Linear Free-Energy Relationships(Substituent Effects, LFERs, or Hammett Plots)O OHXO OX+ H+Qualitative question: How does substituent X affect acidity?As a reminder,O ONH2δ−δ−δ−δ+O ONO2δ+δ+δ+δ−resonance-destabilizedElectron-donating groupsdecrease acidity.resonance-stabilizedO ONO2induction-stabilizedElectron-withdrawing groupsincrease acidity.Linear Free-Energy RelationshipsQualitative question: How does substituent X affect acidity?X =NH2CH3HBrCF3NO2less acidicmore acidicKapKa4.20 6.3 x 10-5M4.863.42 3.8 x 10-4M1.4 x 10-5MΔGoKaO OHXO OX+ H+ΔG05.8 kcal/mol4.7 kcal/mol6.7 kcal/molLinear Free-Energy RelationshipsLouis Hammett turned this into a quantitative question:Can we construct a mathematical relationship between substituent X and acidity? (Can effect of substituent on ΔGoand Kabe expressed mathematically?)Is relationship for one reaction related to that for other reactions?ΔGoKaO OHXO OX+ H+Linear Free-Energy RelationshipsΔGoKaO OHXO OX+ H+Hammett’s Hypothesis, Part 1:For each substituent X, there is a characteristic free-energy differencelog10Ka(X)Ka(H)-ΔΔGo(X)2.303RT== σ(X)“Hammett parameter”X = HX = NO2ΔGo(NO2)ΔGo(H)δ+ΔΔGo(X) = ΔGo(X) - ΔGo(H)Linear Free-Energy RelationshipsHammett’s Hypothesis, Part 1:ΔGoKaWe can define a set ofconstants σ such thatlog10Ka(X)Ka(H)= σ(X)XNH2HBrNO2σ-0.66 Ka(NH2) < Ka(H)0 (by definition)0.230.78 Ka(NO2) > Ka(H)So far, this is just math.Not a big deal.O OHXO OX+ H+Linear Free-Energy RelationshipsHammett’s Hypothesis, Part 2:These exact same constants σ apply to other (only somewhat related) reactions, such thatlog10Ka(X)= ρσ(X)X+ H+OOHXOOHere, different reaction…but same general substituent effects!σlog10Ka(X)Ka(H)ρ = 0.489(ρ < 1 meansless sensitive tosubstituents thanbenzoic acid Ka)This is a big deal.KaKa(H)Linear Free-Energy RelationshipsHammett’s Hypothesis, Part 2:These exact same constants σ apply to other (only somewhat related) reactions, such thatlog10Ka(X)Ka(H)= ρσ(X)X+ H+OOHXOOσlog10Ka(X)Ka(H)ρ = 0.489ρ = 0.212Remarkably, relationship between substituent σ and equilibrium stays linear.Ka(Denominator can actually be any constant.)Linear Free-Energy RelationshipsHammett’s Hypothesis, Part 2:log10Ka(X)K0= ρσ(X)Overall:ρ > 0:Equilibrium has same pattern as benzoic acid Ka’s;Electron-withdrawing substituents increase Ka,Electron-donating substituents decrease Ka.ρ > 1: More sensitive to substituents than benzoic acid Ka’s.0 > ρ > 1: Less sensitive to substituents than benzoic acid Ka’s.ρ < 0:Equilibrium has opposite pattern as benzoic acid Ka’s;Electron-withdrawing substituents decrease Ka,Electron-donating substituents increase Ka.(actually possible to use any constant in denominator)Linear Free-Energy RelationshipsOOH OO+ H+XXKaIf substituent effect is fundamentally different, then different set of σ values may be required.OOXδ+/−δ+/−δ+/−δ+/−Pattern of stabilization/ destabilization is the same for σmeta;Resonance less important,Induction more important.Linear Free-Energy Relationships:KineticsRemarkably, σ can be used for rate constants too.log10kXkH= ρσ(X)rate constants!ΔΔG‡(X) = ΔG‡(X) – ΔG‡(H)ΔG‡(H)ΔG‡(X)E-ΔΔG‡(X)2.303RT=reaction coordinateLinear Free-Energy Relationships:Kineticslog10kXkH= ρσ(X)-ΔΔG‡(X)2.303RT=For example:OOEtXOOXOHEtOH++kXρ = 2.61ρ> 0;As with benzoic acid acidity,EWGs increase rate constant,EDGs decrease rate constant.Linear Free-Energy RelationshipsHO OEtXOOOEtXHOδ−δ−O OEtXHOδ+δ-O OHXElectron-withdrawing X destabilizes (δ+)C=O.Destabilizes Csp3 in transition state less.So, kEWG> kH.Just like benzoic acid Ka’s. So ρ > 0.ΔG‡(H)ΔG‡(EWG)‡log10kXkH= ρσ(X)Linear Free-Energy RelationshipsDirect resonance of changing charge in TS addressed by σ+, σ-.H3C CH3XClH3C CH3XOHH3O+(SN1)H3C CH3XH3C CH3XClδ+δ−rate-determiningstepResonance stabilization particularly important in TS.Resonant e-donors stabilize TS,increase k.Linear Free-Energy RelationshipsH3C CH3XClH3C CH3XOHH3O+(SN1)H3C CH3Xrate-determiningstepσ+accounts for direct resonance with phenyl substituents.Reference is cumyl chloride hydrolysis (this reaction).-log10kXkH= ρσ+(X)Negative sign (for σ+ only) meansσ values same direction as benzoic acids.Linear Free-Energy RelationshipsSummary:ρ > 0:Process has same pattern as benzoic acid Ka’s;Electron-withdrawing substituents increase Kaor rate k,Electron-donating substituents decrease Kaor rate k.ρ < 0:Process has opposite pattern as benzoic acid Ka’s;Electron-withdrawing substituents decrease Kaor rate k,Electron-donating substituents increase Kaor rate k.log10Ka(X)= ρσ(X)Ka(H)orlog10kXkH= ρσ(X)Linear Free-Energy RelationshipsKeep in mind: For multistep kinetics,Effect of substituent is between starting material and rate-determining transition state.ΔG‡(H)ΔG‡(X)Method is frequently used to identify rate-determining step/transition state.Can also be used to identify change inrate-determiningtransition