William L. Hase

On non‐RRKM unimolecular kinetics: Molecules in general, and CH3NC in particular

Monte Carlo rate constants for model CH3NC isomerization, determined at 200, 100, and 70 kcal/mole, disagree with theoretical predictions. Also, three different approximate methods of generating initial conditions at 200 kcal lead to divergent results. The molecule does not appear to us to obey the random lifetime assumption of conventional unimolecular rate theory at any of these energies. A discussion is given of the systematics of this kind of effect, and comments are made on the relationship between our results and those obtained in the laboratory.

Simulations of Gas-Phase Chemical Reactions: Applications to SN2 Nucleophilic Substitution

Computer simulations and animations of the motion of atoms as a chemical reaction proceeds give a detailed picture of how the reaction occurs at a microscopic level. This information is particularly useful for testing the accuracy of statistical models, which are used to calculate various attributes of chemical reactions. Such simulations and animations, in concert with experimental and ab initio studies, have begun to provide a microscopic picture of the intimate details of a particular class of gas-phase ion-molecule bimolecular reactions known as SN2 nucleophilic substitution. In these reactions, a nucleophile is displaced from a molecule by another nucleophile. The dynamical model of SN2 reactions that emerges from the computer studies, and its relation to statistical theories, is discussed here.

Imaging nucleophilic substitution dynamics.

Anion-molecule nucleophilic substitution (SN2) reactions are known for their rich reaction dynamics, caused by a complex potential energy surface with a submerged barrier and by weak coupling of the relevant rotational-vibrational quantum states. The dynamics of the SN2 reaction of Cl– + CH3I were uncovered in detail by using crossed molecular beam imaging. As a function of the collision energy, the transition from a complex-mediated reaction mechanism to direct backward scattering of the I– product was observed experimentally. Chemical dynamics calculations were performed that explain the observed energy transfer and reveal an indirect roundabout reaction mechanism involving CH3 rotation.

Ab initio classical trajectories on the Born-Oppenheimer surface: Hessian-based integrators using fifth-order polynomial and rational function fits

Classical trajectories can be computed directly from electronic structure calculations without constructing a global potential-energy surface. When the potential energy and its derivatives are needed during the integration of the classical equations of motion, they are calculated by electronic structure methods. In the Born–Oppenheimer approach the wave function is converged rather than propagated to generate a more accurate potential-energy surface. If analytic second derivatives (Hessians) can be computed, steps of moderate size can be taken by integrating the equations of motion on a local quadratic approximation to the surface (a second-order algorithm). A more accurate integration method is described that uses a second-order predictor step on a local quadratic surface, followed by a corrector step on a better local surface fitted to the energies, gradients, and Hessians computed at the beginning and end points of the predictor step. The electronic structure work per step is the same as the second-ord...

Ab initio classical trajectory study of H2CO→H2+CO dissociation

Abstract Classical trajectories for H 2 CO→H 2 +CO dissociation have been calculated directly from ab initio molecular orbital computations at the HF/3-21G and HF/6-31G** levels of theory, without constructing a global potential energy surface. The classical equations of motion were integrated on the local fifth-order polynomial surfaces fitted to the energies, gradients and hessians computed at the beginning and end points of each step along the trajectory. The calculated vibrational and rotational energy distributions and average impact parameter of the products are in very good agreement with experiment. The relative translational energy is higher than experiment because the barrier is overestimated at both levels of theory.

A simple model for correcting the zero point energy problem in classical trajectory simulations of polyatomic molecules

A simple model is proposed for correcting problems with zero point energy in classical trajectory simulations of dynamical processes in polyatomic molecules. The ‘‘problems’’ referred to are that classical mechanics allows the vibrational energy in a mode to decrease below its quantum zero point value, and since the total energy is conserved classically this can allow too much energy to pool in other modes. The proposed model introduces hard sphere‐like terms in action–angle variables that prevent the vibrational energy in any mode from falling below its zero point value. The algorithm which results is quite simple in terms of the cartesian normal modes of the system: if the energy in a mode k, say, decreases below its zero point value at time t, then at this time the momentum Pk for that mode has its sign changed, and the trajectory continues. This is essentially a time reversal for mode k (only!), and it conserves the total energy of the system. One can think of the model as supplying impulsive ‘‘quantu...

