Equilibrium of Homochiral Oligomerization of a Mixture of Enantiomers. Its Relevance to Nonlinear Effects in Asymmetric Catalysis

Kinetic Rationalization of Nonlinear Effects in Asymmetric Catalytic Cascade Reactions under Curtin-Hammett Conditions

Observations of nonlinear effects of catalyst enantiopurity on product enantiomeric excess in asymmetric catalysis are often used to infer that more than one catalyst species is involved in one or more reaction steps. We demonstrate here, however, that in the case of asymmetric catalytic cascade reactions, a nonlinear effect may be observed in the absence of any higher order catalyst species or any reaction step involving two catalyst species. We illustrate this concept with an example from a recent report of an organocatalytic enantioselective [10 + 2] stepwise cyclization reaction. The disruption of pre-equilibria (Curtin-Hammett equilibrium) in reversible steps occurring prior to the final irreversible product formation step can result in an alteration of the final product ee from what would be expected based on a linear relationship with the enantiopure catalyst. The treatment accounts for either positive or negative nonlinear effects in systems over a wide range of conditions including "major-minor" kinetics or the more conventional "lock-and-key" kinetics. The mechanistic scenario proposed here may apply generally to other cascade reaction systems exhibiting similar kinetic features and should be considered as a viable alternative model whenever a nonlinear effect is observed in a cascade sequence of reactions.

Data Science Meets Physical Organic Chemistry

ConspectusAt the heart of synthetic chemistry is the holy grail of predictable catalyst design. In particular, researchers involved in reaction development in asymmetric catalysis have pursued a variety of strategies toward this goal. This is driven by both the pragmatic need to achieve high selectivities and the inability to readily identify why a certain catalyst is effective for a given reaction. While empiricism and intuition have dominated the field of asymmetric catalysis since its inception, enantioselectivity offers a mechanistically rich platform to interrogate catalyst-structure response patterns that explain the performance of a particular catalyst or substrate.In the early stages of an asymmetric reaction development campaign, the overarching mechanism of the reaction, catalyst speciation, the turnover limiting step, and many other details are unknown or posited based on related reactions. Considering the unclear details leading to a successful reaction, initial enantioselectivity data are often used to intuitively guide the ultimate direction of optimization. However, if the conditions of the Curtin-Hammett principle are satisfied, then measured enantioselectivity can be directly connected to the ensemble of diastereomeric transition states (TSs) that lead to the enantiomeric products, and the associated free energy difference between competing TSs (ΔΔG⧧ = -RT ln[(S)/(R)], where (S) and (R) represent the concentrations of the enantiomeric products). We, and others, speculated that this important piece of information can be leveraged to guide reaction optimization in a quantitative way.Although traditional linear free energy relationships (LFERs), such as Hammett plots, have been used to illuminate important mechanistic features, we sought to develop data science derived tools to expand the power of LFERs in order to describe complex reactions frequently encountered in modern asymmetric catalysis. Specifically, we investigated whether enantioselectivity data from a reaction can be quantitatively connected to the attributes of reaction components, such as catalyst and substrate structural features, to harness data for asymmetric catalyst design.In this context, we developed a workflow to relate computationally derived features of reaction components to enantioselectivity using data science tools. The mathematical representation of molecules can incorporate many aspects of a transformation, such as molecular features from substrate, product, catalyst, and proposed transition states. Statistical models relating these features to reaction outputs can be used for various tasks, such as performance prediction of untested molecules. Perhaps most importantly, statistical models can guide the generation of mechanistic hypotheses that are embedded within complex patterns of reaction responses. Overall, merging traditional physical organic experiments with statistical modeling techniques creates a feedback loop that enables both evaluation of multiple mechanistic hypotheses and future catalyst design. In this Account, we highlight the evolution and application of this approach in the context of a collaborative program based on chiral phosphoric acid catalysts (CPAs) in asymmetric catalysis.

