Model studies of force-dependent kinetics of multi-barrier reactions

Abstract

According to transition state theory, the rate of a reaction that traverses multiple energy barriers is determined by the least stable (rate-determining) transition state. The preceding ('inner') energy barriers are kinetically 'invisible' but mechanistically significant. Here we show experimentally and computationally that the reduction rate of organic disulphides by phosphines in water, which in the absence of force proceeds by an equilibrium formation of a thiophosphonium intermediate, measured as a function of force applied on the disulphide moiety yields a usefully accurate estimate of the height of the inner barrier. We apply varying stretching force to the disulphide by incorporating it into a series of increasingly strained macrocycles. This force accelerates the reduction, even though the strain-free rate-determining step is orthogonal to the pulling direction. The observed rate-force correlation is consistent with the simplest model of force-dependent kinetics of a multibarrier reaction.

Mechanical gating of a mechanochemical reaction cascade

“…2 were calculated at the uMPW1K/6-311+G(d) level of the DFT in CPCM model of the reaction solvent using complete conformational ensembles in pseudo-harmonic approximation3563. The model chemistry was chosen because it reproduced the experimental free energies of activation of isomerization of cis -2,3-dimethyl-1,1-dichlorocyclopropane in DMF and diphenyl ether, and of the electronic activation energies of dissociation of cis cyclobutane-1,2-dicarboxylic acid and isomerization of cis -2,3-dimethyl-1,1-dichlorocyclopropane in vacuum calculated at the uCCSD/6-31G(d)//uCCSD/jun-cc-pVTZ and uCCSD/6-311+G(d)//uCCSD(T)/jun-cc-pVTZ levels of theory, respectively (Supplementary Tables 1 and 4).…”

“…Both experimental672427303132333435363738 and theoretical2939404142434445464748 studies have been conducted to understand force-coupled reactivity and mechanisms, and these investigations provide valuable insights into the design of mechanophore response. One concept for a useful reactivity response is mechanochemical gating, in which one mechanophore (a molecular gate) initially prevents another mechanophore (substrate) from experiencing force delivered along a polymer backbone.…”

Molecular Mechanochemistry: Engineering and Implications of Inherently Strained Architectures

“…This is because the relative energy of the rate-determining transition state (one of the two transition states) and therefore the activation free energy are hardly affected by force. More recently, the same group reported the reduction of organic disulfides that were also incorporated in stiff stilbene based macrocycles by phosphines in water [108]. The reaction involves two steps: (1) the reactants go through transition state 1 to yield a thiophosphonium intermediate, which is a force-dependent step; (2) the intermediate proceeds over transition state 2 and gives the products, which is the ratedetermining step in the absence of force and depends on pH.…”

“…In addition, there are several advantages of the macrocyclic force probe. First, it is compatible with a broad range of functional groups, including cyclobutane [44,106], cyclopropane [103], disulfide [107,108], sulfonate [109], ester [110], and catalytic ligand [111], which allows investigation into various chemical reactions. Second, the restoring force can be adjusted by varying the length and/or conformational flexibility of the linker, up to hundreds of pico-Newtons (Fig.…”

Polymer Mechanochemistry

“…When the force in (1) is defined as the restoring force of an internal molecular degree of freedom, it is plausible to equate the first-order (∂G/∂f ) and second order (∂ 2 G/∂f 2 ) Taylor coefficients to the strain-free values of this molecular coordinate and of its harmonic compliance, The validity of the Taylor-expansion approach is typically tested computationally by comparing ΔG ǂ correlations calculated explicitly with the values predicted by (1) truncated at the second order using either single-conformer or ensembleaveraged distances and compliances of various internal coordinates in the strainfree initial and transition states. These tests indicate that the predictive capacity of the Taylor expansion approach depends critically on the selection of the internal molecular coordinate whose restoring force is used in the equation [26][27][28]. Fortunately, it appears that the same type of coordinate is appropriate for all reactions of the same mechanism (e.g., S N 2 displacements) [29].…”