En Route to Topologically Interesting Porphyrins

Abstract

Topology is a major area of mathematics concerned with spatial properties that are preserved under deformation. When applied to chemistry it allows stretching the bonds and bending the structure, but no breaking. Porphyrins are a group of organic molecules of which many occur in nature. For instance, the heme group of myoglobin and hemoglobin is one specific type of porphyrin that can be found in the human body. A porphyrin molecule is a macrocyclic molecule that consists of four pyrroles, attached to each other by methine bridges. There are various synthetic ways to make different porphyins. One goal in this research is to incorporate functional groups so that bridges can be introduced into the porphyrin. A doubly bridged porphyrin can be flattened into a plane by appropriate distortion with no crossing the bonds. This is called ?topologically planar.? By inserting a metal into the center of the porphyrin, we are making a topologically non-planar molecule, which means that no matter how we stretch and distort the bonds, there are at least two bonds that must cross over each other. The beauty and importance of this experiment is the marriage between math and science, topology from math and organic synthesis from chemistry.