Mechanisms and Dynamics of Reactions Involving Entropic Intermediates

Unlike conventional intermediates that are local minima on a PES, entropic intermediates involve a flat region on the potential surface (favorable entropically) and the necessity to decrease entropy to exit from this region of the PES. Entropic intermediates are not potential energy minima. We have proposed timing criteria to differentiate dynamically concerted from dynamically stepwise reactions. A mechanism is described as dynamically concerted if all bonding changes are complete in less than 60 fs, but dynamically stepwise otherwise. This criterion is complementary to the usual definition of concerted based on potential energy surface (one or two barriers). Entropic intermediates are often involved in dynamically stepwise reactions. An entropic intermediate is defined as a free energy minimum that is not a potential energy minimum; the favorable entropy in this region of the potential surface is responsible for the increased lifetime of this species. Enabled by molecular dynamics simulations, entropic intermediates have been identified for several types of reactions, particularly pericyclic reactions. This review highlights recent advances in the mechanistic and dynamic investigations of organic and biosynthetic pericyclic reactions that involve entropic intermediates. We have proposed timing criteria to differentiate dynamically concerted from dynamically stepwise mechanisms. These criteria complement the usual definitions of concertedness based on energetics and bonding changes along the potential surface. An entropic intermediate is defined as a free energy minimum that is not a potential energy minimum; the favorable entropy in this region of the potential surface is responsible for the increased lifetime of this species. Enabled by molecular dynamics simulations, entropic intermediates have been identified for several types of reactions, particularly pericyclic reactions. This review highlights recent advances in the mechanistic and dynamic investigations of organic and biosynthetic pericyclic reactions that involve entropic intermediates. We have proposed timing criteria to differentiate dynamically concerted from dynamically stepwise mechanisms. These criteria complement the usual definitions of concertedness based on energetics and bonding changes along the potential surface. a new chemical species AB, each molecular entity of which is formed by direct combination of two separate molecular entities A and B in such a way that there is change in connectivity, but no loss, of atoms within the moieties A and B. [IUPAC Gold Book (https://doi.org/10.1351/goldbook.A00138)]. there is some difference in the English meaning (occurring at different times or the same time, respectively) and how this word is used in chemistry. First we give the IUPAC definition: a concerted process in which the primitive changes concerned (generally bond rupture and bond formation) have progressed to the same extent at the transition state is said to be synchronous. The term figuratively implies a more or less synchronized progress of the changes. However, the progress of the bonding change (or other primitive change) has not been defined quantitatively in terms of a single parameter applicable to different bonds or different bonding changes. The concept is therefore in general only qualitatively descriptive and does not admit an exact definition except in the case of concerted processes involving changes in two identical bonds. [IUPAC Gold Book (https://doi.org/10.1351/goldbook.S06219)]. This is basically the definition used by Dewar [36Dewar M.J.S. Studies of the mechanisms of some organic reactions and photoreactions by semiempirical SCF MO methods.Faraday Discuss. Chem. Soc. 1977; 62: 197-209Crossref Google Scholar], but a proper use of the term would be to equate synchronous to our dynamically concerted, and asynchronous to our dynamically stepwise. This however, is not the general usage of this terminology at this time. (or post-transition state bifurcation); ‘a bifurcating surface is one for which a single transition-state structure leads to two products. For such a situation, intrinsic reaction coordinate (IRC) calculations often indicate that this transition-state structure is directly connected to a second transition-state structure that is itself connected directly to both of the two products. In some cases where bifurcations are suspected, reaction coordinates generated in this way lead directly to one product, but flat plateau regions are often encountered along such a pathway. Navigating along a bifurcating surface presents a molecule with a choice as to which branch of the bifurcating pathway to follow, a more complicated situation than following a surface with a single pathway downhill from a transition-state structure, and a choice that determines which product will ultimately predominate’ [82Hong Y.J. Tantillo D.J. A potential energy bifurcation in terpene biosynthesis.Nat. Chem. 2009; 1: 384-389Crossref PubMed Scopus (95) Google Scholar]. two or more primitive changes are said to be concerted (or to constitute a concerted process) if they occur within the same elementary reaction. Such changes will normally (though perhaps not inevitably) be ‘energetically coupled’. (In the present context the term ‘energetically coupled’ means that the simultaneous progress of the primitive changes involves a transition state of lower energy than that for their successive occurrence). In a concerted process the primitive changes may be synchronous or asynchronous. [IUPAC Gold Book (https://doi.org/10.1351/goldbook.C01234)]. the Cope rearrangement is the thermal isomerization of a 1,5-diene leading to an isomeric 1,5-diene. The main product is the thermodynamically more stable regioisomer. the formation of a cyclohexene from the cycloaddition of a diene and a dienophile (alkene, alkyne, or hetero analog). The reaction may be concerted or stepwise. a 5-alkylidenecyclopentadiene. the effect of isotopic substitution on a rate constant is referred to as a kinetic isotope effect. For example, in the reaction of A + B to C, the effect of isotopic substitution in reactant A is expressed as the ratio of rate constants kl/kh, where the superscripts l and h represent reactions in which the molecules A contain the light and heavy isotopes, respectively. Within the framework of transition state theory and with neglect of isotopic mass on tunneling and the transmission coefficient, kl/kh can be regarded as if it were the equilibrium constant for an isotope exchange reaction between the transition state [TS]‡ and the isotopically substituted reactant A, and calculated from their vibrational frequencies as in the case of a thermodynamic isotope effect. Isotope effects like the above, involving a direct or indirect comparison of the rates of reaction of isotopologues, are called ‘intermolecular’, in contrast to intramolecular isotope effects, in which a single substrate reacts to produce a non-statistical distribution of isotopomeric product molecules [IUPAC Gold Book (https://doi.org/10.1351/goldbook.K03405)]. a reaction in which all bonding changes occur in concert on a closed curve. (synonymous with energy hypersurface); a geometric hypersurface on which the potential energy of a set of reactants is plotted as a function of the coordinates representing the molecular geometries of the system. Such a diagram is often arranged so that reactants are located at the bottom left corner and products at the top right. the aliphatic Claisen rearrangement is a [3,3]-sigmatropic rearrangement in which an allyl vinyl ether is converted thermally to a 4-pentenal. in Evans-Polayni or Eyring theories describing elementary reactions it is usually assumed that there is a transition state between the reactants and the products through which an assembly of atoms (initially composing the molecular entities of the reactants) must pass on going from reactants to products in either direction. In the formalism of ‘transition state theory’ the transition state of an elementary reaction is that set of states (each characterized by its own geometry and energy) in which an assembly of atoms, when randomly placed there, would have an equal probability of forming the reactants or of forming the products of that elementary reaction. The transition state is characterized by one and only one imaginary frequency (corresponding to a negative force constant). Adapted from the IUPAC Gold Book (https://doi.org/10.1351/goldbook.T06468).