Trajectory calculations, reaction path potential energy surfaces

Rather than using transition state theory or trajectory calculations, it is possible to use a statistical description of reactions to compute the rate constant. There are a number of techniques that can be considered variants of the statistical adiabatic channel model (SACM). This is, in essence, the examination of many possible reaction paths, none of which would necessarily be seen in a trajectory calculation. By examining paths that are easier to determine than the trajectory path and giving them statistical weights, the whole potential energy surface is accounted for and the rate constant can be computed. 

Much of the theoretical work in molecular dynamics has been based on potential energy surfaces that have been calculated for individual reactions. Dynamical calculations are then carried out for various initial states of the reacting molecules. For a reaction A + B—C, for example, one chooses a particular vibrational and rotational state for the molecule B-C, and particular translational states for A and B-C. Other details of the collision between the two are also selected. One then calculates, on the basis of dynamics, the path that the system takes on the potential energy surface. A diagram or mathematical description that describes the motion of a reaction system over a potential energy surface is known as a trajectory. Ideally the dynamical calculations are based on quantum mechanics, but this presents difficulty and more often classical calculations are made there is good reason to conclude that not much error is then introduced. Even when the trajectories are obtained classically, the initial states of the reactants are usually selected on the basis of quantum theory. 

In addition to the reaction coordinate mapped out by the DRC, the minimum energy path from transition state to reactants or products is of interest. As with the DRC originating at the transition state, this path is coordinate-system independent. The calculation to determine the minimum energy path starts in a similar manner to the DRC calculation, only after the initial displacement, all velocities are annulled at every step. This results in the system moving perpendicular to the energy contours in mass-weighted coor nate space. Sutime independent, and are called intrinsic reaction coordinates (IRC). For a review of potential energy surfaces for polyatomic reaction dynamics, see ref. 59. 

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