Nonstatistical dynamics on the caldera

Abstract

We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations at several different energies confirm the existence of the "dynamical matching" phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a "stretched" version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the "dynamical matching" phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.

Labelling and determination of the energy in reactive intermediates in solution enabled by energy-dependent reaction selectivity

“…The second is that it is possible under some circumstances to control the behavior of reactive intermediates through the choice of their synthesis. This was already clear from Carpenter’s work on dynamic matching, 11 but the current work greatly expands the possibilities since there is no required involvement of nonstatistical dynamics. A third implication is that the interpretation of experimental observations such as isotope effects or other selectivity from short-lived reactive intermediates may need to consider the history of the intermediate.…”

“…A more interesting potential source of error is that the ring opening of 1 may be subject to non-statistical dynamics. 10,11,12,13,26 That is, the short lifetime of 1 may not allow sufficient time for statistical IVR. This would violate a central assumption inherent in the RRKM predictions.…”

“…The nonstatistical energy distribution after a transition state can also steer the products derived from short-lived intermediates to provide memory effects, either through the selective activation of a part of a molecule 10 or by the process of dynamic matching. 11, We have previously shown how the consideration of the amount of excess energy and its distribution is required to understand the reactions of intermediates in solution. 12,13 …”

Stereoselectivity in a series of 7‐alkylbicyclo[3.2.0]hept‐2‐enes: Experimental and computational perspectives

“…The observed lack of epimerization in the 7‐alkylbicyclo[3.2.0]hept‐2‐enes might be attributed to (1) a significant difference in energy between the endo and exo stereoisomers that favors the exo epimer thermodynamically and/or (2) as Carpenter suggested, the presence of rotational bias from the angular momentum following the breaking of the C1‐C7 bond . A comparison of the computational enthalpy of formation values (Tables and S3) shows that for most of the alkyl substituents, the endo epimer is actually lower in energy.…”

“…Although Carpenter proposes that these diradical species possess small amounts of excess energy, the “exact distribution” of this energy is highly influential on the product distributions. Carpenter and collaborators have also correlated this “dynamic matching” phenomenon of a preferred exit channel related to the initial trajectory of the bond cleavage with a quantum mechanical analog, whereby the momentum of the probability electron density dictates the product outcome. This analysis is consistent with Carpenter's earlier assessment that the si product would form preferentially to the sr product in the [1,3] sigmatropic rearrangement of exo ‐7‐methylbicyclo[3.2.0]hept‐2‐ene.…”