Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model

Abstract

The activation strain or distortion/interaction model is a tool to analyze activation barriers that determine reaction rates. For bimolecular reactions, the activation energies are the sum of the energies to distort the reactants into geometries they have in transition states plus the interaction energies between the two distorted molecules. The energy required to distort the molecules is called the activation strain or distortion energy. This energy is the principal contributor to the activation barrier. The transition state occurs when this activation strain is overcome by the stabilizing interaction energy. Following the changes in these energies along the reaction coordinate gives insights into the factors controlling reactivity. This model has been applied to reactions of all types in both organic and inorganic chemistry, including substitutions and eliminations, cycloadditions, and several types of organometallic reactions.

Keywords: chemical reactivity; computational chemistry; quantum chemistry; reaction mechanisms; transition states.

Figure 1

The activation‐strain model exemplified using a metal‐mediated C−X bond activation: ${\Delta E^{\ne }=\Delta E}_{\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}}^{\ne }$ [reactant 1]+ ${\Delta E}_{\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}}^{\ne }$ [reactant 2]+${\Delta E}_{\mathrm{i}\mathrm{n}\mathrm{t}}^{\ne }$ .

Figure 2

Activation strain or distortion/interaction diagram for S_N2 reactions, showing the position of transition states (filled dots) and inflection points of the reaction‐strain and interaction curves (blue circles). In (a) and (b), the black curves denote the same reference reaction system with a moderate nucleophile X⁻ and a moderate leaving group Y. In (a), the green curves show the effect of using a better nucleophile but keeping the moderate leaving group. In (b), the red curves show the effect of using a poorer leaving group Y but keeping the moderate nucleophile.

Figure 3

a) Schematic activation strain diagram for the four transition states (TS) of the E2 and S_N2 reactions of a weak and a strong base X⁻ (i.e. low‐ and high‐energy HOMO) with identical substrates CH₃CH₂Y, showing for each TS the base–substrate HOMO–LUMO gap. b) The substrate LUMO is C^α−Y and antibonding C^β−H. c) S_N2 distortion reduces the antibonding C^α−Y overlap and thus lowers the LUMO energy. d) E2 distortion lowers the substrate LUMO even more because both C^α−Y and C^β−H antibonding overlap are reduced.

Figure 4

Correlation between the computed activation energies of Diels–Alder reactions of aromatic dienes with maleic anhydride and the distortion energies (left) and energies of the reaction (right).

Figure 5

Transition states of Diels–Alder reactions of cyclopentadiene with enones. Computed at the M06‐2X‐6‐31G(d) level. Energies in kcal mol⁻¹.25a.

Figure 6

Correlation between the activation energies and distortion energies for Diels–Alder reactions of cyclopentadiene with cycloalkenes (red) and cycloalkenones (blue). Both exo (small symbols) and endo (large symbols) are included.

Figure 7

(U)M06‐2X/6‐31+G(d,p)‐optimized transition states for concerted and stepwise parent Diels–Alder reaction and dehydro analogues.

Scheme 1

SPAAC reaction of aromatic azides with bicyclononyne (BCN).

Figure 8

Examples of mutually orthogonal reactions. Reaction (a) is fast for tetrazines, but not azides. Reaction (b) is fast with azides, but not tetrazines.34d Reaction (c) is faster with tetrazines.

Scheme 2

Alder‐ene reaction (XY is, e.g., C₂H₄, C₂H₂, CH₂NH, CH₂O).

Figure 9

Reaction potential energy surfaces (a) and activation strain diagrams (b,c) of the oxidative insertion of Pd (black), Pd(PH₃)₂ (blue), and Pd[PH₂(CH₂)₂PH₂] (red) into the C−H bond of methane. The dots indicate the position of the TS.

Figure 10

Energies and distortion/interaction analysis of transition states (TS37 and TS38) of the [Pd(PH₃)₂]‐mediated oxidative addition to the C−Cl bond of aryl chloride 36. Energies are in kcal mol⁻¹.

Figure 11

Energies and distortion/interaction analysis of the transition states of the [Pd(PH₃)₂]‐mediated oxidative addition to the C−Br bond of aryl bromide 39. Energies are in kcal mol⁻¹.

Figure 12

Stereoselective oxetene ring opening catalyzed by a chiral phosphoric acid.

Figure 13

Transition states for oxetane ring‐opening reactions. These are overlapped on the catalyst structure on the right.

Figure 14

Structures of indolynes.

Figure 15

B3LYP/6‐31G(d)‐optimized structures of 4,5‐indolyne, 5,6‐indolyne, 6,7‐indolyne, and the transition structures (TS56 and TS57) for the addition of aniline to 4,5‐indolyne.

Figure 16

Optimized structures of 3‐methoxybenzyne and 3‐methoxycyclohexyne obtained using M06‐2X/6‐311+G(2d,p) and PCM(THF). The sites of the nucleophilic attack are shown.

Figure 17

Energy terms involved in Marcus theory (left) in comparison to the D/I model (right).

Scheme 3

Oxidative addition by direct oxidative insertion (OxIn) or by nucleophilic substitution (S_N2).

Figure 18

Activation strain model for solution‐phase reactions with solute–solvent interactions: a) The vacuum PES of the solute reaction system ΔE _solute plus the solvation interaction between the solute and solvent ΔE _solvation yield the solution‐phase PES ΔE _solution. b) The vacuum PES of the solubilized reaction system is analyzed by decomposing into the strain and interaction.

Figure 19

Left: Energy diagram for an intramolecular reaction. Right: distortion/interaction model for an intramolecular reaction with the tether removed.