Mirror-symmetry breaking in the Soai reaction: a kinetic understanding

Abstract

Kinetic modeling using nonlinear differential equations is proposed to analyze the spontaneous generation of enantiomeric excess in the autocatalytic addition of diisopropylzinc to prochiral pyrimidine carbaldehydes (Soai reaction). Our approach reproduces experimentally observed giant chiral amplification from an initial enantiomeric excess of <10(-6)% to >60%, high sensitivity and positive response to the presence of minute amounts of chiral initiator at concentrations <10(-14) M, and spontaneous absolute asymmetric synthesis from achiral starting conditions. From our numerical simulations using kinetic schemes derived from the Frank model, including stereospecific autocatalysis and mutual inhibition, we have shown that it is possible to reproduce the mirror-symmetry-breaking behavior of the Soai reaction under batch conditions leading to a bimodal enantiomeric product distribution. Mirror-symmetry breaking was found to be resistant to a loss of stereoselectivity up to 30%. While the mutual inhibition between enantiomers seems to originate from the presence of dimerization equilibria, the exact nature of the autocatalytic stereoselective process still remains to be revealed. From the kinetic viewpoint, simple autocatalysis involving monomers as the catalytic species is consistent with all reported experimental effects of the Soai reaction.

Scheme 1.

The Soai reaction. R = H, CH₃, t-Bu–CC–, or (CH₃)₃Si–CC–.

Fig. 1.

Time evolution of the involved species in model 1, illustrating the consequence of mirror-symmetry breaking in a typical simulation starting from achiral conditions and by using an appropriate set of parameters: [A]₀ = 1 M, [R]₀ = [S]₀ = 0, k₀ = 10^–6 s^–1, k₁ = 1 M^–1·s^–1, and k₂ = 100 M^–1·s^–1.

Fig. 2.

Mirror-symmetry breaking and amplification of ee in model 1. [A]₀ = 1 M, k₀ = 10^–6 M^–1·s^–1, k₁ = 1 M^–1·s^–1 and μ = 1. Curve A, [R]₀ = [S]₀ = 0 (no catalyst added); curve B, [R]₀ = 5.05 × 10^–3 M and [S]₀ = 4.95 × 10^–3 M (1% of catalyst, ee = 1%); curve C, [R]₀ = 5.50 × 10^–3 M and [S]₀ = 4.50 × 10^–3 M (1% of catalyst, ee = 10%); curve D, [R]₀ = 4.95 × 10^–2 M and [S]₀ = 5.05 × 10^–2 M (10% of catalyst, ee = –1%; note that because of a dilution effect by the high autocatalyst concentration the final ee does not reach –100%). For the sake of clarity data points corresponding to curves B, C, and D have been smoothed.

Fig. 3.

Predicted molecular structures of the heterochiral dimer RS (Left), kcal·mol^–1 and of the homochiral dimer SS or RR (Right), kcal·mol^–1.

Fig. 4.

Aldehyde consumption vs. time in an NMR-monitored Soai reaction (○) (ref. 16) fitted by model 2 (continuous line) and by model 3 (broken line). Initial concentrations (M): [A] = 1.92 × 10^–2 and [Z] = 0.04; rate parameters model 2 {model 3}: k₀′ = 5.2 × 10^–3 {3.7 × 10^–3} M^–1·s^–1; k₁′ = 69 M^–2·s^–1 {k₆ = 154 M^–2·s^–1, k₇ = 2.1 × 10^–4 M^–2·s^–1}; k₂ = 4.5 × 10⁵ {9.2 × 10⁵} M^–1·s^–1; k₃ = 5.2 × 10^–2 {6.4 × 10^–4} s^–1; k₄ = 4.8 × 10³ {1.1 × 10⁴} M^–1·s^–1; and k₅ = 21 {6.4 × 10^–4} s^–1. The first seven data points have not been taken into account.

Fig. 5.

Effect of catalyst enantiomeric purity. (a) Simulated reaction heat flows vs. time by model 2. Continuous line, enantiopure catalyst; dotted line, racemic catalyst. The relation between the heat flow maxima is around 50%. (b) Normalized heat flows vs. fraction conversion. The enantiopure and racemic catalyst curves are nearly superimposed. (c) Percent ee vs. fraction conversion for the case ee(cat) = 43%; ▪, experimental results from ref. . For all simulations, the rate constants were the same as in Fig. 4 except k₃ = 1.0 × 10² s^–1; [A]₀ = [Z]₀ = 0.2 M; and [R}₀ + [S]₀ = 2.0 × 10^–2 M.