My current research is associated with trying to better understand the behavior of OClO, which is believed to play an important role in the depletion of stratospheric ozone. By using multidimensional wave packet propagations with accurate ab initio potential energy surfaces, I hope to gain insight into the reaction dynamics of this molecule so that we can understand the role OClO plays in the destruction of the ozone layer.
Controversy has surrounded the OClO molecule since it was first studied over 50 years ago. Anomalously large peaks from the asymmetric stretch vibration are seen in the absorption spectrum, and two models have been developed to explain their presence. The first model assumes that there is minimal vibrational interaction among the three vibrational modes of OClO and the anomalous peaks are explained by the presence of a barrier in the potential well along the asymmetric stretch coordinate, thereby creating a double-well. The second model does not rely upon a double-well, but instead explains the anomalous peaks by assuming strong coupling of the asymmetric stretch vibration to the intense symmetric stretch vibration. Since the two models predict very different reaction dynamics, it is important to discern which model is correct before trying to make predictions of OClO chemistry in the stratosphere.
Most experimentalists prefer to work with the most convenient model available in order to explain their experimental results. Since the double-well model assumes that there is little coupling among the vibrational modes it is very easy to work with because each vibration can be treated independently of the others. Various double-well models have been successful in explaining experimental results.
Interestingly, though, recent ab initio calculations suggest that there is no double-well along the asymmetric stretch coordinate of the potential energy surface. By including coupling among the three vibrational modes and performing a full 3-D calculation using the ab initio surface, I have been able to demonstrate that the ab initio potential also reproduces the experimental absorption spectrum.
I am currently performing calculations that will produce Raman spectra based upon the various potential energy surfaces which exist for OClO. These calculated spectra will be compared with recent experimental Raman spectra and will provide a more definitive conclusion regarding which potential most accurately describes the behavior of OClO.
The final phase of my research will include exact rotation-vibration coupling to calculate a low-temperature absorption spectrum based upon the various potential energy surfaces for OClO. This will not only provide further evidence for the determination of the most accurate potential energy surface, but will also enable researchers to better determine which areas of the potential may be in need of further refinement.
Wave packet propagation is a useful technique for solving quantum mechanical problems over a wide range of applications. Since very few quantum mechanical problems can be solved exactly, each propagation technique can only provide an estimate to the actual solution. For a propagation algorithm to be useful it must be fast in addition to being accurate. With most algorithms a high accuracy can be reached by taking a small time step between propagation calculations. However, if the time step is too small too much time is needed to reach a final answer, so a balance between speed and accuracy is needed for each algorithm. In addition, the parameters of the energy spectrum I am interested in calculating must be taken into account, since the energy range of the spectrum determines the maximum time step that can be taken, and the energy resolution of the spectrum determines the length of time that the wave packet must be propagated.
The different propagation techniques I have studied include the Feit & Fleck split operator method, a time dependent modified Cayley method, a second-order differencing scheme, an iterative Lanczos reduction, and a Chebyshev polynomial expansion. Various coordinate systems have been used for the propagations, including normal coordinates, Jacobi coordinates and Radau coordinates. Finally, different methods for calculating the kinetic energy of the system have been explored, including FFT's and various finite-difference schemes.
When normal coordinates can be used, the Feit & Fleck split operator propagation technique, using FFT's to calculate the kinetic energy, is the most robust and fastest of the various combinations studied. However, normal coordinates do not preserve the symmetry of the OClO molecule and therefore cannot always be relied upon to produce accurate results. In such cases Radau coordinates must be used, and in order to reproduce the reflectional symmetry of the angle coordinate a finite-difference scheme must be used to find the kinetic energy, rather than an FFT. We use a 25-point finite difference method because we found it gave the best compromise between accuracy and speed. Since FFT's cannot be used with Radau coordinates the split operator propagation technique is no longer viable; a Chebyshev expansion is instead used to propagate the wave packet.
Useful Links
Introduction to quantum mechanics.
My research poster presented at the ACTC conference in 1999.