Chemical Dynamics and Bond-Order Potentials
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rials scientists and engineers. A discussion of the bond-order formalism and how it can be related to both solid-state structure and chemical dynamics follows. The article ends with a discussion of two applications of this formalism, modeling chemical dynamics near a shock front and the reactive chemistry of diamond deposition.
Potential-Energy Surfaces and Chemical Dynamics Chemists have used the concept of a potential-energy surface to model and understand few-body chemical dynamics for many years. The earliest example is probably the work presented in the seminal 1936 paper by Hirschfelder, Eyring, and Topley1 where they used classical trajectories to model the reaction H + H 2 -* H2 + H. Although the potential-energy surface used is crude by cur-
A-B
rent standards (it has a nonphysical well that yields a stable H 3 molecule), it did establish some of the critical ideas still used today to understand and model chemical dynamics. Illustrated in Figure 1 are potentialenergy contour surfaces, similar to those introduced by Hirschfelder, Eyring, and Topley for a hypothetical three-body reaction A + BC ->• AB + C.
(1)
A linear configuration is used for the three atoms, and the x and y axes correspond to the bond lengths A-B and B-C. The contours illustrate lines of equipotential much like those used to denote equal elevation on a topographical map. Indeed, the analogy to the topology of the earth is a useful one. The areas of low potential energy, which are analogous to a topological valley, dominate the dynamics at low energies while the areas of high potential energy, which can be envisioned as mountains, generally only influence atomic dynamics at hyperthermal energies. A chemical reaction like that given by Equation 1 would begin at the lower right corner of Figure la and proceed to the left, as illustrated by the arrows. Successful chemical reaction requires a trajectory that passes from the horizontal valley from where the reaction is initiated to the vertical valley at the left of the figure. The lowest energy reaction path, which is illustrated by the dashed line, proceeds over the saddle point. This point, the potential energy for which establishes the classical barrier height, is
Stretch
Q
A —B D i s t a n c e
A-B Distance
Figure 1. Potential-energy contour diagram for the reaction given by Equation 1. Contour lines are in electron volts, (a) Thermoneutral reaction; (b) exothermic reaction.
MRS BULLETIN/FEBRUARY 1996
Chemical Dynamics and Bond-Order Potentials
-3 4 Reactants Q)
A + BC
Products AB + C
/
''.
5 Symmetric Barrier
CD
6
.Barrier Position', Shifts Toward Reactants; Lower Height
7 Exothermic Reaction
8 0
Reaction Path Figure 2. Energy along the reaction path for the reaction given by Equation 1. The dashed and dotted lines refer to Figures 1a and 1b, respectively.
crucial in determining the probability for reaction. Again analogy with geological topology is helpful in understanding dynamics: A hiker wanting to take the easiest route between valleys would attempt to hi
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