Hyperpositive non-linear effects: enantiodivergence and modelling

The chiral ligand N-methylephedrine (NME) was found to catalyse the addition of dimethylzinc to benzaldehyde in an enantiodivergent way, with a monomeric and a homochiral dimeric complex both catalysing the reaction at a steady state and giving opposite product enantiomers. A change in the sign of the enantiomeric product was thus possible by simply varying the catalyst loading or the ligand ee, giving rise to an enantiodivergent non-linear effect. Simulations using a mathematical model confirmed the possibility of such behaviour and showed that this can lead to situations where a reaction gives racemic products, although the system is composed only of highly enantioselective individual catalysts. Furthermore, depending on the dimer's degree of participation in the catalytic conversion, enantiodivergence may or may not be observed experimentally, which raises questions about the possibility of enantiodivergence in other monomer/dimer-catalysed systems. Simulations of the reaction kinetics showed that the observed kinetic constant k_obs is highly dependent on user-controlled parameters, such as the catalyst concentration and the ligand ee, and may thus vary in a distinct way from one experimental setup to another. This unusual dependency of k_obs allowed us to confirm that a previously observed U-shaped catalyst order vs. catalyst loading-plot is linked to the simultaneous catalytic activity of both monomeric and dimeric complexes.

An asymmetric reaction consisting of competing monomeric and dimeric catalysts may explain enantiodivergent non-linear effects.

Supramolecular Chiral Aggregates Exhibiting Nonlinear CD-ee Dependence

Although a linear relationship between the optical activity (normally the CD signal) and the enantiomeric excess (ee) of chiral auxiliaries has been the most commonly observed dependence in dynamic supramolecular helical aggregates, positive nonlinear CD-ee dependence, known as the "majority-rules effect" (MRE), indicative of chiral amplification, has also been well documented and to some extent understood. In sharp contrast, the negative nonlinear CD-ee dependence has been much less reported and is not well understood. Here, the state of the art of both the positive and negative nonlinear CD-ee dependence in noncovalently bound supramolecular helical aggregates is summarized, with the hope that the vast examples of supramolecular aggregates showing positive nonlinear dependence, in terms of the methods of investigations, variations in the structure of the building block (single species or multiple species), and theoretical modeling using the mismatch penalty energy and helix reversal penalty energy, would help to guide the design of building blocks to form aggregates showing negative nonlinear dependence, and thus to understand the mechanisms. The potential applications of those functional supramolecular aggregates are also discussed.

Requiem for the Rate-Determining Step in Complex Heterogeneous Catalytic Reactions?

The concept of the rate determining step, i.e., the step having the strongest influence on the reaction rate or even being the only one present in the rate equation, is often used in heterogeneous catalytic reactions. The utilization of this concept mainly stems from a need to reduce complexity in deriving explicit rate equations or searching for a better catalyst based on the theoretical insight. When the aim is to derive a rate equation with eventual kinetic modelling for single-route mechanisms with linear sequences, the analytical rate expressions can be obtained based on the theory of complex reactions. For such mechanisms, a single rate limiting step might not be present at all and the common practice of introducing such steps is due mainly to the convenience of using simpler expressions. For mechanisms with a combination of linear and nonlinear steps or those just comprising non-linear steps, the reaction rates are influenced by several steps depending on reaction conditions, thus a reduction in complexity to a single rate limiting step can lead to misinterpretations. More widespread utilization of a microkinetic approach when the reaction rate constants can be computed with reasonable accuracy based on the theoretical insight, and availability of software for kinetic modelling, when a system of differential equations for reactants and products will be solved together with differential equations for catalytic species and the algebraic conservation equation for the latter, will eventually make the concept of the rate limiting step obsolete.

Possible Physical Basis of Mirror Symmetry Effect in Racemic Mixtures of Enantiomers: From Wallach’s Rule, Nonlinear Effects, B–Z DNA Transition, and Similar Phenomena to Mirror Symmetry Effects of Chiral Objects

Effects associated with mirror symmetry may be underlying for a number of phenomena in chemistry and physics. Increase in the density and melting point of the 50%L/50%D collection of enantiomers of a different sign (Wallach’s rule) is probably based on a physical effect of the mirror image. The catalytic activity of metal complexes with racemic ligands differs from the corresponding complexes with enantiomers as well (nonlinear effect). A similar difference in the physical properties of enantiomers and racemate underlies L/D inversion points of linear helical macromolecules, helical nanocrystals of magnetite and boron nitride etc., B–Z DNA transition and phenomenon of mirror neurons may have a similar nature. Here we propose an explanation of the Wallach effect along with some similar chemical, physical, and biological phenomena related to mirror image.

