Mentor: Professor Michelle Francl
In recent years, the lines between the “distinct” fields of the various natural sciences (physics, chemistry, biology, geology, and mathematics) have become blurred. The increasing cooperation between the different fields has allowed some questions to be answered that perhaps previously seemed unanswerable. This summer I will be beginning my thesis research on molecular moebius strips, which I will be exploring from a quantum mechanical as well as a mathematical perspective.
In my research this summer I will be using a computer program called Gaussian 03 to find approximate solutions to the Schrödinger equation, which yields information about various physical properties of the molecule in question, such as the geometrical form of the molecule that corresponds to the lowest energy of the molecule. The molecules that I will be completing computations on are composed of between 15 and 30 benzene rings (or regular hexagons with carbon atoms at the vertices) and have the topological form of cylinders and moebius strips. The goal of the research is to determine the lowest energy geometry of the molecules. A comparison of the energies of the corresponding cylinders and moebius strips will allow us to determine what the addition of the half-twist costs energetically. These computations will be completed using at least two different computational models.
In addition to these computations, I will also begin attempting to figure out why the half-twist in a moebius band is localized, or in other words why the half twist is not distributed throughout the strip evenly. In order to do this I will first learn techniques in topology and differential geometry by reading textbooks on the subjects, including When Topology Meets Chemistry by Erica Flapan. One goal of this summer's research is to understand Erica Flapan's book, so that I can move forward when I continue this work throughout the next school year.