Finding the minimal-energy configuration of N-body clusters with
K-body interactions is an NP-hard problem.
Computer-assisted searches are quickly becoming overwhelmingly
complicated when N gets large. In this situation it is prudent to find
necessary criteria for minimality that can be employed to test
computer-outputs for optimality. In the talk I present some monotonicity
results that are obeyed by minimizers, and apply them to test various
cluster models used in physical chemistry. This includes Lennard-Jones
clusters, Baxter's sticky-hard-sphere clusters, H20 clusters with TIP5P
pair interactions, and also a cluster model with a mix of Lennard-Jones
pair and Axilrod–Teller three-body interactions. This is joint work
with David Wales from Cambridge University.
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