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AnalysisofRadicalsbyEPR

SchoolofChemistry,EaStChem,UniversityofSt.Andrews,St.Andrews,Fife,UK

1INTRODUCTION

1.1BackgroundandScope

Allradicalscontainoneormoreunpairedelectrons (UPEs),eachwithitsownmagneticdipolemoment arisingfromitsspin.Radicalsarethereforeparamagneticandpossessnetspinmomentsthatcan interactwiththemagneticcomponent(B1 )of incidentelectromagneticradiation.Thisinteraction givesrisetoelectronparamagneticresonance(EPR) spectra,oneofthemostversatileandusefultechniquesforstudyingradicals.ThereisacloseanalogybetweenEPR(alsocalled ESR,EMR )andthe morefamiliarnuclearmagneticresonance(NMR) spectra.Thisarticlefocusesontheisotropicspectraobtainedfromorganicmonoradicalsandradical ionsinsolution.Numeroustextbooksandmonographsareavailablecoveringanisotropicspectra, electronnucleardoubleresonance(ENDOR)spectra,pulsedEPRtechniques,andrelatedtopics.1–4

Paramagneticresonanceabsorptionwasfirst observedonaCuCl2 2H2 OsamplebyZavoiskii usingradiofrequencyirradiationandalowfield.5 Continuouswave(CW)EPRinstrumentsoperatinginthemicrowaveregionatabout9GHz withmagneticfieldsofabout300mT(X-band) weretheworkhorsesofthetechniqueuntilaround thestartofthetwenty-firstcentury.Sincethen highfield/highfrequencyspectrometers,pulsed spin-excitationspectrometers,doubleresonance instruments,andsoonhavebecomecommercially availableandareenablingEPRtoexpandintonew

areasofbiologyandmaterialsscience.Extensive andvaluabletablesofEPRdata,particularlyfor organicradicalsatX-band,havebeenpublishedin theLandolt–B ¨ ornsteinseries.6

1.2BasisoftheEPRTechnique

InaCWEPRexperiment,theparamagneticsample isplacedinastaticmagneticfield B0 where itisirradiatedwithelectromagneticradiationof frequency ν havingoscillatingmagneticcomponent B1 .Thestaticmagneticfieldisscannedandthe electronundergoestransitionsbetweenavailable energylevels.Thesetransitionsoccurwhenthe energyoftheincidentphotons(h ν )matchesthe separationoftheenergylevels( E ).

= h ν (1)

Ateachtransition,powerisabsorbedfromthe incidentmicrowaveradiationandthisisdetected andamplified.TheEPRspectrumisusuallya displayofthefirstderivativeofthisabsorptionasa functionoftheappliedmagneticfield.

Theenergiesoftheelectronandnucleardipoles intheradicalareproportionaltothestrengthof thestaticfieldandalsodependontheirorientations withrespecttoit.Radicalsofsmalltomoderatesize undergorandomBrownianmotioninfluidsolvents andthisusuallyaveragestheanisotropiesofthe Zeemanandhyperfinecouplingstozero.Under theseconditions,andtakingthestaticmagneticfield tobeinthe z -direction,theenergiescanbeobtained

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fromthespinHamiltonian ˆ H giventofirstorderby (2)7–9 :

ˆ H = g βe BSz + ai Iz ,i S (2)

Thefirsttermin(2)representstheelectron Zeemaninteractionandcontainsthedimensionless spectroscopicsplitting g -factor, βe ,the Bohrmagneton (aconstantequalto eh/ 4π me c ), B thevectorof themagneticfield,and Sz ,thespinangularmomentumoperatoroftheUPEinthe z -direction.The constants ai aretheisotropichfsconstantsthatquantifytheisotropicinteractionoftheelectronwith eachmagneticnucleus.Theycanbepositiveornegativebutonlythemagnitudesaredirectlyaccessible fromEPRmeasurements(thesignscanbedeterminedbyNMR).Thespinoperators, Sz and Iz , actonthespinwavefunctionstoyieldeigenvalues ms =± 1/2 and mI =−I , I + 1, , I forthe electronandnuclearcomponents,respectively.The availableenergylevelsaregivenby(3):

iso = gβe Bms + ms ai mI ,i (3)

where B isthefieldatresonance.Theresonance linesappearintheEPRspectrumatthefollowing fields:

= B0 ai mI ,i (4)

Inthecaseofaradicalcontainingnomagnetic nuclei,(3)yields Eiso = g βe Bms .Radiationinduces transitions,thatis,changesintheorientationofthe electronspinrelativeto Bz ,betweenthelowerand theupperenergylevels.Since ms =− 1/2 and + 1/2 forthelowerandtheupperlevels,respectively, E becomes g βe B andhencetheconditionforanEPR transitionisasfollows:

E = h ν = g βe B (5)

Consideraradicalcontainingtwo I = 1/2 nuclei coupledtotheUPEwithhfs a1 and a2 (a1 > a2 ).

Equation(4)indicatestherewillbefourresonance

fieldsat B1 = B0 1/2a1 , B2 = B0 1/2a2 , B3 = B0 + 1/2a2 ,and B4 = B0 + 1/2a1 .TheallowedEPR transitionsarethoseinwhich ms altersby ±1,while thenuclearspinsstayunchanged( mI = 0).The spectrumwillconsistoffourlinesseparatedby a1 and a2 asshowninFigure1.Sinceeachnuclear

= 1/2

= 1/2

Figure1 Energylevelsandtransitionsforamono-radical containingtwospin1/2nuclei.ThecorrespondingEPRspectrum isbelowthefieldaxis.

spinstateisequallyprobable,thefourlinesareof equalintensity.

Forradicalswithgroupsoftwo,three,four, andsoonofequivalentnuclei,thecorresponding spectraaretriplets,quartets,quintets,andsoon withintensitiesaccordingtothecoefficientsof thebinomialseries.Forradicalswithseveral nonequivalentsetsofnucleiandwithnucleihaving I > 1/2,theEPRspectracanbeextremelycomplex; suchspectraareoftenincompletelyresolvedand analyzingthemisanontrivialtask.Second-order spectra,sometimescontainingadditionallines,are obtainedforradicalswithrelativelylargevalues of ai 10

1.3RelaxationPhenomenaandLineShapes

Whenelectromagneticradiationinteractswithan assemblageoffreeradicalsinamagneticfield,there isanequalprobabilityofspinflipfromtheupper orthelowerlevel.Fornetabsorptionofradiation, givinganobservableEPRspectrum,itisnecessary fortheretobemoreelectronsinthelowerstate. Theratioofthenumberofspinsinthelowerlevel

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E
B

(NL )tothenumberofspinsintheupperlevel(NU ) isdeterminedbytheBoltzmanndistribution:

Aslongastheassemblageofradicalsremains inthermalequilibrium, NL willexceed NU andnet absorptionwillensue.Althoughtheenergygapat X-band g βe B issmallincomparisonwiththeaveragethermalenergy kT ,sophisticatedinstrumentationensuresthatEPRisaverysensitivetechnique. Insolution,radicalconcentrationsof10 8 Mcan routinelybedetectedand,underfavorablecircumstances(simplespectra,lowtemperatures)nanomolarconcentrationscanbestudied.

Whenasampleofradicalsabsorbsradiation, thenumberintheupperlevelwillincreaseuntil NU = NL ,oreven NU > NL ,forlargeenergypulses. When NU = NL ,therewillbezeronetabsorption ofmicrowaveradiationandtheEPRspectrumwill shrinktozero.Inthissituation,thespectrumissaid tobe“saturated”andthisoccursformostradicals athighenoughpoweroftheincidentmicrowave radiation.Thereexistmechanismswherebythe electronsintheupperlevelloseenergytothe surroundingmedium,orinternally,suchthatthey returnor“relax”tothelowerlevel.Thelossof excessenergytothesurroundingstakesplaceby anexponentialdecay,whichischaracterizedby thespin–latticerelaxationtime τ1 .Thespin–lattice relaxationtimeisrelatedtothemeanlifetimeof agivenspinstateandsohasaneffectonthe linewidth.

AccordingtotheHeisenberguncertaintyprinciple,the“width”orenergyrange δ E ofashort-lived excitedstateisnotwelldefinedbutisrelatedto itslifetime τ by τδ E = h /2π .Acertainbroadeningwillbeobservedintheresonancetransitionand, onsubstitutionfromPlank’sequation,thefollowing relationshipsareobtained: ν ≈ 1 τ or B ≈

Thiskindoflinebroadeningiscalled lifetime broadening anddefinesthe minimum linewidth foragivensystem.Spin–latticeinteractionsare particularlyimportantforradicalsincondensed phaseswherethespinsystemcanbedirectly

coupledtothevibrationsofthelattice(phonons). Inthiscase, τ in(7)willbedominatedby τ1 Influidsolution,themotionsofthesolvent moleculesprovidealessefficientthermalsinkand asecondprocessknownas spin–spinrelaxation usuallyplaysamoreimportantrole.Magnetic interactionsbetweennucleiandelectrons,and betweenlikespins,areanextremelyefficientmeans ofrelaxingbothnuclearandelectronspins.This dipolarinteractioncauses mutual spinflipssothat thelifetimeofspinsintheupperstateislimited, butthetotalnumberofspinsinthestateremains thesame.Itfollowsthatthisspin–spinrelaxation, withrelaxationtime τ2 ,contributestothelifetime broadeningoftheresonancelinebutdoesnotaffect thelevelofsaturation.Forfreeradicalsinsolution, itisoften τ2 thatlimitsthelinewidth;thatis, B = h /g βe τ2

Deeperinsightintospinrelaxationisobtained fromsolutionstotheBlochequationsforthe timedependenceofthemagneticmomentof anensembleofspinsundertheconditionsof EPRexperiments.11,12 TheBlochequationsfurnish expressionsforthereal(χ )andimaginary(χ ) partsofthemagneticsusceptibilityoftheensembleofradicalsintermsofjustthetworelaxation times τ1 and τ2 .Therealpart χ relatestothe EPR dispersionspectrum ,whichislessusefulthan the absorptionspectrum andisrarelyrecorded.The expressionobtainedfor χ relatingtotheconventional absorptionspectrum farfromsaturationis

χ = χ0 τ2 ω0 1 + τ2 2 γe 2 (B0 B

χ0 isthebulkstaticmagneticsusceptibility, ω0 is theangularfrequencyofthemicrowaveradiation atresonance(ω = 2πν ),and γe (=−2π g βe /h ) isthemagnetogyricratiooftheelectron.The power P absorbedperunitsamplevolume(V ) bytheensembleofradicalsfromthemicrowave radiationis

= 1 ωχ B1 2 µ0 V (9)

where µ0 isthemagneticpermeabilityofthe vacuum.Theexpression(8)takestheformofa LorentzianfunctionandthisistheEPRlineshape observedunderconditionsofslowfieldsweepand withpowerlevelsbelowsaturation.Withthese conditions,thelinewidthathalfheight( B1/2 )is

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givenby(10):

B1/2 = 2 γe τ2 = 31/2 Bpp (10)

Equation(9)showsthatthepowerabsorbedby thesampleisproportionalto χ ,andthereforetothe numberofparamagneticspeciespresent.Thepower absorbedbythewholesample(Pw ),duringascan throughthewholeEPRspectrum,isgivenby P dB whichisameasureoftheareaundertheabsorption curve.Hence,thenumberofspinsinasampleis proportionaltotheintegraloftheabsorptioncurve, orthedoubleintegralofthemoreusuallyrecorded firstderivativespectrum.

InarealCWEPRspectrumofaradicalin solution,thelinesareoftenLorentzianornearly Lorentzianinshape(Figure2).However,when additionalfactorscomeintoplaysuchasslight anisotropiesduetoinefficienttumbling,unresolved hyperfineinteractionsfromsubstituentsorthe surroundingliquid,orstaticdipolarinteractions, thelineshapestendtoGaussian,inwhichcasethe linewidthsaregivenby(11):

B1/2 = 2(π ln2)1

Figure2 GaussianEPRlineshape;(a)absorptioncurve,(b)first derivative.AnalogousLorentzianlineshapes(c)and(d).Notethe differencebetween B1/2 andthepeaktopeaklinewidth Bpp

2ISOTROPIC g-FACTORS

ThefieldexperiencedbyanUPEwilldifferfrom thestaticmagneticfield B becauseoflocalfields, whichmaybepermanentormaybeinducedby theexternalmagneticfield.Toallowforthis,the dimensionless g -factorof(3)isunderstoodtobe variable.Theeffectivefieldcanbewrittenas

eff = (1 σ)B = g ge B (12)

Here, σ istheanalogofthe“chemicalshift” parameterofNMRspectroscopyanditisreplaced by g inEPRspectroscopy.Orbitalangularmotion oftheUPEisanimportantcontributortothe localfield.Inmanytransitionmetalions,spin–orbit couplingislargesothat g deviatesgreatlyfrom ge (2.00232).Formostorganicradicalsinsolution, ontheotherhand,thegroundstatehaszeroorbital angularmomentumandsotheisotropic g isclose to ge .However,inthemajorityofradicals,asmall amountoforbitalangularmomentumfromexcited statesismixedincausing g -factorstodivergefrom ge .Theobserved g -factorsaresensitivetothelocal environmentsurroundingtheUPEandcanbeused forradicalcharacterizationinmuchthesameway aschemicalshiftsfromNMRspectroscopy.

Experimentally,the g -factorofaradicalcanbe determinedfromtheEPRspectrumbytheuseof(5). Thisrequiresthemeasurementofthefrequency ν andthefield B withanaccuracybeyondthatofmost commercialspectrometers.Itisnormal,therefore, toaddastandardofknown g -factor(inacapillary tube,orotherwise)tothesampleoftheunknown radicalsuchthatspectraofboththestandardand unknownaresimultaneouslyscanned.Symmetrical spectrafreefromdistortionsarerequiredforthe uncorrectedfieldsatthecenterofthestandard(BS ) andthecenteroftheunknown(BX )tobereadoff thespectrum.Theunknown g -factor gX canthenbe obtainedfrom(13):

X = gS gS (BX BS ) BS (13)

StandardradicalsfrequentlyusedincludeDPPH (g = 2 00354inPhHsoln.),perylene(g = 2 00257 inconc.H2 SO4 ),weakpitch(g = 2 0028inKCl powder),andTEMPONE(g = 2 0062inPhH

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B
g

2.0002.0022.0042.0062.0082.0102.0122.014

Peroxyl, ROO • Thiyl, RS • Nitroxide, R2NO • Sulfonamidyl, RSO2NR

Sulfonyl, RSO2 • Aryloxyl, ArO • Aminyl, R2N • Iminyl, RC = N • Silyl, R3Si • Alkyl, R3C • Free electron, e

P-centered, R2P •, R4P • Acyl, RC=O • Diazenyl, RN=N •

2.0002.0022.0042.0062.0082.0102.0122.014

Figure3 Centralrangesofisotropic g -factorsoforganicradicalsinsolution(datafromRef.6). soln.).Thecentralrangesfor g -factorsofcommon radicaltypesarepresentedinFigure3.

