Methods of obtaining minimal energy configurations of many-particle systems are presented. As a model system, interactions between β-cyclodextr in (CD) and a varying number of water molecules are investigated using the "rigid molecule approximation" of the molecular mechanics (MM) approach. To minimize the intermolecular interaction energy, as described by a 1-6-12 Coulomb-Lennard-Jones potential (including additional terms for H-bond formation), a simplex algorithm, a Monte Carlo method, a simulated annealing (SA) procedure and a genetic minimization (GM) (or evolutionary) procedure have been used. The numerical convergence behavior of these methods, depending on the characteristics of the investigated system and the parametrizations are described and discussed with respect to the results obtained using the C7 symmetry of the CD molecule and H-bond formation between water and the peripheral hydroxyl groups. The simplex procedure appears to be unreliable for larger systems. The GM algorithm yields excellent results for small systems but needs excessive memory and time with increasing system size. For systems of three and more water molecules, the SA algorithm yields results closest to the absolute energy minimum. The results obtained from this method may be used to calculate thermodynamic quantities of the considered system.
ASJC Scopus subject areas
- Applied Microbiology and Biotechnology
- Chemical Engineering(all)