On the dynamics of state selected unimolecular reactions: Chloroacetylene dissociation and predissociation

Classical trajectories have been used to investigate the dynamics of chloroacetylene dissociation and predissociation. Monte Carlo techniques were used to study dissociation from initial state selected energy distributions. Calculations using different initial distributions show that on a 10−12 sec time scale the HC stretch internal coordinate is decoupled from the remaining internal coordinates. A simulation of chloroacetylene dissociation following S1→S0 internal conversion gives a rate constant in agreement with the RRKM theory. A comparison is made between these results and experimental ones.

Trajectory studies of SN2 nucleophilic substitution. II. Nonstatistical central barrier recrossing in the Cl−+CH3Cl system

For the Cl−+CH3Cl SN2 nucleophilic substitution reaction transition‐state theory predicts that crossing the central barrier region of the potential‐energy surface is the rate‐controlling step. In this work classical trajectories are initialized at the central barrier. Four different models are considered for the potential‐energy surface. A significant amount of central barrier recrossing is observed in the trajectories, which suggests that transition‐state theory is an incomplete model for calculating the Cl−+CH3Cl SN2 rate constant. Two types of recrossings are observed in the trajectories: intermediate recrossings in which trajectories linger near the central barrier and complex recrossings in which trajectories trapped in the Cl−⋅⋅⋅CH3Cl complex return to the central barrier region. Intermediate recrossings are important if, in the trajectory initial conditions, zero‐point energy is added to the vibrational modes orthogonal to the reaction coordinate. Rice–Ramsperger–Kassel–Marcus (RRKM) theory predict...

Trajectory studies of SN2 nucleophilic substitution. I. Dynamics of Cl−+CH3Cl reactive collisions

Classical trajectories were used to study the dynamics of the Cl−+CH3Cl→Cl−‐‐‐CH3Cl association and the Cl−+CH3Cl→ClCH3+Cl−substitution reactions. Substantial deviations are found between the underlying microscopic dynamics of the reactions and the assumptions of statistical rate theories. The energy dependence of the trajectory rate constant for the majority of Cl−‐‐‐CH3Cl→Cl−+CH3Cl dissociation is in accord with a model in which only the Cl−‐‐‐C stretch and the two Cl−‐‐‐CH3Cl bend modes are active degrees of freedom. At 300 K the trajectory rate constant for Cl−+CH3Cl→Cl−‐‐‐CH3Cl association is approximately forty percent smaller than that of microcanonical variational transition state theory, with the difference increasing with an increase in temperature. For thermal conditions substitution occurs by an indirect mechanism in which the reactive system is initially trapped in the Cl−‐‐‐CH3Cl potential well. The cross section for this process decreases dramatically as the reactant relative translational energy is increased. The effect of rotational energy is less precipitous. Exciting the C–Cl stretch normal mode of CH3Cl opens up a direct substitution mechanism without trapping in either of the two potential wells. There is a significant decrease in the cross section for this direct substitution when CH3Cl is rotationally excited.

Classical mechanics of intramolecular vibrational energy flow in benzene. IV. Models with reduced dimensionality

The classical mechanics of intramolecular relaxation of benzene CH(D) local mode overtone states is studied with the molecular models HC3, DC3, and H3C3. These reduced dimensionality models provide one means to correct for the improper classical mechanical treatment of zero‐point motion in complete benzene models. They give significantly smaller homogeneous linewidths for the low energy CH(D) overtones than found from previous classical trajectory calculations for C6H6/C6D6 models. The n=3 and 5 linewidths for the DC3 model are less than 1 cm−1, while for the HC3 and H3C3 models these linewidths are approximately 5–10 cm−1. The energy transfer pathways for the deuterated and nondeuterated models are substantially different. A gradation of couplings are observed from the trajectories. For the low energy HC3/H3C3 overtones a CCH bend is initially the mode most strongly coupled to the excited CH bond, while for the higher overtones it is the B1 CC stretch. In the relaxation of the H3C3 overtones, five modes ...