Rajca Spin Coupling to Magnetism

7/27/2019 Rajca Spin Coupling to Magnetism

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m. .W. 1004, gq.871-893 871Organic Diradicais and Poiyradicais: From Spin Coupling to Magnetism?

Andrzej RajcaDsperbmnt Of c!?"y, hwstiy O f IlkbraSk.9. Lhooh. "&a 885880301

Recalved August 11, l@@3" i M"cr@t R ecal ved Fe M w y 17, 7@@4

Confenfs1. Introduction 8 7 12. Spln Coupling and ChemicalBond 8 7 2

8 7 34. Measuremant of Electron Spin Coupling: What 8 7 43. Spln Coupling and Organlc MagnetismIs the Ground State and by How Much?

A. Bulk Magnetization and SusceptibilityE. ESR SpectroscopyC. Other Methods fo r Determination of SpinStates

5. DkadicaisA. Slmple Dhadicab: Ferromagnetic vsAntiferromagnetlcCoupling UnltsE. Stable Diradicals: Sterlc Shlelding.Heteroatom Perturbatlon. Multiple CouplingUnitsC. QuantitativeUsage of SpinCoupllng Unlts

6. Trk and TetraradlcalsA. TriradicaisE. Tetraradicals

7. Star-Branched and Dendrltlc Polyradicais.Toward Nanometer-Size Slngie MoleculeOrganic Magnetic ParticleA. Star-BranchedHepta- and DecaradlcaisE. Dendritic Polyradlcals with 7. 15, and 3 1Sltes for Ferromagnetically CoupledElectrons

8. Defects and Spin CoupllngA. Spin-Coupllng PathE. Multiple Coupllng path

9. Polyradical Polyanions: Spin Coupling vsElectron Localization10 . Insight into the Eiecbonlc SbuctureAssociated with High Spln via Population ofNonbonding MOs11 . High-Spin Organic Ions and Polycarbenes12 . Conclusions and Perspecthres

8 7 48 7 78 7 78 7 88 7 88 8 0

8 8 28 8 38 8 38 8 48 8 5

8 8 58 8 6

8 8 68 8 68 8 78888 8 9

8 8 98 9 0

Diradicalsandpolyradicals are moleculesthatpossesstwo or more weakly interacting "unpaired" electrons,each formally associated with different atomic centersin a molecule. Diradicals are common intermediatesof chemical reactions and have received perpetualattention over the years.'3 Triradicals, tetraradicals,and higher radicals are relatively rare, and until severalyears ago, only a few of them were known.'.6Di- and polyradicals are a class of molecules that areespecially relevant to a multidisciplinary frontier ofscience concerned with weak interatomic/intermolecu-lar interactions in large systems. Many interestingphenomena in condensed matter are associated withweak interactions between electrons and/or nuclei0009-2685/94/07944871$14.00/0

fA&zejRa]Cawas m i n Walbrzych, Poland. in 1959. Hegraduatedfrom Polbchnlka Wroclawska (Poland) n 1981 (M.S.). In 1982.he Wned Laren M. Toiberi's group at Kentucky (Ph.D. 1985).Subsequently, he was a Miller Fellow an d Lecturer wlth AndrewSbeitwieser at Berkeley (1985-1988) . Before he joined theUniversity of Nebraska chemistry faculty In 1992. he was on thefacuityatKansasStateUniverslty. wherehewasawardedaCamilleand Henry Dreytus Teacher-Scholar Award.leading to a characteristicstate (e.g., with a long-rangeorder, frozen disorder, etc.) in macroscopic or meso-scopicensembles.m Thus, for an ambient temperaturesuperconductor, magnet, etc., t he characteristic energyof the interaction leadingto order should be -1 kcal/mol, that is, >RT at ambient temperature. Theseinteractions are quite weak compared to the typicalbond dissociation energy of 102 kcal/mol.

'The molecular approach" to studying such macro-scopic and mesoscopic phenomena consists of thefollowing sequence: (1)a small molecule with simpleelectronic structurewith two weakly interacting entities(e.g., unpaired electrons), (2) a larger molecule withseveral interacting entities,(3)mesoscopic-size moleculewith added complexities, (4) assembly of molecules tosupramolecular clusters, monomolecular layers, or bulksolids. Studyof organic di- and polyradicals in relationtomagnetismisoneofmanyexamplesofthisapproa~h.~Other examples are found in model studies for molecularrecognition, hydrogen bonding in biologicalstructures,etc.1 The goals of such an approach, through rationaldesign and synthesis of molecules, molecular ensembles,films, etc., are to prepare materials with superiorproperties compared to their existing 'natural" or"conventional" counterparts and to gain better insightto the most complex systems.

This review is focused on molecules with two or more'unpaired" electrons on carbon and other first rowelementa; the transition metal organometallics areexcluded. Theother organic molecules with unpaired"electrons, which are relevant to interactions between"unpaired" electrons such as carbenes, nitrenes, andcertain ions, are briefly mentioned in section 11.8 99 4 A Chemical Socieiy


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872 Chemical Reviews, 1994, Voi. 94 , No. 4 R a j aS =0) functions; for S =0, the symmetry of the spatialpart leads to large probability for fiiding an electronbetween the nuclei. This symmetric spatial part of thewave function can be approximately illustrated by aHartree-Fock a-bonding orbital in H2. The spatial partof the S =1wave function possesses a node betweenthe nuclei, similarly to the a-antibonding orbital in H2.

[Electronic Wave Function]= [Space] x [Spin] =A

Qualitatively,weakly interacting unpairedelectronssuggestpresence of near-degenerate low-lying electronicstates of different spin for di- and polyradicals.Determining the spin of the ground and low-lyingexcited states, as well as the energy gaps between thelow-lying states, is the primary goal of the experimentalmeasurements. The energy gaps and spin can beinterpreted in terms of spin coupling between theunpaired electrons. Application of the molecularapproach should lead to insight about spin couplingin meso- and macroscopic size structures.Because many interesting phenomena in magnetismrely on the competition between the interaction involv-ing a large number of magnetic moments (typically,associated with spins of unpaired electrons) andthermal motion, di- and polyradicals with spin cou-plings, which are comparable or larger than kT in theaccessible temperature range, are particularly relevant.Furthermore, the special role of ferromagnetic spincoupling n bonding and magnetism implies importanceof di- and polyradicals with high-spin ground states.2. Spln Coupilng and Chem ical Bond

For a pair of electrons, their total spin (S) an beeither S =1 (parallel spins) or S =0 (antiparallelspins); n terms of spin multiplicity,2s+1, hese spinvalues correspond to triplet and singlet, respectively.In regard to the lowest energy state, the reference canbe made to either ferromagnetic ( S =1)or antiferro-magnetic ( S =0) spin coupling. The energy differencebetween the singlet and triplet s tates (AEsT)measuresthe strength of the spin coupling. (Spin-orbit couplingeffects are neglected.) Thus, a chemical bond may beviewed as an extreme case of antiferromagnetic cou-pling, and A&T can be a measure of the bond strength.llIt is challenging to achieve and understand a strongferromagnetic coupling, which is antithesis tobonding.

Energy Spin Multiplicitys 2 s t 1

O t O si*tThe case of antiferromagn etic couplingThe origin for preponderance of antiferromagneticcoupling (chemical bonding) is well established.12Because electrons are indistinguishable particles withspin, S = l/2, the electronic wave function must beantisymmetric ( A ) , ha t is, interchanging coordinatesof any pair of electrons should not change the prob-ability for finding an electron, but does change the signof the wave function. Typically, it is a good ap-proximation to write electronic wave function as productof the two parts, space and spin , each part eithersymmetric (S ) or antisymmetric ( A ) . The antisym-metric product, space X spin , may be either A X S orSX A . For two electrons and two nuclei, i.e., a chemicalbond, these two products correspond to triplet(parallelspin, S =1)and singlet (antiparallel spin,

SxA aD-Therefore, the spin preference, S =0 vs S =1, isassociated with the distribution of electrons with respectto nuclei; thus, electrostatics, not the magnetic interac-tions between the magnetic moments of electrons,determines the spin of the lowest energy state (groundstate).l3 For H2, the ground state is singlet ( S =0) atall internuclear separations; this is not only the resultof the above simplistic analysis of symmetry of the exact

two-electron wave function but alsothe result of rigorousmathematical proof for kinetic/electrostatic energyHamiltonian for H2 as well.14Singlet ground states are found in an overwhelmingmajority of nonmetallic molecules; however, for systemswith more than two electrons, S =1ground states arepossible in rare cases. Examples are C (atomic carbon),0 2 , CH2 (carbene), etc.2JsThe preference for S =0 vs S =1ground state canbe illustrated by applying the above symmetry argu-ments to a simple two-orbital two-electron model. Whenno restrictions are placed upon the orbitals, they overlapin phase; the spatial part of the two-orbital wavefunction is symmetric and the S=0ground state results,i.e., hydrogen atoms forming a chemical bond in Hz(two 1s orbitals). When the orbitals are restricted tobeing orthogonal, they will overlap out-of-phase; thespatial part of the two-orbital wave functionwll possessa node and the S =1ground state will be obtained, i.e.,in C (two 2p orbitals).

s =o S = lTriplet ground state for C, which possesses half-occupied degenerate atomic orbitals, isa manifestationof Hunds rule.ls The extension of the rule to moleculeswith half-occupied degenerate molecular orbitals (MO)appears straightforward because MOs an be madeorthogonal. Examples of such an extension is foundin those diradicals, where a pair of half-occupiednear-degenerate (or degenerate) nonbonding MOs(NBMOs) must have their lobes coincide significantly(non-disjointMOs).n fact, very strong ferromagneticcoupling may be obtained in such diradicals, with AESTon the order of 10kcal/mol. The complication is that,for some diradicals, the half-occupied NBMO s can beselected in such a way tha t their lobes coincide to verysmall extent (disjoint MOs). n those cases, the


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Organic Dlradicals and Polyradlcalsexchange integral is small and, consequently, the spincoupling is small (the S = 0 and S = 1 are neardegenerate).ls The examples are provided by twor-conjugated diradicals, trimethylenemethane (TMM)and tetramethylenethane (TME).

