David M. Wardlaw

Unimolecular reaction rate theory for transition states of partial looseness. II. Implementation and analysis with applications to NO2 and C2H6 dissociations

Implementation of RRKM theory for unimolecular dissociations having transition states of any degree of looseness is described for reactions involving dissociation into two fragments. The fragments may be atomic, diatomic, or polyatomic species. Action-angle and internal coordinates for the transitional modes of the reaction, transformations to Cartesian coordinates, and other calculational aspects are described. Results for the NO2-->NO+O reaction are presented, including the dependence of the microcanonical rate constant on the bond fission and bending potentials for model potential energy surfaces. Illustrative calculations for the C2H6-->2CH3 reaction are also given.

RRKM reaction rate theory for transition states of any looseness

Unimolecular rate theory for various types of reactions is implemented for any looseness of transition state. Quantum states are counted for all but the “transitional” modes, their phase space being counted via Monte Carlo sampling. The rate constant k_(EJ) is then weighted with the initial E and J distributions.

A semiclassical approach to intense-field above-threshold dissociation in the long wavelength limit. II. Conservation principles and coherence in surface hopping

This paper is a companion to our recently published semiclassical formalism for treating time-dependent Hamiltonians [J. Chem. Phys. 105, 4094 (1996)], which was applied to study the dissociation of diatomic ions in intense laser fields. Here two fundamental issues concerning this formalism are discussed in depth: conservation principles and coherence. For time-dependent Hamiltonians, the conservation principle to apply during a trajectory hop depends upon the physical origin of the electronic transition, with total energy conservation and nuclear momentum conservation representing the two limiting cases. It is shown that applying an inappropriate scheme leads to unphysical features in the kinetic energy of the dissociation products. A method is introduced that smoothly bridges the two limiting cases and applies the physically justified conservation scheme at all times. It is also shown that the semiclassical formalism can predict erroneous results if the electronic amplitudes for well-separated hops are ...

A SEMICLASSICAL APPROACH TO INTENSE-FIELD ABOVE-THRESHOLD DISSOCIATION IN THE LONG WAVELENGTH LIMIT

A new semiclassical formalism has been developed to treat Hamiltonians having explicit time dependence, with particular application to the dissociation of diatomic ions in intense laser fields. Based on this formalism, a hopping algorithm is presented which specifies how classical trajectories should be moved between coupled electronic surfaces. The theory is laid out in a rigorous, general form and an analysis is also presented for the case where only two electronic surfaces are strongly coupled. In addition, valuable physical insight into the hopping process is obtained by considering the theory in a number of physically relevant limiting cases. From this insight a number of guidelines are proposed which detail the manner in which trajectory hopping should be implemented when time‐dependent potential energy surfaces are present, including the effects of phase coherence and conservation principles.

Role of angular momentum in statistical unimolecular rate theory

Abstract A variety of topics is reviewed with an emphasis on assessment of models and discussion of their underlying physical assumptions, rather than on an overview of applications. Different treatments of angular momentum in the Rice-Ramsperger-Kassel-Marcus theory are surveyed and compared for tight and flexible transition states. The influence of angular momentum on thermal reaction rates is examined within the framework of variational transition state theory. The vibrational/rotational adiabatic theory of unimolecular decomposition is discussed. Various models for product energy distributions are summarized. The nature of non-thermal distributions of reactant angular momentum, arising from particular experimental techniques, is examined. A brief discussion of theoretical studies of vibrational/rotational coupling in the reactant and at the transition state is provided. The review attempts to unify advances in the fields of neutral and ion unimolecular decomposition.

Canonical flexible transition state theory revisited

A simple formula for the canonical flexible transition state theory expression for the thermal reaction rate constant is derived that is exact in the limit of the reaction path being well approximated by the distance between the centers of mass of the reactants. This formula evaluates classically the contribution to the rate constant from transitional degrees of freedom (those that evolve from free rotations in the limit of infinite separation of the reactants). As a result of this treatment, the formula contains the product of two factors: one that exclusively depends on the collision kinematics and one that exclusively depends on the potential energy surface that controls the transitional degrees of freedom. This second factor smoothly varies, in the classical limit, from harmonic oscillator to hindered rotor to free rotor partition functions as the potential energy surface varies from quadratic to sinusoidal to a constant in its dependence on the relative orientation angles of the fragments. An applica...