Enantioselective copper-catalyzed azide-alkyne click cycloaddition to desymmetrization of maleimide-based bis(alkynes)

A copper catalyst system derived from TaoPhos and CuF2 was used successfully for catalytic asymmetric Huisgen [3+2] cycloaddition of azides and alkynes to give optically pure products containing succinimide- and triazole-substituted quaternary carbon stereogenic centers. The desired products were obtained in good yields (60-80 %) and 85:15 to >99:1 enantiomeric ratio (e.r.) in this click cycloaddition reaction.

Theoretical models of nonlinear effects in two-component cooperative supramolecular copolymerizations

The understanding of multi-component mixtures of self-assembling molecules under thermodynamic equilibrium can only be advanced by a combined experimental and theoretical approach. In such systems, small differences in association energy between the various components can be significantly amplified at the supramolecular level via intricate nonlinear effects. Here we report a theoretical investigation of two-component, self-assembling systems in order to rationalize chiral amplification in cooperative supramolecular copolymerizations. Unlike previous models based on theories developed for covalent polymers, the models presented here take into account the equilibrium between the monomer pool and supramolecular polymers, and the cooperative growth of the latter. Using two distinct methodologies, that is, solving mass-balance equations and stochastic simulation, we show that monomer exchange accounts for numerous unexplained observations in chiral amplification in supramolecular copolymerization. In analogy with asymmetric catalysis, amplification of chirality in supramolecular polymers results in an asymmetric depletion of the enantiomerically related monomer pool.

Enantiomeric self-recognition in homo- and heterodinuclear macrocyclic lanthanide(III) complexes

The controlled formation of lanthanide(III) dinuclear μ-hydroxo-bridged [Ln(2)L(2)(μ-OH)(2)X(2)](n+) complexes (where X = H(2)O, NO(3)(-), or Cl(-)) of the enantiopure chiral macrocycle L is reported. The (1)H and (13)C NMR resonances of these complexes have been assigned on the basis of COSY, NOESY, TOCSY, and HMQC spectra. The observed NOE connectivities confirm that the dimeric solid-state structure is retained in solution. The enantiomeric nature of the obtained chiral complexes and binding of hydroxide anions are reflected in their CD spectra. The formation of the dimeric complexes is accompanied by a complete enantiomeric self-recognition of the chiral macrocyclic units. The reaction of NaOH with a mixture of two different mononuclear lanthanide(III) complexes, [Ln(1)L](3+) and [Ln(2)L](3+), results in formation of the heterodinuclear [Ln(1)Ln(2)L(2)(μ-OH)(2)X(2)](n+) complexes as well as the corresponding homodinuclear complexes. The formation of the heterodinuclear complex is directly confirmed by the NOESY spectra of [EuLuL(2)(μ-OH)(2)(H(2)O)(2)](4+), which reveal close contacts between the macrocyclic unit containing the Eu(III) ion and the macrocyclic unit containing the Lu(III) ion. While the relative amounts of homo- and heterodinuclear complexes are statistical for the two lanthanide(III) ions of similar radii, a clear preference for the formation of heterodinuclear species is observed when the two mononuclear complexes contain lanthanide(III) ions of markedly different sizes, e.g., La(III) and Yb(III). The formation of heterodinuclear complexes is accompanied by the self-sorting of the chiral macrocyclic units based on their chirality. The reactions of NaOH with a pair of homochiral or racemic mononuclear complexes, [Ln(1)L(RRRR)](3+)/[Ln(2)L(RRRR)](3+), [Ln(1)L(SSSS)](3+)/[Ln(2)L(SSSS)](3+), or [Ln(1)L(rac)](3+)/[Ln(2)L(rac)](3+), results in mixtures of homochiral, homodinuclear and homochiral, heterodinuclear complexes. On the contrary, no heterochiral, heterodinuclear complexes [Ln(1)L(RRRR)Ln(2)L(SSSS)(μ-OH)(2)X(2)](n+) are formed in the reactions of two different mononuclear complexes of opposite chirality.