Foranunknownradical,the g -factorisavaluableindicatoroftheprincipalsiteoftheUPE.The rangesofvalues(Figure3)occurbecauseadditional functionalgroupsinthevicinityoftheUPEaffect thespin–orbitcoupling.Afewradicalssuchas acyl,diazenyl,andsomephosphorus-centeredradicalshave g -factors <ge .MostC-andSi-centered radicals,andradicalions,have g -factorsofabout 2.0026,butmultiplesubstituentssubstantially increasethis.Nitrogen-centeredradicalsincluding iminylsandaminylshave g -factorsintherange 2.003–2.004.Nitroxides(aminoxyls)arethemost commontypeofpersistentradicalandtheyhave verycharacteristic g -factorsaround2.006.Most aryloxylradicalsandsemiquinoneradicalanions have g -factorsaround2.0045.Manyalkylperoxyls havelarge g -factorscloseto2.015.Extensive tablesofisotropic g -factorsformanyradicaltypes canbefoundinRef.6.

3INTERPRETATIONOFCOMPLEXSPECTRA

AtX-band,theappliedfield B islargecompared toalmostallhfs,soisotropicspectrashowa

symmetricalclusterofresonancelinesaroundthe centralfield B0 .Asetofhfs(ai ;analogousto j in NMRspectroscopy)quantifiestheelectron–nuclear interactions.ForradicalsinwhichtheUPEinteracts withonlyafewsetsofnuclei,thespectracan beinterpretedandthe ai valuesdeterminedby simpleinspectionofthemultipletsthatappear. Thelineheightsshouldalsobesymmetrical,but non-idealitycanresultfromslowtumblingofthe radicals.Seriousasymmetryusuallyindicatesthat spectrafromtwoormoreradicals,withdifferent g -factors,aresuperimposed.Hyperfinesplittingsare usuallyexpressedinmilliteslaorGauss[a (G) = 10a (mT)]butcanalsobereportedinMHz[a (MHz) = 1 3996ga (mT)].

Thefollowingrulesarehelpfulinanalyzing spectra:

1.Theseparationbetweenthetwooutermostlines athighfield(orlowfield)isalmostalwaysthe smallesthfs.Note,however,thattheoutermost lowintensitylinesmaybehiddeninnoise.

2.Thespectralextent Bw istheseparation betweenthelowandhighfieldoutermostlines andfor I = 1/2 nuclei,itisgivenby Bw = ni ai ,where i = 1, ... , N .Here, N isthe numberofsetsofequivalentnucleiand ni isthe numberofequivalentnucleiwithhfs ai

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a1 = 0.12 mT

a2 = 0.42 mT

a3 = 0.61 mT

a4 = 1.10 mT

3.Aspectrumwithacentrallineindicatesthe presenceofanevennumberof I = 1/2 nuclei. However,thepresenceofcentrallinedoesnot excludeanoddnumberofnuclei.

ForthemodelspectrumshowninFigure4,the twooutermostlinesformadoubletwithseparation0.12mTandsothisisthesmallesthfs a1 . Thedoubletpatternindicatesthatthisresultsfrom interactionwithone I = 1/2 nucleus.Atripletsplittingfromtwo I = 1/2 nucleistarts0.42mTupfield fromthefirst(a2 ).Adoubletfromone I = 1/2 nucleusstarts0.61mTupfieldagain(a3 ).Themeasuredspectralextent Bw is3.77mT.Thus,thefinal hfscanbefoundfromthedifference: Bw [1 × 0 12 + 2 × 0 42 + 1 × 0 61] = 2 20mT.Inspection showsthatthiscorrespondstoa1:1:1triplet withhfs1.10mTfroman I = 1nucleus(N, a4 ).Inthisspecies,therefore,theUPEinteracts withtwononequivalentH-atoms,aCH2 group, andanN-atomasexpectedfortheradicalanion of5-ethyl-2-nitrothiophene.Analysessuchasthis shouldbeconfirmedbycomputersimulationofthe spectrumusingoneofthefreelyavailablepackages forisotropicspectra.(TheWINEPRSimFoniapackageisfreewareavailablefromBrukerCorporation andrunsintheMSWindowsenvironment).13

Definitiveanalysesofcomplexandimperfectly resolvedspectrapresentformidableproblems.It

maybepossibletodeduceoneortwoofthe ai valuesusingtheaboverules.TheWinsim2002software,andtheMATLAB-basedpackageEasySpin,14 areparticularlyusefulbecausetheydirectlyread experimentalEPRspectrafromseveraldifferentfile formats.Thesimulatedspectrumiscomparedwith theexperimentalspectrumandacorrelationcoefficientisoutputtedasameasureofthegoodnessof fit.ApplicationoftheWinsim2002autocorrelation functiontotheexperimentalspectrumprovidesalist ofhyperfineparameters.Thelistcontainsallthe required ai valuesfortheunknownradicalmixed upwithsumsanddifferencesofthe ai values.On thebasisofthislist,alikelysetof ai canoftenbe guessedandtheresultingsimulationcomparedwith experiment.Helpinestimatingappropriate ai valuescanalsoobtainedfromliteraturedataformodel radicalsorfrom abinitio computedhfs.Byworking throughseveraliterationsofinputted ai andcomparisonofthesimulatedandexperimentalspectra,it isoftenpossibletoobtaingoodsimulationsofeven verycomplexspectraofunknownprovenance.

Indifficultcases,itisnecessarytoobtain andcomparespectrafromaseriesofradical isotopomers.Deuterium(D, 2 H)has I = 1and since a (H)/a (D) = [µD /ID ]/[IH /µH ] = 6 5substitutionofHbyDusuallymeansthehfsfromthesubstitutedH-atomisremoved(towithinthelinewidth) orbecomesasmallersetof1:1:1triplets.15

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Bw = 3.77 mT
Figure4 Deductionofhyperfinesplittings ai fromanEPRspectrum.

Asimplifiedspectrum,whichiseasiertointerpret, oftenresults.Similarsimplificationcanbeachieved bysubstitutionof 14 N(I = 1)by 15 N(I = 1/2). Occasionally, 17 O(I = 5/2)hasbeenintroduced inplaceof 16 O(I = 0)toconfirmthesiteofan O-atom,notablyinperoxylradicals.16,17

4INTERPRETATIONOFISOTROPIC

HYPERFINESPLITTINGS

4.1TheOriginofHyperfineSplitting

Themagnitudeoftheisotropicinteractiondepends ontheprobabilityoffindingtheelectronatthe nucleus.Clearly,thishingesonthecharacterof theorbitalcontainingtheUPE.Ingeneral,the spinsofelectronsandnucleiarecoupledbythe Fermi contactinteraction ,whichrepresentsthe energyofthenuclearmomentinthemagneticfield producedatthenucleusbythespinningelectron. TheHamiltonianoperatorcorrespondingtothisis givenby(14)

ˆ Hc = 8π 3 g β gn βn δ(

TheDiracdeltafunction δ(r ) ensuresthatthis isonlyeffectivewhentheelectronhasafinite probabilityofbeingatthenucleus.Thus, ˆ Hc only hasfinitevaluesfors-orbitalsbecausep-,d-,f-,and soonorbitalshavezerodensityatnuclei,andhence onlyelectronswithsomes-charactercaninteract withthecorrespondingnucleus.Thehfsderived from(14)takestheform

molecularframework.Thisphenomenon,knownas spinpolarization ,canbeunderstoodbyreferenceto aC–Hfragmentformingpartofa π -radical.Two arrangementsofthespins(a)and(b)arepossible (Figure5).However,becauseofexchangecoupling betweenthe π -and σ -orbitals,arrangement(a)is slightlylowerinenergy.

In(a),thetwospinsontheC-atom(α )are parallel,leadingtoafavorableexchangeinteraction. Hence,thereisaslightexcessof α -spininthe σ -orbitalandacorrespondingexcessof β -spin intheH-atom’ss-orbital.The α -spinonthe π -orbitalinduces β -spinattheH-atomandhence thespindensityattheH-atomisnegative,and soistheH-atomhfstothe π -electron.In(a), the α -spinofthe π -electroninduces α -spininthe σ -orbitalcenteredontheC-atomandhencethe hyperfinecouplingtothe 13 C-nucleus(I = 1/2)will bepositive.

McConnellshowedthatthehfs a (H)ofH-atoms in π -typeradicalsaredirectlyproportionaltothe π -electronspindensities ρπ inthep-orbitalsofthe C-atomstowhichtheyareattached18,19 :

a (H) = Q ρπ (16)

where ρ (rn )isthe spindensity evaluatedoverthe volumeofthenucleus.

In π -typeneutralradicals(methyl,allyl,cyclohexadienyl,etc.),aromaticradicalions,andsimilarspecies,theUPEsarecontainedin π -molecular orbitals(MOs)thatextendovermuchofthemolecularframework.The π -MOshaveanodeinthe planeoftheradical,wheremanyoftheH-atoms, 13 C,andothermagneticnucleireside.Atfirstsight, itappearsthatelectron–nuclearcouplingshouldbe zero,butinpracticeexchangeforcesbringabout couplingofthe π -electronwith σ -electronsinthe

Therelationshiphasbeentestedformanydiverse seriesof π -typeradicalsandradicalionsand reasonablelinearityresultedwith Q usuallyinthe range 2.2to 2.9mT.20 Thissimplerelationship enablesaroughpictureofthedistributionof unpairedspininafreeradicaltobebuiltupfrom theexperimentalhfsof“reporter”H-atoms.

4.2HyperfineSplittingfromNucleiTwoor MoreBondsfromtheUPE

ThedistancesofH-atomsfromaradicalcenter, whichmayormaynotbepartofa π -delocalized

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Figure5 SpinpolarizationinaC–Hfragmentofa π -radical.

3, staggered

4, eclipsed

Scheme1 ConformationsofR2 C• CH2 β R radicals. system,areusuallyindexedasshownin 1 (Scheme1).

Thus,Hα areonebondawayfromthe π -orbital containingtheUPE,whileHβ ,Hγ ,Hδ ,and soonaretwo,three,four,andsoonbonds, respectively,removedfromtheradicalcenter.For Hβ -atoms,interactionwiththeUPEoccursmainly byahyperconjugativemechanism.The π -orbital containingtheUPEhascorrectsymmetryfordirect overlapwiththe σ -orbitaloftheCβ –Hβ bond (2a,Scheme1).ThismechanismimpliesthatHβ hyperfinesplittingsshouldbepositiveandthishas beenconfirmedbyNMRexperiments.Thedirect natureoftheoverlapin 2a, b leadstosizeable β -hfs, whichareoftenlargerthan α -hfs.Forexample,in theethylradical,wherethereisfreerotationabout theCα –Cβ bond,themeasured a (Hα )is2.24mT, whereasthe a (Hβ )islargerat2.69mT.

Innonrigidradicals,adegreeoftorsionabout theCα –Cβ bondtakesplaceinsolution.Theextent ofoverlap,andhencethemagnitudeof a (Hβ ), willdependonthedihedralangle θ betweenthe π -orbitalandtheCβ –Hβ bond(2b).Thisangle varieswiththerateofinternalrotationaboutthe Cα –Cβ bond,whichdependsontemperature.It followsthat a (Hβ )arealsosignificantlytemperature dependent.Extensivestudiesofalkylradicals21,22

haveshownthat β -hfsfollowaKarplustype relationship(17):

a (H β ) = A + Bcos2 θ (17)

ConstantAissmall(<0.4mT)andcanoften beneglected; B is ≈5 0mTforC-centered radicals.Therearetwoparticularcases:(i) R2 C• –CH2 β R wheretherearetwo β -H-atoms and(ii)R2 C• –CHβ R2 withone β -H-atom.For (i)thevalueof θ is60◦ whenR eclipsesthe π -orbital(4)and30◦ whentheconformation isstaggered(3).Forfreerotation,theaverage valueof θ is45◦ .Ifthepreferredconformationis eclipsed(4), a (Hβ )willbeintherangeA + 1/4B toA + 1/2B,andwill increase towardthelatter withincreasingtemperature.Ifthepreferred conformationisstaggered, a (Hβ )willbeinthe rangeA + 3/4BtoA + 1/2Bandwill decrease towardthelatterwithincreasingtemperature.In case(ii),thelimitsarewider,thatis,fromAto A + B.Theseexpectationvaluescanbeusefulfor determiningthepreferredconformationaboutthe Cα –Cβ bondsofnonrigidradicals.Forexample, theEPRspectrumofthe n -propylradicaldisplayed a (Hα ) = 2 21and a (Hβ ) = 3 32mTat100K. Onincreasingthetemperatureto200K, a (Hβ ) droppedto2.92mT.Itfollowsthatthepreferred conformationofthe n -propylradicalisstaggered 3 Ontheotherhand,fortheCH3 SCH2 CH2 • radical a (Hβ )increasedfrom1.35mTat150Kto1.49mT at205Kshowingthatitspreferredconformationis eclipsed 4.Ingeneral,radicalsRXCH2 CH2 • tend toadoptconformation 3 ifXisafirstrowelement but 4 ifXisfromthesecondorsubsequentrows oftheperiodictable.

Longerrangehfsgenerallydecreasewiththe numberof σ -bondsbetweentheH-atomandUPE. Hfsfrom γ -H-atomsarenormallymuchsmaller [< 1/10 × a (Hα )].Ingeneral,theprerequisitefor observationofasubstantiallong-rangehfsisa “frozen”conformation(ontheEPRtimescale). MostEPRstudiesoflong-rangehfshaveinvolved bicyclicorpolycyclicradicalsinwhichtherigid structuresplaceparticularH-atomsatsitesthat arefavorableforhyperfineinteractions.23–26 For example,inthebicyclo[2.2.1]heptylsemidioneradicalanion 5 alarge γ -hfsof0.65mTwasobserved fortheindicatedHγ (Scheme2).

Generally, γ -H-atomsforwhichthe σ -bondsand theorbitalcontainingtheUPEadopta“W-plan”

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Scheme2 Largelong-rangehyperfineinteractions.

