James T. Hynes

The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models

The time correlation function (tcf) formulas for rate constants κ derived via the stable states picture (SSP) of chemical reactions are applied to a wide variety (a–d) of gas and solution phase reaction models. (a) For gas phase bimolecular reactions, we show that the flux tcf governing κ corresponds to standard numerical trajectory calculation methods. Alternate formulas for κ are derived which focus on saddle point surfaces, thus increasing computational efficiency. Advantages of the SSP formulas for κ are discussed. (b) For gas phase unimolecular reactions, simple results for κ are found in both the strong and weak coupling collision limits; the often ignored role of product stabilization is exposed for reversible isomerizations. The SSP results correct some standard weak coupling rate constant results by as much as 50%. (c) For barrier crossing reactions in solution, we evaluate κ for a generalized (non‐Markovian) Langevin description of the dynamics. For several realistic models of time dependent fri...

Constrained reaction coordinate dynamics for the simulation of rare events

Abstract A computationally efficient molecular dynamics method for estimating the rates of rare events that occur by activated processes is described. The system is constrained at “bottleneck” regions on a general many-body reaction coordinate in order to generate a biased configurational distribution. Suitable reweighting of this biased distribution, along with correct momentum distribution sampling, provides a new ensemble, the constrained-reaction-coordinate-dynamics ensemble, with which to study rare events of this type. Applications to chemical reaction rates are made.

Intramolecular vibrational relaxation and spectra of CH and CD overtones in benzene and perdeuterobenzene

A theoretical model is presented for the vibrational dynamics of highly excited CH and CD overtones in benzene and perdeuterobenzene. The origin, path, and time scale for the overtone relaxation are described. The critical near resonant interaction responsible for the energy flow from an excited CH(D) oscillator to the ring is a Fermi resonance coupling, identified by Sibert, Reinhardt, and Hynes [Chem. Phys. Lett. 92, 455 (1982)]. Quantum overtone spectra are calculated both from time independent and time dependent perspectives and good qualitative agreement is found with the experimental overtone spectra of Reddy, Heller, and Berry [J. Chem. Phys. 76, 2814 (1982)]. Some expected consequences for future experiments on benzene and related systems are indicated.

Solvation dynamics for an ion pair in a polar solvent: Time‐dependent fluorescence and photochemical charge transfer

The results of a molecular dynamics (MD) computer simulation are presented for the solvation dynamics of an ion pair instanteously produced from a neutral pair, in a model polar aprotic solvent. These time‐dependent fluorescence dynamics are analyzed theoretically to examine the validity of several linear response theory approaches, as well as of various theoretical descriptions (e.g., Langevin equation) for the solvent dynamics per se. It is found that these dynamics are dominated for short times by a simple inertial Gaussian behavior, a feature which is absent in many current theoretical treatments, and which is related to the approximate validity of linear response theory. Nonlinear aspects, such as an overall spectral narrowing, but a transient initial spectral broadening, are also discussed. A model photochemical charge transfer process is also briefly considered to elucidate aspects of the connection between solvation dynamics and chemical kinetic population evolution.

Why Water Reorientation Slows without Iceberg Formation around Hydrophobic Solutes

The dynamics of water molecules next to hydrophobic solutes is investigated, specifically addressing the recent controversy raised by the first time-resolved observations, which concluded that some water molecules are immobilized by hydrophobic groups, in strong contrast to previous NMR conclusions. Through molecular dynamics simulations and an analytic jump reorientation model, we identify the water reorientation mechanism next to a hydrophobic solute and provide evidence that no water molecules are immobilized by hydrophobic solutes. Their moderate rotational slowdown compared to bulk water (e.g., by a factor of less than 2 at low solute concentration) is mainly due to slower hydrogen-bond exchange. The slowdown is quantitatively described by a solute excluded volume effect at the transition state for the key hydrogen-bond exchange in the reorientation mechanism. We show that this picture is consistent with both ultrafast anisotropy and NMR experimental results and that the transition state excluded volume theory yields quantitative predictions of the rotational slowdown for diverse hydrophobic solutes of varying size over a wide concentration range. We also explain why hydrophobic groups slow water reorientation less than do some hydrophilic groups.

