Atomistic models of materials provide accurate total energies.
Practical applications, however, often
require extremely long time scale simulations.
Structural optimization of an atomic cluster
requires a simulated annealing run whose
length scales exponentially with the number of atoms in the cluster.
Here, the 60 atom carbon buckyball is formed from random
coordinates in our computer simulation.
How we do it
The genetic algorithm.
Inspired by the Darwinian evolution process, a population of
structures is maintained. New
generations are produced by `mating' clusters and selecting the lowest
energy relaxed children.
Carbon clusters in a tight-binding model.
We found fullerene cages starting from random coordinates, including
the 60 atom buckyball illustrated above.
The mating procedure.
We use a cut and mating operation. The parent clusters
are split in half and the child is created from one half of each
parent. Mutations may also be applied.
At left, we show some of the structures our algorithm generates
for twenty carbon atoms. At right, the lowest energy structure is
found only when mutations are added.
We have applied the physical cut-and- mating genetic
algorithm to other systems, including point charges on a sphere
(Thomson problem), lattice spin glass models in 2D and 3D, and