig. 3(B), this ismainly due to the angular variation (step 2–4) sinceupon decreasing bond distances (step 5 and 6) both

M. Rodrıguez et al. / Polyhedron 19 (2000) 2483–24912488

frontier orbitals increase in energy, but in similar magni-tudes.

The second distortion described consisted, first, on themodification of bond angles for terminal ligands, reach-ing 120° (see Fig. 4, steps 2–3), and then increasingCu�Cl bond distances (steps 5–6). The final step of thisdistorsion was a tbp type of geometry, frequently ob-served in real cases. The angular alteration produced astrong increase on the gap, which was then progressivelydecreased as the distances were elongated. Nevertheless,the final geometry still possesses a much higher gap thanthe initial. Again, the dCu metal orbitals involved changefrom dx 2−y 2 type to dz 2, and an effective overlap isobserved between the two Cu metal centers through boththe bridging chlorines.

It is worth mentioning that in the present case, the twodistortions described produce a substantial increase inthe energy gap with regard to the ideal model.

3.2.3. Perpendicular basesThe first distortion studied in this case involved the

variation of the Cu�Cl�Cu bond angle for the apicalbridging chloro ligand, maintaining the rest of thestructural parameters constant except, obviously, theCu�Cl(apical) bond distance. Upon applying this varia-tion the gap remains constant, in agreement with the factthat the orbitals belonging to this ligand do not partic-ipate in the frontier orbitals (see Fig. 1(C)).

A second variation consisted on the same type ofdistortion, but now applied to the Cu�Cl(basal) bond

angle (see Fig. 5). In this case, a direct relationshipbetween the bond angle and the energy gap was found.That is, as the angle decreases (from 94.18 to 86.10), theenergy gap increases, nearly linearly, from 0.045 to 0.140eV (see Walsh diagram in Fig. 5(B)).

A third distortion consisting on synchronized variationof both apical and basal Cu�Cl�Cu bond angles gave thesame results as in the previous case, as expected.

3.3. Magneto-structural correlations

Structural and magnetic data for a series of dinucleardichlorobridged copper complexes are presented in Table1. As can be observed, either ferromagnetic or antiferro-magnetic coupling can be found for real compounds.Those of PAR type of geometry present, in general,smaller values of DES-T than the coplanar bases geometrydimers.

Two different type of correlations between structureand magnetic properties for dichlorobridged copperdimers can be found in the literature. One of them relatesthe magnetic interaction to a/R (Fig. 6(A)) [51], wherea represents the Cu�Cl�Cu angle, and the second onefinds a dependence of DES-T on the angle a (Fig. 6(B))[52]. In both cases, it can be noticed that the majority ofcomplexes are situated along two different lines. There-fore, there are no simple structural parameters thatcan correlate structure and magnetic properties. Acloser examination of the graphs reveals that com-plexes with the same type of geometry are gathered

Fig. 4. Distortion from the parallel bases ideal model II. (A) Schematic diagram showing the applied distortion from sqp through a modificationof the indicated bond angles and distances. (B) Walsh diagram showing the energy as function of angle (step 2–3) and bond (step 4–6) variations(step 1: initial idealized parallel bases; step 2 and 3, aa=15 and 30°, respectively; step 3, 4, 5 and 6 Cu�Cl bond distance 2.51, 2.60, 2,8 and 3.04,respectively). (C) Drawing of HOMO and LUMO frontier orbitals obtained in step 6.

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Fig. 5. Distortion from the perpendicular bases ideal model. (A) Schematic diagram showing the applied distortion through a modification of theindicated bond angle. (B) Walsh diagram showing the energy as function of the aa angle (step 3: initial idealized perpendicular bases; step 1, 2,4 and 5, aa=94.18, 91.47, 88.56, and 86.10°, respectively). (C) Drawing of HOMO and LUMO frontier orbitals obtained in step 1.

close to straight lines, and that complex[Cu2(dpt)2Cl2]Cl2 (34) [25], which is the only one withperpendicular bases arrangement, is not placed close toany of the previous lines. The line that fits the magneticbehavior of complexes with a coplanar bases type ofgeometry (graph in Fig. 6(A)) has a slope of −95.54cm−1/(°/A, ) and an intercept at 41.56°/A, . In the graphin Fig. 6(B), the corresponding straight line has a slopeof −48.65 cm−1/° and the intercept at 95.1°.

For this geometry, the modification of the Cu�Cl�Cubond angle, either above or below 90°, produces asignificant increment of the gap (see Section 3.2.1).Since all complexes reported to date, and belonging tothis type of symmetry, have Cu�Cl�Cu bond angleshigher than 90°, it follows that the higher theCu�Cl�Cu bond angle the more antiferromagneticcharacter, which is actually what is found experimen-tally (see Fig. 6(B)) [52].