Chemical Reviews, 1994, Vol. 94 , No. 4 873ensembles with predominantly ferromagnetic couplingbut with either maximum or zero spontaneous mag-netizations indicates th at ferromagnetism at T >0 isnot possible for a one-dimensional (1D)chain of spins.22In two- and three-dimensional (2D and 3D) spinensembles ferromagnetism is possible; however, in 2D ,this prediction is highly model dependent and Tcs tendto be lowera23Intramolecular ferromagnetic spin coupling is ex-ceptionally large (compared to transition metal dimers)for some organic diradicals. If such large ferromagneticcouplings can be maintained in polyradicals with 2Dor, most likely, 3D-extended structures, then bulkorganic magnets with high TC ambient temperature)are achievable. Examples of suitable structures arehighly cross-linked polymers; in 1968,Mataga proposedsome relevant 2D structures.24 A combination of highTC nd very low density of unpaired electrons would beunusual; dilute alloy ferromagnets, e.g., 0.196 Fe in Pd,has rather low T c . ~ ~Another option is to use mono-, di-, and polyradicalsas components of molecular or macromolecular solids.Unfortunately, the intermolecular ferromagnetic spincouplings discovered to date are rather weak, with someex~eptions.~6*~he first organic ferromagnet, whichis based upon neutral organic monoradicals, possessesvery low TC 0.60 Kh2-Interesting magnetic phenomena in systems whichcontain a mesoscopic number of spins (e.g., nanometer-size magnetic particles) are of both fundamental andtechnological interest.31 Recent examples are theoreti-cal prediction and experimental confirmation forquantum mechanical tunneling of magnetizationthrough magnetic anisotropy barrier on a mesoscopic~cale.3~Mesoscopic organic polyradicals are promising argetsbecause their size can be rigorously controlled by organicsynthesis. Furthermore, their anisotropy barriers canbe more easily evaluated because of the negligible spin-orbit coupling effects for nonlinear three-coordinatecarbon-based radicals.33 Consideration of classicalmagnetic dipole-dipole interaction gives the shapeanisotropy barrier (EA) s follows:

TMM I ILarge AEST

YTME I IA

Small ESTWhen the interaction between the pair of selectedMOs is small because of their disjoint nature ordifference in energy (e.g., TME), interaction betweenotherMOs,ncluding unoccupied ones, should be takeninto account; that is, electron correlation (e.g., withrespect to restricted Hartree-Fock MOs) may becomeimportant. Then, predictions of the ground state, S =1 vs S =0, are problematic; the problem is furtherdiscussed in section 5.Finally, it can be shown that symmetry properties ofthe wave function allow one to write a spin-couplingHamiltonian for spins S1 and S2 as

The negative sign and factor of 2 are one of thetraditional choices,l9 e.g., J > 0, 51 = SZ = l / 2 ,correspondstothe S=1ground statewhich is separatedby an energy gap of 25 from the S =0 excited state(PEST=2J) . Equation 2.1 is frequently referred to asHeisenberg (o r Heisenberg-Dirac) Hamiltonian. Itsderivation is straightforward for SI =S2 = l / 2 andorthogonal orbitals.20

H =-2JS1*S2 (2.1)

3. Spln Coupllng and Organic MagnetismMost recent research on organic di- and polyradicalsis also tailored toward discovery of novel magneticmaterials and understanding important aspects ofmagnetism. While comprehensive discussion of mag-netism isbeyond the scope of this article, selected issuesrelevant to organic radicals are mentioned.Many interesting magnetic phenomena involve spincoupling of a macroscopic number of electron spins (andother interactions), in competition with thermal exci-tations. An example is ferromagnetically orderedmaterial below Curie temperature, Tc, hich possessmany important features, including ferromagnetic spincoupling (e.g., pairwise parallel spins) and spontane-ous magnetization (e.g., net number of parallel spins).Consideration of thermal energy versus pairwise spincoupling with spin-coupling constant J for example,eq 2.1) gives an order of magnitude estimate for Tc;that is, kTc =J.21 owever, the sufficient strength offerromagnetic spin coupling is merely one of theprerequisites for ferromagnetism. Consideration of spin

EnergytQ

Iw 1When attempting to invert magnetization in nanometer-size elongated-shape ferromagnetic particles, theintermediate configuration has a relatively high pro-portion of the unfavorable side-by-side vs a lowproportion of the favorable head-to-tail dipole orienta-tions. Besides the more elongated shape, other factorsshould increaseEA = (number of unpaired electrons)

(unpaired electron density)2 (3.1)Application of organic polyradicals to interestingproblems in magnetism of solids poses an obvious


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874 Chemical Reviews, 1994, Voi. 94, No. 4 R a j asynthetic challenge, especially when the 2D and 3Dstructures are needed in some cases. Most importantly,strong ferromagnetic spin coupling found in diradicalsmust be maintained in their higher homologues.4. Measurem ent of Elec tron Spin Coupling:What Is the Ground State and by Ho w Much?

As discussed in section 2, spin coupling in a diradicalmay be described by Heisenberg Hamiltonian, H =-US1432 (eq 2.1))where "J" s spin-coupling constant.The ground-state total spin (5') is S =1 for J >0(ferromagnetic coupling) and S =0 for J k T . The most importantmethod of measurement of J relies on detecting therelative thermally induced populations of the states ofdifferent spin; whenJ - T , the changes in populationsbetween different spin states will be the most pro-nounced and, therefore, the J will be determined withthe greatest accuracy.The temperature range of most spectroscopic andmagnetic measurements is limited by, on the one side,difficulty n attaining temperatures in the neighborhoodof absolute zero and, on the other side, instability ofpolyradicals. Typically, temperatures between 2 and300 K are readily accessible; in terms of energy permole, 0.004


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Organlc Dlradlcals and Polyradicaisa numerical two-parameter fi t to eq 4.1, even if theamount of polyradical is unknown. Alternatively, ifthe amount of the polyradical is known, S may beobtained by a one-parameter fit to eq 4.1 or, lessaccurately, calculated from Mmt. The data is usuallyshown as magnetization, M vs HIT, or "normalized"magnetization (equivalentto Brillouin function),M/M,vs HIT (Figure 1B). The reliability of the value of Sdepends on number of the fitting parameters, theirinterdependence, and the HIT range; the type of theBrillouin plot used to display the results as in Figure1 (A vs B) is irrelevant.B&) for large values ofSshow very similar curvature.Only approximate values of large S may be obtained bythe above procedures, if the amount of polyradical isunknown. In the more favorable case, where the amountof radical is known, all experimental errors in measure-ment of Msathave to be less than (1/2S)100% to obtainthe spin,S f lIz,.g., for S =10- ess than 5 % . Finally,in the limit of infinite S , Brillouin function (eq 4.1)becomes Langevin function.39Polyradicals with S = 0 and large IJ1 should beinvestigated using other techniques; for all otherpolyradicals with extreme values of "J",magnetizationfollows the Brillouin functions with appropriate valuesof S. For odd-electron S = / z polyradicals, distinctionbetween the strong antiferromagnetic and uncoupled(weakly coupled) polyradical is made by evaluating Mthat is, the amount of polyradical should be determinedindependently.When polyradicals with different values of S arepresent in the sample, M does not follow any Brillouinfunction.40 M or a polyradical with spin, S, is relatedto the product, S*Bs(x),which, in the limit of smalland largeHIT, s related toS(S+1)and S, espectively.Consequently, addition of magnetizations, MI =constl*S1*Bsl(x) and MZ=constz*Sz*Bsz(x),for anypair of polyradicals with different spins (SI# SZ) ,cannot be related to the product S*Bs(x). For example,for an equimolar mixture of two polyradicals withdifferent spins, S1# SZ,molar magnetization followsBrillouin functions corresponding to S' =[ ( l+2A)1/z- 13,where A =S1(S1+1)+Sz(S2+11,a t small HITand S" =(SI+&)I2 at argeHIT, Le., there is a crossoverfrom the larger, S', to smaller, S", function withincreasingHIT. Analogous results are easily obtainedfor mixtures of more than two-spin systems.Spin values can also be determined by thermallyperturbing population of the m, sublevels. In the limitof small HIT,eq 4.1 can be shown to give rise to simpleCurie plot (eq 4.2).36

x =Ng2F2S(S+1)/3kT (4.2)In connection with eq 4.2, the susceptibility data arefrequently plotted as xT vs T ; S for polyradical isobtained from the value of xT. Alternatively, aneffective magnetic moment (peff=2.84(~T)'/~)an bedefined. The amount of polyradical must be knownaccurately, and for isolated polyradical, one data pointmight be sufficient to determine value of S .b. Intramolecular Interactions, J =k T

For weakly coupled (smallSsorJ = T )polyradicals,it is possible to perturb population of both the m,sublevels and the ground vs excited states of different

Chemical Reviews, 1994, Vol. 94 , No. 4 875Scheme 1

Eigenvalues (Ei)

spin using variable H and T. Therefore, Brillouinfunctions (eq 4.1) and Curie plots (eq 4.2) are notapplicable; more general equations, which include eqs4.1 and 4.2 as special cases, should be used. Thederivation is outlined below, using a diradical as anexample.(1)Write Hamiltonian (Heisenberg, Ising,XU, tc.);Heisenberg is used here(4.3)

(2 ) Find eigenvalues corresponding to the total spin,S =SI+ Sz, and magnetic quantum number, m,=S ,S - 1, ...,S. The solution of the Hamiltonian (eq 4.3)for a pair of spins, S1 and SI, can be written as%E(S,m,) =gpBm,,Hz- J[S(S+1)- Sl(Sl+1)-In th is example, S1 =SZ='/z and S =0 , l and m,=1, 0, -1, and for J C 0, the energy diagram shown inScheme 1 s obtained.(3)Calculate partition function [Z=Cexp(-Ei/kT)]where Ei are eigenvalues from eq 4.4 (relative to the S=0 energy level, Scheme 1):

Z =1+exp(2J/kT)[l+ 2 cosh(gpBH/kT)] (4.5)(4) Calculate magnetization (M NkT(G I nZ / b l l ) ~ )

H =gFL,s$z - 2JSlSz

S,(S, +1) l (4.4)

for 1mol of diradical:M =2 N g p ~inh(gpBHlkT)/[exp(-2J/kT)-1

2 c~sh(g~BH/kT)l4.6)(5) Calculate static magneticsusceptibility ( x=M/H).x is typically measured at low magnetic fields (smallH) r at high temperature (large T);Le., HIT is small.Therefore, the following approximations for hyperbolicfunctions, sinh(x)= and cosh(x)=1, are appropriate.Thus, x for 1mol of diradical is

x =2N8p2/3kT[l +('l3)exp(-2JIkT)1-' (4.7)This is a well-known Bleaney-Bowers expre~sion.~~Equation 4.7 should be treated as an approximateversion of eq 4.6, especially, at low temperatures; a t Tc 2 K and for J =0, the xT from eq 4.7 is too high by-1% a t H =0.5 T and -10% at H =2 T.