(a) (b)

Figure6 (a)EPRspectrumofbicyclo[1.1.1]pentylradical 6 inliquidDTBPat240K.(Theintensitydifferenceofthetwo multipletsisduetoaCIDEPeffect.)(b)Spectrumofcubyl radical 7 inliquidDTBPat245K.

conformation(see 5 and 8)showsubstantialhfs. TheEPRspectraofthebicyclo[1.1.1]pentylradical 6 andthecubylradical 7 (Figure6)werequite remarkableinthathugehfsof6.96mTwere observedforthesingleHγ of 6 (theintensity differenceofthetwomultipletsisduetoaCIDEP effect.)27,28 and0.63mTforthesingleHδ of 7, 29,30 becauseofmultipleW-planthroughbondand throughspaceinteractions.

Smalllong-rangehfsareoftenresolvablein acyclicradicals,21,31,32 andinradicalscontaining oxygen,usuallyinanetherlinkage.33–35 Many alkaneradicalcationsin“rigid”conformationsin lowtemperaturematricesexhibitlargelong-range hfs.36

In n -propanesolvent,inthetemperaturerange 90 < T < 125Ktumblingremainsfastforsmallto medium-sizedradicals,butinternalrotationsmay cease,sothatlong-rangehfscanberesolved.37 Inthe“rigid”conformationsadoptedatthese temperatures γ -H-atomssituatedtrans(W-plan) withrespecttothesinglyoccupiedmolecularorbital (SOMO)showlargehfs.Forexample,threeof the γ -H-atomsoftheneopentylradicalexhibit a (Hγ ) = 0 40mTand,evenmoreremarkably,the uniqueHγ ofthe2,2,3-trimethylbutylradical 8 had a (Hγ ) = 0 80mT.38,39

4.3QuantumChemicalComputation ofEPRParameters

ThestraightforwardpictureofjustoneUPEina particularorbitalinteractingwithnearbymagnetic nucleiisagrossoversimplification.40 Infact,radicalscontainmanyelectronsallofwhosespins interacttosomeextent.Foramorecomplete andaccuratepicture,allthepopulatedmolecular orbitalshavetobetakenintoaccountinevaluatingthespindensity ρ (rn ),whichisactually thenetdifferencebetweenthe α -spinand β -spin atthenucleus.In-depthtreatmentsofthecalculationofEPRparameterscanbefoundinthecompilationeditedbyKaupp etal 41 ModernquantummechanicalMOpackagesbasedonDFT,or other abinitio methods,cancomputeoptimum geometriesoffreeradicals,togetherwiththeenergiesandeigenvectorsassociatedwiththeiroccupied(andvirtual)orbitals.42,43 Considerableeffort hasgoneintofindingthemosteffectivequantum mechanicalmodelsandbasissets44,45 forthecomputationofisotropicEPRparameters.46–48 MethodsbasedontheunrestrictedKohn–Sham(UKS) approachtoDFTareamongthemostefficient. Quadraticconfigurationinteraction(QCI)andcoupledcluster(CC)methodsgiveaccurateresultsbut arenotpracticalformedium-orlarger-sizedradicals(>10non-hydrogenatoms).Hybridfunctionals suchasthepopularB3LYPandtheparameter-free PBE0modelprovidegooddescriptionsoftheEPR spectraofmanytypesofradicals.Acombined PBE0/QCISDapproachisrecommendedformore accurateworkwithspeciescontainingseveralheteroatomssuchasnitroxides.Particularbasissets suchasEPR-II,49 andthemuchlargertriple-zeta

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BASICCONCEPTSANDMETHODOLOGIES

qualityEPR-III,50 usuallyenablegoodagreement ofcomputedandexperimentalhfstobeachieved forH-atoms.However,forheteroatoms(eventhe firstrowN,F)considerablymorecomputational effortisoftenrequired.Anumberofwell-tried electronicpackagesarenowavailabletoimplement thequantummechanics(QM)computationsincludingGAMESS-UK,51 Jaguar,52 andSpartan.53 The Gaussian03and09seriesofpackages54 areconvenientbecauseisotropicandanisotropicspindensitiesandhfsaredirectlycomputedandspindensity mapscanbeplotted.

Forexample,the1,3-dimethylimidazolyldihydroborylradical 9 wasgeneratedbyH-atomabstraction fromthecorrespondingHNC-boraneandexhibited theisotropicEPRspectrumshowninFigure7at 245K.55 Themolecularstructurewasoptimized usingtheDFTmethodwiththeB3LYPfunctional andthe6-31+G(d)basissetandisshownin 9 (Figure7).ThecorrespondingmapsoftheSOMO andspindensity,computedwiththesamegeometry buttheEPR-IIIbasisset,areshownas 10 and 11 ThecomputedFermicontacthfsarecomparedwith theexperimentalparametersbelowandgiveafair ideaoftheachievablelevelofagreement: Hfs/mT

5GEOMETRIESATCα OFC-CENTERED RADICALS

Theground-statestructureatCα ofcarbon-centered radicalsmaybeplanar 12 suchthattheUPE occupiesa p -typeorbital,thatis,theradicalhas π -character.Alternatively,theradicalmaybepyramidal 13 suchthattheUPEoccupiesahybridorbital of σ -character(Scheme3).TheEPRhfsofadjacentmagneticnucleicanbeveryhelpfulindistinguishingbetweenthesealternatives.Table1shows experimentalparametersforarchetypeC-centered radicalswithvarioussubstituents.

The a (13 Cα )areparticularlyvaluablebecause theygiveadirectmeasureoftheamountof s -characterintheSOMO. 13 C(I = 1/2)ispresent inorganicradicalswithanaturalabundanceof 1.1%;thus,signalsfromtheinteractionofUPE withthisnucleusaccompanythemainspectrum assmallsatellitesoneithersideofthemain 12 Clines.Fortransientradicals,the 13 Csatellites areusuallyundetectableinthenoise,soisotope enrichmenthastobeemployed.Fortheseriesof radicals • CHn Me3 n ,the a (13 Cα )valuesincrease onlyslightlywithincreaseinthenumberofMe groups(Table1). 13 Cα andHα hfsusuallyshow smalltemperaturedependenciesthatresultfrom vibrationalmotions,particularlyfrominversionsat f

12, p-radical 13, s-radical

Scheme3

Geometriesof π -and σ -radicals.

Table1 EPRparametersforsubstitutedmethylradicals.a

Radical a (13 Cα ) a (Hα ) a (X) g -factor

• CH2 –H3.85 2 30—2.0026

• CH2 –Me3.91 2 24—2.0027

• CH2 –NH2 1 320.5(14 N)2.0029

• CH2 –OH4.53 1 801.0(17 O)2.0032

• CH2 –F5.48 2 116.43(F)2.0045

• CH(Me)2 4.13 2 21—2.0026

• CH(OMe)2 10.1 1 36——

• CHF2 14.9 +2 228.42(F)2.0041

• CF3 27.2—14.2(F)2.0031

• CMe3 4.52——2.0026

a hfsinmillitesla;datafromRef.6.NotethatEPRspectragivethe magnitudebutnotthesignofhfs.

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theradicalcenter.Theseinversionbarriersarevery low,sotheaveragestructuresareplanaronthe EPRtimescale;however,pyramidalstatesmakean increasingcontributionasthenumberofMegroups increases.56,57

Forthefluoromethylseriesofradicals,Table1 showsthat a (13 Cα )increasesstronglyasthenumber ofF-substituentsincreases.Thus,theextentof pyramidalityof(13),measuredbytheangle φ , increasesasthenumberofF-atomsincreases.The large a (13 Cα )for • CF3 (27.2mT)indicatesthat thisradicalisessentiallytetrahedralwiththesp3 orbitaloftheUPEpointingtowardonecorner ofthetetrahedron.Notethatthe a (F)and a (Hα ) valuesalsoincreaseastheradicalsbecomemore pyramidal.Inspectionofthe a (13 Cα )and a (Hα )data forradicalswithoxygensubstitutionrevealsthat thiselementalsoinducespyramidalityattheradical centerandthesameisprobablytrueofnitrogen substituents.

Thelarge a (13 Cα )hfsforvinyl58 andacyl radicals59 (Scheme4)showthattheUPEoccupies orbitalswithsubstantial s -characterandthatthese radicalsarebent.ForacylradicalsRC• = O,the a (13 Cα )hfsincreasealongtheseries R = Me < NH2 < OBut < F.Thedegreeofbendingatthe radicalcenterincreaseswiththeelectronegativity ofthesubstituent,justaswithalkylradicals.

ThehfsofCα -andHα -atoms(Scheme4) showthatcyclohexyl,cyclopentyl,andcyclobutyl radicalsareessentiallyplanar.Fortheseringsizes, substitutionbyoneO-atomadjacenttotheradical centerinducessignificantpyramidalityandtwo O-atomsinduceevenmore s -character.Bywayof contrast,the a (13 Cα )and a (Hα )dataforcyclopropyl andcyclopropenyldisclosethattheseradicalsare bent,asistheoxiranylradical.

Bridgeheadradicals26 are,ofcourse,necessarily pyramidalandtheirEPRspectrashowlarge a (13 Cα ) values.60 Interestingly, a (13 Cα )constantsdisplay alinearcorrelationwiththeNMRonebond Cα –H(1 JC–H )couplingsintheparentbridgehead hydrocarbons.Similarlinearcorrelationshavebeen foundbetweentheNMR 1 JC–H dataofmethanes,61 silanes,62 phosphines,63 andaldehydes64 andthe EPRhfsoftheradicalsformedbylossofthe H-atoms.MortonandPrestonprovidedatomic parameters ψ 2 (0),togetherwiththeisotropichfs forunitspindensityinthes-orbitals,ofnuclei oftheelementsfromHetoBi.65 Comparisonof

Scheme4 Thehfs(millitesla)forvinyl,acyl,andcycloalkyl radicals.6

experimentalEPRparameterswiththisdatacanbe veryhelpfulfordeducinglocalgeometries.

6EPRSTUDYOFRADICAL CONFORMATIONSAND CONFORMATIONALINTERCHANGE

NMRspectroscopyisrecognizedasanextremely valuabletoolforstudyingtheconformationsof moleculesandbiomoleculesandtheirdynamicprocesses.The“timescale”ofEPRismuchshorter thanthatforNMRsothatfasterdynamicprocesses withfreeenergiesofactivationmuchlowerthan thosegenerallymeasurablebyNMRbecomeaccessible(see StructuresandReactivityofRadicals FollowedbyMagneticResonance).Muchimportantworkhasbeencarriedout,mainlywithproteinsandotherbiomoleculeslabeledwithnitroxide freeradicals(see UnderstandingDNARadicals EmployingTheoryandElectronSpinResonance Spectroscopy).ThissectionfocusesonEPRstudies

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oftheconformationsoftransientspecies.Theuse ofKarplustyperelationshipsfordeducingpreferred conformationsisoutlinedinSection4.2.

SmallenergybarrierstohinderedinternalrotationsaboutCα –Cβ bondscanbedeterminedfrom theexperimentaltemperaturedependencesof a (Hβ ). Torsioninaradical • CH2 –CHR2 isgovernedbya twofoldsinusoidalpotential.Eachwellcontainsa numberoftorsionalstatesandaboveeachbarrier thereexistsasetofrotationalstates.Theobserved a (Hβ )isaweightedaveragetakenoverallthepopulatedstates.QuantummechanicalmethodsofderivingthisaveragearedescribedbyFessenden66,67 andKochi.68 However,forlowbarriers,a“classicallimit”approachgenerallygivesthesame resultsasthemorecumbersomequantummechanicalprocedures.69,70 Thebarriertorotationabout theCα –Cβ bond(V0 )canbeestimatedbyfitting theobservedtemperaturedependenceof a (Hβ )with valuescalculatedfrom(18): a (Hβ ) = A + 1/2B + 1/2B cos2θ0 I1 (λ) I0 (λ) (18)

where I1 (λ) and I0 (λ) aremodified(hyperbolic) Besselfunctions, λ = V0 /kT ,and θ0 isthevalue of θ atthepotentialminimum.(ForVo < circa 2.5kJmol 1 (20)maybeapproximatedby: a (Hβ ) = A + 1/2B + 1/2B cos2θo [λ/2 λ3 /16].) A and B areknownfromtheKarplusequationand V0 isvariedsoastoobtainthebestfitbetween experimentalandcalculated a (Hβ )overtheaccessibletemperaturerange.Bythesemeans,barriers, generallyintherange5 0 > V0 > 1 0kJmol 1 , havebeenobtainedformanyalkylradicals.

Internalrotationbarriershigherthan ∼10kJmol 1 generallyleadtoselectiveline broadeninginX-bandEPRspectra.(EPRobservationofselectivelinebroadeningalsodepends onthemagnitudeofthedifferenceinthehfsof theexchangingmagneticnuclei.)Thisoccurswhen thelifetimesoftheconformationalstatesbecome comparabletothereciprocalofthedifferenceinthe hfsoftwoexchangingH-atoms.Whenthebarrierto internalmotionishigherstill,separateEPRspectra willbeobservedforeachconformationalstate. PioneeringEPRstudieswereundertakenonthe conformationsofpersistentcyclic-semidiones71 and nitroxides.72,73 EPRdatafortransientcyclicradicals includingcyclohexyl,74,75 othercycloalkyl,76–78 andcycloalkenyl79 provedusefulforchartingthe

Figure8 CWEPRspectrafromcycloalkylmethylandcyclohexylacylradicals.(a)Spectraofcyclohexylmethyls 14e,a at 240Kin t -BuPhsolution.(b)and(c)secondderivativespectraof 4-t -butylcyclohexylacylradicals 16e,a at140Kincyclopropane. conformationalchangescausedbytheintroduction oftheplanarradicalcenterintoeachtypeofring. AvaluableEPRspectroscopictechniquefor studyingtheconformationsofrings,unperturbed bythepresenceofaplanarradicalcenter,involves usingtheCH2 • moietyasaspinprobe.80 Thesmall, neutral,CH2 groupofacycloalkylmethylradical, c -Cn H2n 1 CH2 • ,causesminimalperturbation oftheadjacentring.Thecyclohexylmethylradicalexistsasapairofconformers 14e and 14a inwhichtheCH2 • groupisintheequatorialand axialorientations,respectively.TheEPRspectrum ofthecyclohexylmethylradical(Figure8a)showed alargedoubletriplet(E)fortheequatorialradical 14e accompaniedbyaminoramountofasecond doubletriplet(A)fortheaxialradical.Themain differencewasthattheaxialradical 14a hada largerdoublethfsfromHβ andthisenabledthe twospectratoberesolved.Sterichindrancefrom the syn -axialhydrogens(Hδ )of 14a resultedin anincreasedtorsionalbarrierandconsequentlythe largeHβ hfs.Fromtherelativeconcentrationsof thetwospecies 14e and 14a,theconformational freeenergydifferenceoftheCH2 • group( G0 300 ) wasfoundtobe3.0kJmol 1 .Themethodwas alsoapplicabletocycloalkylmethylradicalswith ringsizesuptoatleast15,81 tocycloalkenylmethylradicals(15e,a,Scheme5),82 andtocyclohexylacylradicals(16e,a)83 (Scheme5,Figure8b andc).

