Chapter 6 - Electronic Spectroscopy of Molecules.pdf

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1. Electronic Spectroscopy of Molecules
ElectronicSpectraofDiatomicmolecules
TheBorn-OppenheimerApproximation
UsingtheBorn-Oppenheimerapproximation,thetotalenergyofadiatomicmoleculemaybe
written:
E
total=E
electronic+E
vibration+E
rotation (1)
whichimpliesthattheelectronic,vibrational,androtationalenergiesofamoleculearecompletely
independentofeachother.Achangeinthetotalenergyofmoleculemaythenbewritten:
ΔE
total=ΔE
elec.+ΔE
vib.+ΔE
rot. J
or
ΔƐ
total=ΔƐ
elec.+ΔƐ
vib.+ΔƐ
rot. cm
‒1
(2)
Theapproximateordersofmagnitudeofthesechangesare:
ΔƐ
elec.≈ΔƐ
vib.×10
3
≈ΔƐ
rot.×10
6
(3)
andsoweseethatvibrationalchangewillproducea‘coarsestructure’androtationalchangesa
‘finestructure’onthespectraofelectronictransitions.

2. VibrationalCoarseStructure
IgnoringrotationalchangesmeansthatwerewriteEq.(1)as
E
total=E
elec.+E
vib.J
or
Ɛ
total=Ɛ
elec.+Ɛ
vib.cm
‒1
(4)
Moreover,wecanwrite:
Ɛ
total=Ɛ
elec.+(ʋ+
1
2
)ϖ
e‒x
e(ʋ+
1
2
)
2
ϖ
ecm
‒1
(ʋ=0,1,2,……) (5)
Ananalyticalexpressioncaneasilybewrittenforthespectrum.FromEq.(5)wehave
immediately:
ΔƐ
total=ΔƐ
elec.+ΔƐ
vib.
Therefore
ʋ
spec=(Ɛ'–Ɛʺ)+{(ʋ'+
1
2
)ϖ'
e‒x'
e(ʋ'+
1
2
)
2
ϖ'
e}
‒{(ʋ''+
1
2
)ϖ''
e‒x''
e(ʋ''+
1
2
)
2
ϖ''
e} cm
‒1
(6)
and,providedsomehalf-dozenlinescanbeobservedintheband,valuesforϖ'
e,x'
e,ϖ''
e,and
x''
e,aswellastheseparationbetweenelectronicstates,(Ɛ'–Ɛʺ),canbecalculated.

3. Figure:Thevibrational‘coarse’
structureofthebandformed
duringelectronicabsorptionfrom
theground(ʋʺ=0)statetoa
higherstate.
TheenergylevelsoftheEq.(5)are
showninthisfigurefortwoarbitrary
valuesofƐ
elec..
Thisfiguresuggeststhattheground
statecanusuallyundergoatransition
toseveralexcitedstates,andeach
suchtransitionwillbeaccompaniedby
abandspectrumsimilartothisfigure.

4. The Franck-Condon Principle
TheFranck-Condonprinciplestatesthatanelectronictransitiontakes
placesorapidlythatavibratingmoleculedoesnotchangeits
internucleardistanceappreciablyduringthetransition.
Figure:Theprobabilitydistributionforadiatomicmoleculeaccordingto
thequantumtheory.Thenucleiaremostlikelytobefoundatdistances
apartgivenbythemaximaofthecurveforeachvibrationalstate.
TheFigureshowsthevariationofψ
2
with
internucleardistance,whereψisthevibrational
wavefunction.Ifadiatomicmoleculeundergoesa
transitionintoanupperelectronicstateinwhichthe
excitedmoleculeisstablewithrespectto
dissociationintoitsatoms,thenwecanrepresent
theupperstatebyaMorsecurvesimilarinoutline
tothatofthegroundelectronicstate.

5. The Franck-Condon Principle
Figure:TheoperationoftheFranck-Condonprinciplefor(a)
internucleardistancesequalintheupperandlowerstates,(b)
upperstateinternucleardistancealittlelessthanthatinthelower
state,(c)upperstatedistancealittlegreaterthaninthelower,and
(d)upperstatedistanceconsiderablegreater.
Figureshowsfourpossibilities.Figure(a)shows
theupperelectronicstatehavingthesame
equilibriuminternucleardistanceasthelower.
NowtheFranck-Condonprinciplesuggeststhat
atransitionoccursverticallyonthisdiagram.
Figure(b)showsthecasewheretheexcited
electronicstatehasaslightlysmallerinternuclear
separationthanthegroundstate.Avertical
transitionfromʋ''=0levelwillbemostlikelyto
occurintotheuppervibrationalstateʋ'=2.
InFigure(c),theexcitedelectronicstatehasa
slightlylargerinternuclearseparationthanthe
groundstate,buttheresultingtransitionsand
spectrumaresimilar.
InFigure(d),theupperstateseparationisdrawn
asconsiderablygreaterthanthatinthelower
stateandweseethatthevibrationallevelto
whichatransitiontakesplacehasahighʋ'
value.