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878 Chemical Reviews, 1994, Vol. 94 , No. 4 Rajathe Hamiltonian and connectivity should be explored.For example, for tetraradical (four S =l/2 centers), theequations analogous to eq 4.7 are distinctly differentfor colinear, triangular, square, butterfly, or tetra-hedral connectivity of the radical centers.36 Interpre-tations of the magnetic interactions, based upon eq 4.7and its analogues, are very sensitive to the quality ofthe magnetic data. Proper calibrationof the instrumentand accurate weight, purity, and correction for dia-magnetism of the sample and the sample holder areimportant.43

1.0

0 . 8

c, 0 . 6sd\ .4

0. 2

0 . 00 4 8

H (Teila)Figure 2. Plot of normalized magnetization, MIMmt vsmagnetic field,H,at temperature,T =2 K using eq 4.6. Thecurves from left to right correspond to a diradical with J / k=200, 2, 0, -0.5, -1, -2, -4, -10 K.

1 2 ah . 7 - bh2 0. 8i\

0. 8av 0.4x

0.2

0. 00 60 10 0 16 0 2 0 0 260 300

T (Kelvin)Figure 3. Plotof the product of magnetic susceptibilityandtemperature vs temperature (xT s 79. x is obtained fromeq 4.7; he curves correspond to the following values of Jlk(Kelvin): (a ) 500, (b)200, (c) 2, (d)-10, and -4, -2, -1, -0.5.J / k =500 K corresponds t o J =1 kcal/mol.

Equations 4.6 and 4.7 are quite sensitive to themagnitude of J


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Organic Diradlcais and Polyradicals Chem ical Reviews, 1994, Vol. 94 , No . 4 877

0 . eY 1

0 . 0 I0 6 10 16 2 0

H ( T e a l a )Figure 4. Plot of normalized magnetization,MIM, vsmagnetic field,H , at temperature, T =1K for J l k =-4.0 Kfor an intermolecular antiferromagnetic interaction(4withinan isolated pair of tw o high-spin (S=1)diradicals. M forone mole of diradical: M = Ngp&exp(z) sinh(x) +exp(3z)(sinh(x)+2 sinh(2x))]/[l+ exp(z)(l+2 cosh(x))+exp(3z)(l+2 cosh(x) +2 cosh(2x))]) where z =2 J / k T andx =g p f l / k T .B. ESR Spectroscopy

ESR spectroscopy had a crucial role in the discoveryof a triplet excited state (S =1). It is a common toolfor study of S >0 states in di- and po1yradicals.MBecause the intensity (I)of the ESR signal is relatedto magnetic susceptibility (x) s x = A"J ESRspectroscopy may be used similarlytothe bulk magneticmeasurements, as described above.a** However, quan-titative ESR measurements (spin counting) are rarebecause determination of Aeonst,which may be routinefor S = l/2, is difficult for S > l / ~ . ~ypical ESRmeasurements involve temperature perturbation ofeither m , sublevels in high-spin polyradicalsor popula-tion of the ground vs excited states of different spin.In the first case, I a 1/T,which is analogous to eq 4.2,is followed, and in the second case, I 0: 1/T[1 +(1/3)exp(-2J/kT)l-1, which is analogous to eq 4.7, isfollowed for a diradical. (ForS >1,equations similarto 4.7 can be derived.) Thus, when Ivs 1/T ollows thestraight line a t cryogenic emperatures, the ground state(typically, high spin) is separated by either a very largeor a very small energy gap (compared to kT) from theexcited states. If the curvature in the I vs 1/Tplot isdetected, then, the gap between the ground and excitedstates is comparable to kT and can be obtained fromthe fit equations analogous to eq 4.7. Thus, asdiscussedpreviously by Berson,S1 elucidation of the spin statesusing I vs 1/T dependence is ambiguous in manydiradicals. Furthermore, even if the curvature in theI vs 1/T is detected, it is almost always assumed tooriginate in intramolecular spin coupling.62 Suchinterpretations can be confirmed by dilution experi-ments.53One of the attributes of ESR spectroscopy is electron-electron dipolar coupling that provides characteristicspectral pattern.51 (Other terms in spin Hamiltonian,such as g anisotropy and A anisotropy, are lessimportant for most high spin organic polyradicals.)Typically, spectra are obtained in dilute, rigid media,

where polyradicals are randomly oriented with therespect to external magnetic field (e.g., frozen solution).However, even partial orientation of the molecules mayimprove spectral resolution." The transitions aretypically observed between the neighboringm,sublevels(Am,=1)but, the formally forbidden, weak transitionsbetween more distant m, sublevels (Am, =2 , 3) aresometimes detected. Because the number of m , sub-levels is 2 s +1 (spin multiplicity), these Am , =2, 3(half-field, hird-field) transitions are of great value todemonstrate the detection of a spin state with S 1 1and S 2 /2, respectively. Dipolar couplings, which arecharacterized by two parameters, D and E (sometimes,Elhc =0), will affect all observable Am , transitions; atleast for Elhc =0andsmall p/hc (, he spectral patternsfrom dipolar couplings in Am, =n for spin =S and Am ,=n +1 or spin =(S +1/2) transitions appear similar.55More rigorously, computer simulations of ESR spectra,withD,E,and S (spin) among several parameters, allowfor determination of spin states of the observed species?'In particular, a spectrum of a thermally populated S>0 excited state can be detected.%C. Other Methods for Determination of SplnStates

Magnetic susceptibility (x) an also be estimatedusing either contact shift or susceptibility shift, asdetected by solution NMR sp ec tr o~ co py .~ ~istinctionbetween the contact shift and susceptibility shift andknowledge of the amount (concentration)of the polyrad-ical must be accurate.Contact shift originates n hyperfine electron-nuclearcoupling (A), which splits NMR transition; for oneunpaired electron, two NMR lines are shifted by+('/2)A and -(l/z)A from their position in the absenceof the hyperfine coupling. Typically, he electron spin-lattice relaxation times are shorter by several orders ofmagnitude, compared to h/ A, and the two lines collapseinto one at the chemical shift which is weighted byBoltzman population of the electron m, ublevels. Themeasurement of this shift (contact shift) compared tothe appropriate diamagnetic reference reveals therelative population of the electron m , sublevels at agiven magnetic field (H) and temperature (2'9. For apolyradical with spin, S, this contact shift is%

The expression n the first square bracket correspondsto eq 4.2 for magnetic susceptibility. Similar to the eqs4.7 vs 4.2, an equation for the contact shift in a weaklycoupled diradical is obtained by substituting S =1 neq 4.9 and multiplying eq 4.9 by an additional factor,[l + (1/3)exp(-W/kT)l. Such an equation may beparticularly useful for determination of the spincoupling in singlet ground state diradicals because offavorable NMR line widths.se NMR line widths thatare too broad are oneof the limitationsformeasurementof contact shifts. Small hyperfine coupling (spindensity) at the observed nucleus, smallYN (2H s betterthan lH), fast electron spin-spin exchange (e.g., higherconcentration and temperature, solvent with unpairedelectrons) are among the factors sharpening the para-magnetic NMR lines.Contact shifts allow for determination of spin densi-ties in polyradicals.60 Also, impurities in samples of


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878 Chemical Reviews, 1994, Vol. 94 , No. 4polyradicals may be quantified, which is important forother types of measurements.Susceptibility shift arises because the NMR chemicalshift for a given nucleus (i.e., the effective magneticfield at the nucleus at a given frequency) depends notonly on microscopic environment of the nucleus butalso bulk properties of the sample such as its magneticsusceptibility, shape, orientation with the respect tothe applied magnetic field, et^.^^ This is the basis forEvans method for measurement of bulk magneticsusceptibility.61 Evans method is widely used byinorganic chemists to determine kefffor ransition metalcomplexes in solution; recently, it was applied tounstable polyradicals.62 For a sample, which is con-tained in narrow tube parallel to the external magneticfield (modern high-field NMR spectrometer), magneticsusceptibility (xm n emu/g) is determined from thefollowing equation61

xm =3 A 6 / ( 4 ~ ~ )x0 +xo(do- ,)/c (4.10)where c is concentration (in g/mL),x o s diamagneticsusceptibility of the solvent, and A6 is the chemicalshift difference (measured for solventor inert reference)between the solution (density, d 8) and pure solvent(density,do ) . The third term in eq 4.10 can be omittedwith negligible error for highly paramagnetic com-pounds.6l A6 should be corrected for the presence ofother diamagnetic solutes and the contact shift of thesolvent (or the reference) should be negligible. Forexample, A6 for diradical dianion 59 (R =H) in Me20is significantly ess than expected because of substantialcontact shift.63Typically, an assembly of two concentric tubes is used.The concentration of the solution should be sufficientto obtain easily measurable A6, but not too excessive,in order to avoid large NMR line broadening. Theconcentration should be known exactly at the tem-perature of the measurementf2 for variable-tempera-ture measurements, it is convenient to use a solventwith its density as a function of temperature knownaFor polyradicals with 14


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Organic Dlradicals and Polyradlcals Chemical Reviews, 1994, Vol. 94, No. 4 8791 o(fcuDj i....... ..........1 .......... n = 2 , 3@ i,acuD.........

