Karl Fails and Dr. Richard Rowley, Chemical Engineering
The purpose of this study was to examine a new method for predicting elementary gas-phase reaction rates using molecular dynamics simulations. The diatomic substitution reaction: 
was to be used as a test model for its simplicity. Molecular dynamics simulations were to be used to calculate the motion of the interacting atoms. Any associations, dissociations and substitutions were to be counted and recorded.
As with all molecular dynamics simulations, the most important aspect of this project was using an appropriate potential energy model. The forces between molecules were then found from the gradient of the potential energy. The motion of all atoms is governed by a potential energy field. The energy field around an atom is created by the interaction of that atom with the surrounding atoms. This potential energy field depends on the spacial configuration of the neighboring atoms as well as the type of interactions that occur. Types of interactions include relatively short range interactions found in bonds as well as longer range interactions like hydrogen bonding and dispersion forces (van der Waal’s forces). Many of these atomic potential energies have been studied extensively and accurate mathematical models have been developed. For molecular dynamics simulations the assumption of a “pair-potential” is often used. This assumption implies that the presence of atom X does not effect the interaction between atoms Y and Z.
At the inception of this project, a hybrid potential energy model encompassing both the bonding and dispersion regimes was developed. This model used the pair-potential assumption as described above. An appropriate molecular dynamics code was generated and used to simulate a reaction system. A few simulations were run to observe what behavior the model would predict. It was quickly discovered that as the reaction system progressed in time, the atoms formed a giant “cluster.” Because the model only included pair interactions, the fact that a given atom was already bonded to one atom did not energetically dissuade the atom from bonding with another and then another and so on. It was realized that a new, more complex model must be developed that encompassed three-body interactions.
With this discovery, the main focus of the project shifted to the development of an accurate three-body potential energy model. It was decided that ab-initio calculations would be used to generate this model. The commercial software package Gaussian 98 was used to perform all of the ab-initio calculations. Ab-initio calculations use several simplifying assumptions to solve Schrödinger’s equation for the probable configuration of electrons in a given system. From these results, a potential energy for the given atomic configuration can be calculated.
To create the three-body potential energy model, ab-initio energies were to be calculated for all possible triplets (Br-Br-Br, Br-Br-Cl, Br-Cl-Cl, Cl-Cl-Cl) at various distances and configurations. These results were then to be fit to a three-dimensional function with the three interatomic distances as independent variables. At the present time, this work has been completed for the Cl-Cl-Cl triplet. The other triplets are at varying levels of completion.
Though the original idea for the potential energy model was proven to be insufficient and inaccurate and the project is not yet complete, the project can still be judged a success. Important information on three-body interactions of reacting systems has been generated and can be the basis for future work in this area.