Analysis and application of potential energy smoothing and search methods for global optimization

Global energy optimization of a molecular system is difficult due to the we ll-known "multiple minimum" problem. The rugged potential energy surface (P ES) characteristic of multidimensional systems can be transformed reversibl y using potential smoothing to generate a new surface that is easier to sea rch for favorable configurations. The diffusion equation method (DEM) is on e example of a potential smoothing algorithm. Potential smoothing as implem ented in DEM is intuitively appealing and has certain appropriate statistic al mechanical properties, but often fails to identify the global minimum ev en for relatively small problems. In the present paper, extensions to DEM c apable of correcting its empirical behavior are systematically investigated . Two types of local search (LS) procedures are applied during the reversin g schedule from the smooth deformed PES to the undeformed surface. Changes needed to generate smoothable versions of standard molecular mechanics forc e fields such as AMBER/OPLS and MM2 are also described. The resulting metho ds are applied in an attempt to determine the global energy minimum for a v ariety of systems in different coordinate representations. The problems stu died include argon clusters, cycloheptadecane, capped polyalanine, and the docking of a-helices. Depending on the specific problem, potential smoothin g and search (PSS) is performed in Cartesian, torsional, or rigid body spac e. For example, PSS finds a very low energy structure for cycloheptadecane with much greater efficiency than a search restricted to the undeformed pot ential surface. It is shown that potential smoothing is characterized by th ree salient features. As the level of smoothing is increased, unique minima merge into a common basin, crossings can occur in the relative energies of a pair of minima, and the spatial locations of minima are shifted due to t he averaging effects of smoothing. Local search procedures improve the abil ity of smoothing methods to locate global minima because they facilitate th e post facto correction of errors due to energy crossings that may have occ urred at higher levels of smoothing. PSS methods should serve as useful too ls for global energy optimization on a variety of difficult problems of pra ctical interest.