Nonequilibrium solvation effects on reaction rates for model SN2 reactions in water

Molecular dynamics (MD) simulations of the model SN2 reaction Cl−+CH3Cl→ClCH3+Cl− in water, and variants thereof, are presented. The resulting transmission coefficients κ, that measure the deviations of the rates from the transition state theory (TST) rate predictions due to solvent‐induced recrossings, are used to assess the validity of the generalized Langevin equation (GLE)‐based Grote–Hynes (GH) theory. The GH predictions are found to agree with the MD results to within the error bars of the calculations for each of the 12 cases examined. This agreement extends from the nonadiabatic regime, where solvent molecule motions are unimportant and κ is determined by static solvent configurations at the transition state, into the polarization caging regime, where solvent motion is critical in determining κ. In contrast, the Kramers theory predictions for κ fall well below the simulation results. The friction kernel in the GLE used to evaluate the GH κ values is determined, from MD simulation, by a fixed‐parti...

On the Molecular Mechanism of Water Reorientation

We detail and considerably extend the analysis recently presented in Science 2006, 311, 832- 835 of the molecular mechanism of water reorientation based on molecular dynamics simulations and the analytic framework of the extended jump model (EJM). The water reorientation is shown to occur through large-amplitude angular jumps due to the exchange of hydrogen (H)-bond acceptors, with a minor contribution from the diffusive H-bond frame reorientation between these exchanges. The robust character of this mechanism with respect to different water models is discussed. We fully characterize these jump events, including the distributions of trajectories around the average path. The average path values and the distributions of the jump time and the jump amplitude, the two key parameters in the Ivanov jump model component of the EJM, are determined. We also discuss the possibility of selectively exciting water molecules close to the jump event, of interest for ultrafast infrared experiments. In addition to a comparison of predicted reorientation times with experimental results, the reorientation time temperature dependence is discussed. A detailed description of the pathway free energetics for the water reorientation is presented; this is used to identify the jump rate-limiting step as the translational motion in which the initial H-bond of the reorientating water is elongated and the new H-bond acceptor water approaches.

Molecular‐dynamics simulation for a model nonadiabatic proton transfer reaction in solution

It is shown how a dynamical theory for proton transfer rates in solution can be implemented in a molecular‐dynamics simulation for a model reaction system. The reaction is in the nonadiabatic limit, in which the transfer occurs via quantum tunneling of the proton. The importance of the coupling of the proton to the solvent and to an intramolecular vibration is illustrated, and the simulation results are successfully compared with analytic rate‐constant expressions in several limiting regimes.

Molecular dynamics of a modelSN2 reaction in water

Molecular dynamics are computed for a model SN2 reaction Cl−+CH3Cl→ClCH3+Cl− in water and are found to be strongly dependent on the instantaneous local configuration of the solvent at the transition state barrier. There are significant deviations from the simple picture of passage over a free energy barrier in the reaction coordinate, and thus, a marked departure from transition state theory occurs in the form of barrier recrossings. Factors controlling the dynamics are discussed, and, in particular, the rate of change of atomic charge distribution along the reaction coordinate is found to have a major effect on the dynamics. A simple frozen solvent theory involving nonadiabatic solvation is presented which can predict the outcome of a particular reaction trajectory by considering only the interaction with the solvent of the reaction system at the gas‐phase transition barrier. The frozen solvent theory also gives the transmission coefficient κ needed to make the transition state theory rate agree with the...

Reactive modes in condensed phase reactions

The rate constant k for condensed phase chemical reactions is found when a saddle point normal mode analysis holds and when the dynamic solvent forces are of the generalized Langevin type. If the reactive and nonreactive modes are uncoupled, the deviation of k from its transition state value ktst is governed by the nonadiabatic friction on the reactive mode. In the more typical case where the modes are coupled k/ktst is governed by an effective nonadiabatic reactive mode friction which completely accounts for intramode coupling. Some simple illustrations of mode coupling effects on k are given.The rate constant k for condensed phase chemical reactions is found when a saddle point normal mode analysis holds and when the dynamic solvent forces are of the generalized Langevin type. If the reactive and nonreactive modes are uncoupled, the deviation of k from its transition state value ktst is governed by the nonadiabatic friction on the reactive mode. In the more typical case where the modes are coupled k/ktst is governed by an effective nonadiabatic reactive mode friction which completely accounts for intramode coupling. Some simple illustrations of mode coupling effects on k are given.