L........... ..........2

3-0*i , a c u j..........L.............>4to be more effective, compared to their ferromagneticcounterparts.The presence (non-Kekule structures) vs absence(Kekule structures) of important open-shell resonancestructures suggests strong ferromagnetic vs strongantiferromagnetic coupling for diradicals with onecoupling unit.83The strength of the ferromagnetic coupling is alsoelucidated by the MO theory as outlined by Bordenand Davidson.18 Both 1 and 3 possess a pair of half-occupied nonbonding MOs (degenerate or near de-generate). TheseMOs ay be orthogonal and have tocoincide at oneormore atomic sites (non-disjointMOs);this leads t o the strong ferromagnetic coupling (section2).*Another approach is to invoke the concept of spinpolarization within either valence bond (VB) or MOtheory;@ n the latter case, UHF method or limitedelectron correlation are used. Heuristically, spindensities at he adjacent atomic centers in ?r-conjugatedsystem prefer opposite signs,a and j3,which correspondto antiferromagnetic coupling for nonorthogonal 2porbitals. Such spin polarization should lead to theaj3aj3.B pattern in alternate systems. If the number ofa ites (na, arrows up) is greater compared to j3 sites(nB, arrows down), he ne t spin S results. Accordingto Ovchinnikov85

s =(n,- ng)/2 (5.1)Counting arrows up and arrows down in 1 and 3shows that both diradicals should be S =1. Anotherway to apply eq 5.1 is to count the number of atomiccenters between the sites with unpaired electrons inone of the important resonance structures; if thisnumber is odd,as n 1 and 3, hese unpairedelectronsare ferromagnetically coupled. Unfortunately, eq 5.1does not address the strength of spin coupling.The concept of spin coupling unit may be extendedinto diradicals with multiple coupling units. Such unitsmay be connected either parallel or sequentially. It isexpected that the former will not weaken spin couplingand the later will lead to a weak spin coupling.Spectroscopic studies of dimethylenecyclobutadiene(6),which is an example of ferromagnetic coupling viatwo parallel coupling units, suggest a triplet ground

state;%AESTfrom semiempirical calculations is com-parable tothat found for a single-couplingunit analogue,lasb This is in agreement with theory;6 ossesses non-disjoint half-occupied MOs nd application of eq 5.1givesS =1. An example for antiferromagnetic coupling,which is an analogue of 6, s benzene; AEST=90 kcal/mol implies stronger antiferromagnetic coupling com-pared to b~ ta di en e . ~~

- .......7 -?r-Conjugation in polyenes, which is an example forantiferromagnetic coupling through sequentially con-nected coupling units, has been thoroughly studied overthe years.88 Decrease of -AEsT upon addition of onecoupling unit is moderate, e.g., from 74.3 for butadieneto 60.2 kcal/mol for he~atriene.~~~erivatives ofdiradicals based upon the sequential 1,Cconnection ofone, two, and three benzene units are singlet groundstates;89 for 12,AEST=1 kcal/mol was found by theobservation of a thermal population of a triplet state,using ESR spectroscopy.waThe sequential connection of ferromagnetic couplingunits such as 1,l-connected ethylenes or 1,3-connected

benzenes corresponds to diradicals 13-17. Among thosediradicals, 13, 16, nd their derivatives are known. 13is a ground state riplet according to ESR spectroscopicstudies.91 Ab initio calculations support this assignmentof the ground state and predict AEST=1 kcal/mol;however, for a planar structure, the singlet groundstate is ~alculated.9~imilarly, weak ferromagneticcoupling is claimed in 16; SR Curie studies on impuresamples in a rather narrow temperature range giveAEST=0.3 kcal/molqw Thus, coupling is weak for twosequentially connected ferromagnetic coupling units.The nature of this weak coupling, i.e., ferromagneticvs antiferromagnetic, is difficult to predict because, asfor most weak interactions, slight structural or mediumchanges may matter. For diradicals with sequentiallyconnected ferromagnetic coupling units, the half-occupied nonbonding MOsmay be chosen in such away that they do not coincide at any of the atomiccenters (disjointMOs). xchange interaction betweenthese twoMOs s small, leading to weak spin coupling(section 2). Therefore, other small interactions (be-tween other MOs), such as those accounted for byelectron correlation, may have a significant effect; inmany instances, these interactions favor singlet groundstates. Equation 5.1 predicts a singlet ground stateand a triplet ground state for diradicals with two andthree sequential ferromagnetic coupling units, respec-tively.


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880 Chemical Reviews, 1994, Vol. 94 , No. 4 Rajcadiradicals 20-23, eq 5.1 provides a simple guide whereto attach the groups with unpaired electrons in orderto control spin coupling. Similarly, numerous otherdiradicals based upon homologues of naphthalene(anthracene, phenanthrene, etc.) can be designed.Dougherty has recently reviewed methylene-baseddiradicals 24 and 2KSn Strength of their ferromagneticspin coupling decreases as the C-(CH2)-C angle in-c r e a s e ~ . ~ ~his is reminiscent of analogous angledependence in copper dimer^.^^^^^Dowd proposed nonalternant diradicals containinga cyclopentadienyl moiety.% Ab initio calculations oncyclopentadienyltrimethylenemethane (CPTMM) re-veal a 3B2 riplet ground state, which is approximatelydescribed as a cyclopentadienyl and methyl radicals1,l-connected o ethylene.99bBecause cyclopentadienylcan be viewed as a spin diluted methyl radical, AESTfor CPTMM, which is a few kilocalories per mole, isless than PEST for 1.

v/8 1n=2,3

R Rmdecreased couplingXY V3 14

R .RxpqRR

R = H , 15 R = H , 17R = P h , 16

n=2,3very weak coupling

The sequential and parallel connectivity of ferro-magnetic coupling units are also found in a singlediradical. Examples are 18 and 19. Solid-state NM R0

p/ \180 0

19

1..._..... 1.

spectroscopy of matrix-isolated 18establishes its singletground state with -AEsT >1 kcal /m01.~~ his is inagreement with ab initio calculations on 18 (AEsT=5kcal /mo P) and planarized 13.92194 Diradical 19, forwhich molecular models suggest an approximatelyplanar structure, is unknown; isit a singlet ground state?Diradicals based upon other ferromagnetic couplingunits, presumably weaker than ethylene and benzene,are known, e.g., the naphthalene moiety (20-23) andmethylene (24 and 25).g5*g6n the naphthalene-based

& &022

&x1A.23

/x\0 X/=.

B. Stable Dlradicals: Steric Shleldlng,Hetero atom Pertu rbatio n, Multiple Coupling UnitsBecause stable monoradicals are known, the simplestdesign for stable diradicals is to couple two stablemonoradicals via a spin coupling unit. 1,3-Connectionof benzene with two phenylmethyl moieties correspondsto Schlenk hydrocarbon 26,100-102which is almostcompletely oligomerized at ambient temperature. Heat-ing, followed by rapid cooling, of oligomerized 26 intoluene gives an ESR spectrum at 77 K; Curie studiesabove77 K suggest ha t a minor species possesses tripletground state.lo3 Triphenylmethyl isalmost completelyassociated in solution; the dimer CC bond is betweenthe triphenylmethyl site in one radical andpara positionin the benzene ring of the other radical. Therefore,steric shielding of sites para with respect to triaryl-

methyl sites for unpaired electron in 26 should improvestability of polyarylmethyl diradicals.l@JJOl

R =H, x =ti, 27R =Me, X = H. 28R = i-pr.x =H,29R =Me, X =Me, 30R =C F ~ . =H, 31

CI U CI

bl3324 25

R =alkyl, aryl, vinylX =oxo, halogen All diradicals 27-33 show intense triplet ESR pectrain frozen solutions; only small amounts of doublet


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Organic Dlradlcals and Polyradlcals Chemical Reviews, 1994, Vol. 94. No. 4 881pure solids; magnetic susceptibility studies up toambient temperature give penclose to the theoreticalvalue of 2.83 p~ for S =1 state. Similar studies on28-30 are complicated by the presence of S = '/zimpurities, predominantly arising from partial associa-tion of diradicals in the solid state;IM magnetic sus-ceptibility data for 28 and 30 are best fit withintermolecular antiferromagnetic interaction betweentwo S =1 diradicals (dimer), which possess strongintramolecular ferromagnetic coupling.lWb Magnetiza-tion studies of 28 (Figure 5) and 29 in frozen THF (2-MeTHF) at 2, 5 , and 10 K indicate good fit to a S =1Brillouin curve and show a constant magnetic momentbetween 3 and 80 K. A very weak antiferromagneticinteractions are seen below 3 K (0 =-0.1 K); becausea S = 1 Brillouin curve is followed, these weakinteractions are intermolecular (section 4).1Mb