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, a(2Ha) = 2.15 mT

(Hb) = 3.04 mT

15e, a(Hb) = 3.37 mT

,

(Hb) = 4.29 mT

16e, X = CH2, R =

a(Hb) = < 0.1 mT

a(2H) = 0.16 mT

, X = CH2, R = H

(Hb) = 0.22 mT

(2H) = 0.37 mT

Scheme5 Axialandequatorialcycloalkylmethyland cycloalkylacylradicals.

7EXCHANGEBROADENINGAND INTERNALMOTIONS

Section1.3establishedthat,forradicalsinsolution, spin-statelifetimesaregovernedbyspin–spinrelaxationphenomenawithcharacteristictime τ2 .For Lorentzianlines,andwithpowerwellbelowsaturation,(10)yields B1/2 = 2/γe τ2 .Internalrotations, ringinversions,andotherintramolecularprocesses altertheelectronspin–nuclearspininteractionand hencecandrasticallymodify τ2 .Somelines,but notothers,maybeselectivelybroadened,dependingonthetypeofmotion.Sincetheratesofinternal motionsdependontemperature,theEPRlinewidths ofsuchradicalsarealsotemperaturedependent. Theamplitudeofagivenlineinafirstderivative spectrumisinverselyproportionaltothesquareof thelinewidth,sosmallchangesinthelattercan leadtostrikingchangesinspectralappearance.For example,thehydroxymethylradicalexistsasa1:1 mixtureofthe2equivplanarconformations 17a and 17b atlowtemperatures.Intheslowexchange limitat150K(Figure9),theEPRspectrumappears asadouble,doubledoubletfrominteractionofthe UPEwithtwononequivalentHX andHY andthe

Scheme6 Interchangeofthetwoplanarconformersofthe hydroxymethylradical.

hydroxylhydrogenHβ (Scheme6; a (HX ) = 1.765, a (HY ) = 1 853, a (Hβ ) = 0 216mT).84 Atahigh enoughtemperature,torsionsabouttheC–Obond arefastleadingtorapidexchangeofHX andHY .In thefastexchangelimitat >200K,HX andHY are equivalentandthespectrumisasharptripletofdoublets.

Atintermediatetemperatures,broadeningofthe centrallinesappears.Maximumbroadening(coalescence)isreachedatabout165K,wheretherateof interchangeofHX andHY isequaltothefrequency separationoftheinnerlines(a (HY ) a (HX ) = 0.088mT = 0.25 × 106 Hz).

Whenexchangebroadeningisduetointerchange oftwospeciesofequalenergy,aswith 17a and 17b,theforwardandbackwardrateconstants(k ) areequal.Therateconstantforinterchangecan besimplyderivedfromthedifferenceinthehfs ofHX andHY andthelinewidth.85 Otherkinds ofselectiveEPRlinebroadeningwithdifferent characteristicsareattributabletodifferenttypesof internalmotions.86 Software,basedonrelaxation matrixtheory,canbeobtainedforsimulatingthe linebroadeningofmorecomplexprocesses.87

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Figure9 Temperature-dependentlinewidthsintheEPRspectrumofHO–CH2 •

Scheme7 “Frozen”conformeroftheneopentylradical.

Theneopentylradical 18 providedaparticularly strikingexampleofexchangebroadening.88 Above 210K,theinternalrotationsabouttheCα –Cβ bond, andaboutthethreeCβ –Cγ bonds,areallinthefast exchangelimit,sothesolutionEPRspectrumof 18 consistsofatriplet(a (2Hα ) = 2 14mT)having eachcomponentsplitinto10linesfromthe9equiv Hγ (a (9Hγ ) = 0.096mT).Inthetemperaturerange 210–106K,exchangebroadeningisobservedasa resultofhinderedrotationofthethreeMegroups abouttheirCβ –Cγ bonds(Figure10).By96K,the “rigid”conformation 18a,b isreached,inwhichthe Megrouprotationsarefrozenwith3equivtrans Hγ t havinglargehfsbecausetheyareinW-plan sites(a (3Hγ t ) = 0 404mT)and6equivgauche Hγ g (a (6Hγ g ) = 0 062mT).Internalrotationabout theCα –Cβ bondcontinuesrapidlyevenat96K becauseofthelowsixfoldbarrier.Figure10shows

aselectionofexchangebroadenedexperimental EPRspectraintherange106–210Kalongside computersimulationsobtainedwithathree-jump modelhavingallforwardandreverserateconstants equal.AnArrheniusplotoftherateconstants yieldedanactivationbarrierof15.4kJmol 1 anda pre-exponentialfactorof1012 6 s 1 fortheinternal Merotations.Activationbarriersintherange 8–40kJmol 1 forgrouprotationsaboutC–C,22,37 C–N,89,90 andC–Obondshavebeendetermined bysimilarmeansaswellasinversionbarriersfor severaltypesofrings.79,80,82,91

8EPRSPECTRAOF HETEROATOM-CENTEREDRADICALS

IsotropicEPRspectrahavebeendescribedfor manytypesofradicalscontainingelementsfrom thefirstandsecondrowsoftheperiodictable. ThissubsectionsurveysradicalsinwhichtheUPE residesmainlyonaparticularheteroatomandthose inwhichspinispartlydelocalizedawayfromthe principalheteroatom.Anisotropicspectrahavebeen obtainedfrommanyradicalscenteredonelements fromthethirdandsubsequentrowsoftheperiodic table,92,93 butsolutionspectratendtobebroad,and comparativelyfewhavebeenreported.

Figure10 EPRspectraofthecentralcomponentofthetripletfromtheneopentylradical(18).Left:Experimentalspectraatthe indicatedtemperatures.Right:Simulatedspectrawiththeindicatedrateconstants.[AdaptedwithpermissionfromK.U.Ingold, etal., J.Phys.Chem.,1986, 90,2859–2869.Copyright1986AmericanChemicalSociety.]

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8.1SpectrafromTransientBoron-and Aluminum-CenteredRadicals

Triarylboronradicalanions[Ar3 B] • areofinterestbecausetheyareisoelectronicwithneutral C-centeredradicalsAr3 C• .EarlyEPRstudies showedthat[H3 B] • (19)had a (11 B) = 1.99mT and a (3H) = 1 52mT94 whilefortheanalog 20 a (11 B) = 0.78mTwasobtained.95 TheUPE ismainlyonboronandthelow a (11 B)values suggestthattheseare π -typespecieswithplanar geometryatboron.94,96 Otherclassesoftransient boron-centeredradicalsthathavebeenextensively studiedbyEPRspectroscopyinsolutioninclude thephosphine-borylradicals(21),97,98 dialkyl sulfide-borylradicals(22),99 andamine-borylradicals(23).100–103 Thesespeciesweregeneratedby H-atomabstractionfromthecorrespondingligated boranesandgaverisetowell-definedspectraoften showingstructurefrom 10 B(I = 3,19.9%)aswell as 11 B(I = 3/2,80.1%);seeFigure11a.104,105

Theequilibriumgeometriesoftheboroncenters of 21 and 22 (Scheme8)areplanar,ornearlyso, asjudgedbythe 11 BandHα hfs(Table2).In contrasttothis,thelarger 11 Bhfsofamine-boryls 23 (Table2)indicatedapyramidalarrangementof theligandsaboutboron.

EPRspectroscopyshowedtheamineborylradicals 23 tobethemostreactive;theyunderwent β -scissionmorereadilythanisoelectronicalkylradicalsandrearrangedrapidlytoaminyl-boraneradicals.Theirnucleophilliccharacterwasconfirmedby alaserflashphotolysis(LFP)studyofthekinetics ofvariousreactions.106

Scheme8 Selectedboron-centeredradicalsandions.

N -Heterocycliccarbeneborylradicalscontainingimidazoleandtriazoleringsweregenerated byH-atomabstractionfromthecorresponding N -heterocycliccarbeneboranes,55,107 andbyreductionofanalogouscations.108 TheisotropicEPR parametersofmodel 24 (Table2)andothers, togetherwithDFTcomputations,showedthemto beplanar π -delocalizedspecies,inwhichtheUPE isdelocalizedfromboronintothe π -systemof theadjacentheterocyclicrings.KineticEPRstudies revealedthattheirbimolecularself-terminationand halogenabstractionreactionswerestronglyinfluencedbystericshieldingoftheboroncenter.

ApartfromanisotropicEPRstudies,109,110 afew alaneradicalanionsweregeneratedinsolution byH-atomabstractionfromMX3 AlHsalts.111 Comparisonofthe a (27 Al)hfs(IAl = 5/2)for AlH3 −• (Table2)withthatcalculatedforunit populationoftheAl3sorbital(98.5mT)112 showed thatitssemi-occupiedorbitalhasabout16%3s charactersothatitdeviatessomewhatfromplanar.

8.2SpectrafromTransientSilicon-, Germanium-,andTin-CenteredRadicals

(a)

(b)

Figure11 (a)EPRspectrumofthe(MeO)3 P → B• HBu-t radicalat240Kincyclopropaneshowingsignalsfrom 11 B and 10 Bcontainingisotopomers(a (11 B) = 1 34, a (10 B) = 0 45, a (Hα ) = 1 55, a (31 P) = 3 96, a (9H) = 0 09mT).104 (b)EPR spectrumofthe α -tocopheroxylradical 49

Spectroscopicstudiesofsilylradicalshaveoften beenplaguedbythebuildup,duringphotolysis,of spectrafromsecondarypersistentradicalsthatmask transientspecies.Inmanyspectra,thesatellites from 29 Si[naturalabundance4.7%, I (29 Si) = 1/2]wereobserved,andtheEPRparametersfor somemodelradicalsarelistedinTable3.113–119 Thevaluesof a (29 Si)forH3 Si andalkylsilyl radicals(∼18mT)are ∼25%thatexpectedforunit UPEpopulationoftheSi3sorbital(∼80mT). Therefore,theSOMOoftheseradicalshasabout

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BASICCONCEPTSANDMETHODOLOGIES

Table2 EPRparametersofmodelboron-andaluminum-centeredradicalsandanions.a

Radical g -factor a (11 Bor 27 Al) a (2H) a (31 Por 14 N) a (other)

H3 B−• (19)—1.991.52(3H)——

X3 P → BH2 • (21,X = Et)2.00201.761.684.36—

X3 P → BH2 • (21,X = Me2 N)2.00201.671.634.250.20(3N)

X3 P → BH2 • (21,X = MeO)2.00191.471.664.39—

Me2 S → BH2 • (22,R = Me)2.00172.321.66—0.09(6H)

Me3 N → BH2 • (23,X = Me)2.00225.130.960.140.14(9H)

Et3 N → BH2 • (23,X = Et)2.00234.751.300.220.22(6H)

NHC → BH2 • (24,R = Me)2.00280.671.200.41(2N)0.12(2H),0.25(6H)

H3 Al • 2.002515.420.70(3H)—— (t -BuO)3 Al • 2.001530.07——— a hfsinmT;datafromRef.6andreferencesinthetext.

Table3 EPRparametersofmodelsilicon-,germanium-,andtin-centeredradicals.

Radical g -factor a (29 Sior 73 Geor117,119 Sn) a (Hα ) a (other)Reference

H3 Si• 2.003218.200.79—113

Me2 (H)Si• 2.003118.301.700.72(6H)114

Me3 Si• 2.003118.30—0.63(9H)120

F2 (H)Si 2.0013—8.997.78(2F)115

F3 Si• 2.000349.8—13.66(3F)113

Ph3 Si• —15.0——120 (Me3 Si)3 CSi(• )HOH2.002521.223.780.013(27H)113 (Me3 Si)3 CSi(• )HF2.002624.144.07—113

H3 Ge• 2.00737.51.5—116a Me3 Ge• 2.0107——0.55(9H)117

Ar3 Ge• 2.00846.84—0.07(Me,Hm )118b

H3 Sn• 2.01738.02.6—120a Me3 Sn• 2.0163——0.31(9H)119 a Datafromanisotropicsolid-statespectra.

b Ar = mesityl.

1/4 s-characterandtheradicalsarepyramidal(25, Scheme9),incontrasttotherelatedC-centered radicals.Introductionofanelectronegativeligand X(suchasForOH)confersgreaterp-character ontheSi–Xbondandcorrespondinglygreater s-characterontheremainingSi–Hbondsandthe SOMO.Thepyramidalcharacterisincreasedand both a (Hα )and a (29 Si)areincreased(Table3). Theintroductionofphenylsubstituentsdoesnot greatlyaffecttheconfigurationatSibutthereis significantdelocalizationofunpairedspinintothe aromaticrings.Itwasshownthatforagoodrangeof speciesalinearrelationshipexistsbetween a (29 Si) and 1 J (SiH)oftheparentsilanes.120

EPRspectrahavealsobeenobtainedfora significantnumberofgermanium-andtin-centered radicals(Table3).Comparisonofthe 73 Ge(I = 9/2, 7.8%)and117,119 Sn(I = 1/2,7.6,8.6%)hfswith theexpectedvaluesforunitoccupationofthe4sor

Scheme9 PyramidalstructuresofSi,Ge,andSncentered radicals.

5sorbital(Ge = 53 0mT,Sn ∼326mT)indicated pyramidalityforbothtypesofradical(26, 27; Scheme9).

8.3SpectrafromTransientNitrogen-and Phosphorus-CenteredRadicals

Aminylradicals(R2 N• )andthecorresponding aminiumradicalcations(R3 N•+ )areisoelectronic

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Table4 EPRparametersforaminyl,oxyaminyl,thioamiyl,andacylaminyl(amidyl)radicalsandaminiumradicalcations.

