  A new theoretical approach is described for the inverse self-assembly
problem, i.e., the reconstruction of the interparticle interaction from a given
structure. This theory is based on the variational principle for the functional
that is constructed from a free energy functional in combination with Percus's
approach [J. Percus, Phys. Rev. Lett. vol.8, 462 (1962)]. In this theory, the
interparticle interaction potential for the given structure is obtained as the
function that maximizes the functional. As test cases, the interparticle
potentials for two-dimensional crystals, such as square, honeycomb, and kagome
lattices, are predicted by this theory. The formation of each target lattice
from an initial random particle configuration in Monte Carlo simulations with
the predicted interparticle interaction indicates that the theory is
successfully applied to the test cases.
