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Published in issue 30, 2009 of Dalton Transactions

Image reproduced with permission of Christophe Coperet Papers published in this issue include: A combined picture from theory and experiments on water oxidation, oxygen reduction and proton pumping Per E. M. Siegbahn and Margareta R. A. Blomberg, Dalton Trans., 2009, DOI: 10.1039/b903007g Mechanisms of C–H bond activation: rich synergy between computation and experiment Youcef Boutadla, David L. Davies, Stuart A. Macgregor and Amalia I. Poblador-Bahamonde, Dalton Trans., 2009, DOI: 10.1039/b904967c Are tetrathiooxalate and diborinate bridged compounds related to oxalate bridged quadruply bonded compounds of molybdenum? Malcolm H. Chisholm and Namrata Singh, Dalton Trans., 2009 DOI: 10.1039/b901734h Molecular recognition in Mn-catalyzed C–H oxidation. Reaction mechanism and origin of selectivity from a DFT perspective David Balcells, Pamela Moles, James D. Blakemore, Christophe Raynaud, Gary W. Brudvig, Robert H. Crabtree and Odile Eisenstein, Dalton Trans., 2009 DOI: 10.1039/b905317d Visit the Dalton Transactions website for more cutting-edge inorganic and organometallic research

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PAPER www.rsc.org/dalton | Dalton Transactions

Ligand field torque: a p-type electronic driving force for determining ligandrotational preferences

Robert J. Deeth,* Anna E. Anastasi and Kris Randell

Received 13th March 2009, Accepted 27th May 2009First published as an Advance Article on the web 23rd June 2009DOI: 10.1039/b905154f

Transition metal complexes with triply-degenerate T ground states are formally Jahn–Teller active butdo not usually display the significant bond length distortions familiar from their E ground statecounterparts like d9 Cu(II). The electronic ‘asymmetry’ for T-state systems lies in the dp orbitals, whichinteract with the ligands relatively weakly compared to the stronger s-type interactions for E-statesystems. However, in combination with asymmetric M-L p bonding, T-type systems have an additionalmechanism for relieving the electronic strain. Density functional theory, ligand field theory and ligandfield molecular mechanics calculations are used to show how rotations around the M–L bonds canaffect their p–p (dp–Lp) interactions and lead to significant energy lowering. For example, d6

[Fe(OH2)6]2+, which has a 5Tg state in cubic Th symmetry, ‘distorts’ to an S6 structure 4.4 kcal mol-1

lower in energy (by DFT) but with six equal Fe–O distances via Fe–O rotations of ~ 20◦ and thusmasquerades as an apparently regular geometry. Using model systems, we show that this effect is notrestricted to formally Jahn–Teller active complexes. The combination of asymmetric p bonding andasymmetric dp orbital occupations can generate an M–L ‘torque’ worth up to 6 kcal mol-1 per bondwhich can ‘lock’ the ligand in a particular orientation relative to the partially-occupied d orbital(s). Theeffect is particularly marked for imidazole, the donor group of histidine, which, in a model low-spin d5

Fe(III) system, shows almost no orientational preference in its neutral form but a very strong (~6 kcalmol-1) orientational preference in its deprotonated form.

Introduction

The Jahn–Teller effect (JTE) is ubiquitous in coordination chem-istry. In Oh symmetry, for example, most dn configurations areformally ‘Jahn–Teller active’ (Table 1). They generate either E orT orbitally degenerate ground states, depending on whether the‘asymmetry’ in the d orbital occupations is in the s-type eg orp-type t2g orbitals.

While the original concepts of Jahn and Teller were publishedmore than 70 years ago,1 the Jahn–Teller effect continues to attractgreat interest.2 The most-studied transition-metal-based Jahn–Teller effects, and certainly the ones which are easy to spot, arethe geometrical changes associated with the Jahn–Teller distortion(JTD) of a s-type E ground state system. Six-coordinate d9 Cu(II)is probably the best known example3 where the coupling betweenthe 2Eg term and the Jahn–Teller-active eg vibrational mode (an2Eƒe vibronic coupling problem) leads to the familiar tetragonallyelongated 4 + 2 geometry. (Fig. 1)

The competing factors involved in ‘s-type’ JTDs, especiallyin copper(II) chemistry, were established some time ago3–5 whileCarver et al.6 have recently examined high-spin d4 species like[Mn(OD2)6]3+, which, while superficially similar to their d9 coun-terparts, have a more complex electronic structure which requiresconsideration of the mixing of an excited 3T1 state into the 5Eƒeproblem.

