(112d) Development and Application of a Heuristic to Study Heterogeneous Nucleation Mechanisms

The key tool for understanding the properties of discrete atomic and
molecular clusters is identifying their energetic
global minimum configuration. However, even for simple pair potential models
the search for the global minimum has been shown to be a member of the
so-called "NP-hard" class of problems.[1]
Additional studies[2][3][4]
have estimated that the growth in the number of local minima is of the order ~exp(N), where N is the number of components. Moreover,
the sequence of global minima as a function of the size of the cluster
typically forms a set whose members vary dramatically in morphology. This gives
rise to the frequent occurrence of magic numbers in cluster growth experiments.
These observations demonstrate that in order to solve this optimization problem
efficiently, unbiased heuristic methods are needed. The algorithms that have
shown the most promise include: simulated annealing,[5]
Monte Carlo basin hopping[6] and genetic (or evolutionary)
algorithms (GA or EA).[7] Each class of algorithm has been
successful at locating the global minima in a variety of different chemical
contexts using a diverse range of potential energy functions. However, in some
cases they still scale poorly with system size. In addition, because of their
stochastic nature they do not guarantee that the global minimum will be found
for any particular simulation. To address the issues of scalability and
efficiency in global optimizations of atomic and molecular clusters we develop
and carefully assess a heuristic that combines the genetic algorithm with
quenched molecular dynamics simulations against a series of benchmark
systems.  We then summarize the results
of using the algorithm to find the species responsible for initiating a novel
cooperative heterogeneous nucleation mechanism.