Fig. 6. Magneto-structural correlations: (A) DES-T (cm−1) versus a/R (°/A, ) and (B) DES-T (cm−1) versus a (°) for Cu(m-Cl)2Cu dimers.

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In sharp contrast, for this arrangement, a change ofthe local copper geometry from sqp by tbp practicallydoes not change the gap. As a consequence of this,complexes 21, 22, 23, 25 and 27, bearing coplanar basestype of geometry, deviate from the established linearity(see Fig. 6(B)) basically due to the type of distortiondepicted in Fig. 2(A), which involves a deviation, fromtheir original position, of the apical ligand (with a sa

angle) and of one of the terminal basal ligands (with asb angle), leading to a tbp type of geometry aroundeach copper atom. The complexes undergoing this typeof distortion show an enhancement of the forecastedferromagnetic character, then being placed on the rightside of the straight line in Fig. 6(B). This is in agree-ment with the overlap theory proposed by Khan [54,55]in which this type of distortion is responsible for theincrease of the effective Cu�Cl�Cu orbital overlap (theapical ligands also contribute to the HOMO andLUMO orbitals, see Fig. 2(B)) and, as a consequence,of the ferromagnetic contribution to the coupling con-stant J.

EH calculations for the ideal parallel bases type ofgeometry (Fig. 1(B)) show that the magnetic interactionbetween the copper metal centers will take place mainlythrough a p* type of interaction between the Cu dx 2−y 2

and the apical pCl orbitals. Therefore in this geometryvery small magnetic coupling constants (J) are expectedwhich again is consistent with the experimental valueslisted in Table 1. What is interesting in this case, is thatsmall geometric deviations produce large gaps as shownin Fig. 3 and Fig. 4. As a consequence of those twoeffects, the complexes adopting this type of symmetryare randomly scattered close to the x axis. Complex 21[53], was originally assigned as forming part of thecorrelation followed by the compounds marked withrhombus in Fig. 6(A) [51].The fact that this complex inboth graphs (Fig. 6(A and B)) is aligned close to thecomplexes with the coplanar type of geometry demandsa reexamination of its geometrical classification. In-deed, a careful inspection of its structural parameterscombined with its magnetic properties clearly showsthat it is much better defined as having a coplanar basestype of geometry with a slight distortion of the local Cugeometry towards tpb. This result invalidates the em-pirical magnetostructural correlation proposed early byHatfield and coworkers [51]. It is also worth mention-ing that complexes 1, 13, 16, 18 and 19, which alsobelong to the parallel bases type of geometry, are theones situated farther from the x-axis. This is due to thepresence of other coordinating atoms than N, whoseoverall effect is an increase of the antiferromagneticcharacter.

Up to now there is only one fully characterizedcomplex that presents the perpendicular bases type ofgeometrical arrangement [25]. For this complex, asmentioned in a previous section, only orbitals of the

basal Cl bridging ligand participate in frontier orbitals.Thus from a magnetic point of view the system can bedescribed as having only one bridging ligand. Howeverthe apical Cl has a key role in overcoming the sterichindrance leading to a Cu�Cl(basal)�Cu bond angle ofonly 91.4°. For a monobridged core the Cu�Cl�Cubond angle would be much higher due to steric repul-sions and therefore this would substantially changemagnetic properties. As a result of this low angle, theoverlap between dCu−pCl(basal)−dCu is very similar forboth frontier orbitals thus yielding relatively close ener-gies. This similarity of energies for the HOMO andLUMO orbitals is in turn consistent with the experi-mental ferromagnetic behavior displayed by thecomplex.

In contrast with the coplanar bases type of symme-try, here the decrease of the Cu�Cl(basal)�Cu angle from94.18 to 86.10° produces a nearly linear increase of thegap. Therefore if more complexes existed with this typeof symmetry, this theoretical analysis would predict avery good magneto-structural correlation with theCu�Cl(basal)�Cu angle.

As a summary, complexes bearing the Cu(m-Cl)2Cucore need to be classified in terms of their relativearrangement of square pyramids into coplanar, paralleland perpendicular bases. EH calculations indicate thatin each case a completely different type of orbitals isinvolved in their respective frontier orbitals. Distortionsfrom ideal models provides understanding of the differ-ent structural parameters that influence the energy gapbetween frontier orbitals and therefore allows to fore-cast the behavior of their magnetic properties.

Acknowledgements

This research has been supported by DGICYT ofSpain through grants PB96-0467 and PB96-0163.CIRIT of Catalunya is also gratefully acknowledged foran aid SGR-3102-UG-01 and for the allocation of a FIdoctoral grant to M.R.

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