C2 - C2 Collisions

In 1996, I performed some simulations of C2 - C2 collisions. The two molecules were each given an initial translation velocity corresponding to 3.52 eV per molecule. To simulate an initial temperature, random velocities (with total mean zero) were given to the inidividual atoms. These random velocities corresponded to about 1% of the total initial kinetic energy. The potential energy was modelled with a semi-empirical* potential function for carbon-clusters. This function requires a term to be computed for every triple of atoms. This is quite managable for small systems. To accurately resolve the collision, variable timestepping is used. The numerical integration scheme is a 4th-order time-reversible variable-stepsize method, based on the Adaptive Verlet method**.

* T. Takai, C. Lee, T. Halicioglu, and W.A. Tiller, A Model Potential Function for Carbon Systems, J. Phys. Chem. 94 , 4480--4482 (1990).

** W. Huang and B. Leimkuhler, The Adaptive Verlet Method, SIAM J. Sci. Comput. 18 , 239--256 (1997).

Here is a movie showing the collision. Bonds are drawn between any two atoms within bonding distance. The red bonds signify new bonds created via the high-speed collision. (69k mpeg)

Here are some results in the form of graphs (click to enlarge):

Energy Error

Variation in Step

Kinetic Energy

Potential Energy

Separation Distances

Minimal Separation

At such high-energies, this system seems to be rather dependent upon the initial conditions. If I put a light spin on the first molecule, I get drastically different results. Here is a movie showing this result. (122k mpeg)