Semiclassical Dynamics of Constrained Systems

Under the direction of William H. Miller at The University of California, Berkeley, I worked on applying the semiclassical initial value representation [1] to systems with arbitrary holonomic constraints.

The semiclassical initial value representation (SC-IVR) was originally developed by W.H. Miller in the early 1970s. As computers have improved, it has re-emerged as a practical method to include approximate quantum effects in a wide range of dynamical molecular properties. P.-N. Roy has recently explored the idea of adding constraints to the SC-IVR [2], and I've been working on possible improvements to the framework he developed.

I believe that this project may be especially useful in the study of clusters. Many potential energy surfaces for clusters (including my previous work on H2-benzene) are based on a rigid monomer approximation. Adding constraints to the SC-IVR will open up a new method to study dynamical quantum effects for such potential surfaces.

A few more details (from my Graduate Research Conference, presented 19 April 2007):

  • GRC Abstract [PDF; 81 kB]
  • GRC Slides [QuickTime; 57.7 MB] Assuming your QuickTime Player works like mine, you'll have to click/press the right arrow to advance each slide build (sometimes more than once due to invisible builds).
  • GRC Sound [MP3; 18.9 MB] The first minute or so is Prof. Harris expressing his opinion on the art in the newly-opened Stanley Hall. Questions start after about 18 minutes, and the whole thing is about 20 minutes 30 seconds.

If you choose to view the slideshow, there are a couple of slides at the end about pseudo-inverses. There wasn't time to talk about them in my GRC, but I put those slides in with the (vain) hope that someone would ask a question about them.

References:
[1] William H. Miller. J. Phys. Chem. A 105 (2001) 2942.
[2] Ben B. Harland and Pierre-Nicolas Roy. J. Chem. Phys. 118 (2003) 4791.