Radical g -factor a (14 N) a (Hα ) a (Hβ ) a (Hother ) Reference

H2 N• 2.00461.522.54(2H)——121

Me2 N• 2.00441.48—2.74(6H)—122 1-Aziridinyl2.00431.25—3.07(4H)—123 1-Pyrrolidinyl—1.43—5.42(2H)—124 2.71(2H)

PhNH• 2.00340.771.29(1H)—0.20(2H),0.62(2H),0.82(1H)125

H3 N+• —1.962.74——126

Me2 NH+• 2.00361.922.273.42(6H)—122

Me3 N+• 2.00361.47—2.73(9H)—122

EtON• H2.00501.202.000.31(2H)—127

MeON• Me2.00481.43—2.19(3H)0.26(3H)128

EtON• Ph2.0441.09——0.16(2H),0.48(3H),0.16(2H)127 t -BuSN• Me2.00731.25—1.64(3H)—129

PhSN• Bu-t 2.00701.18——0.1(3H)130

MeC(= O)N• Me2.00551.49—2.95(3H)0.13(3H)131

MeC(= O)N• Bu-t 2.00441.57——0.27(3H)132

withalkylradicals.Onlyafewprimaryalkylaminyls RHN• havebeendetectedinsolution,butprimary arylaminylsArHN• andmanysecondaryalkylaminylsandarylaminylshavebeenstudied;EPR parametersforaselectionofmodelspeciesare displayedinTable4.121–132

Thedataindicatethatalkylaminylradicalsare bentandthatinarylaminylstheUPEisdelocalizedintothearomaticrings.Theground-statestructuresofthesimpleaminiumradicalcationsare planar(28),unlikethepyramidalparentamines. Alkoxyaminylandthioaminylradicalshavesmaller a (14 N)valuesthanaminylsasmightbeexpected. Amidylradicals(acylaminyls)havelarger a (14 N) andthetemperaturedependenceofthe a (Hβ ) of modelradicalsshowedthattheyhave π -typestructures 29 (Scheme10).131,133,134

Iminylradicals(R2 C=N• )areisoelectronicwith vinylandformylradicals 30135 (Scheme10).These areall σ -typeradicalsbuttheUPEinformylis containedinanorbitalwithsubstantials-character (30),whereastheSOMOofiminylshaspractically purep-character(31, 32).EPRdataissetout inScheme10formethaniminyl 31, 136 andmodel iminyls 32, 137 33, 138 and 34. 139 Numerousmore compleximinylshavebeencharacterizedbyEPR spectroscopyandthekineticsoftheircyclization reactionshasbeeninvestigated140,141 (see Radical KineticsandClocks).

SeveralN-basedspeciesinwhichtheUPE issharedbetweentwoormoreN-atomsare

importantorganicintermediates.Hydrazylradicals arederivativesofhydrazine,andtheEPRdata fortheparent 35, 142 andanalogs 36143 and 37136 (Scheme10)showthattheUPEisfairly evenlydistributedbetweenbothN-atoms,probablybecauseofacontributionfromstructures R2 N–NH• ↔ R2 N+• =NH .Otherwise,hydrazyls resembleaminylsandthegeometryisflattenedat bothN-atoms,asrequiredbytheir π -structures. SampleEPRdataisalsodisplayedinScheme10 fordiazenylradical 38, 144,145 andtriazenyl 39146 in whichtheUPEisalsodistributedtoalltheN-atoms. Hugevarietiesofaminoxylradicals(nitroxides, R2 N–O• )andiminoxylradicals(R2 C=NO• ) have beeninvestigatedandmanyarepersistentorstable(see Nitroxide-MediatedPolymerizationand itsApplications and NitroxidesinSyntheticRadicalChemistry).TheirEPRspectraareoutsidethe scopeofthisarticle.147

ScarcelyanyalkylphosphinylradicalR2 P• has beenobservedinfluidsolutionbutPh2 P• [a (31 P) = 7 87mT]hasbeendetectedinthesolidphase atlowtemperatures.148 Afewphosphonylradicals,suchas(EtO)2 P• O[g = 2 0018, a (31 P) = 68 86mT],havealsobeencharacterized.149 Incontrasttothis,manyphosphoranylradicals(R4 P• ), mostlygeneratedbyadditionofneutralradicals tophosphorus(III)compounds,havebeenstudiedbyEPRspectroscopy.150,151 Thespectrareveal thatthelocalgeometryaroundphosphorusvaries markedly,dependingonthenatureoftheattached ligands.152,153 Atoneextreme,themajorityof

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30

a(13C) = 13.4

a(Ha) = 13.2

33 g = 2.0029

a(14N) = 0.96

a(6Hg ) = 0.14

31 g = 2.0028

a(14N) = 0.97

a(2Hb ) = 8.52

a(31P) = 51.93

(2Hap) = 19.87

(2Heq

32 g = 2.0029

a(14N) = 1.02

a(Hb ) = 8.20

a(3Hg ) = 0.25

34 g = 2.0031

a(14N) = 0.90

a(Hb ) = 8.01

H2N NH Me2N NH H2N NPh

37 g = 2.0035

a(N2) = 0.88

a(H1) = 1.63

a(N2) = 1.15

a(H1) = 1.37

a(N1) = 1.17 a(N1) = 0.96 a(N1) = 0.96 a(N2) = 1.15 a(H1) = 1.37 a(6H2) = 0.69

a(H2) = 0.43

a(H2) = 0.16

a(6H2) = 0.69

PhN N H3CN N NCH3

38 g = 2.0002

a(N1) = 2.25 1 2

a(N2) = 0.95 a(N2) = 1.16

a(2Hm) = 0.12

39 g = 2.0021 a(2N1,3) = 0.39 a(6H) = 0.77

Scheme10 StructuresandEPRparametersforN-centered radicalsandrelatedspecies(seetextforsourcereferences).

phosphoranylsadopttrigonalbipyramidylstructures 40 – 45 (Scheme11)withtwoligandsapical,two equatorial,andthefinalequatorialpositionoccupiedbyanorbitallobe(TBP).Thelargehfsfor 31 Pandapicalligands(Scheme11)showthatmost ofthespindensityisassociatedwiththesesites. Theprincipalatomicorbitalsthatcontributetothe SOMOofTBPphosphoranylsareillustratedin 44b and 45b.Attheotherextreme,somephosphoranylssuchasPh3 P• Cladoptstructuressuchas 46 withlocalC3v symmetryatphosphorus.154 Inthis case,theSOMOisaP–Clσ *orbitalasshownin 46 (Scheme11).155 Quantitativeinformationabout

Scheme11 EPRparametersforphosphoranylradicals(seetext forsourcereferences).

ligandapicophilicities,stereochemicalpermutations, β -and γ -scissionprocesses,andotherreactionshas beenobtainedbyEPRmethodsformanyphosphoranyls.

8.4SpectrafromTransientOxygen-and Sulfur-CenteredRadicals

Hydroxyl(HO• ) andalkoxylradicals(RO• ) arenot detectableinsolutionbecauseofunsuitablerelaxationtimes.Aryloxylradicals,semiquinone,and semidioneradicalanionsareveryimportantbiochemicalspeciesandmanyderivedfromphenolicnaturalproductshavebeenexaminedbyEPR

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47 g = 2.0046

a(H2,6) = 0.66

a(H3,5) = 0.19

a(H4) = 1.02

48 g = 2.0042

a(H3,5) = 0.17

a(3H) = 1.11

49 R = phytyl

g = 2.0046

a(3H) = 0.60

a(3H) = 0.46

a(3H) = 0.10

a(2H) = 0.15

50a, g = 2.0146

a(17O1) = 2.18

a(17O2) = 1.64

52 g = 2.0049

a(3H) = 0.06

53 g = 2.0050 a(2H) = 0.08 a(3H) = 0.17

g = 2.0151 a(Hb) = 0.51

54 g = 2.0045

a(2Ho) = 0.03

a(2Hm) = 0.13

a(Hp) = 0.05

Scheme12 StructuresandEPRparametersofradicalscentered onoxygenandsulfur.

spectroscopy.EPRparametersforphenoxyl 47 and thearyloxyl 48,derivedfromtheartificialantioxidantBHT,aredisplayedinScheme12.156 The well-resolvedspectrathatcanbeobtainedaretypifiedbythatfromthechromanyloxylradical 49 derivedfromthenaturalantioxidant α -tocopherol (Figure11b).TheEPRparametersshowthatthese are π -typespeciesinwhichspinisextensivelydelocalized.

Peroxylradicals(ROO• )areeasilyformedbythe extremelyrapidcouplingofC-centeredradicalswith dioxygen.Signalsfromperoxylsoftenaccompany theEPRspectraofalkylradicalsunlessalltraces ofoxygenareexcluded.Theyareeasytoidentifybecauseoftheircomparativelylarge g -factors (∼2 015).EPRspectraofperoxylshavebeen observedfromawiderangeofcompoundsincludingalkanes,alkenes,substitutedalkanes,lipids, aromatics,andothers.157,158 Thespectraareusuallybroad,andlinewidthsarehighlydependenton temperature,solventviscosity,andthepresenceof

derivativespectrum.

residualoxygen.Figure12showsthespectrumof thecyclohexylperoxylradical 51 infirstandsecond derivativemodes.159

Theisotropichfsofperoxyl 17 O isotopomers160,161 (Scheme12)indicatethat spindensityispartitionedbetweenbothoxygens, butmoreresidesontheterminalO1 .Thestructures 50a,b giveareasonablerepresentationofthe SOMOshowingthatperoxylsare π -radicals.

EPRspectraforthiylradicals(RS• )andsulfinyl radicals(RSO• )haveonlybeenobtainedinlowtemperaturematrices.However,well-resolvedsolution EPRspectrahavebeenrecordedforsulfonylradicals(RS• O2 )generatedinavarietyofways162 from sulfinicacids,163 sulfonylchlorides,andsulfonate esters(Scheme12).Thehfsdisclosespindistributionthatistypicalofradicalswithapyramidal centeratsulfur(52, 53).164,165

9KINETICEPRSPECTROSCOPY

9.1RadicalDecayCurvesandConcentration Measurement

ThegrowthanddecayofEPRsignalscanbe monitoredasafunctionoftimewhentheEPR setupentailsradicalgenerationbyUVlight(orother radiation).Whentheirradiationcommences,the signalgrowsinandonshutteringthelightthesignal decays.Figure13showsatypicalexperimentin whichtheNHC-borylradical 55 wasgeneratedfrom irradiationoftheNHC–BH3 precursorandDTBPin theEPRresonantcavity.TheCWspectrumshown wasrecordedandthenthefieldwassettothevalue

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Figure12 EPRspectrumofthecyclohexylperoxylradical 51 in cyclopropaneat150K.(a)Firstderivativespectrum.(b)Second

BASICCONCEPTSANDMETHODOLOGIES

DPPHorgalvinoxyl(DIS ).Themicrowavepower, modulationamplitude,receivergain,scanrange ( HR /mTcm 1 ),andtemperatureoftheparticular radical(TR /K)arenoted.Thesamesampletube isthenfilledtothesamelevelwiththestandard solutionwhichisthenscannedundersimilar conditionsatthesamepowerandmodulation amplitude.TheconcentrationofR• canthenbe obtainedfrom(19):

[R• ] = [S• ] × DIR

Figure13 FirstderivativeEPRspectrumofradical 55 in PhBu-t at245K;theinsetshowsthegrowthanddecayofthe signalasafunctionoftime.Theintegralanddoubleintegral(DI, red)areshownbeneath.

nearthemaximumsignalintensitymarkedbyan arrow.Thespectrometertimeconstantwasadjusted toavaluemuchlessthanthehalf-lifeoftheradical (tc = 1 28ms).Timescansthenenabledgrowthand decaycurvessuchasthatshownintheinsettobe obtained.

Absoluteradicalconcentrationsareusually neededforkineticinformationtobededucedfrom suchdecaycurves.Accordingto(9)(Section1.3), thepowerabsorbedbyasampleisproportional totheimaginarypartofthesusceptibility(χ ), andhencetothenumberofparamagneticspecies present.Theradicalconcentrationistherefore proportionaltotheintegraloftheabsorptioncurve, orthedoubleintegralofthefirstderivativespectrum.Fordependableconcentrationmeasurements, thespectraldatamustbeobtainedonsamplesof volumelessthanorequaltothesensitivevolume ofthecavityandforsignalsbelowmicrowave powersaturation.Theconcentrationofaparticular radical[R• ]canbeobtainedbycomparingits doubleintegralDIR tothatofaknownconcentrationofastandardpersistentradical(S• )suchas

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DIS × GainS

GainR

× HR 2 HS 2 × RubyS RubyR

Theterm HR 2 / HS 2 equals1.0,exceptwhen thespectrumofR• wasrecordedwithafield scaledifferentfromthestandard. TR /TS allowsfor anytemperaturedifferencebetweentheparticular radicalandthestandard.IfR• wasinasolvent differentfromthestandard,variationsincavityQ canbecorrectedforbynormalizingtheR• andS• spectrawithrespecttothesignal(atcirca200mT) fromasinglecrystalofsyntheticruby,positioned off-centerinthemicrowavecavity.Therubyterm canusuallybeneglectedifR• andS• wereboth inhydrocarbonsolvents.ThewholeS• spectrumis doublyintegratedbut,ifonlyafractionoftheR• signalwasaccessible,thenthemultiplierFconverts totheDIoftheentireR• spectrum.

Mostsmall,unhindered,neutralradicalsdecay influidsolutionswithhalf-liveswithin1–2ms. Aspecialtechniquethatenablesmanyidentical radicaldecaystobecollectedandaveraged,soas toimprovesignaltonoiseratio,wasdevisedfor thissituation.67 Applicationsofthetechniqueto manydiversekineticproblemswerereportedby Ingoldandcoworkersinanoutstandingseriesof papers.166–168

Intheabsenceofasuitablereactionpartner,most radicalsdecaybycombinationanddisproportionationprocesseswhicharesecondorderinradical concentration.Fischerandcoworkersenhancedthe kineticEPRmethodinseveralwaysanddevelopeda modulationapproach.169,170 Therateconstantsthey obtainedforalkylradicalterminations(2kt )inmany differentsolventsareamongthemostaccurately known.Thisdataestablishedthatthetermination ratesofsmallradicalsareinverselyproportionalto solventviscosityandthattheseprocessesarediffusioncontrolled,171 whichresultsin2kt ≈ 5 × 109

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× TR TS × F (19)

M 1 s 1 influidsolventsatambienttemperature. Therateconstant(2kt = 8.7 × 109 M 1 s 1 at 298K)andArrheniusparametersfor t -butylradicalterminationin n -heptane:172 log(2kt /M 1 s 1 ) = 11.63–9.61(kJmol 1 )/2.3RThavebeenwidely usedas“clock”parametersforcalibratingthe dynamicsofotherradicalreactions.KineticEPR isusuallylessprecisethanLFPbuthasthe advantagesofgoodresolutionandhighspecificity. KEPRdoesnotrequirethepotentiallyawkward reporterchromophoresinradicalsthatareneeded withtheLFPmethod(see RadicalKineticsand Clocks).

