Revisiting Textbook Azide-Clock Reactions: A “Propeller-Crawling” Mechanism Explains Differences in Rates

An ongoing challenge to chemists is the analysis of pathways and kinetics for chemical reactions in solution, including transient structures between the reactants and products that are difficult to resolve using laboratory experiments. Here, we enabled direct molecular dynamics simulations of a textbook series of chemical reactions on the hundreds of ns to μs time scale using the weighted ensemble (WE) path sampling strategy with hybrid quantum mechanical/molecular mechanical (QM/MM) models. We focused on azide-clock reactions involving addition of an azide anion to each of three long-lived trityl cations in an acetonitrile–water solvent mixture. Results reveal a two-step mechanism: (1) diffusional collision of reactants to form an ion-pair intermediate; (2) “activation” or rearrangement of the intermediate to the product. Our simulations yield not only reaction rates that are within error of experiment but also rates for individual steps, indicating the activation step as rate-limiting for all three cations. Further, the trend in reaction rates is due to dynamical effects, i.e., differing extents of the azide anion “crawling” along the cation’s phenyl-ring “propellers” during the activation step. Our study demonstrates the power of analyzing pathways and kinetics to gain insights on reaction mechanisms, underscoring the value of including WE and other related path sampling strategies in the modern toolbox for chemists.

Figure S2: Overall workflow of the weighted ensemble (WE) strategy.The weighted ensemble (WE) strategy involves running multiple trajectories in parallel and iteratively evaluating trajectories for resampling after a short time interval τ .Configurational space is divided into bins along a progress coordinate and the goal of the resampling procedure is to split or merge trajectories to yield a target number of trajectories per bin.Trajectory weights (indicated by circle sizes) are rigorously tracked such that no statistical bias is introduced in the dynamics, enabling direct calculation of rates from the simulation.For each of the reactions in this study, five WE simulations were initialized from five structures randomly selected from a set of 50 unassociated-reactant configurations sampled by a conventional simulation and run for N = 500 iterations with a two-dimensional progress coordinate, τ = 0.5 ps, and a target number of 5 trajectories/bin to generate a sufficient number of pathways to yield statistically robust rates (see Methods).Table S1: Computed rate constants for azide addition to each of the three cations.Rate constants were directly computed from WE simulations and reported as averages from five independent WE simulations with uncertainties that each represent the 95% credibility region from Bayesian Bootstrapping. 1 Overall reaction rate constants (k rxn ) from experiment were previously measured by others using laser-flash photolysis. 2 experiment simulation cation Movies S1-S3: Movies of the most probable reaction pathways for addition of azide anion to the (S1) 4-OCH 3 -T + , (S2) T + , and (S3) 4-CF 3 -T + cations.These movies reveal a greater range of azide crawling among the three phenyl-ring "propellers" of the cation for the lessreactive 4-OCH 3 -T + cation relative to the T + and 4-CF 3 -T + cations.

Figure S3 :
Figure S3: Progress coordinate, state definitions, and binning scheme used for WE simulations of the azide-clock reactions.As mentioned in Methods, we used a two-dimensional progress coordinate consisting of the minimum separation distance between any nitrogen of the azide anion and (i) the central carbon of the cation, and (ii) any carbon of the cation.Shaded regions indicate state definitions for the reactants (pink), ion-pair intermediate (purple), and product (blue).Bins were positioned every 1 Å from 4 Å to 22 Å along the first dimension and from 4 Å to 5 Å in the second dimension.To focus sampling on the ratelimiting activation step involving rearrangement of the ion-pair intermediate to the product, a radial binning scheme was used for the region between 1.6 Å and 4 Å in both dimensions, positioning radial bins from (1.6 Å, 1.6 Å) to (4 Å, 4 Å) at 1 o intervals.

Figure S4 :
FigureS4: Time evolution of k rxn for azide addition to each cation.A cumulative average of k rxn for each reaction shows that the rate constants begin to level off after 250 ps (500 WE iterations).The jump in the rate-constant estimate at 251 ps (WE iteration 501) is due to reweighting for a steady state using the WESS procedure.After reweighting, 50 ps (100 WE iterations) of additional simulation reveals that the rate constant average levels off further, suggesting our estimates are reaching convergence.

Figure
Figure S5: (A)Resonance models predict the dominant product to involve addition to the central carbon atom of the cation.Addition to various phenyl "propeller" carbons is possible, but would form an unstable product with a nonaromatic ring.(B) Ratios of probabilities for azide addition to propeller carbons relative to addition to the central carbon of the cation calculated from WE simulation.

Figure S6 :
Figure S6: Each dendrogram (tree diagram) reveals clusters of pathways that are more related to each other than to other pathways in terms of sequence of configurations visited (see Methods).To obtain distinct classes of pathways, a horizontal line (dashed line) was positioned to maximize the distance separation between nodes in the dendrogram.