Global Energy Minima of Molecular Clusters Computed in Polynomial Time with Semidefinite Programming

The global energy minima of pure and binary molecular clusters with 5–12 particles interacting pairwise are computed in polynomial time as a function of only the two-particle reduced density function (2-RDF). We derive linear matrix inequalities from the classical analogue of quantum N-representability constraints to ensure that the 2-RDF represents realistic N-particle configurations. The 2-RDF reformulation relaxes a combinatorial optimization into a convex optimization that scales polynomially in computer time. Clusters are optimized with a code for large-scale semidefinite programming developed for the quantum representability problem [ D. A. Mazziotti Phys. Rev. Lett. 93 213001 (2004)].