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)10.1103/PhysRevLett.93.213001].