Undergraduate Thesis

Here is my undergraduate thesis, called "Instantaneous Normal Mode Analysis on Arbitrary Configuration Manifolds," which was advised by Richard Stratt. I tried to make it somewhat palatable to both chemistry/physics and mathematics audiences. Here are the slides from my thesis defense.

Here is a visualization tool that illustrates an example I worked out after the thesis's completion. It is the "spherical pendulum" in which the potential energy $V$ of a rotating rigid linear molecule is given by $V(\theta,\phi) = 1 - \cos(\theta)$, where $(\theta,\phi)$ are spherical coordinates using the physics convention. In the visualization, the black rod represents the dynamics (pay attention only to the end of the rod, which is on the sphere) when worked out according to the (coordinate-system-invariant) INM theory I formulated in my thesis, and the red rod represents the dynamics worked out in the original way. Note the coordinate-system-invariant INM theory gives dynamics that make much more physical sense.

Below is another illustration of how the coordinate-system-invariant INM theory differs from the original theory. I computed the autocorrelation function of angular position in the case of a freely rotating acetylene molecule (with moment of inertia I = 2.37e-46 kg m^2) using the original INM theory (in blue) and the coordinate-system-invariant INM theory (in red). I showed in my thesis that my coordinate-system-invariant INM theory is exact in the case of free rotation, so the red curve represents the true angular position autocorrelation function. The function computed using the original INM theory disagrees at a reasonable time scale with the true autocorrelation function, even though the two agree at very short (and of course, very long) time scales.