A molecular dynamics simulation reveals the occurrence of nonstatistical dynamical effects in the ring-opening and subsequent [1,5] H migration of bicyclo[2.1.0]pent-2-ene. The symptoms of the effects do not show up in the overall kinetics or product branching ratios of the reaction, which are well explained by a master-equation analysis, but in an oscillatory preference for migration of the two methylene hydrogens. It is predicted that these oscillations could have an observable effect on final product ratios in isotopically labeled analogues, and that the effect might be greater in certain solvents than in the gas phase.

A number of methods proposed in the past few years have been aimed at accelerating the sampling of rare events in molecular dynamics simulations. We recently introduced a method called Boxed Molecular Dynamics (BXD) for accelerating the calculation of thermodynamics and kinetics ( J. Phys. Chem. B 2009, 113, 16603−16611). BXD relies upon confining the system in a series of adjacent “boxes” by inverting the projection of the system velocities along the reaction coordinate. The potential of mean force along the reaction coordinate is obtained from the mean first passage times (MFPTs) for exchange between neighboring boxes, simultaneously providing both kinetics and thermodynamics. In this paper, we investigate BXD in the context of its natural relation to a kinetic master equation and show that the BXD first passage times (FPTs) include different time scales—a fast short time decay due to correlated dynamical motion and slower long time decay arising from phase space diffusion. Correcting the FPTs to remove the fast correlated motion yields accurate thermodynamics and master equation kinetics. We also discuss interrelations between BXD and a recently described Markovian milestoning technique and use a simple application to show that, despite each method producing distinct nonstatistical effects on time scales on the order of dynamical decorrelation, both yield similar long-time kinetics.

The acetyl + O2 reaction has been studied by observing the time dependence of OH by laser-induced fluorescence (LIF) and by electronic structure/master equation analysis. The experimental OH time profiles were analyzed to obtain the kinetics of the acetyl + O2 reaction and the relative OH yields over the temperature range of 213−500 K in helium at pressures in the range of 5−600 Torr. More limited measurements were made in N2 and for CD3CO + O2. The relative OH yields were converted into absolute yields by assuming that the OH yield at zero pressure is unity. Electronic structure calculations of the stationary points of the potential energy surface were used with a master equation analysis to fit the experimental data in He using the high-pressure limiting rate coefficient for the reaction, k∞(T), and the energy transfer parameter, ⟨ΔEd⟩, as variable parameters. The best-fit parameters obtained are k∞ = 6.2 × 10−12 cm−3 molecule−1 s−1, independent of temperature over the experimental range, and ⟨ΔEd⟩(He) = 160(T/298 K) cm−1. The fits in N2, using the same k∞(T), gave ⟨ΔEd⟩(N2) = 270(T/298 K) cm−1. The rate coefficients for formation of OH and CH3C(O)O2 are provided in parametrized form, based on modified Troe expressions, from the best-fit master equation calculations, over the pressure and temperature ranges of 1 ≤ p/Torr ≤ 1.5 × 105 and 200 ≤ T/K ≤ 1000 for He and N2 as the bath gas. The minor channels, leading to HO2 + CH2CO and CH2C(O)OOH, generally have yields <1% over this range.

Non-TST behavior has recently attracted a great deal of attention. If such behavior is general, then the standard way in which synthetic chemists rationalize and predict reactivity and selectivity would be at least partially invalid. The work in this article was inspired by recent results which highlighted a departure from the predictions of TST for rationalization of the regiochemical outcome of the hydroboration reaction mechanism, suggesting that the isomeric product ratios arise because of nonstatistical dynamical effects (J. Am. Chem. Soc. 2009, 131, 3130−3131). We suggest, based on new calculations using a weak collision RRKM-Master Equation (ME) model, an alternative interpretation of the experimental results which preserves a statistical reaction model. While it is a common assumption that all intermediates and transition states along the reaction path are in thermal equilibrium with solvent, our ME results show that hot intermediates may react while they are undergoing stepwise relaxation through weak collisions, even in solution. To our knowledge, this work represents the first application of master equation methodology to a solution phase thermal reaction in organic chemistry that cannot be otherwise explained using conventional TST. Explicit modeling of solvent and solute dynamics is often prohibitively expensive; however, the master equation offers a computationally tractable model with considerable predictive power that may be utilized to investigate whether stepwise collisional relaxation is prevalent in other polyatomic systems.