Linear Free-Energy Relationships (Substituent Effects, LFERs, or Hammett Plots)

Transcription

1 (Substituent Effects, LFERs, or Hammett Plots) H + H + Qualitative question: How does substituent affect acidity? As a reminder, δ δ + resonancedestabilized resonancestabilized δ NH 2 δ + δ Electron-donating groups decrease acidity. δ + N 2 δ δ + inductionstabilized Electron-withdrawing groups increase acidity. N 2

2 H ΔG o + H + Qualitative question: How does substituent affect acidity? p ΔG 0 = NH 2 CH 3 H Br less acidic x 10-5 M x 10-5 M 6.7 kcal/mol 5.8 kcal/mol CF 3 N 2 more acidic x 10-4 M 4.7 kcal/mol

3 H ΔG o + H + Louis Hammett turned this into a quantitative question: Can we construct a mathematical relationship between substituent and acidity? (Can effect of substituent on ΔG o and be expressed mathematically?) Is relationship for one reaction related to that for other reactions?

4 δ+ H ΔG o + H + Hammett s Hypothesis, Part 1: For each substituent, there is a characteristic free-energy difference () -ΔΔG o () = = σ() 2.303RT Hammett parameter ΔG o ΔG o (N 2 ) = H = N 2 ΔΔG o () = ΔG o () - ΔG o

5 H ΔG o + H + Hammett s Hypothesis, Part 1: We can define a set of constants σ such that () = σ() NH 2 H Br N 2 σ (NH 2 ) < 0 (by definition) (N 2 ) > So far, this is just math. Not a big deal.

6 Hammett s Hypothesis, Part 2: These exact same constants σ apply to other (only somewhat related) reactions, such that H + H + () = ρσ() ρ = Here, different reaction but same general substituent effects! () (ρ < 1 means less sensitive to substituents than benzoic acid ) This is a big deal. σ

7 Hammett s Hypothesis, Part 2: H These exact same constants σ apply to other (only somewhat related) reactions, such that + H + () = ρσ() ρ = (Denominator can actually be any constant.) () ρ = Remarkably, relationship between substituent σ and equilibrium stays linear. σ

8 Hammett s Hypothesis, Part 2: () = ρσ() (actually possible to use any constant in denominator) verall: K 0 ρ > 0: Equilibrium has same pattern as benzoic acid s; Electron-withdrawing substituents increase, Electron-donating substituents decrease. ρ > 1: More sensitive to substituents than benzoic acid s. 0 > ρ > 1: Less sensitive to substituents than benzoic acid s. ρ < 0: Equilibrium has opposite pattern as benzoic acid s; Electron-withdrawing substituents decrease, Electron-donating substituents increase.

9 H + H + If substituent effect is fundamentally different, then different set of σ values may be required. δ+/ δ+/ δ+/ δ+/ Pattern of stabilization/ destabilization is the same for σ meta ; Resonance less important, Induction more important.

10 : Kinetics E ΔG ΔG () Remarkably, σ can be used for rate constants too. ΔΔG () = ΔG () ΔG k k H = -ΔΔG () 2.303RT = ρσ() reaction coordinate rate constants!

11 : Kinetics Et For example: k ρ = H + EtH k k H = -ΔΔG () 2.303RT = ρσ() ρ > 0; As with benzoic acid acidity, EWGs increase rate constant, EDGs decrease rate constant.

12 δ H δ Et Electron-withdrawing destabilizes (δ+) C=. Destabilizes C sp 3 in transition state less. So, k EWG > k H. Just like benzoic acid s. So ρ > 0. ΔG (EWG) k k H = ρσ() H δ- H Et H Et δ+ ΔG

13 Direct resonance of changing charge in TS addressed by σ +, σ -. Resonance stabilization particularly important in TS. Cl H 3 C CH 3 H H 3 C CH 3 Cl H 3 C CH 3 δ+ δ H 3 + (S N 1) H 3 C CH 3 Resonant e - donors stabilize TS, increase k. rate-determining step

14 σ + accounts for direct resonance with phenyl substituents. Cl H 3 C CH 3 H 3 + H H 3 C CH 3 (S N 1) H 3 C CH 3 rate-determining step Reference is cumyl chloride hydrolysis (this reaction). - k k H Negative sign (for σ+ only) means σ values same direction as benzoic acids. = ρσ + ()

15 () = ρσ() or k k H = ρσ() Summary: ρ > 0: ρ < 0: Process has same pattern as benzoic acid s; Electron-withdrawing substituents increase or rate k, Electron-donating substituents decrease or rate k. Process has opposite pattern as benzoic acid s; Electron-withdrawing substituents decrease or rate k, Electron-donating substituents increase or rate k.

16 Keep in mind: For multistep kinetics, Effect of substituent is between starting material and rate-determining transition state. ΔG ΔG () Method is frequently used to identify rate-determining step/transition state. Can also be used to identify change in rate-determining transition state.