6. Dissociation Energy and Dissociation Products
Figure(a)and(b)showstwoofthewaysinwhich
electronicexcitationcanleadtodissociation.
Figure(a)representsthecasewherethe
equilibriumnuclearseparationintheupperstateis
considerablygreaterthanthatinthelower.The
dashedlinelimitsoftheMorsecurvesrepresent
thedissociationofthenormalandexcited
moleculeintoatoms,thedissociationenergies
being??????
0
′′
and??????
0
′
fromtheʋ=0stateineachcase.
Weseethatthetotalenergyofthedissociation
productsfromtheupperstateisgreaterbyan
amountcalledE
exthanthatoftheproductsof
dissociationinthelowerstate.Thisenergyisthe
excitationenergyofoneoftheatomsproducedon
dissociation.
ʋ
continuumlimit=??????
0
′′
+E
ex.cm
‒1
(7)
Figure(b)illustratesthecaseinwhichtheupper
electronicstateisunstable:thereisnominimum
intheenergycurveand,assoonasamoleculeis
raisedtothisstatebyexcitation,themolecule
dissociatesintoproductswithtotalexcitation
energyE
ex..
Figure:Illustratingdissociationbyexcitation
into(a)astableupperstateand(b)a
continuousupperstate.

7. Rotational Fine Structure of Electronic-Vibration Transitions

10. Figure:Therotationalfinestructureofaparticularvibration-electronictransitionfor
adiatomicmolecule.TheR,P,andQbranchesareshownseparatelyat(a),(b),and
(c),respectivelywiththecompletespectrumat(d).

11. Electronic Angular Momentum in Diatomic Molecules

14. Spectrum of Hydrogen Molecules
Figure:Thesingletandtripletenergylevelsof
thehydrogenmolecule.Oneelectrononlyis
assumedtoundergotransitions,theother
remaininginthe1sσstate.
Thegroundstateofmolecularhydrogencan
bewritten:
Groundstate:(1sσ
g)
21
Σ
??????
+
Alargenumberofexcitedsingletstatesalso
exist:letusconsidersomeofthelowerones
forwhichoneelectrononlyhasbeenraised
fromthegroundstateintosomehigher
molecularorbital,i.e.singlyexcitedstates.
Thuswemayconsiderthethreepossible
excitedstates(1sσ
g2sσ
g),(1sσ
g2pσ
g),and
(1sσ
g2pπ
u).
Taking(1sσ
g2sσ
g)first:herebothelectrons
areσelectrons;henceΛ=λ
1+λ
2=0and,
sinceweareconsideringonlysingletstates,
S=0also.Further,sincebothconstituent
orbitalsareevenandsymmetrical,theoverall
statewillbethesame,andwehave
(1sσ
g2sσ
g)
1
Σ
??????
+
.

15. Now(1sσ
g2pσ
g):hereweagainhavea
1
Σstatesincebothelectronsareσ,buttheoverallstateis
nowodd(u);thismayberationalizedifwethinkofoneelectronasrisingfromahydrogenatomin
theeven1sstateandtheotherfromanodd2pstate,thecombinationofanoddandanevenstate
leadingtoanoveralloddstate.Thus(1sσ
g2pσ
g)
1
Σ
??????
+
.
Finallythe(1sσ
g2pπ
u):nowΛ=λ
1+λ
2=1,sinceoneelectronisinaπstateand,againsinceone
electronoriginatesfroma2porbital,thecombinedstateisu:
1
Π
??????.
Theenergiesofthesethreestatesincreaseintheorderoftheconstituentmolecularorbitals:
1
Σ
??????
+
<
1
Π
??????<
1
Σ
??????
+
Similarstatesareobtainedbyexcitationtothe3sand3pstates,tothe4sand4pstatesetc.Also
forn=3,4,….thereexiststhepossibilityofexcitationtothendorbital.Itmaybeshownby
methodssimilartothoseabovethatinteractionbetween1sandndelectronscanleadtothethree
configurationsandstatesymbolsinincreasingenergy:
(1sσndσ)
1
Σ
??????
+
<(1sσndπ)
1
Π
??????<(1sσndδ)
1
Δ
g
SomeoftheseenergylevelsareshownattheleftoftheFigure.Transitionbetweenthemcanoccur
accordingtotheselectionrules:
1. ΔΛ=0,±1 (1)
ThustransitionsΣ↔Σ,Σ↔Π,Π↔Π,etc.,areallowedbutΣ↔Δ,isnot.
2. ΔS=0 (2)
Forthepresentweareconcernedonlywithsingletstatessothisruledoesnotarise.