Canonical flexible transition-state theory for generalized reaction paths

In previous work (J. Chem. Phys., 995, 103, 2917), simple yet exact formulae for the canonical flexible transition-state theory expression for the thermal reaction-rate constant were derived for all pairings of atomic, linear rigid top, and non-linear rigid top fragments when the distance between the centres of mass of the fragments serves as the reaction coordinate. In this paper, we derive the fundamental modifications required to generalize the reaction coordinate for all fragment-type pairings. That is, the hinge point about which each fragment rotates is no longer constrained to be the centre of mass of the fragment, being in general arbitrarily displaced from the fragment centre of mass. The generalized reaction coordinate is the line connecting the displaced hinge points. It is shown that only the kinetic energy associated with the internal relative motion of the two fragments is affected by a generalized reaction coordinate. The correction to this kinetic energy has a simple functional form whose evaluation for a given fragment-type pairing is straightforward. The ensuing formulae for the canonical rate constant will not be as simple as for the centres-of-mass reaction coordinate case, but are not more difficult to employ computationally. The new theory is applied to the simplest possible fragment-type pairing, atom–diatom, which serves to illustrate the essential features of the method and some of the implications of a generalized reaction coordinate.

Reduction of the two‐dimensional master equation to a Smoluchowsky type differential equation with application to CH4→CH3+H

A master equation (ME) approximation describing the effect of vibrational/rotational (V/R) relaxation on unimolecular reactions in the gas phase is presented. It is demonstrated that some forms of ME can be transformed exactly to an effective two‐dimensional Smoluchowsky type differential equation (SE) in the V/R energy variables, V and R. The SE allows interpretation in a unified way of both weak and strong collision limits. Analytical expressions for the unimolecular reaction rate coefficient ku(T) are derived for simple models of the energy dependence of the microscopic reaction rate k(V,R) and V/R density of states. For realistic k(V,R) (obtained from flexible transition state theory for the reaction CH4→ArCH3+H) the SE is solved numerically. Both numerical and analytical calculations show that the collisional rotational energy transfer can, in principle, affect the rate coefficient ku(T). However, for the particular reaction considered, ku is found to be less sensitive to changes in the average rotat...

Classical analysis of diatomic dissociation dynamics in intense laser fields

The dissociation of a diatomic ion in an intense laser field is studied using a one‐dimensional model with a Morse function representing the nuclear interaction potential, and coupling to a linear dipole moment representing the interaction with the laser field. A perturbative treatment is generally not possible because the field strengths employed are large enough to significantly distort the potential surface. Instead, classical trajectories are used to investigate some qualitative features of the dissociation process, with the goal of introducing some simple models to explain these features. A modified barrier suppression model is proposed which predicts the field strength at which trajectories first start to dissociate, and a ‘‘wagging tail’’ model is proposed which predicts the maximum kinetic energy of the dissociation products. Both these models provide physical insight into the dissociation process, and can be used to qualitatively understand experimental results.

Potential energy function for CH3+CH3⇄C2H6: Attributes of the minimum energy path

The region of the potential energy surface for the title reaction in the vicinity of its minimum energy path has been predicted from the analysis of ab initio electronic energy calculations. The ab initio procedure employs a 6–31G** basis set and a configuration interaction calculation which uses the orbitals obtained in a generalized valence bond calculation. Calculated equilibrium properties of ethane and of isolated methyl radical are compared to existing theoretical and experimental results. The reaction coordinate is represented by the carbon–carbon interatomic distance. The following attributes are reported as a function of this distance and fit to functional forms which smoothly interpolate between reactant and product values of each attribute: the minimum energy path potential, the minimum energy path geometry, normal mode frequencies for vibrational motion orthogonal to the reaction coordinate, a torsional potential, and a fundamental anharmonic frequency for local mode, out‐of‐plane CH3 bending ...