Inorganic Computational Chemistry Group, Department of Chemistry,University of Warwick, Coventry, UK CV4 7AL. E-mail: r.j.deeth@warwick.ac.ukx; Fax: +44 24 76524112; Tel: +44 24 76523187

Table 1 Ground state orbital degeneracies for octahedral dn complexesin high spin (HS) and low-spin (LS) environments

n 1 2 3 4 5 6 7 8 9

HS T T A E A T T A ELS T T A T T A E A E

Fig. 1 Electronic stabilisation energy associated with a tetragonal elon-gation for d9 CuL6 species.

In contrast, reports of ground state geometrical distortions ofp-type systems—i.e. those with a formally triply orbitally degener-ate ground state—which are directly attributed to the JTE are less

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common although significant effects on more sensitive propertieslike magnetization have been reported for T ground state systemslike the [Ti(OH2)6]3+ ion doped into CsGa(SO4)2·12H2O.7 Theusual rationale for no apparent structural changes is that the dp

‘t2g’ orbitals interact with ligand orbitals only relatively weaklyand hence p-type Jahn–Teller distortions are intrinsically small.For example, Reinen et al.8 have studied the [MIIIX6]3- polyhedrain elpasolite A¢2AMX6 systems (A, A¢ = K, Rb, Cs+; M = Ti, V, Co;X = Cl, F) and describe them in terms of Tƒe vibronic coupling(Fig. 2). They conclude that the Jahn–Teller splittings for thesep-type T ground states are about an order of magnitude smallerthan those for E ground states.

Fig. 2 Schematic representation of the first-order potential energy surfacefor Tƒe vibronic coupling. The two components of the eg vibrational modeare shown on the left.

Even to first order, p-type JTEs are much more complicated thans-type effects. Worse still, it is possible to couple the T groundstate with triply-degenerate vibrational modes to give a seriesof Tƒt coupling problems with a bewildering array of possibledistorted geometries. However, given a suitable ligand system, thecomplexity is significantly reduced.

Reports from the Halcrow group on high-spin complexes ofd6 Fe(II) and 2,6-dipyrazolylpyridine and related ligands (Fig. 3),show significant and remarkable angular distortions from ‘reg-ular’ meridonal coordination, which they attribute to the JTE.9

Depending on the counter anion, the twisting of the plane of oneligand relative to the other about the N{pyridine}-Fe-N{pyridine}vector, and the rotation of one ligand about the Fe ion (q and fin Fig. 3), is around 63◦ and 154◦, respectively, versus the ‘regular’values of 90◦ and 180◦.

Fig. 3 Definition of the twist angle, q, and the rotation angle f.

Such clear examples of JTDs in T ground state systems arerelatively rare. So what about the humble [Fe(OH2)6]2+ ion? Thisd6 species possesses a 5Tg ground state in cubic (i.e. Th) symmetryand is therefore formally Jahn–Teller active. However, it is treated

as ‘octahedral’,10 implying that any JTD is relatively insignificant.However, our recent re-evaluation of ligand field stabilisationenergy (LFSE) contributions to the ground states and water-exchange transition states for the M2+ aqua species of the firsttransition series suggest something different.11 Based on idealTh symmetry, the DFT estimate of Doct for [Fe(OH2)6]2+ (and[Co(OH2)6]2+) was about 4000 cm-1 smaller than the ‘accepted’experimental value of about 9000 cm-1.12 In contrast, provided theexperimental values for CrII and CuII are adjusted to take theirstrong Jahn–Teller distortions into account, the DFT Doct valuesfor the VII, CrII, NiII and CuII were in quite good agreement withexperiment.

In this paper, we analyse the source of this discrepancy in detailand show that [Fe(OH2)6]2+ is quite strongly Jahn–Teller stabilised.The ‘trick’ is that ligands like water, which are capable of engagingis asymmetric p bonding, are able to relieve the ‘electronic strain’associated with the JTE by rotations about the M–L vector ratherthan having to alter the M–L bond lengths as demanded in the Eƒes-type JTE. Thus, the ‘distortion’ is less obvious and the Jahn–Teller-stabilised complex masquerades as an apparently regularsystem with six equal M–L bond lengths. The consequences ofsuch ‘torsional stabilisations’ are potentially far-reaching.

