Bond breaking in a Morse chain under tension: Fragmentation patterns, higher index saddles, and bond healing

Influence of second-order saddles on reaction mechanisms

The transition state, a first-order saddle point on the potential energy surface, plays a central role in understanding the mechanism, dynamics, and rate of chemical reactions. However, we recently identified...

Can reactions follow non-traditional second-order saddle pathways avoiding transition states?

We report here an ab initio (CASSCF/6-31+G*) trajectory simulation study on the mechanisms of the denitrogenation of 1-pyrazoline and its subsituted analogue that reveals reaction pathways via a high energy second-order saddle (SOS) region. This mechanism involves the molecule adopting a five-membered planar structure contrary to the traditional boat-like transition state. The SOS offers a trifurcation point where a pathway branches into three, different from the single pathway associated with a transitions state. We observe that the molecules following the SOS path exhibit distinctive dynamical features and form products with high translational energies and low rotational energies compared to those following the traditional pathways. In addition, the SOS pathway provides an alternative mechanism for the formation of stereo-selective products. Interestingly, although the reaction proceeds via a trimethylene diradical intermediate, the simulations show that the product cyclopropane is formed with a major single inversion of the configuration consistent with experimental observations. They also reveal mechanisms that do not follow the minimum energy paths and exhibit non-statistical dissociation dynamics.

The phase space geometry underlying roaming reaction dynamics

Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable amount of time and extracts another hydrogen atom from the molecule prior to dissociation. This phenomenon has been coined roaming and has since been reported in the dissociation of a number of other molecules. In this paper we investigate roaming in Chesnavich's CH 4 + model. During dissociation the free hydrogen must pass through three phase space bottleneck for the classical motion, that can be shown to exist due to unstable periodic orbits. None of these orbits is associated with saddle points of the potential energy surface and hence related to transition states in the usual sense. We explain how the intricate phase space geometry influences the shape and intersections of invariant manifolds that form separatrices, and establish the impact of these phase space structures on residence times and rotation numbers. Ultimately we use this knowledge to attribute the roaming phenomenon to particular heteroclinic intersections.

Roaming dynamics in ion-molecule reactions: phase space reaction pathways and geometrical interpretation

A model Hamiltonian for the reaction CH4(+) -> CH3(+) + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of time-invariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom NHIMS are unstable periodic orbits which, in conjunction with their stable and unstable manifolds, unambiguously define the (locally) non-recrossing dividing surfaces assumed in statistical theories of reaction rates. By constructing periodic orbit continuation/bifurcation diagrams for two values of the potential function parameter corresponding to late and early transition states, respectively, and using the total energy as another parameter, we dynamically assign different regions of phase space to reactants and products as well as to conventional and roaming reaction pathways. The classical dynamics of the system are investigated by uniformly sampling trajectory initial conditions on the dividing surfaces. Trajectories are classified into four different categories: direct reactive and non-reactive trajectories, which lead to the formation of molecular and radical products respectively, and roaming reactive and non-reactive orbiting trajectories, which represent alternative pathways to form molecular and radical products. By analysing gap time distributions at several energies, we demonstrate that the phase space structure of the roaming region, which is strongly influenced by nonlinear resonances between the two degrees of freedom, results in nonexponential (nonstatistical) decay.

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

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 multi-barrier reaction.