Transition state in a noisy environment

Phase-space geometry of the generalized Langevin equation

The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of the system will be constructed, the generalized Langevin equation will be formally rewritten as a pair of coupled ordinary differential equations, and the fundamental geometric structures in phase space will be described. It will be shown that the phase space itself and its geometric structure depend critically on the preparation of the system: A system that is assumed to have been in existence forever has a larger phase space with a simpler structure than a system that is prepared at a finite time. These differences persist even in the long-time limit, where one might expect the details of preparation to become irrelevant.

Solvent-induced acceleration of the rate of activation of a molecular reaction

An increase in the rates of activated processes with the coupling to the solvent has long been predicted through the phenomenological Langevin equation in the weak coupling regime. However, its direct observation in particle-based models has been elusive because the coupling typically places the processes in the spacial-diffusion limited regime wherein rates decrease with increasing friction. In this work, the forward and backward reaction rates of the LiNC<==>LiCN isomerization reaction in a bath of argon atoms at various densities have been calculated directly using molecular dynamics trajectories. The so-called Kramers turnover in the rate with microscopic friction is clearly visible, thus providing direct and unambiguous evidence for the energy-diffusion regime in which rates increase with friction.

Transition state theory for laser-driven reactions

Recent developments in transition state theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, the authors construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to extract time-dependent invariant manifolds that act as separatrices between reactive and nonreactive trajectories and thus make it possible to predict the ultimate fate of a trajectory. They illustrate the power of our approach on a driven Henon-Heiles system, which serves as a simple example of a reactive system with several open channels. The present generalization of transition state theory to driven systems will allow one to study processes such as the control of chemical reactions through laser pulses.

Energy dependence of the roaming atom pathway in formaldehyde decomposition

Recently, a new mechanism of formaldehyde decomposition leading to molecular products CO and H(2) has been discovered, termed the "roaming atom" mechanism. Formaldehyde decomposition from the ground state via the roaming atom mechanism leads to rotationally cold CO and vibrationally hot H(2), whereas formaldehyde decomposition through the conventional molecular channel leads to rotationally hot CO and vibrationally cold H(2). This discovery has shown that it is possible to have multiple pathways for a reaction leading to the same products with dramatically different product state distributions. Detailed investigations of the dynamics of these two pathways have been reported recently. This paper focuses on an investigation of the energy dependence of the roaming atom mechanism up to 1500 cm(-1) above the threshold of the radical channel, H(2)CO-->H+HCO. The influence of excitation energy on the roaming atom and molecular elimination pathways is reported, and the branching fraction between the roaming atom channel and molecular channel is obtained using high-resolution dc slice imaging and photofragment excitation spectroscopy. From the branching fractions and the reaction rates of the radical channel, the overall competition between all three dissociation channels is estimated. These results are compared with recent quasiclassical trajectory calculations on a global H(2)CO potential energy surface.

Probing the cybotactic region in gas-expanded liquids (GXLs)

Gas-expanded liquids (GXLs) are a new and benign class of liquid solvents, which may offer many advantages for separations, reactions, and advanced materials. GXLs are intermediate in properties between normal liquids and supercritical fluids, both in solvating power and in transport properties. Other advantages include benign nature, low operating pressures, and highly tunable properties by simple pressure variations. The chemical community has only just begun to exploit the advantages of these GXLs for industrial applications. This Account focuses on the synergism of experimental techniques with theoretical modeling resulting in a powerful combination for exploring chemical structure and transport in the cybotactic region of GXLs (at the nanometer lengthscale).

Identifying reactive trajectories using a moving transition state

A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic two-dimensional system confirm the efficiency of this approach. The results are compared to the standard fixed transition state dividing surface that is well-known to suffer from recrossings and therefore requires trajectories to be evolved over a long time interval before they can reliably be classified as reactive or nonreactive. The moving dividing surface can be used to identify reactive trajectories in harmonic or moderately anharmonic systems with considerably lower numerical effort or even without any simulation at all.

Stochastic transition states: Reaction geometry amidst noise

Classical transition state theory (TST) is the cornerstone of reaction-rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space, such that it is crossed once and only once by each transition path.