Computational details

Density functional theory (DFT) calculations used the 2008version of the Amsterdam density functional (ADF) program.13

Geometry optimisations employed the spin-unrestricted OPBEfunctional14,15 with basis sets of triple-z plus polarisation (TZP)quality throughout with the frozen core approximation16 (1s–2pon first-row metals, 1s–3d for Rh and 1 s on C, N, and O). DefaultSCF and geometry optimisation convergence criteria were used.Spin contamination for open-shell systems was small as judgedby the calculated expectation value of <S2>, which was alwayswithin a few percent of the appropriate ideal value.

All LFMM calculations were carried out using DommiMOE,17

our extended version of the Molecular Operating Environment,based on MOE2007.

All Cambridge structural database (CSD) searches were carriedout via the EPSRC Chemical Database Service.18

Results and discussion

Complexes of the 2,6-di(pyrazol-1-yl)pyridine skeleton, L1,(Scheme 1) display some remarkable properties. With CuII,substitution at the 3 and 3¢¢ position leads to a change overfrom the normal axially-elongated structure of six-coordinate CuII

complexes with a dx2 -y2 ground state to the much less commonaxially compressed structure with a dz2 ground state.19 With FeII,not only do we see substantial Jahn–Teller distortions but many

Scheme 1

6008 | Dalton Trans., 2009, 6007–6012 This journal is © The Royal Society of Chemistry 2009

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of these complexes, and those with structurally-related ligands,display spin crossover behaviour.20,21

Focusing on the structural chemistry of the iron complexes,Elhaık et al.9 consistently refer to the ‘angular Jahn–Tellerdistortion’. While they report some simple DFT calculations,the analysis is complicated by the non-90◦ bite angles inherentin L1. Thus, there is not a clean separation between s and peffects and the energies of the dp orbitals are affected to someextent by Fe–N s interactions. As a fully quantum method, DFTautomatically describes the whole complex and cannot easily beused to separate M–L s from M–L p effects. Hence, the source ofthe ‘angular’ distortion remains unclear.

There is also the somewhat thorny issue of whether it istheoretically correct to apply molecular modelling methods whichimplicitly assume the Born–Oppenheimer approximation to JTEproblems where, by definition, the electronic and nuclear motionsare coupled.2 In principle, a full vibronic treatment should beconsidered.6,22,23 We take a simpler, pragmatic view and assertthat conventional methods have, and continue to, provide usefulinformation.5,24,25 Returning to the issue of the JTE in Fe(II)complexes, ligand field molecular mechanics (LFMM)26,27 explic-itly and separately parameterises M–L s and p effects via theunderlying angular overlap model (AOM)28 es and ep parameters.Moreover, we can explicitly separate asymmetric p bonding—i.e.that perpendicular to the ligand plane and that in the plane.This is in contrast to the effective Hamiltonian crystal field(EHCF) method.29,30 Although related to LFMM EHFC has onlysymmetric p bonding.

Thus, using the LFMM, Fe–N perpendicular p bonding can beswitched off and on at will. LFMM calculations clearly show ap-bonding effect (Fig. 4), although it is somewhat different to thatobserved crystallographically.

Fig. 4 Effect of p bonding in LFMM optimisations of [Fe(L1)2]2+.

Increasing the Fe–N p^ bonding parameters yields a definitechange in f. However, there does not appear to be much ofa rotation of the two ligand planes. Instead, we see a new‘rudder’ movement, r, coupled with an elongation of one ofthe Fe–N(pyrazolyl) bonds in each ligand. However, the appar-ent difference between X-ray crystal structures and LFMM isprobably not significant. The LFMM parameters have not yetbeen fully optimised plus the potential energy surface is extremelycomplicated with a large number of possible minima. Given thatcrystal packing may exert a small effect but this may be significantgiven the very many possible and energetically similar structures,we do not presume precise agreement between the solid state and

single-molecule LFMM optimisations. Nor is precise agreementrequired. The important observation is that the LFMM-optimisedstructure displays no angular distortion in the absence of M–L pinteractions. This angular distortion is therefore a p-type JTE.