Terminationrateconstantsandequilibrium constantsforradical–dimerequilibriahave beenobtainedformanyclassesofradicals,173 includingB-centeredradicals,55,100 ahugerange ofC-centeredradicalswithmanydifferent structuralfeatures,58,174–176 aswellasother group14element-centeredradicals.177 Similarly,theterminationsofN-andP-centered radicalsincludingaminyls,178,179 amidyls,180 iminyls,141,181 alkoxyaminyls,182 diazenyls,145 and phosphoranyls,151,183,184 havebeeninvestigated byEPR.Theterminationsandradical–dimer equilibriahavealsobeenexaminedfornumerous O-centeredspeciesincludingphenoxyls185,186 and peroxyls.187–189 Mostofthelatter,particularly secondaryandtertiaryalkylperoxyls,terminate manyordersofmagnitudemoreslowlythanthe diffusionlimit.190

AnalternativeEPR-basedmethodofstudying reactiondynamicsreliesontheincreaseofESR linewidthsthatresultsfromdecreasinglifetimeof theobservedradicals.191,192

9.2Steady-StateKineticEPRMeasurements

UVphotolysisofDTBP,neatorinsolution, produces t -BuO radicalsthatareEPR“silent” andsodonotcomplicateEPRspectra.Inthe presenceoftwosubstratesHR1 andHR2 (ortwo sitesinthesamesubstrate),unselectiveabstraction givesrisetotworadicalsthataredestroyedby bimolecularprocesses.Thesteady-statesystemcan berepresentedby(20)–(24):

+ R1• −→ nonradicalproducts(22)

R1• + R2• −→ nonradicalproducts(23)

R2• + R2• −→ nonradicalproducts(24)

Providedbothradicalsaretransientandterminate atthediffusion-controlledlimit(k22 = k23 = k24 ), thefollowingrelationholds: k20 k21 = [R1• ][HR2 ] [R2• ][HR1 ] (25)

TheconcentrationsofHR1 andHR2 ,and/orthe temperature,areadjusteduntil,underconditionsof steady-statephotolysis,spectraofbothradicalscan besimultaneouslyrecorded.Therateconstantratio k20 /k21 canthenbedeterminedfromtheknown substrateconcentrationsandtheratio[R1• ]/[R2• ] obtainedfromtheEPRspectra.Therelativerate datacanbeputonanabsolutescalebyusing astandardradical“clock,”suchascyclopentane plus t -BuO• , 193 asareferencereaction.Many suitableradicalclocks194 havebeencalibratedand compilationsofratedataareavailable173,195–197 (see RadicalKineticsandClocks).

Thedynamicsofaunimolecularreactionofa radical(U• ) tosomerearrangedradical(R• ) can beprobedwhenthespeciesisgeneratedfrom somephotolabileprecursorXUintheabsenceof substrates.

+ R• kUR −→ nonradicalproducts

+ R• kUR −→ nonradicalproducts

Understeady-stateconditionsrelationship(26)is easilyderived:

[R• ] = 2kUR kr + 2kRR [R• ] kr [U• ] (26)

Inprinciple,theradicalconcentrationscanbe variedbychangingtheincidentUVintensity.

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BASICCONCEPTSANDMETHODOLOGIES

Aplotof1/[R• ]against[R• ]/[U• ]thenproduces alineofslope2kRR /kr andintercept2kUR /kr .In practice,theEPRsignalsareusuallytooweakto allowasufficientchangeofradicalconcentrations foraccuratedeterminations.If,however,bothU• andR• terminateatthediffusion-controlledlimit, then2kUR = 2kRR = 2kt and(26)simplifiesto

kr 2kt = [R• ] + [R• ]2 [U• ] (27)

andhence kr /2kt canbedeterminedsimplyfrom EPRmeasurementsoftheU• andR• concentrations. IfR• terminatesatthediffusion-controlledlimitthen itisusuallyaccurateenoughtouseFischer’s2kt datafor t -Bu• in n -heptane,172 correctedforthe differenceintheviscositiesof n -heptaneandthe solventused.198

Rateconstantsformanydissociationsincludingdecarbonylations199,200 andother β -scission processes201,202 havebeenobtainedbythismethod. Forexample,203 i -propylthiylradicals,generatedby UVphotolysisofthecorrespondingdisulfide,added

Scheme13 β -Scissionofthioimidoylradical 56 and ring-openingreactionsofmono-andpoly-cycloalkylmethyl radicals.

Figure14 EPRspectraanddoubleintegralsofthioimidoyl 56 and i -propylradicalsatdifferenttemperatures.(a)At190K;(b) at210K;and(c)at230K.The*indicatesthecentralcomponents ofthe i -propylradicalspectrum.

tocyclohexaneisonitriletoproducethioimidoylradicals 56 (Scheme13).TheEPRspectrumof 56 was observedincyclopropanesolutionat T < 180K (Figure14a).Above ∼190K,thespectrumof 56 wasaccompaniedbythatofthe i -propylradical (Figure14b)andat T > 240Konlythe i -propyl radicalcouldbediscerned.Thissequenceofspectrawasreversibleonloweringthetemperature.The concentrationsof 56 and i -propylwereobtainedat eachtemperaturefromthedoubleintegralsofthe spectrashowninFigure14andbyuseof(19).Then the kd /2kt valuesateachtemperaturewerederived from(27)and,afterinclusionofFischer’s2kt data, gavelog(Ad /s 1 ) = 12.1, Ed = 38kJmol 1 forthe dissociationof 56

Analogoussteady-stateEPRmethods(SEPR) havebeenappliedtothestudyofringopening ofcyclopropylmethyl(58),204,205 cyclobutylmethyl(59),cyclobutenylmethylradicals,206–208 anddominoring-openingreactionsofbicyclo[1.1.1]pentylmethyl(60),209 cubylmethyl (61),29 andanalogs.210,211 SEPRinvestigations ofthekineticsofothertypesofrearrangements,

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Figure15 EPRspectrafromphotosensitizedUVirradiation ofoximeoxalateamide 62 in t -BuPh.Highandlowfield 1:1:1tripletsarefromPhCH=N• (63).Thecarbamoylradical ismarkedby A andtheazetidinylaminylradicalismarkedby C (a)Spectraat220K.(b)Spectraat240K.(c)Spectraat310K. [AdaptedwithpermissionfromG.A.DiLabio, etal.,Org.Lett., 2005, 7,155–158.Copyright2005AmericanChemicalSociety.]

includingarylgroupmigrations,204 andring-closure reactions,136,212,213 havealsobeenpublished.An exampleistheSEPRdeterminationoftherateconstantofanunusual4-exo-cyclizationasillustrated inFigure15.Photolysisofoximeoxalateamide 62,sensitizedwith4-methoxyacetophenone, in t -butylbenzeneat220Kyieldedthe phenyliminylradical 63 andcarbamoylradical A (Scheme14).214

Phenyliminyl 63 appearedasapairof1:1:1 tripletsoneineitherwingoftheEPRspectrum (Figure15).Carbamoyl A contributeda1:1:1 tripletinthecentralregion(Figure15a).Asthe temperaturewasraised,4-exo-cyclizationof A into theoximeetheracceptorbecameimportantand yieldedazetidinylaminylradical C.Thesignals from C (g = 2.0049, a (N) = 1.37, a (1H) = 1.37, a (2H) = 0 25, a (2H) = 0 10mT)dominatedthe EPRspectrumat T = 310K(Figure15c).Therate constantforcyclizationof A wasfoundtobe 3 × 104 s 1 at300K.

Scheme14 4-exo-Cyclizationofacarbamoylradicalontoan oximeetheracceptor.

10DETERMINATIONOFTHERMODYNAMIC PARAMETERSBYEPRSPECTROSCOPY

Radicalenthalpiesofformation( Hf,300 ),radicalstabilizationenthalpies(RSEs),andbond dissociationenthalpies[BDE(R–X)]areuseful parametersforassessingmechanismsandfor planningsyntheses. Relative thermodynamic parameterscanbeobtainedfromEPRmeasurementsofradicalconcentrationsin“radicalbuffer” systems215,216 whereanequilibriumissetup betweentworelatedradicalsandtheirprecursor molecules.Themethodhasbeensuccessfully appliedforthedeterminationofthermodynamic dataforalkanesandalkylradicals,217,218 phenols andaryloxylradicals,219,220 pyridinols,221,222 and pyrimidinols.223

Manymoderatelystablefreeradicalsexistin solutioninequilibriumwiththeirdimers.The equilibriumconstantsofmanysuchsystemshave beendeterminedfromEPRmeasurementsofthe radicalconcentrations.224 RuchardtusedBDE(C–C) valuesderivedfromequilibriumdatatoproduce aself-consistentsetofRSEsthattendtoexpress thedifferenceinstabilityofapurehydrocarbon radicalL3 C• (L = H,alkyl)andthecorresponding substitutedradicalL2 SC• (S = functionalgroup).225 Agoodnumberofempiricalrelationshipsbetween RSEsandspindensitieshavebeensuggested.226–228 ThemostcomprehensivetreatmentbasedonHα hfs fromplanarmono-anddisubstitutedradicals229,230

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BASICCONCEPTSANDMETHODOLOGIES

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Scheme15 Internalrotationinfunctionalizedprimaryradicals.

gavethefollowingrelationshipsforRSEandBDE (kJmol 1 )wherethe a (Hα )areinmillitesla:

RSE = 69.0a (Hα ) 155.0(28)

BDE(C H) = 67.3a (Hα ) + 260.8(29)

Linearrelationshipswerealsofoundfortertiary radicalsinvolvingthehfsfrom β -Megroups. AnotherempiricalEPRmethodforBDEsfocuses onthetorsionbarriers(E0 )abouttheC–X bondsinprimaryradicalsoftypeLn XCH2 • (64, Scheme15).231–233

Thelinearrelationship(updatedforrecentBDE data)foundbetweenthetwoquantitiesisshownin (30).234,235

BDE(Ln XCH2 H)/kJmol 1 = 422 6 0 86E0 (30)

Thecorrelationhasprovedusefulforestimatingand/orcheckingBDEdatainavarietyof circumstances.230,236

11CONCLUSIONS

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RedoxPropertiesofRadicals

1 DepartmentofChemistry,TheUniversityofMalta,Msida,Maltaand

2 DepartmentofChemistry,TheUniversityofWesternOntario,London,Ontario,Canada

1INTRODUCTION

Radicalsarechemicalspeciescontainingatleastone unpairedelectroninanatomicormolecularorbital. Theimportanceofthisclassofreactiveintermediatehasbeendulynotedinchemicalandbiological systems.1,2 Anunderstandingofthereactivityof radicalshasallowedforabetterunderstandingof biochemicalpathwaysincellsandthecauseofmany diseases.3,4 Exploitationofthepropertiesofradicals hasprovidedefficientproceduresforsynthesizing novelmolecularandpolymermaterials.5,6 Ofthe manypathwaysavailabletoradicals,themereloss orgainofasingleelectronisoftremendousconsequenceasityieldsaneven-electronspecieswithdifferentreactivityproperties.Hence,knowledgeofthe redoxpropertiesofradicalsisimperativeforpredictingthefeasibilityforanelectrontransferreaction.7 Furthermore,accurateknowledgeofthestandard potentialsoffreeradicalsalsoallowsfortheestimationofotherpertinentthermodynamicinformation, suchaspKa sandbonddissociationenergies,that maynotbeotherwisereadilyavailable.8

Theionizationpotentialandtheelectronaffinity ofaradicalareameasureofitsdonorandacceptor propertiesinthegasphase.Theoxidationandreductionpotentialofaradicalareameasureofthedonor andacceptorpropertiesinthesolutionphase.In solution,thepropertiesofthesolventcontributeto somevariationintheoxidationandreductionpotentialsmainlyduetodifferencesinthesolvationproperties.Thisarticlefocusesontheredoxproperties

ofradicalsmeasuredinsolutionandontheelectrochemicalandphotoelectrochemicalmethodsused toinvestigateandcharacterizethem.9–15 Thearticle concludeswithup-to-datetablesofstandardreductionandoxidationpotentialsofradicals.Thelast extensivecompilationofliteraturedatawaspreviouslyreportedbytheAarhusgroupin1999.13

Thereareseveraldirectandindirectelectrochemicalmethodsthathavebeendevelopedfortheinvestigationoftheredoxpropertiesoftransientradicals, themajorityofwhicharebasedonacombinationofphotochemicaland/orelectrochemicaltechniques.Thedirectevaluationoftheoxidationand reductionpotentialsofradicalsbyelectrochemical techniquesincludescyclicvoltammetry,whichisby farthemostwidespread,andalsoothercomplimentarytechniques,suchaspolarographyandsecond harmonicalternatingcurrentvoltammetry(SHV). Photoelectrochemicaltechniquesrelyonlightto homolyticallycleaveacovalentbond,whichgeneratestheradicals,andelectrochemicalmeansto detectandstudythem.Thetwomostcommonly employedphotoelectrochemicalmethodsarephotomodulationvoltammetry,inwhichtransientradicals aregeneratedbymodulatedphotolysis,andthermalizedlaserflashphotoejection,inwhichalaser isusedtoinjectelectronsintosolutionbyirradiationofanelectrode.Althoughtrivialtomany,itis oftentakenforgrantedthatnomattertheanalytical techniqueusedtomeasureastandardpotential,it isanintrinsicpropertyofachemicalspeciesand

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Nothing is known of its manners during the breeding season; and we are equally ignorant of the changes of plumage which, like other species, it may undergo at that period.

As I have not had very good opportunities of making myself acquainted with the modes in which the Canvass-backs are obtained for the markets, I here present an account of duck-shooting on the waters of the Chesapeake, published some years ago in the “Cabinet of Natural History,” and of which a copy has been transmitted to me by its author, Dr J. J. S, of Philadelphia, to whom, for this and other marks of attention, I offer my best thanks.

“The Chesapeake Bay, with its tributary streams, has, from its discovery, been known as the greatest resort of water-fowl in the United States. This has depended on the profusion of their food, which is accessible on the immense flats or shoals that are found near the mouth of the Susquehanna, along the entire length of North-East and Elk Rivers, and on the shores of the bay and connecting streams, as far south as York and James Rivers.

“The quantity of fowl of late years has been decidedly less than in times gone by; and I have met with persons who have assured me that the number has decreased one-half in the last fifteen years. This change has arisen, most probably, from the vast increase in their destruction, from the greater number of persons who now make a business or pleasure of this sport, as well as the constant disturbance they meet with on many of their feeding grounds, which induces them to distribute themselves more widely, and forsake their usual haunts.