Steric hindrance in diradicals28-30 and 33 inevitablyleads to substantial out-of-plane distortion. Becauseferromagnetic coupling remains strong (Le., AEST>1kcal/mol) in these diradicals, 1,3-connected benzene isa good ferromagnetic coupling unit.MbSterically hindered derivatives of 16 such as 34 arealso obtained.lo7 Magnetic studies, M vs Hand MT vsT, rule out a singlet ground state with -AEsT >0.004kcal/mol, and the observation of a triplet ESR spectrumimplies some degree of spin coupling. Although thesinglet ground state with very small spin coupling ispossible, the best fitting to eq4.8 suggests riplet groundstates with AEST=0.04 kcal/mol (R =Me) and AEST=0.004 kcal/mol (R =i-Pr). Thus, spin coupling isquite weak in these systems.107bMany stable diradicals contain heteroatoms. Het-eroatom-containing spin sites may be attached to astrong ferromagnetic coupling unit such as 1,3-con-nected benzene or 1,l-connected ethylene. For ex-

ample,E SR spectroscopic studies suggest riplet groundstates for 35 and 36 (X =CH2, Y =O).61J08Ab initiocalculations give a triplet ground state with AEST=10kcal/mol for 36 (X =Y =0);81ae., similar to the all-carbon counterpart, 3. Analogous perturbation in 1,l-connected ethylene systems diminishes ferromagneticcoupling; e.g., calculations suggest tha t 37 is a tripletground state with very smallAESTand alkyl-substitutedderivatives of 37 are ground-state singlets." This isin agreement with E S R spectroscopic studies ondiradicals 38 and 39; that is, derivatives with the mostelectron-withdrawing substituents (and oxo) are E S Rsilent.llOJ1l Although 40 (X =CH2, Y =0) s a tripletground state according to ESR spectroscopic studiesand ab initio calculations,Mb*couble substitution withoxygen(X=Y =0) s predicted to give singlet groundstate.86cJ12 Different behavior of the benzene andethylene coupling unit can be explained in terms ofMO theory;l13 he defining structural factors appear tobe aromaticityof benzene and trengthof C = OvsC 4bond. Berson and co-workers found that heteroatom-substituted diradicals 41 (X =0, s)which are deriva-tives of 13, are singlet ground ~ t a t e 5 . l ' ~ heir all-carbonanalogues 41 (X=C(Me)2) and 42 are triplet groundstates.11sJ16 Ab initio MO calculations suggest that,for diradicals 41 (X=0,NH , CH2, C(Me)Z) and 42, thesign and magnitude of AEST'Smight be related to thesquare of energy gap between the N B M O ' S . ~ ~

A 1.0

0.8

0 . 6c)

;\x 0.4

0.2

0.00 1 2

H/( T- e) (Tesla/K)3

1.00.60.6a\ 0. 4z0.20.0

4

I I I I I0 100 200 3

T ( K )Figure 5. SQUID data for diradical28. (A ) Solution of 28in 2-MeTHF: Plot of normalized magnetization,MIM , vsHI(T - e), compared to the S =1/2,1, SIzBrillouin functions(eq 4.1);0 =-0.09 K.N (B) olid 2 8 xT vs T lot atH =0.5Tesla with fit using a model of pair of two antiferromag-netically coupled S =1 diradicals with partial dim erizationto monoradicals. (Strong intramolecular ferromagnetic andweak intermolecular antiferromagneticcouplings.) Magne-tization (M) and susceptibility ( x =MIH) is calcu lated fromthe following equation (analogousto eq 4.6 and equation incaption of Figure 4) : M = N g p ~ ([exp(z) s inh(x) +exp(3z)(sinh(x)+2 sinh(2x))l/[l +exp(z)( l+2 cosh(x)) +exp(3zMl +2 cosh(x) +2 cosh(2x))l)+NgPB(1 - a)[sinh-( x ) l ( 2 +2 cosh(x ))l where z =WIkT and x =gp&l/kT. Jlk=7 K and CY=0.4 are intermolecu lar pin-couplingconstantbetween diradicals and fraction of diradical in the sample,respectively. Insert shows MIMmtvs HIT plot less contribu-tion from diradical, which is very small a t T =2 K and H


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882 Chemical Reviews, 1994, Vol. 94 , No. 4

HN NH Y

R a j a

36X . c t l 2 , Y . OX = Y = O

35R = H , F

420 41x =W.Y =0X = Y = O X = C(Me)2, S, 0

Di-tert-butyl nitroxide is an air-stable free radical,which is commerciallyavailable. 1,3-Connectionof twonitroxide moieties to benzene gives diradical 43;l17J18magnetic studies find triplet ground state with PEST>1kcal/mol.118 A frozen solution of dinitroxide 44, whichis an analogue of 30, is studied by ESR spectroscopyin the cryogenic temperature range. Temperaturedependence of ESR intensity is interpreted in terms ofintramolecular antiferromagnetic coupling; i.e., a singletground state with a thermally populated tr iplet excitedstate.ll9 Magnetic susceptibility studies of methoxy-substituted dinitroxide 45, either in solid state orpolymer matrix, indicate singlet ground state. The factthat the antiferromagnetic coupling is intramolecularis further confirmed by examination of an X-ray-determined structure; large intermolecular distancesbetween the sites with large spin density are found.120

0 .i k y xO x p : .. x .oR =H, CBu. 43 R = Me. X = Me, 44

R =OMe, X =H,45

Because spin density is localized on nitroxide moiety(approximately equally on oxygen and nitrogen) in*-conjugated nitroxides,121spin coupling is weaker for*-conjugated dinitroxides, e.g., 43-45, compared totheircarbon counterparts (section 5.C) . Other weaklycoupled diradicals,e.g., 46 and 47, are formally obtainedby connecting different heteroatom-based monoradicalsto ferromagnetic coupling units. Stable, but weaklycoupled diradicals, containing several coupling unitsare known, e.g., 48-51; only weak coupling ST C 0.1kcal/mol) is found for these diradicals.122126 In par-ticular, spin coupling through three coupling units, fCU-aCU-fCU and fCU-fCU-fCU should be very weak;therefore, factors other than connectivity (couplingunits) are likely to affect it significantly, especially innonplanar systems (sections 2,5.A, and 5 . 0Dinitroxide 49 gives bulk ferromagnet with T,=1.48K.29

46 47

48 49

50 &C. Quan titative Usage of Spin-Coupling UnitsIn the preceding discussion, we used spin-couplingunits to rationalize qualitatively the type and strengthof spin coupling in diradicals. Now we attempt a morequantitative approach to strong ferromagnetic couplingin diradicals based upon 1,3-connected benzene asferromagnetic couplingunit. We conjecture hat,withinthe l,&connected benzene series, the existing experi-mental and computational data on spin-coupling con-stantJ (orPEST=2 4 or such diradicals may be relatedto electron-nuclear ( e n ) couplings (spin densities) inthe corresponding monoradicals,49 which formallycontain the spin coupling unit of interest: J a (spindensity in ferromagnetic coupling ~ n i t ) ~ . l ~ 7

J =5.0Kcal/mol

e-n coupling estimate ofin C U ferromagnetic J

J =1.3 KcaVmol

Comparison of electron-proton coupling constantsin the benzene rings of benzyl,'% triphenylmethyl,128band tert-butylphenyl nitroxide'w gives the followingratio of spin densities associated with one benzenering: 20107. Therefore, if the result of ab initiocalculation for spin coupling for 3,J =5.0 kcal/mol, is


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Organic Dlradicals and Polyradlcalscorrect, then, the predicted J for 26 and 43 are 5 x(10/20)2- 1.3 and 5 X (7/20)2=0.6 kcal/mol, respec-tively.J values for sterically hindered analogues of poly-arylmethyl diradical26 may be estimated consideringelectron-I3C and electron-proton coupling constantsfor triphenylmethyl,tris(2,6-dimethoxyphenyl)methyl,and perchlorotriphenylmethy1.lwe As far as out-of-plane twisting caused by steric hindrance is concerned,tris(2,6-dimethoxyphenyl)methyl rovides a conserva-tive model for estimating J for alkyl-substituteddiradicals 27-30; among those, 30 is likely to be mosttwisted but, presumably, less than the model mono-radical. Perchlorotriphenylmethyl should be a goodmodel for diradical 33. Notably, the l3C-coupling

Chemical Revlews, 1994, Vol. 94 , No . 4 883proton coupling; e.g., from triphenylaminium to tris-(4-methoxypheny1)aminium y factor of 2.For systems containing heavy elements such as Siand Ge, perturbation of J in diradicals, with 1,3-connected benzene as coupling unit, are examined byusing the following monoradicals.lZsk+ +

I M

= .3 in 6? J =0.6Kcal/molcI Ph&. i n 3 3

increases in increments of about 3 G between mono-radicals. This suggests that the spin density (andelectron-proton coupling constants) in their benzenerings decreases by similar increments.l& Extrapolationof the electron-proton coupling constants from tri-phenylmethyl to the other two model monoradicalsgivesthe followingJ values: (1)diradicals 27-30,1.3 >J >1.0 kcal/mol, and (2 ) diradical 33, J c 0.6 kcal/mol.Ortho substitution with Me or OMe groups in ter t-butylaryl mononitroxides drastically decreases (morethan factor of 2) electron-proton coupling constantsfrom the already low values for the parent tert -butylphenyl nitroxide.l2Ef Consequently, spin couplingthrough 1,3-connected benzene, which is ferromagneticcoupling unit for dinitroxides 44 and 45, should be verysmall (J0.5 kcal/mol) poly-arylaminium systems may be difficult to achievebecause a stabilizingparu substitution with Me0 or C1groups causes a precipitous decrease in the electron-

Hp estimate of J(Gauss) (Gauss) (Kcal/mol)c 2.58 2.80 1.3Si 0.95 1.17 0.2AV e 0.60 0.95 0.1

+

J for the all-carbon diradical should be identical to 26,which is estimated at 1.3 kcal/mol. J for the Siand Geanalogues is predicted to be 0.20 and 0.10 kcal/mol,respectively; should these diradicals be prepared, theirh E s ~ 2 5 =0.4 and W =0.2 kcal/mol are well suitedfor standard ESR spectroscopic and magnetic suscep-tibility measurements.6. Trl- and Tetraradlcals

Strength of the spin coupling (J)n many diradicalscan be obtained by experiment, calculation, andempirical estimate. One of the key questions is whetherstrong spin coupling can be maintained in extendedsystems with more than two sites for unpaired electrons,e.g., is J constant within a homologous series di-, tri-,tetra-, and polyradicals?lWA. Triradicais

Triradicals are relatively rare compared to diradicals.Systems with potentially strong ferromagnetic coupling,which are homologoustom-benzoquinodimethane, fallinto three categories: (1)wo l,&connected benzenesin a linear arrangement, (2) 1,3,5-connected benzene,and (3) three 1,3-connected benzenes in a closed looparrangement.

fi

EQD=J EQD =3J Ea0=3JAssuming that a coupling constant J is associatedwith ferromagnetic (J>0) spin coupling through each1,3-connectivity in benzene, application of HeisenbergHamiltonian (section 4) reveals that the energy gapbetween the ground quartet and lowest excited doublet


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884 Chemical Reviews, 1994, Vol. 94 , No.4state is much smaller (UQDJ) for the lineartopology, compared to AEQD =3J for the other twocases,35 (Coupling constants may be different for thesecond and third topologies.) These energy gaps shouldbe compared to AEST =2J in a diradical. Therefore,linear riradicals are relatively susceptible to thermalpopulation of the lowest excited states and can be usedto measure strong ferromagnetic couplings.The representative examples for the first topologyare polyarylmethyl triradicals 52-55, and trinitroxide56; all possess S = /2 ground states in either solid stateor frozen solution.

