Non-linear Effects in Asymmetric Catalysis: Whys and Wherefores

Sosale Chandrasekhar

doi:10.1038/npre.2012.6947.1

Abstract

AbstractIt is argued that the titled non-linear effects (NLE) may arise whenever the order of the reaction in the chiral catalyst in greater than 1. In a fundamental departure from previous approaches, this is mathematically elaborated for the second order case. (NLE may also be observed if the chiral catalyst forms non-reacting dimers in a competing equilibrium; practically, however, this implies the in situ resolution of the catalyst.) The amplification of enantiomeric excess by NLE implies a relative (although modest) reduction in the entropy of mixing. The consequent increase in free energy apparently indicates a non-equilibrium process. It is suggested, based on arguments involving the chemical potential, that kinetically-controlled reactions lead to a state of “quasi-equilibrium”: in this, although overall equilibrium is attained, the product-spread is far from equilibrium. Thus, both the linear and NLE cases of chiral catalysis represent departures from equilibrium (which requires that the product e.e. = 0). Interesting similarities exist with models of non-equilibrium systems, the NLE cases apparently being analogs of open systems just after the bifurcation point has been crossed.

Highlights

The enhancement of enantiomeric excess (e.e.) is justly a cause for jubilation, but sometimes, for concern too! Whilst asymmetric syntheses clearly aim for the highest possible e.e.’s, unsolicited enhancements of e.e. raise intriguing conceptual issues
Thermodynamic stability is represented by e.e. = 0, and a departure from this theoretical comfort zone implies a higher level of order: it is incumbent on the investigator to explain the origin of the apparent increase in free energy content, and the nature of the intervention that brought it about
The rates of formation of the two enantiomeric products, PR and PS in the reaction in Scheme 1, would be given by eqs. 1 and 2. (We note that two molecules of catalyst are involved in the reaction, the second order dependence, the k’s being rate constants; the treatment extends previous ones as explained in the S.I. section.)[1,2] For the sake of simplicity, at this stage, it is assumed that the reaction of substrate (S) with CR yields only PR, and with CS only PS, i.e. 100% enantioselectivity; CR and CS do not act in concert. (All this implies that only CRMCR and CSMCS react with total selectivity, and that CRMCS is completely unreactive.)

Summary

INTRODUCTION

The enhancement of enantiomeric excess (e.e.) is justly a cause for jubilation, but sometimes, for concern too! Whilst asymmetric syntheses clearly aim for the highest possible e.e.’s, unsolicited enhancements of e.e. raise intriguing conceptual issues. Such examples can be mediated by complexation of two molecules of the chiral catalyst – usually with a metal ion – prior to the reaction (Scheme 1). This leads to the formation of all three diastereomeric dimeric complexes (CR and CS are the enantiomeric catalysts, and M a metal ion): CRMCR, CSMCS and CRMCS. These are, the effective catalytic species in the reaction. These cases, apparently involve a prior in situ resolution of the catalyst, and are considered only briefly further below

RESULTS AND DISCUSSION

CONCLUSIONS

A Critical Assessment of Previous Approaches