Quantum Spheres: Particle-on-a-sphere model for Buckminsterfullerene

c. Michelle M. Francl, 2004

Full module available as PDF from the author at mfrancl@brynmawr.edu

keywords: quantum chemistry • nanotechnology • particle-in-a-box

Primary Literature Reference: This module is based on Chem. Phys. Lett. 1993, 205, 200-206. "A particle-on-a-sphere model for C₆₀ " by Michael R. Savina, Lawrence L. Lohr and Anthony H. Francis.

Background:

The road from organic chemistry to quantum dots, tiny molecular clusters whose electronic wavefunctions mimic those of atoms, turns out to pass briefly through a "galaxy far, far away." For decades it was thought that elemental carbon existed in only two pure forms: graphite and diamond. About 30 years ago, radioastronomers and astrochemists discovered that red giant stars eject substantial amounts of carbon as they switch from "burning" hydrogen to helium. In 1985, Harold Kroto convinced Richard Smalley at Rice University to explore the chemistry using laser vaporization and molecular beams techniques that Smalley's group had developed. In the course of these experiments Smalley's group identified and characterized C₆₀, a new form of elemental carbon, quickly shifting the focus of the research problem from one of the universe's largest structures, to one of its smallest.

Smalley and his co-workers deduced that C₆₀ was a spheroid, in part by assembling paper cut-outs of pentagons and hexagons at the kitchen table while having a beer! In fact, Smalley was not the first to propose that such a carbon structure might be stable. Researchers had already done theoretical calculations to show that C₆₀ would be stable. Smalley's paper in Nature [Nature 1985 318, 162 ], however, showing that these molecules self-assembled and providing a mechanism for their synthesis and isolation catalyzed the development of a new field - nanotechnology. Theory and experiment both continue to provide key insights in this emerging area.

Sample Critical Reading Questions:

• The authors note that "perimeter models" have been developed for cata-condensed hydrocarbons. What is a cata-condensed hydrocarbon? Give an example that is not given in the paper, draw its molecular structure.
• Cut out and build the scale model of buckminsterfullerene attached. How close to a sphere is a buckyball? [Ed: An easy to assemble, scale model is available in Molecular Origami by Robert Hanson; a similar model can be found at the Mathforum]

Sample Problem:

• Draw, to scale, an energy level diagram for benzene based on the perimeter model. Based on what you know from organic chemistry, is this a good model? How well does the first excitation energy calculated from this model match the experimental value (which occurs at roughly 200 nm)?

Culture of Chemistry Feature:

In vivo imaging using quantum dot dyes.