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TheActivationStrainModel

DenmarkGroupMeetingAndrewZahrt

TheActivationStrainModel(ASM)• AlsoreferredtoasDistortionInteractionModel• TheActivationStrainModel:

– Afragmentbasedapproachwhichdecomposesthepotentialenergysurfaceintostrainandinteractionportionsinanefforttounderstandthephysicalpropertiesthatareresponsibleforenergybarriers.

– Leadstorationaldesignofefficientreactions• DevelopedindependentlybyHouk andBickelhaupt

Bickelhaupt etal.,Comput.Mol.Sci.,2015,5,324-343

BeforeUsingtheASM

• BeforeusingASM,first:1. Locatetransitionstateof

interest• ScanFromReactant

2. Performasteepestdescentcalculationtoobtaintheintrinsicreactioncoordinate(IRC)• ScanbacktoLocalMinima

oneachside

UsingtheASM

• ASMdecomposesenergyintotwoterms:o ΔE=ΔEstrain +ΔEinto ΔEstrain =geometricdeformationoffragments(reactants)fromareferencegeometry

o ΔEint =interactionbetweenfragments

o ThetransitionbarrieroccurswhentheslopeofΔEstrain =ΔEint

InterpretingtheActivationStrainDiagram(ASD)

• TwohypotheticalreactionsA(black)andB(blue).

• InteractionenergyisforreactionBismorestabilizingatanygivenpointalongthereactioncoordinate

• Singlepointanalysiswouldyieldoppositeconclusion!

Fernandez,I.;Bickelhaupt,F.M.Chem Soc Rev,2014,43,4953- 4967

UsingMolecularOrbitalTheorytoExplainΔEstrain

• ΔEstrain:MOtheorycanexplainwhystructuraldeformationdestabilizesachemicalspecies.– WalshDiagram

UsingEnergyDecompositionAnalysistoExplainΔEint

• EnergyDecompositionAnalysis:– AdaptedfromMorokuma,Ziegler,andRauk

ΔEint =ΔVelstat +ΔEPauli + ΔEoi (+ ΔEdisp)

– ΔVelstat =ElectrostaticPotentialEnergy• Usuallyattractive(negative)atchemicallyrelevantdistances

– ΔEPauli =PauliRepulsion:ResponsibleforStericRepulsion• Repulsive(positive)

– ΔEoi =OrbitalInteraction:Includeschargetransferandpolarization

• Stabilizing(negative)

– ΔEdisp =DispersionEnergy(arisingfrominducedinstantaneouspolarization)

• Repulsiveat<3.5Å,attractivebeyond3.5Å

Bickelhaupt etal.,Comput.Mol.Sci.,2015,5,324-343

Frontside vsBacksideSN2

• BimolecularNucleophilicSubstitution

Purpose:Toelucidateacausalrelationshipbetweenthereactants’electronicstructureandSN2reactivity

Bento,A.P.;Bickelhaupt,F.M.J.Org.Chem.2008,73,7290-7299

BacksideSN2:PES

Y=Cl;X=F,Cl, Br, I

F>Cl> Br> I


Frontside SN2:PES

Y=Cl;X=F,Cl, Br, I

F>Cl> Br> I


ApplyingASM

• ActivationStrainModeladdressesthefollowingquestions:

1. WhydoestheenergybarrierincreasewhenthenucleophileprogressesfromFtoI?

2. Whatphysicalpropertiesofthereactantsresultinbacksideattackbeingfavoredoverfrontside attack?

ApplyingASMtoAssessNucleophilicity

Y=Cl;X=F,Cl, Br, I

• Strainisconstantthroughoutallcases.

• TSlocationisdeterminedbytheslopeofΔEint


SN2:Nucleophilicity Trend

DominantorbitalinteractionisbetweenoccupiedAOonX– andCH3Y σ*C-Y


SN2:FactorsControllingΔEint

Y=Cl;X=F,Cl, Br, I 1. ΔEoi becomesmorenegativeduetoweakeningofC-Ybond

2. ΔVelstat becomesmorenegativebecauseofpositivechargebuilduponthecarbon.