16. 3. ΔΩ=0,±1 (3)
Thisfollowsdirectlyfrom1and2above.
4.Therearealsorestrictionsonsymmetrychanges.Σ
+
statescanundergotransitionsonlyinto
otherΣ
+
stateswhileΣ
‒
goonlyintoΣ
‒
(orΠ).Symbolically:
Σ
+
↔Σ
+
Σ
‒
↔Σ
‒
Σ
+
Σ
‒
(4)
Andfinally
??????↔?????????????????????????????? (5)
Thetripletstatesofmolecularhydrogenandorderofenergiesas:
(1sσ
g2pσ
g)
3
Σ
??????
+
<(1sσ
g2pπ
u)
3
Π
??????<(1sσ
g2sσ
g)
3
Σ
??????
+
Theseenergylevelsareshownontherightofthefigure.
⁄↔
⁄↔ ⁄↔

17. Chemical Analysis by Electronic Spectroscopy
Figure:Theregionsoftheelectronicspectrumandthetypeoftransitionwhich
occursineach.

19. Re-emission of Energy by an Excited Molecule
Figure:Showingthevariouswaysinwhichan
electronicallyexcitedmoleculecanloseenergy.
Afteramoleculehasundergoneanelectronic
transitionintoanexcitedstatethereareseveral
processesbywhichitsexcessenergymaybe
lost;wediscusssomeofthesebrieflybelow.
1.Dissociation:Theexcitemoleculebreaksinto
twofragments.Nospectroscopicphenomena
areobservedunlessthefragmentsradiate
energybyoneoftheprocessesmentioned
below.
2.Re-emission:Iftheabsorptionprocesstakes
asshownschematicallyinFigure(a),then
there-emissionisjustthereverseofthisasin
(b)oftheFigure.Theradiationemitted,which
maybecollectedanddisplayedasan
emissionspectrum,isidenticalinfrequency
withthatabsorbed.

20. Figurec
1:Thesequenceof
stepsleadingtofluorescence.
Aftertheinitialabsorption,the
upper vibrationalstates
undergoradiationlessdecay
bygivingupenergytothe
surroundings.Aradiative
transitionthenoccursfrom
thevibrationalgroundstateof
theupperelectronicstate.
3.Fluorescence:If,asinpreviousFig.(a),themoleculeisinahigh
vibrationalstateafterelectronicexcitation,thenexcessvibrationalenergy
maybelostbyintermolecularcollisions;thisisillustratedinFig.(c)and(c
1).
Thevibrationalenergyisconvertedtokineticenergyandappearsasheatin
thesample;suchtransferbetweenenergylevelsisreferredtoas
‘radiationless’.Whentheexcitedmoleculehasreachedalowervibrational
state,itmaythenemitradiationandreverttothegroundstate;theradiation
emitted,calledfluorescencespectrum,isnormallyoflowerfrequencythan
thatoftheinitialabsorption,butundercertainconditionsitmaybehigher
frequency.Thetimebetweeninitialabsorptionandreturntogroundstateis
verysmall,oftheorderof10
‒8
s.
Figure:Anabsorptionspectrum(a)
shows avibrationalstructure
characteristicoftheupperstate.A
fluorescencespectrum(b)showsa
structurecharacteristicofthelower
state;itisalsodisplacedtolower
frequencies(butthe0–0transitions
arecoincident)andresemblesa
mirrorimageoftheabsorption.

