# Research with Dr. Rolf Mayrhofer

**An Ab Initio Potential Energy Surface for Argon and Ethylene **

Our research goals are to study the transfer of energy in collisions between rare gases (like argon) and small molecules (in this case ethylene). Basically, we are throwing an argon atom at ethylene at various angles. Then we calculate the energy of the Ar-ethylene system as argon approaches. These potential energies are determined using classical trajectory calculations.

In the example shown below, the angle of argon approach was varied from linear to T-shaped.

The plot below is like a contour map of the potential energy for the various positions of the argon atom relative to the ethylene. The distance between argon and ethylene is represented along the x axis, while the angle of approach is represented along the y-axis.

# Potential Energy Surface for ArHCN

Our research goals are to study the transfer of energy in collisions between rare gases (like argon) and small molecules (in this case HCN). Basically, we throw an argon atom at HCN, and try to determine whether the H will change its position (a process known as isomerization).

The potential energies of various argon-HCN interactions are determined using classical trajectory calculations.

This graph is like a contour map of the potential energy of the Ar-CNH system as the distance between Ar and CNH varies (along the y-axis), and the angle of approach of Ar to CNH changes (along the x-axis).

Graphs like this help us understand the fundamental nature of interactions associates with these types of collisions.

The potential energies used to construct this map were calculated using Gaussian 98 software.

# Using Internal and Jacobi Coordinates to Calculate HO_{2} Vibrational Eigenfunctions

This project focused on determining vibrational eigenfunctions for HO_{2}, which is an important intermediate in ozone destruction, photochemical air pollution, and O_{2} formation in interstellar clouds.

In these calculations, the choice of the coordinate system is very important.

The example of the Hamiltonian shown here (at left) takes into account the coordinates, interactions and momenta of the particles involved in the system.

Using Jacobi coordinates (shown at right), the potential energy of HO_{2} was calculated as the angle and distance of H relative to the O_{2} was varied.

Graphs like this help us understand fundamental energy flow in molecules, and can be used as the basis to predict energies associated with molecular vibration and rotation.

In a sense, we attempt to apply fundamental theory of the interaction of particles to understand the nature of how molecules behave.