The crucial difference between T ground state systems whichshow significant JTE and those which do not, is the nature ofthe p bonding interaction. In particular, asymmetric p bondingencourages a Jahn–Teller stabilisation. However, in contrastto E ground state systems where the nature of the couplingvibration means that the ‘electronic strain’ is relieved throughchanges in bond length, asymmetric p systems have an alternativemechanism–rotation about the M–L bond.

Torsional stabilisation can be substantial. To illustrate this,let us return to [Fe(OH2)6]2+. In Th symmetry—the highestsymmetry point group possible for this system—the dp orbitals aredegenerate. This is the equivalent to the truly octahedral symmetryavailable to symmetric p bonding systems like the MX6 complexesstudied by Reinen et al.8 and defines the reference point for anydiscussion of the JTE.

Assuming Fe-OH2 p bonding occurs only perpendicular to thewater ligand plane and that water is a p donor (ep^ > 0), withinthe angular overlap model (AOM), the three dp orbitals have anenergy of 2ep^. For the high-spin d6 configuration, therefore, thelargest possible electronic stabilisation arises when one of the dp

functions is rigorously non-bonding and is therefore at the energyzero. Our estimate of ep^ for [Fe(OH2)6]2+ is 1400 cm-1 based onDFT calculations.11 Hence, twice this is the maximum possiblechange in the p contribution to the LFSE which corresponds tojust over 8 kcal mol-1.

However, the geometric changes, which lower the LFSE tendto increase unfavourable intra-ligand interactions such that themaximum possible p stabilisation is not realised plus some of theelectronic stabilisation is offset. Thus, while the S6 structure shownin Fig. 5 is a true minimum, the rotations about the Fe–O bondsare only about 20◦. By LFT, the electronic driving force is ~ 5 kcalmol-1 (Fig. 5) but, overall, the ‘distorted’ structure is only 4.4 kcalmol-1 lower (by DFT) than the reference Th system.

Fig. 5 Ligand field stabilisation energy change for d6 [Fe(OH2)6]2+

associated with a geometrical ‘distortion’ from Th to S6 symmetryassuming ep^ = 1400 cm-1.

However, to put this in perspective, the comparable DFT calcu-lations for [Cu(OH2)6]2+, but using C i symmetry for the distorted

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geometry, yield a Jahn–Teller stabilisation of 6.2 kcal mol-1. Thus,rather than the p-type JTE being only a tenth the magnitude ofthe s-type as found for MX6 complexes with symmetric p-bondingligands,8 the energetic stabilisation for [Fe(OH2)6]2+ is about twothirds of the Cu(II) value and yet the structure of [Fe(OH2)6]2+

has six identical Fe–O bond lengths. The complex masquerades asapparently regular. The large magnitude of the p-type Jahn–Tellerstabilisation in high-spin FeII complexes does not appear to havebeen recognised previously.

A more obvious JTD can be forced onto the DFT calculationby imposing a point group symmetry, which precludes bondrotation, D2h for example. Now the orbital degeneracy can onlybe lifted by altering the Fe–O bond lengths resulting in a‘classical’ tetragonally-elongated structure with four short Fe–Obonds at 2.09 A and two longer axial contacts at 2.17 A. Thus,while reasonably large, this distortion is much smaller than for[Cu(OH2)6]2+ consistent with the weaker anti-bonding shifts of thedp orbitals compared to the ds functions.

The driving force for all these geometry changes is the p con-tribution to the LFSE. We can expect an effect whenever we haveasymmetrically occupied dp orbitals (i.e. not ‘high spin’ dp

3 or dp6)

in combination with asymmetric p-bonding ligands. Interestingly,asymmetric p effects are also implicated in determining the spinHamiltonian parameters for the s-type JTE system [Cr(OH2)6]2+31

although, since the dp functions are symmetrically occupied, theyplay no major structural role.