“As early as the first and second weeks in October, the smaller ducks, as the Buffel-head, Anas Albeola; South-southerly, A. glacialis; and the Ruddy or Heavy-tailed Duck, A. rubidus, begin to shew themselves in the upper part of the bay; and by the last of the month, the Black-head, A. Marila; Widgeon or Bald-pate, A.

Americana; Red-head, A. Ferina; and the Goose, A. Canadensis, appear, and rapidly distribute themselves down the bay. The Canvass-back, A. Valisneria, and the Swan, Cygnus Americanus, rarely, unless the weather to the north has been severe, appear in quantities till the middle of November. All these fowl, when first arrived, are thin and tasteless, from their privation during their migration, and perhaps preparatory arrangements, and require some days at least of undisturbed repose, to give them that peculiar flavour for which some of them are so celebrated. During the low tides succeeding their arrival, the birds sit on the flats far from the shores, and rarely rise to the wing unless disturbed; but when the spring-tides render the water too deep for feeding, they commence their career, and pass down the bay in the morning, and return in the evening. Most of these fowl feed on the same grass, which grows abundantly on the shallows in the bay and adjacent waters, and has been called duck-grass, Valisneria Americana. It grows from six to eighteen inches in length, and is readily pulled up by the root. Persons who have closely observed these ducks while feeding, say that the Canvass-back and Black-head dive and pull the grass from the ground, and feed on the roots, and that the Red-head and Baldpate then consume the leaves. Indeed, although the Bald-pate is a much smaller bird than the Canvass-back, it has been seen to rob the latter, immediately on its return from under the water, of all its spoil.

“All these larger ducks are found together when feeding, but separate when on the wing. That they feed on the same grass, is evident from the similarity of flavour; and those most accustomed to the article have a difficulty in deciding on the kind of duck from the taste. Indeed, the Bald-pate is generally preferred by residents.

“By the middle of December, particularly if the weather has been a little severe, the fowl of every kind have become so fat, that I have seen Canvass-backs burst open in the breast in falling on the water;

and spending less time in feeding, they pass up and down the bay from river to river, in their morning and evening flights, giving, at certain localities, great opportunities for destruction. They pursue, even in their short passages, very much the order of their migratory movements, flying in a line, or baseless triangle; and when the wind blows on the points which may lie on their course, the sportsman has great chances of success. These points or courses of the ducks are materially affected by the winds, for they avoid, if possible, an approach to the shore; but when a strong breeze sets them on these projections of the land, they are compelled to pass within shot, and often over the land itself.

“In the Susquehanna and Elk rivers, there are few of these points for shooting, and there success depends on approaching them while on their feeding grounds. After leaving the eastern point at the mouth of the Susquehanna and Turkey Point, the western side of the Elk River, which are both moderately good for flying shooting, the first place of much celebrity is the Narrows, between Spesutie Island and the western shore. These narrows are about three miles in length, and from three to five hundred yards in breadth. By the middle of November, the Canvass-backs in particular, begin to feed in this passage, and the entrance and outlet, as well as many intermediate spots, become very successful stations. A few miles further down the western shore is Taylor’s Island, which is situated at the mouth of the Rumney, and Abbey Island at the mouth of Bush River, which are both celebrated for ducks, as well as swans and geese. These are the most northerly points where large fowl are met with, and projecting out between deep coves, where immense numbers of these birds feed, they possess great advantages. The south point of Bush River, or Legoe’s Point, and Robbin’s and Rickett’s Points near Gunpowder River, are fruitful localities. Immediately at the mouth of this river is situated Carroll’s Island, which has long been known as a great shooting ground, and is in the rentage of a company at a high

rate. Maxwell’s Point, as well as some others up this and other rivers, and even further down the bay, are good places, but less celebrated than those I have mentioned. Most of these points are let out as shooting grounds to companies and individuals, and they are esteemed so valuable that intruders are severely treated.

“It has been ascertained that disturbing the fowl on the feeding flats is followed in most cases by their forsaking those haunts, and seeking others; hence, in the rivers leading to the bay near flying points, they are never annoyed by boat-shooting, either by night or day, and although the discharge of guns from the shore may arouse them for a time, they soon return; whereas a boat or sail in chase a few times, will make them forsake a favourite spot for days.

“From the great number of ducks that are seen in all directions, one would suppose that there could be no doubt of success at any one of the points in the course of flight; but whilst they have such correct vision as to distance, and wide range of space, unless attending circumstances are favourable, a sportsman may be days without a promising shot. From the western side of the bay, and it is there the best grounds are found, the southerly winds are the most favourable; and, if a high tide is attended by a smart frost and mild south wind, or even calm morning, the number of birds set in motion becomes inconceivable, and they approach the points so closely, that even a moderately good shot can procure from fifty to one hundred ducks aday. This has often occurred, and I have seen eight fat Canvassbacks killed at one discharge into a flock, from a small gun.

“To a stranger visiting these waters, the innumerable ducks, feeding in beds of thousands, or filling the air with their careering, with the great numbers of beautiful white swans resting near the shores, like banks of driven snow, might induce him to suppose that the facilities for their destruction were equal to their profusion, and that with so large an object in view, a sportsman could scarcely miss his aim. But, when he considers the great thickness of their covering, the

velocity of their flight, the rapidity and duration of their diving, and the great influence that circumstances of wind and weather have on the chances of success, it becomes a matter of wonder how so many are destroyed.

“The usual mode of taking these birds has been, till recently, by shooting them from the points during their flight, or from the land or boats, on their feeding grounds, or by toling, as it is strangely termed, an operation by which the ducks are sometimes induced to approach within a few feet of the shore, from a distance often of several hundred yards. A spot is usually selected where the birds have not been much disturbed, and where they feed at three or four hundred yards from, and can approach to within forty or fifty yards of the shore, as they will never come nearer than they can swim freely. The higher the tides, and the calmer the day, the better, for they feed closer to the shores and see more distinctly. Most persons on these waters have a race of small white or liver-coloured dogs, which they familiarly call the toler breed, but which appear to be the ordinary poodle. These dogs are extremely playful, and are taught to run up and down the shore, in sight of the ducks, either by the motion of the hand, or by throwing chips from side to side. They soon become perfectly acquainted with their business, and as they discover the ducks approaching them, make their jumps less high till they almost crawl on the ground, to prevent the birds discovering what the object of their curiosity may be. This disposition to examine rarities has been taken advantage of by using a red or black handkerchief by day, and a white one by night in toling, or even by gently plashing the water on the shore. The nearest ducks soon notice the strange appearance, raise their heads, gaze intently for a moment, and then push for the shore, followed by the rest. On many occasions, I have seen thousands of them swimming in a solid mass direct to the object; and by removing the dog farther into the grass, they have been brought within fifteen feet of the bank. When they have

approached to about thirty or forty yards, their curiosity is generally satisfied, and after swimming up and down for a few seconds, they retrograde to their former station. The moment to shoot is while they present their sides, and forty or fifty ducks have often been killed by a small gun. The Black-heads toll the most readily, then the Redheads, next the Canvass-backs, and the Bald-pates rarely. This also is the ratio of their approach to the points in flying, although, if the Canvass-back has determined on his direction, few circumstances will change his course. The total absence of cover or precaution against exposure to sight, or even a large fire, will not turn these birds aside on such occasions. In flying-shooting, the Bald-pates are a great nuisance, for they are so shy that they not only avoid the points themselves, but by their whistling and confusion of flight at such times, alarm others.

“Simple as it may appear to shoot with success into a solid mass of ducks sitting on the water at forty or fifty yards’ distance, yet when you recollect that you are placed nearly level with the surface, the object opposed to you, even though composed of hundreds of individuals, may be in appearance but a few feet in width. To give, therefore, the best promise of success, old duckers recommend that the nearest duck should be in perfect relief above the sight, whatever the size of the column, to avoid the common result of over-shooting. The correctness of this principle I saw illustrated in an instance in which I had toled to within a space of from forty to seventy yards off the shore, a bed of certainly hundreds of ducks. Twenty yards beyond the outside birds of the dense mass, were five Black-heads, one of which was alone killed out of the whole number, by a deliberate aim into the middle of the large flock from a rest, by a heavy well-proved duck-gun.

“Before I leave the subject of sitting-shooting, I will mention an occurrence that took place in Bush River, a few years since. A man whose house was situated near the bank, on rising early one

morning, observed that the river had frozen, except an open space of ten or twelve feet in diameter, about eighty yards from the shore, nearly opposite his house. The spot was full of ducks, and with a heavy gun he fired into it. Many were killed, and those that flew soon returned, and were again and again shot at, till, fearful that he was injuring those already his own, he ceased the massacre, and brought on shore ninety-two ducks, most of which were Canvass-backs.

“To prevent the dogs, whilst toling, from running in, they are not allowed to go into the water to bring out the ducks, but another breed of large dogs of the Newfoundland and water-spaniel mixture are employed. These animals, whilst toling is in progression, or at a point, take apparently as much interest in success as the sportsman himself. During a flight, their eyes are incessantly occupied in watching the direction from whence the birds come; and I have frequently seen them indicate by their manner, the approach of a flock so distant that the human eye would have overlooked it. As the ducks come on, the dog lies down, but still closely observing them, and the moment the discharge occurs, jumps up to see the effect. If a duck falls dead, they plunge to bring it; but many of them wait to see how he falls, and whither he swims, and they seem to be as aware as the gunner, of the improbability of capture, and will not make the attempt, knowing from experience that a bird merely winged will generally save himself by swimming and diving. These dogs usually bring one duck at a time out of the water; but a real Newfoundland, who was with me and my company this autumn, was seen on several occasions to swim twenty yards further, and take a second in the mouth to carry on shore. The indefatigability and ambition of these animals are remarkable, and a gentleman informed me he had known his dog bring, in the space of one hour, twenty Canvass-backs and three Swans from the water, when the weather was so severe that the animal was covered with icicles, and to prevent his freezing be took his great-coat to envelope him. Some

dogs will dive a considerable distance after a duck, but a crippled Canvass-back or Black-head, will swim so far under the water, that they can rarely be caught by the dog; and it often has been observed, that the moment one of these ducks, if merely winged, reaches the surface, he passes under, and however calm, cannot be seen again. To give an idea of the extreme rapidity with which a duck can dive, I will relate an occurrence which was noticed by myself, and a similar one was observed by another of the party the same day. A male South-southerly was shot at in the water by a percussion-gun, and after escaping the shot by diving, commenced his flight. When about forty yards from the boat, he had acquired an elevation of a foot or more from the surface. A second percussiongun was discharged, and he dived from the wing at the flash, and though the spot of entrance was covered by the shot, soon rose unharmed and flew.

“Canvass-backs, when wounded on the streams near the bay, instantly direct their course for it, and there nestle among the grass on the shores till cured, or destroyed by eagles, hawks, gulls, foxes, or other vermin, that are constantly on the search. If a dead Canvass-back be not soon secured, it becomes a prey to the gulls, which rarely touch any other kind. I have seen severe contests take place between crippled Canvass-backs and Gulls; and although a pounce or two generally prevents further resistance, sometimes they are driven off. If the bird is remarkably savoury, the gull makes such a noise, that others are soon collected, when possession is determined by courage or strength.

“Another mode of taking Ducks consists in placing gilling-nets under water on the feeding-grounds, and when they dive for food, their head and wings become entangled in the meshes, and they are drowned. This plan, though successful at first, soon drives the bird from these places; and in some cases, a few applications have entirely prevented their return for some weeks. Paddling upon them

in the night or day produces the same effect, and although practised to some extent on Bush River is highly disapproved of by persons shooting from points. For the last three years a man has been occupied on this stream with a gun of great size, fixed on a swivel in a boat, and the destruction of game on their feeding-flats has been immense; but so unpopular is the plan, that many schemes have been privately proposed of destroying his boat and gun, and he has been fired at with balls so often that his expeditions are at present confined to the night. Sailing with a stiff breeze upon the geese and swans, or throwing rifle-balls from the shore into their beds, is sometimes successful.

“Moonlight shooting has not been a general practice, but as these birds are in motion during light nights, they could readily be brought within range by “honking” them when flying. This sound is very perfectly imitated at Egg Harbour; and I have seen geese drawn at a right angle from their course by this note. They can indeed be made to hover over the spot, and if a captive bird was employed, the success would become certain.

“Notwithstanding the apparent facilities that are offered of success, the amusement of duck-shooting is probably one of the most exposing to cold and wet, and those who undertake its enjoyment without a courage “screwed to the sticking-point”, will soon discover that “to one good a thousand ills oppose.” It is indeed no parlour sport, for after creeping through mud and mire, often for hundreds of yards, to be at last disappointed, and stand exposed on points to the “pelting rain or more than freezing cold,” for hours, without even the promise of a shot, would try the patience of even F’s “glorious nibbler.” It is, however, replete with excitement and charm, and to one who can enter on the pleasure, with a system formed for polar cold, and a spirit to endure “the weary toil of many a stormy day,” it will yield a harvest of health and delight, that the “roamer of the woods” can rarely enjoy.”

Although this far-famed bird was named by its discoverer after the plant Valisneria Americana, on which it partially feeds when on freshwater, its subsistence is by no means dependent upon that species, which indeed is not extensively distributed, but is chiefly derived from the grass-wrack or Eel-grass, Zostera marina, which is very abundant on the shallows and flats along the whole sea-coast. Its flesh seems to me not generally much superior to that of the Pochard or Red-head, which often mingles in the same flocks; and both species are very frequently promiscuously sold in the markets as Canvass-backs.

In the Plate are represented two Males and a Female. In the back ground is a view of Baltimore, which I have had great pleasure in introducing, on account of the hospitality which I have there experienced, and the generosity of its inhabitants, who, on the occasion of a quantity of my plates having been destroyed by the mob during an outburst of political feeling, indemnified me for the loss.

F V, Bonap. Synops. of Birds of the United States, p. 392.

A V, Wils Amer Ornith , vol viii p 103 pl 70 fig 5

F V, Richards. and Swains. Fauna Bor. Amer. iv. Part II. p. 450

C- D, Nuttall, Manual, vol. ii. p. 430.

