Folding Carbon: A Calculus of Molecular Origami

Fullerenes are carbon molecules that form polyhedral cages in many
shapes. The few types have been synthesized have created revolutionary
materials with important uses in medicine, solar cells, energy
storage, printable electronics, and more.

The number of theoretical structures is staggering: For example, there
are 132,247,999,328 different C400 fullerenes, each with its own
chemical and physical properties. Systematic quantum chemical analysis
to find those that could be made in a lab would take millions of years
with current methods.

I propose radically different methods than have so far been attempted,
using combinatorial geometry arising from the rules for how carbon
binds to itself. Solving electronic wave equations directly on these
intrinsic surfaces could let us analyse low-dimensional structures
orders of magnitude faster than is possible today, and search for
materials that have desirable chemical and physical properties in a
systematic way.

I will use the same mathematical tools to find planar molecules that
fold up to desired fullerene structures by autoassembly. The goal is a
method for automatically discovering recipes for chemical synthesis.

Success could radically change how new materials are discovered,
opening for rapid systematical analysis of millions of structures, and
towards directed design of new materials.