Effects from asymmetric p bonding can be seen in systemswhich are not even formally Jahn–Teller active. As part of anotherproject, we are examining dirhodium carboxylate complexes ofgeneral formula [Rh2(O2CR)4X2]n. The LFMM force field is based,in part, on DFT calculations for the hypothetical monomeric[RhL4]m systems. These low-spin d7 species are planar. In general,this can lead to quite complicated electronic structures since theplanar geometry separates the s-antibonding dx2 -y2 orbital fromthe other four d functions but the latter are relatively close together.Only one is singly occupied and relatively minor variations inligand and/or environment can change the singly-occupied orbitalwith a concomitant change in spectroscopic and/or magneticproperties. Planar Co(II) Schiff base complexes are a classicexample.32

We noted from DFT calculations for the simplest model iminecomplex, [Rh(NH=CH2)4]2+ that its highest-symmetry ‘perpen-dicular’ D2d structure (Fig. 6, left) was not the local minimumbut a first-order saddle point. The true minimum has the ligandstwisted about the Rh–N bond by about 27◦ (Fig. 6, right). In

Fig. 6 Computed (DFT) energy changes as a function of singly-occupiedorbital for low-spin d7 Rh(II) model imine complex.

both cases, dz2 was singly occupied—state 1 in Fig. 6—but theenergy change was negligible. In contrast, during the subsequentLFMM parameterisation, the perpendicular structure could bemade the local LFMM minimum depending on the magnitude ofthe d-s mixing parameter which, in turns, determined the relativeposition of the dz2 orbital and hence the nature of the ground state.

For large values of eds, dz2 can be made the lowest energy dfunction and dx2 -y2 becomes the singly-occupied orbital (notethe axis frame definition in Fig. 6). The imine p orbitals alignthemselves parallel to the plane of the singly-occupied dp orbital.Based on DFT calculations for the excited state 2 configuration,corresponding to {dx2 -y2}1, at the twisted and perpendiculargeometries, the strength of this alignment is quite weak at about1.6 kcal mol-1 or only about 0.4 kcal mol-1 per ligand.

Despite this small orientational effect, the RhII complexesillustrate the important principle that ligand p orbitals will tend toalign themselves in the plane of a singly occupied dp functionprovided the latter are asymmetrically occupied so that a netelectronic stabilisation is possible. The process is thus another formof d-electron stereochemical activity33 wherein the orientation ofpartially filled d orbitals ‘locks’ the position of certain ligands.

The planar low-spin d7 RhII systems also hint at the possibilitythat these p-type stabilisation effects could be switched on andoff. For example, a change, which swaps the order of dz2 and thein-plane dp orbital will alter the orientation of the ligand planefrom no particular preference to one where it will prefer to beperpendicular to the coordination plane. The magnitude of thispreference will depend on the strength of the M–L p interaction.

Since dz2 is already higher in energy than the in-plane dp orbital,the RhII system is not a good choice to illustrate this switchingsince dz2 will always be singly occupied—that is, state 1 is muchhigher in energy than state 2. Instead, we have developed a simplemodel Fe complex and consider the change from low-spin d6 tolow-spin d5 to illustrate the possible importance of asymmetric pbonding for complexes undergoing redox. It is already well known,for example, that certain ML2L’4 complexes can undergo redox-induced cis–trans isomerism.34 Our results suggest that redoxchemistry could be associated with other more subtle yet stillsignificant geometrical effects.

The design of the complex shown in Fig. 7 is loosely based onSiegbahn’s simplified electronic model for compound 1 in hemeperoxidases35 where the porphyrin ring is replaced by two anionic[NH(CH)3NH]- moieties. Here, we use a smaller, neutral diimineto lower the symmetry and encourage a splitting between the dxz

and dyz orbitals. The two-fold symmetry of the Fe(diimine)2 unitmakes dxz the highest of the dp set. For low-spin d6 Fe(II), all the dp

orbitals are fully occupied and there is no p electronic stabilisation.

Fig. 7 The orientation of the water p function relative to the upper,singly-occupied dp function, dxz, in the model low-spin d5 Fe complex.

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In contrast, for low-spin d5 Fe(III), dxz is singly occupied and willstabilise the parallel alignment of the water ligand p orbital asshown on the left of Fig. 7. The energy lowering relative to thed6 case is computed with DFT to be 2 kcal mol-1. Comparedto the Rh(II) system, this change is now focused on a singleM–L interaction: 2 kcal mol-1 of ‘torque’ on the Fe–OH2 bondis becoming significant.

