Accurate and fast enumeration of large, combinatorial search spaces presents a central conceptual challenge in molecular design. To address this challenge, an algorithm is developed that guarantees globally optimal solutions to a mixed-integer nonlinear programming formulation for molecular design. The formulation includes novel structural feasibility constraints, while the algorithm provides all feasible solutions to this formulation through the implicit enumeration of a single branch-and-reduce tree. This algorithm is used to provide the complete solution set to a refrigerant design problem posed elsewhere. In addition to rediscovering CFCs, the proposed methodology identifies a number of novel potential replacements of Freon 12.