SteeperDescentofΔEint=EarlierTransitionState=LowerEnergyBarrier


ActivationStrainAnalysisforFrontside vsBacksideAttack

Y=Cl;X=F,Cl, Br, IY=Cl;X=F,Cl, Br, I


SummaryofSN2

1. OrbitalInteractiontermdictatesnucleophilicity– EnhancesstabilizationfromΔVelstat

2. Frontside attackisdisfavoredbecausePaulirepulsionmakestheslopeofEint lesssteep

CaseI:OxidativeAddition

• DirectOxidativeInsertion

• SN2TypeMechanism

Goal:Todeterminehowcatalystactivitydependsonelectronic

structureBickelhaupt,F.M.;J.Comput.Chem. 1999,20,114–128

Pd(0)CatalyzedBondActivationThroughOxidativeInsertion

ΔEǂ /Ea (kcal/mol)

-21.7/2.7

-1.6/6.4

-0.7/7.5

-4.3/9.6

12.6 /21.2

ΔEstrain/Eint (kcal/mol)

55.6 /-77.3

53.5 /-55.1

54.7 /-55.4

8.8 /-13.1

39.4 /-26.8

Diefenbach,A.;Bickelhaupt,F.M.J.Phys.Chem.A.2004,108,8460-8446

StrainandC-(H/C/Cl)BondStretch

ΔEstrain=55.6kcal/mol ΔEstrain=53.5 kcal/mol ΔEstrain=54.7 kcal/mol

ΔEstrain=8.8 kcal/molΔEstrain=39.4 kcal/mol

H-H:1.38ÅStretch:97%

C-H:1.61ÅStretch:47%

C-H:1.63ÅStretch:48%

C-C:1.93ÅStretch:26%

C-Cl:1.97ÅStretch:9%


StrainandC-(H/C/Cl)BondStretch

-30

-20

-10

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

kcal/m

ol

%Stretch

StrainEnergyVs%Stretch

Energyvs%Stretch

ΔEstrain correlateswith%stretch,butΔEǂ doesnot!

ΔEint mustbemorethoroughlyinvestigatedtounderstandreactionbarrier.Diefenbach,A.;Bickelhaupt,F.M.J.Phys.Chem.A.2004,108,8460-8446

EnergyDecompositionAnalysis

ΔEint =ΔVelstat +ΔEPauli + ΔEoi (Allinkcal/mol)

ΔVelstat =-183.7ΔEPauli =208.7






AnalysisofΔEoi


InsertionintoH-H

Orbitalσ*H-H 4dσH-H5s

Eorbital(eV)-2.854-4.193-8.438-3.423

Overlap0.3000.566

Population(e–) 0.439.281.730.45


Eoi =-102.3kcal/mol

InsertionintoC-H

Orbitalσ*C-H 4dσC-H5s

Eorbital(eV)-1.625-4.193-7.435 -3.423

Overlap0.3270.401

Population(e–) 0.369.321.710.38


Eoi =-95.8kcal/mol

InsertionintoC-C

Orbitalσ*C-C 4dσC-C5s

Eorbital(eV)-0.391-4.193-7.303-3.423

Overlap0.1360.213

Population(e–) 0.259.421.830.22


Eoi =-79.9kcal/mol

InsertionintoC-Cl

Orbitalσ*C-Cl 4dσC-C5s

Eorbital(eV)-2.066-4.193-7.142-3.423

Overlap0.0820.144

Population(e–) 0.199.591.910.18


Eoi =-48.7kcal/mol

SummaryofPd(0)CatalyzedBondActivation

ΔEǂ / ΔEstrain /Eint(kcal/mol)

-21.7/55.6 /-77.3

-1.6/53.5 /-55.1

-4.3/8.8 /-13.1

12.6 /39.4 /-26.8

ΔEPauli + ΔEelstat /Eoi(kcal/mol)

25 /-102.3

40.7 /-95.8

35.6 /-48.7

53.5 /-93.3


AnionAssistance


-21.7/55.6 /-77.3

-35.3/56.1 /-91.4

Ox.Ins.-4.3/8.8 /-13.1SN224.5/ 87.5 / -63.2

Ox.Ins.-10.3/9.6 /-19.9SN2-18.5/ 91.8 / -110.3

Diefenbach,A.;deJong,GT,Bickeclhaupt,FM.J.Chem.TheoryComput.,2005,1,286–298

H-HBondInsertion


-21.7/55.6 /-77.3

-35.3/56.1 /-91.4

(ΔEPauli / ΔEelstat)ΔEPauli + ΔEelstat /Eoi

(kcal/mol)

(208.7/-183.7)25 /-102.3

(176.3/-173.6)2.7 /-94.1

PopulationAnalysis:σH-H =1.73σ*H-H =0.43Pd (4d)=9.28Pd (5s)=0.45

PopulationAnalysis:σH-H =1.89σ*H-H =0.57Pd (4d)=9.32Pd (5s)=0.21


Pd-Hdistancedecreasesfrom1.54to1.61

H-HBondInsertion


ReactivitywithC-Xbond



Ox.Ins.-4.3/8.8 /-13.1SN224.5/ 87.5 / -63.2

35.6/-48.738.3/-101.4


ReactivitywithC-Xbond



22.4/-42.344.5/-154.7

Ox.Ins.-10.3/9.6 /-19.9SN2-18.5/ 91.8 / -110.3

ElongationofC-ClbondinTSlowersLUMOenergyby4.6eV.