R a j aisomerism implies out-of-plane distortion; notably,strong ferromagnetic coupling s maintained in this inerttriradical.

R y T

X58I I I0. 0. 0. R = (PhPh)&, X =HR = % f $ X = H

R =xy, X =H6 R = ritronylnitroaide,X =HR = Chiy lni t rodde,X =H. OM eR = PbNN, X =CNAccording to ESR spectroscopy, the linear poly-arylmethyl triradicals 52-55 show negligible thermalpopulation of the low-spin excited states at 100 K;triradical 54 also shows similar behavior at ambient

temperature, according to the x vs T magnetic sus-ceptibility data.55 Therefore, AEQD=J >1kcal/molis in agreement with our empirical estimate for J =1.3kcal/mol and experimental results (2J >1kcal/mol) inthe homologous diradical 29 (section 5) . The dataindicate that strong ferromagnetic coupling is main-tained, although the out-of-plane twisting for thea-conjugated system in 54 is likely to be substantial.Fitting of the x vs T data for trinitroxide 56 to theequation analogous to eq 4.7 (for linear triradical withthe nearest-neighbor interactions only) gives J =0.5kcal/mol, which is the same as the quartet-doubletenergy gap. Consequently, a substantial population ofthe S =/z excited state is found at ambient tempera-ture.l18 The experimental J * 0.5 kcal/mol is inagreement with the empirical estimate of J =0.6 kcal/mol and experimental studies (2J >1kcal/mol) for ahomologous dinitroxide (section 5 ) .Several examples of triradicals 57-58 pertaining tothe second topology have been reported; quartet statesare detected in all cases.l30-133 In the case of a recentperchlorinated triradical57, it is found tha t quartet isa ground state by a significant margin. This impliesAEQD=35>1kcal/mol for 57, which is in agreementwith the empirical estimate of J z 0.6 kcal/mol andexperimental studies (W 1kcal/mol) for the relateddiradical 33 . The steric hindrance is so severe in 57tha t propeller isomers can be is01ated.l~~ ropeller

B. TetraradicalsSeveral high-spin tetraradicals have been reportedso far.52$55@3 Systems with potential for strong ferro-magnetic coupling, which are homologous to m-benzoquinodimethane, fall into three limitingcategories: (1)star-branched, (2) linear, and (3 )closed oop. (Replacement of 1,3-with 1,3,Bconnected

benzenes may give an entry into multiradicals.) Amongthe three topologies only star-branched tetraradicalsare known. ESR spectroscopy and magnetizationstudies suggest quintet ground states ( S = 2) fortetraradicals 59. The most sterically hindered tet-raradical59 (R =i-Pr) is obtained as a stable solid atambient temperature; magnetic studies, which arecomplicated,by impurities, do not indicate appreciablethermal population of low-spin excited states. Thestrong ferromagnetic coupling is still present, in spiteof probable severe out-of-plane distortion of a-conju-gated system.

I W59 @Q

R =H, Me. CPr O Q

63 64 65Application of eq 5.1 to naphthalene, anthracene,and other polycyclic aromatics reveals a plethora ofpossible ferromagnetic coupling units for tetraradicals.The only known example belongs to the first high-spintetraradical 60, which was reported in 1983 by theBerson group. ESR and UV-vis spectroscopic studiesare best interpreted in terms of quintet ground state( S =2 ) with strong ferromagnetic coupling. The otherisomer 61 possesses either nearly degenerate triplet/


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Organic Dlradlcals and Polyradlcalssinglet groundlexcited states, or it is a ground statetriplet by a large margin.The Dougherty group has reported generation andESR studies for series of tetraradicals 62-65, whichcan be considered as a pair of S=1TM Ms linked with1,3-connectedbenzene or methylenes as spin-couplingunits. ESR spectroscopy suggests quintet groundstates(S=2) for all tetraradicals, except for adamantane-based tetraradical 65, which is assigned singlet groundstate by following the ESR signal intensity duringgeneration of tetraradical. A model based upon two-site Heisenberg Hamiltonian is used to correlate thecalculated AEST in localized diradicals with thetriplet-quintet energy gaps(LsEm)n the correspondingdelocalized tetraradicals, that is,J in a tetraradical isscaled by (1/3)2, compared to a diradical, because onlyl /3 of total spin of trimethylenemethane moiety isaffecting the ferromagnetic coupling unit. The fol-lowing AEms are obtained: 2.2, 0.38, and 0.20 kcallmol for 62,63, and 64, respectively; the last value is inexcellent agreement with the ESR spectroscopic Curiestudies.* The results suggest tha t these ferromagneticcoupling units retain their effectivenessupon differentsubstitution. An elegant ESR study on the effect ofsteric hindrance on spin coupling in derivatives of 62have appeared recently.*bVery weakly coupled tetraradicals based upon stableradical moieties are also known.71aJ3a

Chemical Reviews, 1994, Vol. 94 , No. 4 885

7. Star-Branched and Dendrltlc Polyradlcals.Toward Nan om eter-Slze Single Molecule OrganlcMagnetlc ParticleA. Star-Branc hed Hepta- and Decaradlc als

Homologation of star-branched topology for te t-raradical59 (R=H) allows for design of heptaradical66 and decaradical 67.1a ESR and NMFt spectroscopies

t

A 1.0

0 . 8

0. 6Y

;\3 0.4

0.2

0:o

B 1 . 0

0 .6

0 .6c);\z 0.4

0.2

u .

0 1 2 3H/(T-0) ( T e s l a / K )

0.00 1 2 3

H/(T-0) (Teala/K)Figure 6. Plots of normalized magnetization, M/M,, sH/(T e); solid and intercepted lines correspond to fits (eq8.1, method A) and Brillouin function (eq 4.1) plots, respec-tively:40 A) heptaradical66 in 2-MeT HF,p =0.93,O=-0.1K, and (B) ecaradical67 in THF, p =0.95,O =-0.6 K.at high temperatures (100and 140K ) indicate dominantpresence of the S = heptaradical and S = 5decaradical. The absence of a large amount of otherparamagnetic species (thermal population of low spinexcited states) suggests that both polyradicals possesshigh-spin ground states with strong ferromagneticcoupling. Magnetic susceptibility studies give constantmagnetic moment for both polyradicals between 100and 10 K, which excludes intermediate strengths ofspin coupling; an onset of weak antiferromagneticinteractions is observed at T


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886 Chemlcal Reviews, 1994, Vol. 94 , No. 4The high-spin ground states for 66 and 67 can befurther confirmed by considering the possibility ofintramolecular antiferromagnetic coupling betweenmolecular branches. Because such coupling is throughspace, it is expected to be weak. An illustrative modelis provided by three-spin systems with two couplingconstants, strong ferromagnetic J >> 0 and weakantiferromagnetic J(2JI, the ground state is high spin. Therefore, theobserved weak antiferromagnetic interactions are notlikely to originate from through-space interactionsbetween branches of the same molecule.Zero-field splitting parameters ( p /hcJ )n the ESRspectra of decaradical67 and its lower homologues areinversely proportional t o spin ( S ) , .e.,0 : constant +1/S; also, this reflects proportionality of p/hcl tovolume. One of the practical consequences of thisrelationship is that the spectral widths (20, 40, 60,1 2 0 , and 180) remain approximately constant whilethe number of allowed transitions greatly increases inthe series of di-, tri-, tetra-, hepta-, and decaradicals;67 is at the limit of usefulness of conventional continu-ous-wave ESR spectroscopy (randomly oriented media).B. Dendritic Polyradlcals with 7, 15, and 31Sites for Ferro mag netlcally Coupled Electron s

Homologation of linear topology for triradical 53allows for synthesis of dendritic heptaradical 68,pentadecaradical 69, and 31-radical 70.40J37Hepta-,

6a I

+

8. Defects and Spin CouplingAll methods for generation of unpaired electrons inpolyradicals rely on chemical, photochemical, or elec-trochemical reactions that are carried out to generateall unpaired electrons from a suitable precursor.Because the yields of such reactions are not quantitative,for polyradicals with a dozenor more unpaired electrons,there is a significant probability for formation ofpolyradicals with one or more unpaired electronsmissing. The important questions are what is the effectof such defects is on the spin coupling and can veryhigh spin systems be obtained in the presence of defects?

A. Spin-Coupling PathSpin-coupled systems may be viewed as systemscontaining localized spin sites which are linked viathe coupling units (section 5) . When considering spincoupling throughout the systems with more than twosites, it is useful to define, in the best resonance structurefor a-conjugated polyradical, spin coupling pat h as thearray of atoms (orbitals) between any pair of spin sites,which are spin coupled. Two limiting cases with regardto their spin-coupling paths between a pair of non-nearest-neighbor sites are as follows: class I, anadditional site is formally included in the path; class11,no additional spin sites are formally included in thepath. When the spin sites are represented with dotsand the intervening atoms as bars, the following simplegraphs can be obtained.


