Reactive Scattering on a LEPS Surface

In this Demonstration, a model potential energy surface developed by London, Eyring, Polyani, and Sato (LEPS) is used to describe the collinear F +(Subscript[H, 2])-> H-F + H chemical reaction. The particular parameterization is the "Muckerman V" potential. This potential surface is shown as a contour plot. The coordinates are the F-H and H-H bond lengths. The reaction proceeds with (Subscript[r, F-H])being large and (Subscript[R, HH]) being the equilibrium bond-length of (Subscript[H, 2]) . The reaction path (which follows the contour minimum) connects the reactant channel to the product channel. These are separated by a saddle point that gives the configuration of the activated complex or transition state (([F-H-H])^‡) which has energy (Subscript[E, b]) = -357.13 kcal/mol.

We use Newton's equations of motion to describe the collinear F +(Subscript[H, 2])-> H-F + H chemical reaction. The contour plot shows the Muckerman V potential describing this reaction and the thick black line is a scattering trajectory. By varying the angle θ, one selects how the initial kinetic energy is partitioned between the kinetic energy of the incoming fluorine atom and the vibrational kinetic energy of the (Subscript[H, 2]) molecule. This demonstrates the influence of energy distribution amongst reactants in a given chemical reaction.

DETAILS

The modern theory of chemical reaction dynamics links the observed reaction rate to nuclear dynamics occurring on a potential energy surface. Potential energy surfaces are the connection between the quantum mechanical description of the electronic states of the system and the nuclear motion. The potential energy surfaces we will consider here are based upon the Born Oppenheimer approximation, which allows the separation of the motion of the electrons from the motion of the nuclei.

Here we solve the classical equations of motion describing the motion of the nuclei in the F-H-H collision complex to describe the F +(Subscript[H, 2])-> H-F + H chemical reaction.

One of the surprises is that simply having enough E>(Subscript[E, b]) does not ensure a reaction. Here we start a trajectory in the reactant channel with E just above (Subscript[E, b]) and vary the initial velocity vector between 0 and π/2. This changes the relative amount of energy partitioned to the translation of the incoming F atom and the vibrational energy of the initial (Subscript[H, 2]) molecule. When (θ ~ π/2), most of the energy is given to F atom translations and only these trajectories will proceed into the product channel. Here one can see the effect of an "early" transition state on the final energy distribution of product species.

For detailed descriptions of the Muckerman V potential and an in-depth treatment of reactive scattering please refer to:

P. L. Houston, Chemical Kinetics and Reaction Dynamics, Boston: McGraw Hill, 2001.

J. I. Steinfeld, J. S. Francisco, and W. L Hase, Chemical Kinetics and Dynamics, Englewood Cliffs, NJ: Prentice-Hall, 1989.

Contributed by: Eric R. Bittner (University of Houston)

Funded in part by: National Science Foundation under grant CHE-0712981

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