An even better example is the comparison between imidazole(Himid) and its deprotonated form, [imid]-. Given that histidinecoordinates via an imidazole side chain, the system has somebiological relevance. For Himid, the alignment tendency ofthe d5 complex is slightly in favour of the parallel alignment(~1 kcal mol-1) indicating that, for our particular model system,Fe-Himid p bonding is weak. We would not expect a strongorientational preference for Himid. In contrast, the formalnegative charge of deprotonated imidazole significantly enhancesthe interaction with the metal leading to a parallel alignmentstabilisation of nearly 6 kcal mol-1 (Fig. 8). This figure becomeseven more significant compared to the d6 analogues which showa 3.6 kcal mol-1 preference for the perpendicular arrangement.For this model system, deprotonation leads to strong orienta-tional preferences which change as a function of the formal dconfiguration.

Fig. 8 Calculated (DFT) stabilisation of the parallel orientation of theligand p orbital and dxz. Top: L = Himid; bottom: L = [imid]-.

Conclusions

This paper has shown that the combination of asymmetrically-occupied dp orbitals with asymmetric p-bonding ligands canlead to substantial energetic stabilisation. In some cases, such as[Fe(L1)2]2+, these p-type effects are easy to recognise since theygenerate clear structural distortions, which can be seen in, forexample, X-ray crystallographic studies. However, in other cases,such as [Fe(OH2)6]2+, the ‘distortion’ involves motions of the waterligands which take the Jahn–Teller-unstable Th structure to a truelocal minimum with S6 symmetry. The complex thus retains sixidentical Fe–O bond lengths and masquerades as an apparentlyregular structure.

The electronic strain inherent in the Jahn–Teller instability of theT electronic state can thus be relieved by rotations about the M–Lbonds resulting in a significant lowering of the energy—about

two-thirds of the comparable JTE for the Cu(II) analog—butwithout altering the M–L bond lengths.

This p-type stabilisation exerts a ‘torque’ around the M–L bondwhich depends largely on the strength of the ligand’s p bond.Even for simple ligands, DFT estimates suggest energy changes of2–6 kcal mol-1. Moreover, the key feature of asymmetric p bondingligands with asymmetric dp occupations is very common and hencethese p-type stabilisation effects are likely to be quite widespread.

For example, histidine is a good ligand in bioinorganic chem-istry and is also an asymmetric p donor. Our model system[FeF(HNCHCHNH)2L]n+ suggests a minimal p-bonding influenceon ligand orientation for L = imidazole but a very strongorientational (~ 6 kcal mol-1) preference for L = [imid]-. Therecould be a myriad of influences, which have been missed especiallyin computational studies using conventional MM, which does notexplicitly treat p bonding, or its effect, and will thus not generatethe necessary torque on the M–L bonds. Our implementation ofLFMM is unique in that the full AOM M–L bonding scheme hasbeen included. Related implementations such as SIBFA_LF36 andthe extension to GULP37 are limited to s interactions.

Thus, the energy changes associated with bond rotationsof asymmetric p-bonding ligands coordinated to metals withasymmetric dp occupations can be remarkably large. In particular,we are currently exploring the extension of LFMM to Fe(II)spin crossover systems. These materials very often contain Fe(II)coordinated to unsaturated nitrogen ligands20—i.e. asymmetric pdonors. In their high spin d6 forms, they will be susceptible to thekinds of interactions described in this paper. A change of just afew kcal mol-1 could make all the difference.

Notes and references

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R. M. Dickson, D. E. Ellis, L. Fan, T. H. Fischer, C. Fonseca Guerra,S. J. A. van Gisbergen, J. A. Groeneveld, O. V. Gritsenko, F. E. Harris,P. van den Hoek, H. Jacobsen, G. van Kessel, F. Kootstra, E. vanLenthe, V. P. Osinga, P. H. T. Philipsen, D. Post, C. C. Pye, W. Ravenek,P. Ros, P. R. T. Schipper, G. Schreckenbach, J. G. Snijders, M. Sola,D. Swerhone, G. te Velde, P. Vernooijs, L. Versluis, O. Visser, E. vanWezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and T. Ziegler,Scientific Computing and Modelling NV, Free University, Amsterdam,Amsterdam, 2008.

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6012 | Dalton Trans., 2009, 6007–6012 This journal is © The Royal Society of Chemistry 2009

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