Molecular geometry, or the structure of atoms within a molecule, is an important facet of chemistry because it plays a determining role in the chemical properties of a substance. One of the most common explanations for molecular shapes is the valence shell electron pair repulsion theory (VSEPR theory). This states that electron pairs surrounding a central atom repel each other, and thus try to stay as far apart as possible. This summer, Michael Petrey '09 (Decatur, Ga.) is examining another aspect of the question by looking at similarities between molecular structures and Steiner trees.
A Steiner tree, named after the Swiss mathematician Jakob Steiner, is a network of paths that uses the minimum total path distance possible to connect a set of points. Every point must be connected to all the others, and to create the network, extra points (Steiner points) can be added, if they shorten the total distance. By comparing Steiner trees to molecular shape, Petrey hopes to determine whether molecular bond lengths are as short as possible and if the bond angles place the electron pairs as far apart as possible, as stated in VSEPR theory.
In a geometry class last fall, Petrey was studying Steiner trees and noticed that they had a similar shape to those he had seen in molecular geometry. "I decided to see if that was just coincidence or not," he says. A major challenge of his project is the fact that very little previous research has been done combining the two topics. This makes Petrey's work more difficult, but it can be nice as well, he says, since he has the opportunity to work on research that hasn't been done before.
Other than reading the literature that does exist, most of the project involves doing calculations. Petrey was unable to find a math professor with the appropriate background to co-sponsor his project (he is collaborating with Professor of Chemistry Karen Brewer), so he says that the math has been difficult, but so far successful. He has also started working with the math software program Maple to model his calculations in 3-space.
So far, Petrey's findings show that Steiner trees for small molecule shapes, such as the tetrahedral molecule methane, have shorter connections than the molecules themselves. This indicates that other factors influence molecular shape, other than minimizing bond lengths, and that the central atoms in the molecules do not behave like ideal Steiner points. On the other hand, the central atoms of larger macro-molecules such as collagen do act like Steiner points, Petrey says, because there is more room in the molecules themselves.
Although many students have left campus for summer jobs and internships, Petrey is one of 18 students this year who are pursuing research funded by the Emerson Foundation Grant program. Created in 1997, the program was designed to provide students with significant opportunities to work collaboratively with faculty members, researching an area of interest. The students will make public presentations of their research throughout the academic year.
This is the first summer Petrey has spent doing research, and he says he is enjoying the chance to research something he wouldn't have a chance to study in class, as well as the opportunity to be on campus for a new season. During the school year, he co-hosts a radio show and teaches yoga. He also plans to work as a math tutor starting in the fall.
-- by Laura Bramley
A Steiner tree, named after the Swiss mathematician Jakob Steiner, is a network of paths that uses the minimum total path distance possible to connect a set of points. Every point must be connected to all the others, and to create the network, extra points (Steiner points) can be added, if they shorten the total distance. By comparing Steiner trees to molecular shape, Petrey hopes to determine whether molecular bond lengths are as short as possible and if the bond angles place the electron pairs as far apart as possible, as stated in VSEPR theory.
In a geometry class last fall, Petrey was studying Steiner trees and noticed that they had a similar shape to those he had seen in molecular geometry. "I decided to see if that was just coincidence or not," he says. A major challenge of his project is the fact that very little previous research has been done combining the two topics. This makes Petrey's work more difficult, but it can be nice as well, he says, since he has the opportunity to work on research that hasn't been done before.
Other than reading the literature that does exist, most of the project involves doing calculations. Petrey was unable to find a math professor with the appropriate background to co-sponsor his project (he is collaborating with Professor of Chemistry Karen Brewer), so he says that the math has been difficult, but so far successful. He has also started working with the math software program Maple to model his calculations in 3-space.
So far, Petrey's findings show that Steiner trees for small molecule shapes, such as the tetrahedral molecule methane, have shorter connections than the molecules themselves. This indicates that other factors influence molecular shape, other than minimizing bond lengths, and that the central atoms in the molecules do not behave like ideal Steiner points. On the other hand, the central atoms of larger macro-molecules such as collagen do act like Steiner points, Petrey says, because there is more room in the molecules themselves.
Although many students have left campus for summer jobs and internships, Petrey is one of 18 students this year who are pursuing research funded by the Emerson Foundation Grant program. Created in 1997, the program was designed to provide students with significant opportunities to work collaboratively with faculty members, researching an area of interest. The students will make public presentations of their research throughout the academic year.
This is the first summer Petrey has spent doing research, and he says he is enjoying the chance to research something he wouldn't have a chance to study in class, as well as the opportunity to be on campus for a new season. During the school year, he co-hosts a radio show and teaches yoga. He also plans to work as a math tutor starting in the fall.
-- by Laura Bramley