21. 4.Phosphorescence:Thiscanoccurwhentwoexcitedstatesofdifferent
totalspinhavecomparableenergies.ThusinFig.(d),weimaginethe
groundstateandoneoftheexcitedstatestobesinglets(thatisS=0),
whiletheneighbouringexcitedstateisatriplet(S=1).Althoughtherule
ΔS=0forbidsspectroscopictransitionsbetweensingletandtripletstates,
thereisnoprohibitionifthetransferbetweentheexcitedstatesoccurs
kinetically,i.e.throughradiationlesstransitionsinducedbycollisions.
Figured
1showsthesequenceofeventsleadingtophosphorescencefora
moleculewithasingletgroundstate.Thefirststepsarethesameasin
fluorescence,butthepresenceofatripletexcitedstateplaysadecisive
role.Thesingletandtripletexcitedstatesshareacommongeometryatthe
pointwheretheirpotentialenergycurvesintersect.Hence,ifthereisa
mechanismforunpairingtwoelectronspins(andachievingtheconversion
of↑↓to↑↑),themoleculemayundergointersystemcrossing,a
nonradiativetransitionbetweenstatesofdifferentmultiplicity,andbecomea
tripletstate.Wecanexpectintersystemcrossingtobeimportantwhena
moleculecontainsamoderatelyheavyatom(suchasS),becausethenthe
spin–orbitcouplingislarge.
Thusitisthataphosphorescentmaterialwillcontinuetoemitradiation
seconds,minutes,orevenhoursaftertheinitialabsorption.The
phosphorescencespectrumconsistsoffrequencieslowerthanthat
absorbed.
Figured
1:Thesequenceofsteps
leadingtophosphorescence.The
importantstepistheintersystem
crossing,theswitchfromasinglet
statetoatripletstatebrought
aboutbyspin–orbitcoupling.The
tripletstateactsasaslowly
radiatingreservoirbecausethe
returntothegroundstateisspin-
forbidden.

22. Circular Dichroism(CD) Spectroscopy
CircularDichroismisthedifferenceinabsorptionbetweenleftandrighthand
circularlypolarisedlightinchiralmolecules.Achiralmoleculeisonewithalow
degreeofsymmetrywhichcanexistintwomirrorimageisomers.Illustrated
aboveisanexampleofcirculardichroisminglucose,asimplesugar.

23. •Circulardichroism
=ΔA(λ)
=A(λ)
LCPL‐A(λ)
RCPL
•whereλisthewavelength
LCPL=Left-handedcircularlypolarisedlight
RCPL=Right-handedcircularlypolarisedlight
•CDofmoleculesismeasuredoverarangeofwavelengths.
•Usetostudychiralmolecules.
•Analysethesecondarystructureorconformationofmacromolecules,particularlyproteins.
•Observehowsecondarystructurechangeswithenvironmentalconditionsoroninteraction
withothermolecules.
•Measurementscarriedoutinthevisibleandultra-violetregion.
•MoleculecontainschiralchromophoresthenoneCPLstatewillbeabsorbedtoagreater
extentthantheother.
•CDsignaloverthecorrespondingwavelengthswillbenon-zero.
Circular Dichroism(CD) Spectroscopy

24. 
Prism Polarizer

25. Circular Dichroism(CD)

26. CD for Biological Molecules
•Majorityofbiologicalmoleculesarechiral.
•Tounderstandthehigherorderstructuresofchiralmacromolecules
suchasproteinsandDNA.
•Eachstructurehasaspecificcirculardichroismsignature.
•Toidentifystructuralelementsandtofollowchangesinthestructureof
chiralmacromolecules.
•Tostudysecondarystructuralelementsofproteinssuchastheα-helix
andtheβsheet.
•Tocompare2macromolecules,orthesamemoleculeunderdifferent
conditionsanddetermineiftheyhaveasimilarstructure.
•Toascertainifanewlypurifiedproteiniscorrectlyfolded.
•Todetermineifamutantproteinhasfoldedcorrectlyincomparisonto
thewild-type.
•Foranalysisofbiopharmaceuticalproductstoconfirmthattheyarestill
inacorrectlyfoldedactiveconformation.

27. ThesecondarystructureconformationandtheCDspectraofproteinstructuralelements.
Right:apeptideinanα-helix;Left:apeptideinaβ-sheet.Centre:CDspectraforthese
differentconformations.
Themostcommonlyusedunitsaremeanresidueellipticity,(degree·cm
2
/dmol),andthe
differenceinmolarextinctioncoefficientscalledthemolarcirculardichroism,ε
L-εR=Δε
(liter/mol·cm).
Themolarellipticity[]isrelatedtothedifferenceinextinctioncoefficientsby[]=3298Δε.