Deterministic global optimization of molecular structures using interval analysis

The search for the global minimum of a molecular potential energy surface is a challenging problem. The molecular structure corresponding to the global minimum is of particular importance because it usually dictates both the physical and chemical properties of the molecule. The existence of an extremely large number of local minima, the number of which may increase exponentially with the size of the molecule, makes this global minimization problem extremely difficult. A new strategy is described here for solving such global minimization problems deterministically. The methodology is based on interval analysis, and provides a mathematical and computational guarantee that the molecular structure with the global minimum potential energy will be found. The technique is demonstrated using two sets of example problems. The first set involves a relatively simple potential model, and problems with up to 40 atoms. The second set involves a more realistic potential energy function, representative of those in current use, and problems with up to 11 atoms.