The classical trajectory approach to reaction dynamics

Classical mechanics provides a direct route from the potential energy surface to the dynamics of the collision, namely, the (numerical) solution of the classical equations of motion for the atoms. The solution uses Newton s law of motion to determine the position of each atom as a function of time. This output is known as a trajectory. It allows us to visualize how each atom moves as the reaction is taking place. Trajectory computations are carried out for two purposes. First, as a diagnostic of trends, i.e., features of the dynamics arising from different featnres of the surface or from changes in reactants energies, masses, and so 

The essence of the procedure is to choose a set of initial conditions and solve the classical equations of motion for each atom. In other words, one compntes the time-development of the coordinates of each particle by solving the Newton second-order-in-time differential equation of motion. To do so we need the force acting on each atom. The force is computed as the change in the potential when that atom is displaced. Here is where we need to know the potential as a function of the positions of the atoms. An equivalent method for generating a trajectory is to solve Hamilton s equation for the position and the momentum. There are 

At the other extreme, if you have access to a virtual reality room you can view the reaction taking 

Along the trajectory one knows tiie position and velocity of each atom. These completely specify the mechanical state of the system, so it is possible to compute all the observables of interest. But this determinism carries with it an imphcation. A classical trajectory has a completely definite outcome. The colhsion is either reactive (meaning that the new bond distance is short whereas the old bond distance is long) or it is not reactive. The products come out in a definite angle. Their internal energy is sharply defined, and so on. What gives rise to all the distributions that we have been talking about  

The sampling of initial conditions for the purpose of executing an average over them is often done by a so-called Monte Carlo (i.e., a random selection) procedure. Thus the computation of tiie observable dynamical quantities the 

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