  We formulate statistical-mechanical inverse methods in order to determine
optimized interparticle interactions that spontaneously produce target
many-particle configurations. Motivated by advances that give experimentalists
greater and greater control over colloidal interaction potentials, we propose
and discuss two computational algorithms that search for optimal potentials for
self-assembly of a given target configuration. The first optimizes the
potential near the ground state and the second near the melting point. We begin
by applying these techniques to assembling open structures in two dimensions
(square and honeycomb lattices) using only circularly symmetric pair
interaction potentials ; we demonstrate that the algorithms do indeed cause
self-assembly of the target lattice. Our approach is distinguished from
previous work in that we consider (i) lattice sums, (ii) mechanical stability
(phonon spectra), and (iii) annealed Monte Carlo simulations. We also devise
circularly symmetric potentials that yield chain-like structures as well as
systems of clusters.