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Cwwnic Dkadicals and PoiyadicalsCiaSSI --ccc &,/&

0 0 0ciassi' TIT-w

Among all polyradicds known to date, class I high-spin polyradicals show stronger spin coupling comparedto the class I1 polyradicals. The important differencebetween the two classes is the effect of defects; in aclass I spin system, a single defect may disrupt the strongspin coupling but, in class 11, the coupling, which isalready weak in defect-free systems, may be furtherweaken.Dendritic polyradicals are an example of a class Isystem. Their ferromagnetic coupling path includesboth 1,3-connected benzenes and the arylmethyl radicalcenters. Consequently, the failure to generate one ofthe unpaired electrons, i.e., having an sp3-hybridizedcarbon at one of the arylmethyl sites as a defect, mayinterrupt the strong ferromagnetic coupling and drasti-cally lower the spin value for the polyradical. Defectsat he inner sites are especially detrimental,for example,in pentadecaradical 69 one such defect divides thepolyradical into "uncoupled" parts with significantlylower spin; e.g., three parts with S = 3/2, 3/2, and */2.Defects at the peripheral sites are relatively innocuous.Notably, about half of the spin sites in dendriticpolyradicals such as 69-70 are peripheral, amuch morefavorable situation compared to linear chain polyradi-cals.138 /--nm

In the presence of defects, polyradicals may consistof many spin systems with different spin values.Magnetic data for such samples are not straightforwardto interpret; e.g., magnetization da ta do not adhere toany single Brillouin function (section 4).40The following model may be used for clans I polyrad-icals with defects. Random occupation by an unpairedelectron of each site with probability p is assumed; pX 10036 is the yield per center for generation of unpairedelectrons. The probabilities, NSk,or finding an selectronspinsystem (S =4 2 ) n apolyradicalmoleculewith k sites are used as weighing factors for the Brillouinfunctions, B.lz; thus, magnetization per mole of polyrad-ical,M, sM =NgfiB(N:Bl/2 +N?Bz/z +...+N+l~B(~_l,lz

NKkBk/.J (8.1)N) can be evaluated by two different methods (A andB).

Chemical Revlews. 1994, Vol. 94 , No. 4 887Method A. For polyradicals wi thp closeto 1(90+%yield per site), polyradicals with a small number ofdefectswilldominate the sample. Probabilityof ri dinga polyradical with k sites and j defects is (kj)p(k-j'(lp)'; for example, heptaradicals with 0, 1, 2, 3, and 4defects for p =0.93 will account for essentially wholesample: p' +7ps(l- p )+21p5(l-p )2+35p4(1 P ) ~+35p3(1- ) 4=0.99998. For each polyradical with jdefects, all configurations for defects are enumerated,and numbers of spin systems with S =k/2 , (k- 1)/2,..., 2 , ' /z are found. In order to obtainNSk,he eachnumber of the spin systems with S= / 2 for polyradicalwith j defects is multiplied by p(k-Jl(l p)j and theproducts are added with respect to j.40Method B. For polyradicals with small or interme-diate values of p , method A may become exceedinglylaborious as thousands of spin systems in polyradicalswith large number defects may need to be enumerated.A more direct method to find NSks illustrated, usinga polyradical with linear connectivity. Probability forhaving s sites occupied and g sites unoccupied isp8(l- p)g; in a k site chain, there is k - s - 1ways todis tributes site spin systems, which are flanked by anemptysiteateachend. Therearetwowaystodistributes site spin systems, which are a t the end of the chainand are flanked by only one empty site. Therefore, forlinear k site chain:

N , L = ( k - ~ - l ) p * ( 1 - ~ ) ~ + 2 p ' ( l - ~ )8.2)Efforts toward high-spin polymers, based upon linearconnectivity in class I and I1 systems, may be futile,unless the following issues are addressed first: (1)development of highly efficient methods for generationof radical centers, i.e., even better than the carbanionmethod for polyarylmethyl~~~nd (2 ) search for classI1 strongly coupled spin system.

6. Multiple Coupling PathsAnother approachto the problem of defects may relyon the class Isystems withmultiple spin-couplingpaths.A simple connectivity is "closed loop" (ring),where twopaths exist. For high-spin systems, interesting ex-amples are structures based upon triradicals 57-58 andmacrocyclic calixarenes, which correspond to 1,3-connected p~lya ryl met han es. ~~~uch connectivities are

72 73oblivious to one defect; two defects may interrupt theircoupling paths. We label such polyradicals as 1-proof.(Linear and branched connectivities are 0-proof in thisterminology.) Annelation of 'closed loops" gives ex-tended networks and lattices with greater resistance to


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888 Chemlcal Revlews, 1994. Vol. 94 . No. 4defects. The Mataga polymerz4may be represented asa hexagonal2D lattice and is 5-proof. Multiply strandedconnectivities based upon annulated calixf4larenesoffer less resilience to defects: 2-strand is 1-proof, and3- and oligo-strand is 2-proof. 2-Strand can be modifiedby closure into a closed loop with 3-proof connectivity.The smallest 2-strand loop, based upon 1,3,5-connectedbenzene as coupling unit, corresponds to o h symmetriccubooctahedrane, a CmHe parent hydrocarbon. An-other way to describe this cage isas wo calix[4larenes,one at the bottom and one at the top, with fouradditional CHz linkers. A plethora of other less-symmetric cages are possible by closure of variousstrands of calixarenes.

may be described by a model based upon HeisenbergHamiltonian and localized spin sites. As a test forelectron localization, addition of one or more electronsto a polyradical to form polyradical polyanions areconsidered. Each additional electron corresponds toan extra negative charge. Will the charge/spin belocalized or delocalized? How is spin coupling betweenthe remaining unpaired electrons affected by thenegative charge?From a more general point of view, understanding ofthe factors involved in spin coupling in polyradicalsshould permit a rational design of spin-coupled struc-tures. An interesting example for such design arestructures for electron transfer (or electrical conductiv-ity),i.e.,thequestioniswhethertheypeandmagnitudeof spin coupling is related to aptitude for electrontransfer. For example, two extreme cases of thestrongly antiferromagnetically and ferromagneticallycoupled chains (or networks) of spins can be considered.As one or more electrons are added to the chain, willthe type and magnitude of the spin coupling betweenthe electron spins along the chain be preserved? Willthe added electron@) delocalize over the chain or tendto localize, tha t is, how is electron transfer affected bythe ferro- vs antiferromagnetic spin coupling along thepathway?

2-Strand

Mataga polymer 3-Strand

Cubooctahedrd cage C60H48In the C ~ H Bage, 1 2benzhydryl CHZs re potentialsites for unpaired electrons; the corresponding polyrad-ical, which would have benzene rings twisted by 90out-of-plane in each benzhydryl moiety, would be aninteresting test for 3D r conjugation and for themechanism of ferromagnetic spin coupling.An intermediate approach, which is a compromisebetween the synthetic efficiency of dendrimers and

resistance to defects of closed loops, is embodied inhomologation of 71 into polyradicals 74 and 75, whichmay be referred to as hypercyclomers. All the above

74

75polyradicals are 1-proof;for polyradicals 71,74, and 75with two defects, spin coupling is interrupted in about21%, l o % , and 4% of each homologue, respectively.This is unlike in 0-proof dendritic structures where theanalogous percentages are approximately 75% for allhomologues.9. Polyr adical Polyanlons: Spin Coupling vsElectron Delocalization

As far as the currently available evidence suggests,spin coupling in polyarylmethyl high-spin polyradicals

t-@@@@@@

The simplest system possesses two sites, e.g., adiradical, which after addition of an electron becomesradical anion. Several radical anions, which are derivedfrom diradicals with strong antiferromagnetic coupling,have been studied. Examples are semiquinone radicalanions,41a Wursters salts,41b and their all-carbonanalogues, which are topologically related to 4.9 ESRstudies of the last two examples show spin/chargedelocalization on the ESR time ~cale.7~J~Radical anion and radical cation of perchlorinated10 are also found delocalized on the ESR time scale byBallester and co-workers. Notably, perchlorobiphenylshows 8 7 O out-of-plane twisting in solid state. Thissevere steric hindrance dramatically weakens antifer-romagnetic coupling in the related diradical (14


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Organic Dlradicals and Polyradicalsthe related p01yradicals.l~~~mportant tests, whichawait experimental realization, are radical ions basedupon diradicals with coupling through two or moreferromagnetic coupling units such as 34.14Spectroscopy of more complex radical ions, whichare studied by the Miller and the Nelson groups, isreminiscent of inorganic mixed-valence complexes.1&J&Another interesting example is a spiro-conjugatedradical anion prepared by Maslak and co-workers;l&bits delocalization on the ESR time scale can be relatedto antiferromagnetic spin coupling in a related spiro-conjugated tetraradi~al.~"Because the electron-coupling par t of the theory isvery similar for both electron transfer and energytransfer, it is not surprising that the energy transferbetween porphyrins and other electrophores, which arelinked via 1,3-,1,2-, and 1,4-connected benzene-basedbridges, is the slowest for the 1 , 3 - ~ a s e . ~ ~ ~he relation-ship between the spin coupling and electron delocal-ization is also found in some models for magnetism,e.g., there is an isomorphism between a two-levelquantum mechanical system and the Ising model. Inparticular, adjacent antiparallel spins in the Ising modelcorrespond to tunneling between two spatial states (inanalogy to electron transfer in radicalThe search for the systems with extremely fastelectron-transfer rates may not be the most importanttask; as Nature teaches us, it is far more important tobe able to control the rate of the electron transfer. Thespin-coupled di- and polyradical systems should providenovel opportunities in this field.

Chemical Revlews, 1994, Vol. 94 , No . 4 888UV-vis spectra for the above polyanions and theirselected alkyl-substituted derivatives (more stericallyhindered) show a strong absorption, A =500 nm.79114Molar absorptivities, which are determined for selectedmono-, di-, tetra-, and decaanions, are found to beproportional to the number of arylmethyl fragments(molecular ~harge).~OCyclic voltammetry and various pulse techniquesreveal two, three, and four reversible oxidations at about-1.3 V for dianions, trianions, and tetraanions, respec-

tively.149 For example, consecutive three oxidations oftrianion give radical dianion, diradical anion, andtriradical. Further oxidation of polyradicals occurs atmuch more positive potentials (>1V). The potentialrange between polyanion and polyradical is 0.2, 0.4,and 0.5 V for dianions, trianions, and tetraanions.Although these potential differencesare small comparedto most ?r-conjugated systems, they are about 1orderof magnitude more than the predicted values forcompletely independent arylmethyl a n i o n ~ . ~ ~ J ~The above evidence suggests that l,&connectedpolyarylmethyl-based polyanions may be viewed asensembles of weakly interacting arylmethyls. Such anelectron localization is also found in the relatedpolyradical polyanions (precedingsection). Therefore,similar conclusions should apply to the correspondingpolyradicals; in particular, the "localized spin" spin-coupling models such as Heisenberg Hamiltonian andrelated models, should be adequate. It is reasonable toconclude that the values of "J" n the series di-, tri-,tetra-, and higher radicals are either constant or showvery slow decrease.Presumably, the electronic structure, which is as-sociated with electron localization on arylmethyl frag-ments in 1,3-connectedpolyarylmethyls, may also applyto other strongly coupled high-spin systems.