Resultsinbetter4d– σ*orbitaloverlap.

SummaryofOxidativeAddition

• TheinterplaybetweenStrainandInteractionDictateReactionbarriers:– H-Hhashigheststrainenergy,butlowestactivationenergywhileC-Clhassecondlowestbarrierwithlowestinteractionenergy

• AnionassistancesteepensΔEint curve,resultinginanearliertransitionstateandalowerenergybarrier.

Intermission

CaseIIa:ExoSelectiveDielsAlder

Gouverneur,V;Houk,K.etal.JACS,2009 ,131, 947–195

ExovsEndoSelectivity


Distortion– InteractionAnalysis

Thereactantsintheendopathwayaremoredistortedthantheexo pathway,resultinginexo

selectivity.


StraininTransitionState

Higherdistortioninendo pathwayisduetoamoreasynchronousTS


SummaryofExoSelectiveDielsAlder

Distortion/Interactionanalysisleadstoa

straightforwardmodeltoexplainselectivity


CaseIIb:MO4 Cylcoaddition toEthylene

• 3+2vs2+2• Itwasknownthat3+2wastheoperativepathway• ItwasalsoknowsthatAminebasescatalyzedthereaction• Distortion/InteractionAnalysisandEnergyDecomposition

Analysisemployedtoexplain:– Themechanismofaminebasecatalysis– Reactivitydifferencesbetweenselectedmetals

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

32TSvs22TS(OsO4)

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

32TSvs22TS(OsO4):uncatalyzed

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

• OOsO bondanglesequallydistorted

• Os-Obondin22TSmoredistorted

• 22TSlaterthan32TS

32TSvs22TS(OsO4):catalyzed

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

• 32TSislessdistortedthaninuncatalyzedcase

• 22TSmoredistortedthanuncatalyzed case

DistortionInteractionAnalysis:32TSUncatalyzed Case

• OsO4 remainsapprox5kcal/mol distortedthanethylenethroughouttheentiresurface

DistortionInteractionAnalysis:Uncatalyzed Case

• PositiveInteractionEnergy!

CurrentAnalysis• AnsweredQuestions:

Q:Whyisthe3+2TSpreferredoverthe2+2TS?A:The3+2pathwayhasanearlier,lessdistortedTS.

Q:Whydoesthepresenceofanamineligandcatalyzethereaction?A:TheamineNH3OsO4 complexisdistortedlessintheTS,resultinginalowerenergybarrier

• UnansweredQuestions:– Howdoweinterpretpositiveinteractionenergy?– CanthereactivityofOsmiumbeunderstoodintermsofits

electronicstructure?• Cansimilaranalysisexplainthereactivityofothermetals?

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

AbsolutelyLocalizedMolecularOrbitalInteractionDecompositionAnalysis

• ALMO-EDA:ΔEint =ΔEFRZ+ΔEPOL + ΔECT + ΔEHO

– ΔEFRZ:FrozenElectronDensities:IncludesCoulombicinteractionandexchange/correlation.

– ΔEPOL:Polarization– ΔECT:ChargeTransfer– ΔEHO:Higherorderorbitalrelaxationeffects(includesallinductioneffects)

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

Positive interaction energy

ComparisonAcrossMetals:Distortion,InteractionandEnergyBarrier

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

EDAatNonstationaryPoints

Ess,D. J.Org.Chem.,2009 ,74,1498-1508

Distortion/InteractionCurve

MO4 Cylcoaddition toEthylene:Summary

• ChargetransferfromethylenetoOsO4 ismostefficientbecauselow-lyingLUMOofOsO4

• MnO4– isanactiveoxidantbecauseofitsearlyTS

– Lowstrain

• TcO4– andReO4

– arelessactivebecauseoftheirlaterTS.– ΔEint developsmoreslowlyduetolessstabilizationfromchargetransfer

Summary

• ASMorDistortion/Interactionanalysiscanbeusedinavarietyofwaystoshowthephysicaloriginofenergybarriers– FrequentlyusedwithEDA

• ThePEScanbedecomposedinmultipledifferentways:– Methodofdecompositionisatthediscretionofthepractitioner

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