Adult Male. Plate

CCCI. Fig. 1, 2.

Bill as long as the head, deeper than broad at the base, the margins parallel, slightly dilated towards the end, which is rounded, the frontal angles rather narrow and pointed. Upper mandible with the dorsal line at first straight and declinate, then slightly concave, direct for a short space near the tip, where it is incurved, the ridge broad and concave at the base, narrowed at the middle, enlarged and convex

at the end, the sides nearly erect and concave at the base, becoming anteriorly more and more declinate and convex, the edges curved upwards, with about 50 lamellæ, the unguis small and oblong. Nostrils submedial, linear-oblong, rather large, pervious, near the ridge, in an oblong depression covered with soft membrane. Lower mandible flattened, being but slightly convex, with the angle very long and rather narrow, the dorsal line very short and straight, the erect edges with about 55 inferior and 105 superior lamellæ, the unguis obovato-elliptical.

Head rather large, compressed, convex above. Eyes small. Neck of moderate length, rather thick. Body full, depressed. Wings small. Feet very short, strong, placed rather far behind; tarsus very short, compressed, anteriorly with narrow scutella continuous with those of the middle toe, and having another series commencing half-way down and continuous with those of the outer toe, the rest reticulated with angular scales. Hind toe small, with an inner expanded margin or web; middle toe nearly double the length of the tarsus, outer a little shorter. Claws small, compressed, that of the first toe very small and curved, of the third toe larger and more expanded than the rest.

Plumage dense, soft, blended. Feathers of the upper part of the head small and rather compact, of the rest of the head and neck small, blended, and glossy. Wings shortish, narrow, pointed; primary quills strong, tapering, the first longest, the second almost as long, the rest rapidly diminishing; secondary quills broad and rounded, the inner elongated and tapering. Tail very short, much rounded, or wedge-shaped, of fourteen feathers.

Bill black, with a tinge of green. Iris bright carmine. Upper part of the head, and a space along the base of the bill dusky; a small transverse band of white on what is called the chin; the rest of the head, and the neck all round, for more than half its length, of a rich brownish-red. A broad belt of brownish-black occupies the lower part of the neck, and the fore part of the body, of which the posterior part

is of the same colour, more extended on the back than under the tail. Back and scapulars white or greyish-white, very minutely traversed by undulating black lines; wing-coverts similar but darker. Alular feathers greyish-brown. Primary quills brownish-black, tinged with grey towards the base; the shaft brown. Secondaries ash-grey, whitish, and undulated with dark grey towards the end; five of them also having a narrow stripe of black along their outer margin. Tail brownish-grey, towards the end ash-grey. The lower parts white, the sides and abdomen marked with fine undulating grey lines, of which there are faint traces on most of the other feathers. The feet are greyish-blue tinged with yellow.

Length to end of tail 22 inches, to end of wings 20, to end of claws 25; extent of wings 33; wing, from flexure, 9 3/4; tail 2 10/12; bill along the back, measured from the tip of the frontal process to the end of the unguis, 3; lower mandible along the edge 2 7/12; tarsus 1 3/4; first toe 6/12, its claw 5/12; middle toe 2 10/12, its claw 5/12; outer toe scarcely shorter; inner, 7/12 shorter. Weight 3 3/4 lb.

Adult Female. Plate CCCI. Fig. 2.

The Female has the bill coloured as in the male; the iris reddishbrown; the feet lead-grey; the upper parts greyish-brown; the top of the head darker, its anterior part light reddish; the chin whitish; the neck greyish-brown, as are the sides and abdomen; the breast white; wing-coverts brownish-grey; primary quills greyish-brown, dusky at the end; secondary quills ash-grey, five of the inner with an external black margin, the innermost greyish-brown like the back, and with some of the scapulars faintly undulated with darker. Tail greyish-brown, paler at the end; axillars and smaller under wingcoverts white, as in the male.

Length to end of tail, 20 1/4 inches, to end of wings 18 1/2, to end of claws, 23 1/4; extent of wings, 30 3/4: wing from flexure, 9 1/4. Weigh 2 3/4 lb.

This species is very closely allied to the Pochard, or Red-headed Duck, Fuligula Ferina, but is much larger, and differs in having the bill proportionally higher at the base, and less dilated towards the end. The colours are also generally similar, but present differences. The upper parts of the Canvass-back are much whiter than those of the Pochard; the head of the former is dusky above, of the latter uniform with the neck; and the white spot on the chin is wanting in the Pochard.

The Digestive and Respiratory Organs of a male shot near Baltimore present the following characters.

The upper mandible is broadly and deeply concave. The tongue, which is thick and fleshy, as in other ducks, is 2 2/12 inches long, its sides parallel, slightly sloping, and furnished with two series of bristly filaments; its base with numerous straight conical papillæ directed backwards, its upper surface marked with a broad median groove, the lower flat, its extremity formed by a thin semi-circular appendage, a quarter of an inch in length. The œsophagus passes along the right side of the neck, for six inches has a diameter of 5/12 then dilates to 9/12, so as to form a slight crop, again contracts as it enters the thorax, and in terminating forms the proventriculus, which is 1 3/4 inches in length, with oblong glandules, generally a twelfth of an inch in length. The stomach is a very large and powerful gizzard, of a broadly elliptical form, with extremely thick lateral muscles, the left being 11/12 in thickness, the right 10/12, the tendons large and strong. The transverse diameter of the gizzard is 2 11/12 inches, the longitudinal, from the cardiac orifice to the bulge of the inferior

muscle, 2 1/12. Its cuticular lining is of very dense texture, and rugous; the grinding plates opposite the lateral muscles about half a twelfth thick, and slightly rugous. The intestine, which is 5 feet 9 inches in length, first forms in the usual manner the duodenal fold, at the distance of 5 inches from the pylorus, encloses the pancreas, receives the biliary ducts, and passing under the right lobe of the liver, proceeds backward beneath the kidneys, is convoluted in several large folds, and finally from above the stomach, passes in a direct course to the anus. Its coats are thick, its inner surface villous, and its diameter is considerable, being in the first part of the duodenum 9/12, then for two feet from 5/12 to 4/12, enlarged again to 6/12, and so continuing to the rectum, which is 6 inches long, 1/2 inch in diameter, and ends in an enlargement or cloaca, about an inch in diameter. The cœca, which commence at the distance of 6 inches from the anus, are 8 inches long, slender, 2/12 in diameter for 3 inches, afterwards about 3/12, with the extremity obtuse. The œsophagus and stomach contained young shoots of Zostera marina, and in the latter were numerous particles of quartz.

The trachea, when moderately extended, measures 10 inches in length, and is furnished with strong lateral or contractor muscles, a pair of cleido-tracheal, and a pair of more slender sterno-tracheal. Its diameter at the upper part is 4 1/2 twelfths, it gradually contracts to 3 1/2 twelfths, enlarges to 4 1/2 twelfths, and at the distance of 7 1/4 inches from the upper extremity, forms a dilatation about an inch in length, and 7/12 in its greatest diameter, but composed of distinct rings, then contracts to 5/12, and ends in a bony and membranous expansion, forming on the left side an irregular thin disk, convex towards the right, and flattened towards the left where it is membranous. The expansions of the trachea are thus similar to those of the Red-breasted Merganser, but of less extent; the rings

are of equal breadth on both sides, but alternately overlap each other, one side being partially concealed by the corresponding sides of those above and below it, while the other stands exposed. The lower larynx is formed of ten united rings, together with the bony and membranous expansion described. The tracheal rings, rather broad and osseous, are 118; the half-rings of the bronchi about 16.

DUSKY DUCK.

A O, G.

PLATE CCCII. M F.

This species, which is known in all parts of the United States by the name of “Black Duck,” extends its migrations from the Straits of Belle Isle, on the coast of Labrador, to the province of Texas. Strange as the fact may appear, it breeds in both these countries, as well as in many of the intermediate districts. On the 10th of May 1833, I found it breeding along the marshy edges of inland pools, near the Bay of Fundy, and, on Whitehead Island in the same bay, saw several young birds of the same species, which, although apparently not more than a week old, were extremely active both on land and in the water. On the 30th of April 1837, my son discovered a nest on Galveston Island, in Texas. It was formed of grass and feathers, the eggs eight in number, lying on the former, surrounded with the down and some feathers of the bird, to the height of about three inches. The internal diameter of the nest was about six inches, and its walls were nearly three in thickness. The female was sitting, but flew off in silence as he approached. The situation selected was a clump of tall slender grass, on a rather sandy ridge, more than a hundred yards from the nearest water, but surrounded by partially dried saltmarshes. On the same island, in the course of several successive days, we saw many of these ducks, which, by their actions, shewed that they also had nests. I may here state my belief, that the

Gadwall, Blue-winged Teal, Green-winged Teal, Mallard, American Widgeon, and Spoon-billed Duck, all breed in that country, as I observed them there late in May, when they were evidently paired. How far this fact may harmonize with the theories of writers respecting the migration of birds in general, is more than I can at present stop to consider. I have found the Black Duck breeding on lakes near the Mississippi, as far up as its confluence with the Ohio, as well as in Pennsylvania and New Jersey; and every one acquainted with its habits will tell you, that it rears its young in all the Eastern States intervening between that last mentioned and the St Lawrence, and is of not less frequent occurrence along the margins of all our great lakes. It is even found on the Columbia River, and on the streams of the Rocky Mountains; but as Dr R has not mentioned his having observed it in Hudson’s Bay or farther north, we may suppose that it does not visit those countries.

On arriving in Labrador, on the 17th June 1833, we found the Dusky Ducks in the act of incubation, but for nearly a month after, met with no young birds, which induced me to suppose that this species does not reach that country at so early a period as many others, but lingers behind so as to be nearly four weeks later than some of them. At the end of four weeks after our arrival, all the females we met with had young broods, which they led about the fresh-water ponds, and along their margins, either in search of food, or to secure them from danger. None of these broods exceeded seven or eight in number, and, at this early period of their life, we found them covered with long soft down of a deep brown colour. When alarmed they would dive with great celerity several times in succession, but soon became fatigued, made for the shore, ran a few feet from the water, and squatted among the grass, where they were easily caught either by some of our party, or by the Gulls, which are constantly on the look-out for such dainty food. At other times, as soon as the mother apprehends danger, she calls her young around her, when the little

things form themselves into a line in her wake, and carefully follow her in all her movements. If a Hawk or a Gull make a plunge towards them, she utters a loud cry of alarm, and then runs as it were along the surface of the water, when the young dive as quick as lightning, and do not rise again until they find themselves among the weeds or the rocks along the shores. When they thus dive, they separate and pursue different directions, and on reaching the land lie close among the herbage until assured, by the well-known voice of their parent, that the danger is over. If they have often been disturbed in one pond, their anxious mother leads them overland to another; but she never, I believe, conducts them to the open sea, until they are able to fly. The young grow with remarkable rapidity, for, by the middle of August, they almost equal their parents in size; and their apprehension of danger keeps pace with their growth, for at the period of their southward migration, which takes place in the beginning of September, they are as wild and as cunning as the oldest and most experienced of their species. Each brood migrates separately; and the old males, which abandoned the females when incubation commenced, set out in groups of eight or ten. Indeed, it is not common to see birds of this species assemble in such flocks as their relatives the Mallards, although they at times associate with almost all the fresh-water Ducks.

The males, on leaving the females, join together in small bands, and retire into the interior of the marshes, where they remain until their moult is completed. My young friend C brought me a pair shot on the 4th of July, in Labrador, in so ragged a state that very few feathers remained even on the wings. On his approaching them, they skimmed over the surface of the water with such rapidity, that when shot at they seemed as if flying away. On examining these individuals I found them to be sterile, and I am of opinion that those which are prolific moult at a later period, nature thus giving more protracted vigour to those which have charge of a young brood. I

think, Reader, you will be of the same opinion, when I have told you, that on the 5th of July I found some which had young, and which were still in full plumage, and others, that were broodless, almost destitute of feathers.

As many of the nests found in Labrador differed from the one mentioned above, I will give you an account of them. In several instances, we found them imbedded in the deep moss, at the distance of a few feet or yards from the water. They were composed of a great quantity of dry grass and other vegetable substances; and the eggs were always placed directly on this bed without the intervention of the down and feathers, which, however, surrounded them, and which, as I observed, the bird always uses to cover them when she is about to leave the nest for a time. Should she be deprived of her eggs, she goes in search of a male, and lays another set; but unless a robbery of this kind happens, she raises only a single brood in the season. But although this is the case in Labrador, I was assured that this species rears two broods yearly in Texas, although, having been but a short time in that country, I cannot vouch for the truth of this assertion. The eggs are two inches and a quarter in length, one inch and five-eighths in breadth, shaped like those of the domestic fowl, with a smooth surface, and of a uniform yellowish-white colour, like that of ivory tarnished by long exposure. The young, like those of the Mallard, acquire the full beauty of their spring plumage before the season of reproduction commences, but exhibit none of the curious changes which that species undergoes. Although the Dusky Duck is often seen on salt-water bays or inlets, it resembles the Mallard in its habits, being fond of swampy marshes, rice-fields, and the shady margins of our rivers, during the whole of its stay in such portions of the Southern States as it is known to breed in. They are equally voracious, and may sometimes be seen with their crops so protruded as to destroy the natural elegance of their form. They devour, with the greatest eagerness, water-lizards,

young frogs and toads, tadpoles, all sorts of insects, acorns, beech nuts, and every kind of grain that they can obtain. They also, at times, seize on small quadrupeds, gobble up earth-worms and leeches, and when in salt water, feed on shell-fish. When on the water, they often procure their food by immersing their head and neck, and, like the Mallard, sift the produce of muddy pools. Like that species also, they will descend in a spiral manner from on high, to alight under an oak or a beech, when they have discovered the mast to be abundant.

Shy and vigilant, they are with difficulty approached by the gunner, unless under cover or on horseback, or in what sportsmen call floats, or shallow boats made for the purpose of procuring water-fowl. They are, however, easily caught in traps set on the margins of the waters to which they resort, and baited with Indian corn, rice, or other grain. They may also be enticed to wheel round, and even alight, by imitating their notes, which, in both sexes, seem to me almost precisely to resemble those of the Mallard. From that species, indeed, they scarcely differ in external form, excepting in wanting the curiously recurved feathers of the tail, which Nature, as if clearly to distinguish the two species, had purposely omitted in them.

The flight of this Duck, which, in as far as I know, is peculiar to America, is powerful, rapid, and as sustained as that of the Mallard. While travelling by day they may be distinguished from that species by the whiteness of their lower wing-coverts, which form a strong contrast to the deep tints of the rest of their plumage, and which I have attempted to represent in the figure of the female bird in my plate. Their progress through the air, when at full speed, must, I think, be at the rate of more than a mile in a minute, or about seventy miles in an hour. When about to alight, they descend with double rapidity, causing a strong rustling sound by the weight of their compact body and the rapid movements of their pointed wings. When alarmed by a shot or otherwise, they rise off their feet by a

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