10. Insight into the Electro nic StructureAssociated with High Spin via Population ofNonbonding MO'sMost of the high-spin polyradicals studied to dateare characterized by half-occupied nonbonding (NB)molecular orbitals (MO). Full NBMO occupationcorresponds to polyanions; their intermediate occupa-tions corresponds to polyradical po lya ni ~ns .~~ecause

4 4 t t Tetraradicalt t $.f t i Diradi cal Dianion- - -A----

# tf t i Tetraanion----population of NBMOs should not significantly changebonding, an insight into the electronic structure ofpolyradicals should be obtained by study of the relatedpolyradical polyanions and diamagnetic polyanions.14NMR, UV-vis, and electrochemical studies for theseries of carbo polyanions, which are related to tris-(4-tert-butylpheny1)methylnd polyradicals 27,59 (R=H), and 67 are primarily ons side red.^^ Arylmethylcarbons in these mono-, di-, tetra-, and decaanionspossess large negative charge as evidenced by upfield13C NMR chemical shifts; notably, the chemical shiftrange is only a few parts per million. Because similarclustering of 13CNMR resonances is observed for othercarbons bearing substantial negative charge, it isconcluded tha t extension of conjugation in this seriesdoes not perturb the electron density distribution.79

1 1. Hlgh-Spin Organic Io ns and PolycarbenesThe discussion of the spin coupling would not becomplete without a t least mentioning carbenes, nitrenes,ions, and other molecules capable of possessing high-spin ground states. Polycarbenes have repeatedly beenreviewed in recent y e a r ~ . ~ J ~Iwamura, Itoh, and their co-workers have preparedand characterized high-spin polycarbenes with up tonine carbene centers (S = 9) in matrix.lsl Trulyremarkable features of these spin systems are thepaucity of defects, due to efficiency of the photochemicalgeneration of polycarbenes from their diazo precursors,and possibility for manifestation of magnetic anisotropyon a slow time scale at the molecular level.151 Severalexamples of other di- and polycarbenes, and theirnitrene analogues have been studied to elucidate thefactors affecting spin c~upl ing .l~ ~-l "First triplet states of antiaromatic ions were detectedby ESR spectroscopy in early 196Os.la Among deriva-tives of cyclopentadienyl cations, benzene dications,and benzene dianions both singlet and triplet groundstates were found; he spin of the ground state is affectedby both substituents and medium.'"JM Such moleculesplayed an important role in Breslow's pioneeringexperimental attempts toward an organic ferromag-Many selected S = l / 2 radical anions and radicalcations are stable at ambient temperatures and/or on

net,166,157


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890 Chemical Reviews, 1994, Vol. 94, No. 4air; they are readily prepared by one-electron reductionor oxidation of appropriate p r e c u r ~ o r s . ~ ~ ~ J ~ ~olaronsin some electrically conducting n- or p-doped polymerscan also be considered as radical ions.% Such radicalions are promising building blocks for stable polyradi-cal species with both high and low spin. Their stabilityand generation of unpaired electrons via redoxprocesses, which may be thermodynamically controlled,should have advantages in preparation of extendedstructures with very small density of defects.For biselectrophoric molecules,159which are obtainedby linking two anthracene radical anions via short alkylchain bridges or two naphthalene radical anions via1,3-connected benzene bridges, or related examples,triplet states are detected by ESR s p e c t r o s ~ o p y . ~ ~ ~ ~ ~Topology of the bridging by alkyl chain appears to bei m ~ 0 r t a n t . l ~ ~ ~lso, in mixtures of di-, tri-, andtetraanions of di-, tri-, and tetra(g,lO-anthrylenes),triplet, quartet, and quintet states were detected infrozen a 2-MeTHF solution at T =150 K using ESRspectroscopy.lm In most of the above examples, it isnot clear what is the spin of the ground state and howit is effected by ion pairing.161J62High-spin states ( S=2.5) wee also found in a p-dopedpolymer, which before doping consisted of short polyenechains linked via 1 &connected benzene bridges; themagnetization measurements were carried out down toT =2 K.163Interpretation of spectroscopic and magnetic data inthe radical ion systems may potentially be complicatedby disproportionation equilibria, e.g., for a tripletground-state pair of radical ions in equilibrium withsinglet dianion and singlet neutral species.162

Rajcadevelopment of ultra-high yield methods for generationof polyradicals. Although some interesting magneticphenomena are not restricted by dimensionality, long-range ferromagnetic order implies spin coupling in atleast two dimensions. Rational organic synthesis ofextended two- and three-dimensional extended struc-tures, with repetitive macrocyclic ring closures, will bechallenging.Further insight into a relationship between spincoupling and electron transfer using polyradicals maybe gained and, ultimately, better understanding ofphenomena associated with electrical conductivity mayresult. From a broader perspective, it should beemphasized that both magnetism and superconductiv-ity are unsolved problems and understanding a knownrelationship between them may be critical to thesolution.

12. Conclusions and Perspectiv esIn the past decade significant progress towardunderstanding of spin coupling in di- and polyradicals

has been made. High-spin polyradicals (strong ferro-magnetic coupling) are most interesting because se-lected n-conjugated hydrocarbon di- and polyradicalsare among species with strongest ferromagneticcouplings to date. Although n-conjugated systems aretraditionally viewedas examples of delocalized bonding,high-spin 1,3-connected arylmethyl polyradicals arehighly localized as indicated by studies of polyradicals,polyanions, and polyradical polyanions; that is, exten-sion of their conjugation and moderate out-of-planedistortion do not lead to a major change in electronicstructure. This suggests that such polyradicals may beviewed as ensembles of arylmethyl monoradicals;consequently, simplistic concepts such as spin sites,coupling units, and coupling paths, in conjunction withsimple spin-coupling models, are useful in elucidationof spin coupling.Weak spin coupling in n-conjugated di- and polyrad-icals is far less understood; in particular, factors otherthan molecular connectivity, which is a dominantcontributor in strong spin coupling, may be decisive.Qualitative determination of spin coupling in ho-mologous high-spin polyradicals and their localizedelectronic structure suggest that strong ferromagneticspin coupling(J)hould be maintained in mesoscopic-size or extended structures. Preparation of very highspin polyradicals requires a careful design of molecularconnectivity to minimize impact of defects and further

Acknowledgments. The important contributions tothis field of study have been made by my co-workersnamed in the references. I acknowledge the Divisionof Chemistry and Division of Materials Research of theNational Science Foundation for the supportof researchon polyarylmethyl polyradicals. I acknowledge theCamille and Henry Dreyfus Teacher-Scholar Programfor the award. Acknowledgment is also made to thedonors of the Petroleum Research Fund, administeredby the American Chemical Society, for the partialsupport of this work. I thank Professors W. T.Borden,D. A. Dougherty, H. Iwamura, and J.Veciana for kindlyproviding preprints of their papers.References

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New York, 1986.(49) The ESR signal intensity for oraanic radicals is related toparamagneticsusceptibiliG (no corrections for diamagnetism areneeded).(50) Example of EPR spin counting for S > I/*: Juarez-Garcia, C.;Hendrich, M. P.; Holman, T. R.; Que, L.; Munck, E. J.Am. Chem.SOC.991, 113, 518.(51) Beraon,J. A. In The Chemistry of Quinoid Compounds; Peta i, S.,Rappaport, Z., Eds.; Wiley: 1988; Vol. 11, Chapter 10.(52) Standley, K. J.; Vaughan, R. A. Electron Spin RelaxationPhenomena in Solids; Plenum Press: New York, 1969. Reference48, Chapter 9.(53) (a) Both m agnetization a nd paramagnetic susceptibility, which arerelated to ESR intensity (ref 49), show similar temperaturedependence for intra- an d intermolecular spin coupling (section4.A). (b) Achieveme nt of spin equilibrium , especially for photo-chemicallygenerated di- and polyradicals adicals in frozen matricesat ow temperatures, isimportant:Bush, L. C.; Heath, R. B.; Berson,J. A. J. Am. Chem. Soc. 1993,115,9830.(54) ESR spectrosco py in orient ed media: Yagi, M.; Uchida, K. S.;Higuchi, J. J.Magn. Res. 1987, 71, 303. Neumann, R; Hugerat,M.; Micheli, S.; Natt, A.; Bernitz, M.; Levanon, H. Chem. Phys.Lett. 1991, 182, 249.(55) Rajca,A.; Utamapanya, S.J . Am. Chem. SOC.993,115,2396.

(56) (a) Jacob , J. S.; Shultz, D. A.; J ain , R.; Novak, J.; Doug herty, D.A. J. Am. Chem. SOC.993, 115, 1744. Novak, J. A.; Jain, R.;Doughe rty,D. A.J.Am. Chem.SOC.989,111,7618. (b) Silverman,S. K.; Dougherty, D. A. J. Phys. Chem. 1993,97, 13273.(57) (a) LaMar, G. .; Horrocks, D.; H olm, R. NMR of ParamagneticMolecules; Academic Press: New York, 1973. (b) Recent reviewon paramagnetic NMR: Westlund, P.-0. In Nuclear M agneticResonance; The Royald Society of Chemistry: London, 1991;Vol.20, Chapter 14, p p 452-49

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Rajca Spin Coupling to Magnetism

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