This summer I have an internship in theoretical and computational chemistry at the University of Vienna through a program called Partnership in International Research and Education (PIRE). Every summer the PIRE program takes place in either Pisa, Italy; Santiago de Compostela, Spain; or Vienna, Austria. For the program, undergrads work with PhD students on various theoretical and computational chemical projects. I am working with another undergrad from the University of New Mexico and a PhD student from Yale University. We are using classical mechanics to model a simple reaction, the reaction of a hydrogen atom with a hydrogen molecule (H + H_{2} → H_{2} + H). Classical mechanics is much less computationally intensive than quantum mechanics, allowing the properties of larger reactions to be calculated faster than is possible with quantum mechanics alone. However, classical mechanics is inadequate for completely describing this system as some quantum effects interfere. One of those effects is tunneling: a reaction can occur even when there is insufficient kinetic energy for the reaction to occur classically. Ultimately, the purpose of this research is to create a quasiclassical means of including tunneling in calculations without having to do an exact quantum calculation.

Most of the work accomplished so far this summer has been done to replicate the most accurate quasiclassical calculations that have been previously. In order to do a quasiclassical calculation of the reaction, the three atoms involved are placed along a collinear energy surface that is a function of the two internal coordinates (the distance between the first atom and the second atom and the distance between the second atom and the third atom). Two graphs of the energy surface are shown. For some initial kinetic energy of the impacting atom, the initial position of the impacting atom is varied randomly within a range that corresponds to a complete vibration of the reactant molecule. Then, multiple reaction trajectories are run and the percentage of successful reactions for the given energy is noted. Classically, no reaction can occur unless the impacting particle has enough energy to reach the saddle point, the highest point along the reaction trajectory on the energy surface. A graph of a successful trajectory is shown.

The eventual goal of this project is to utilize a concept called Ring Polymer Molecular Dynamics (RPMD) to include tunneling. Each particle can be represented by a number of beads in a ring of harmonic springs. In the limit of an infinite number of beads, these systems are equivalent to an exact quantum calculation. Although the center of mass of the beads may never be above the energy barrier, different beads may at different times pass over the barrier. Further work will see whether this method can approximate the exact quantum results with a computationally reasonable number of beads.