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JcouplingSpin-spinCouplingdipole-dipoleinteraction:
magneticdipoleinteractionbetweennucleidirectlySpin-spinCoupling:
Itwilloccurbetweentwomagneticallyactivenucleithatareconnectedthroughchemicalbonds.Wecanseeitfortwoatomsdirectlyconnected,orforatomsthat‘see’oneanotheracrossseveralbonds.
CouplingsareperhapsthemostimportantparameterinNMR,astheyallowustoelucidatechemicalstructure.I
SJ0I
SJ=0ExampleEthanol:
CH3CH2OHThreesinglets
Thespectrumisaresultofspin-spincoupling(scalecoupling)JCoupling
TheresonancefrequencyofHa
depends
onwhethertheadjacent
Hb
hasspinup
ordown.
Thefrequencyseparationbetweenthe
twopeaksiscalledJ(scalarcoupling
constant)
(typically
0~15Hz).
Thecouplingconstantisindependentof
BoandisreportedinHz.JCoupling
TheresonancefrequencyofHa
depends
onwhethertheadjacent
Hb
hasspinup
ordown.
Thefrequencyseparationbetweenthe
twopeaksiscalledJ(scalarcoupling
constant)
(typically
0~15Hz).
Thecouplingconstantisindependentof
BoandisreportedinHz.ExampleEthanol:
CH3CH2OHSpin-spincouplingtellsushowmanynucleithereareneartoagivennucleus.JCouplingPascalTriangle11112113311464115101051JCouplingIfaprotoninteractswithtwodifferentsetsofequivalentprotons,themultiplicitywillbe: —spinsystem,AnMmXp
(m+1)(p+1)ConsiderCH3CH2CH2I
—H=1.02;H=1.86;H=3.17-CH3;1:2:1triplet(frommethyleneCH2)-CH2;quartetoftriplets–12lines(3+1)(2+1)-CH2;1:2:1triplet(frommethyleneCH2)CouplingbetweenSetsofSpins:JCouplingFactorsaffectthesizeofJ:ThenumbersofbondsinvolvedThedihedralangleφ,forvicinalprotonsTheconfigurationsTheconformationsKarplusEquationJcouplingsprovideanestimationofmolecularconformation!J(θ)=Acos2(θ)+Bcos(θ)+CA,B,andCareempiricallyderivedparameters.JCouplingEAXAXA1A2A1A2BoJ=0J<0E4E3E2E1A1A2n(A1)=n(A2)A2A1n(A2)n(A1)A1A2n(A1)n(A2)J=0J>0J<0Analysisofspin-spincoupling:Analysisof1stOrderSystemsCH3CH2CH3CH2J(Hz)4.5ppm1.5ppmEthylacetate(CH3COOCH2CH3):Nuclei
A
iscoupledto
n
identicalnucleiX(ofspin1/2),
A
willshowupas
n+1
linesinthespectrum.Sincewehavethesameprobabilityoffindingthesysteminanyofthestates,andstatesinthesamerowshaveequalenergy,theintensitywillhavearatio
1:2:1
fortheCH3,andaratioof
1:3:3:1
fortheCH2.PascalTriangle11112113311464115101051Inaspinsysteminwhichwehaveacertainnucleicoupledtomorethanonenuclei,allfirstorder,thesplittingwillbebasicallyanextensionofwhatwesawbefore.SaythatwehaveaCH(A)coupledtoaCH3(M)witha
JAM
of7Hz,andtoaCH2(X)witha
JAX
of3Hz.Webasicallygoinsteps.Firstthebigcoupling,whichwillgiveaquartet:Thenthesmallcoupling,whichwillspliteachlineinthequartetintoatriplet:Thisiscalleda
tripletofquartets
(bigeffectisthelast…).Analysisof1stOrderSystems7Hz)3Hz
Analysisof2ndOrderSystems1234ABnZnAnBWhatwehavebeendescribingsofarisaspinsysteminwhich
Dn>>J.B0
Dn
Dn
~
J
Averysimplewaytodetermineifwehavean
AB
systemisbylookingattheroofingeffect:coupledpairswillleantowardseachother,makingalittleroof:ROOFAswithan
AX
system,
JAB
istheseparationbetweenlines
1and2or
3and4:|JAB|=|f1-f2|=|f3-f4|Now,thechemicalshiftsofnucleiAandBarenotatthecenterofthe
doublets.They'llbeatthecenterofmassofbothlines.Thiscanbecalculatedasfollows.Being
Dn
thenA
-nB
chemicalshiftdifference:Dn2=|(f1-f4)(f2-f3)|nA
=nZ-Dn/2
nB
=nZ+Dn/2I1I2I3I4I2I3|f1-f4|==I1I4|f2-f3|Magnetic&ChemicalEquivalenceAswesawlasttime,wecandoaverysimplefirstorderanalysisofthisspinsystem,becauseweassumedthatallCH2protonswere‘equal’,andallCH3protonswere‘equal’.Wecaneasilyseethattheyarechemicallyequivalent.Additionally,wehavefreerotationaroundthebond,whichmakestheirchemicalshiftsandcouplingsequal.Soineffect,thecouplingofanyprotoninCH2toanyprotonintheCH3will
bethesame.Magnetic
equivalence:Anethoxygroup(-O-CH2-CH3)
ChemicalEquivalence:Thenucleigroupswhosechemicalshiftsareequalarechemicalequivalence.
d(CH2)>>d(CH3)
A2X3system
Wehave2magneticallyequivalent1HsontheCH2,and3ontheCH3.The
2JHH
coupling
iszerointhiscase,becausetheenergiesforanyofthe
three
protonsisthesame.Weuse
A
torefertotheCH2protons,and
X
torefertotheCH3protonsbecausethey
haveverydifferentds.Westartwiththeletter
Aforthemostdeshieldedspin.Magnetic&ChemicalEquivalenceCH2F2isanotherexampleofan‘AX’typesystem.Inthiscase,the1Hsandthe19Fsare
equalnotduetorotation,buttosymmetryaroundthecarbon.It’san
A2X2
system.
ForCH2F2,wecanalsocomparethecouplingstocheck
the1Hsand19Fsareequivalent:
JH1F1=JH1F2=JH2F1=JH2F2.Allduetotheirsymmetry.Symmetry
noRotationdHa
=
dHb
dFa
=
dFbduetothegeometryofthiscompoundJHaFa
JHaFb
JHbFa
JHbFbTheenergylevelsfor
Ha
andHb
aredifferent(notdegenerateanymoreasinCH3),andwehave
JHaHb
≠0.For
Ha,wehave
JHaFa,JHaFb,and
JHaHb.For
Hb,wehave
JHbFa,JHbFb,and
JHbHa.CH2F2H2C=CF2A2X2AA'XX'1H-NMRData:3componentsChemicalshift-eachnonequivalenthydrogengivesauniquesignal.J-Scalecouplingsproducesplittingpatterncorrelatedwithm
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