Curls research at Rice involved the fields of infrared and microwave spectroscopy.  Curls research inspired Richard Smalley to come to Rice in 1976 with the intention of collaborating with Curl.  In 1985, Curl was contacted by Harold Kroto, who wanted to use a laser beam apparatus built by Smalley to simulate and study the formation of carbon chains in red giant stars. Smalley and Curl had previously used this apparatus to study semiconductors such as silicon and germanium. They were initially reluctant to interrupt their experiments on these semiconductor materials to use their apparatus for Kroto's experiments on carbon, but eventually gave in.
They indeed found the long carbon chains they were looking for, but also found an unexpected product that had 60 carbon atoms.  Over the course of 11 days, the team studied and determined its structure and named it buckminsterfullerene after noting its similarity to the geodesic domes for which the architect Buckminster Fuller was known. This discovery was based solely on the single prominent peak on the mass spectrograph, implying a chemically inert substance that was geometrically closed with no dangling bonds. Curl was responsible for determining the optimal conditions of the carbon vapor in the apparatus, and examining the spectrograph.  Curl noted that James R. Heath and Sean C. OBrien deserve equal recognition in the work to Smalley and Kroto.  The existence of this type of molecule had earlier been theorized by others, but Curl and his colleagues were at the time unaware of this.  Later experiments confirmed their proposed structure, and the team moved on to synthesize endohedral fullerenes that had a metal atom inside the hollow carbon shell.  The fullerenes, a class of molecules of which buckminsterfullerene was the first member discovered, are now considered to have potential applications in nanomaterials and molecular scale electronics. Robert Curls 1985 paper entitled "C60:  Buckminsterfullerine", published with colleagues H. Kroto, J. R. Heath, S. C. O’Brien,  and R. E. Smalley, was honored by a Citation for Chemical Breakthrough Award from the Division of History of Chemistry of the American Chemical Society, presented to Rice University in 2015. The discovery of fullerenes was recognized in 2010 by the designation of a National Historic Chemical Landmark by the American Chemical Society at the Richard E. Smalley Institute for Nanoscale Science and Technology at Rice University in Houston, Texas.
After winning the Nobel Prize in 1996, Curl took a quieter path than Smalley, who became an outspoken advocate of nanotechnology, and Kroto, who used his fame to further his interest in science education, saying, "After winning a Nobel, you can either become a scientific pontificator, or you can have some idea for a new science project and you can use your newfound notoriety to get the resources to do it. Or you can say, Well, I enjoy what I was doing, and I want to keep doing that." True to that humility, when asked by the President of Rice what he would like, following the Nobel announcement, he asked that a bike rack be installed closer to his office and laboratory.