Distance and angular holonomic constraints in molecular simulations

Abstract

Finding the energy minima of systems with constraints is a challenging problem. We develop a minimization method based on the projection operator technique to enforce distance and angle constraints in minimization and reaction-path dynamics. The application of the projection operator alone does not maintain the constraints, i.e., they are slightly violated. Therefore, we use the SHAKE-methodology to enforce the constraints after each minimization step. We have extended θ -SHAKE for bend angles and introduce ø-SHAKE and χ-SHAKE to constrain dihedral and out-of-plane angles, respectively. Two case studies are presented: (1) A mode analysis of united-atom n-butane with various internal degrees of freedom kept frozen and (2) the minimization of chromene at a fixed approach toward the catalytic site of a (salen)Mn. The obtained information on energetics can be used to explain why specific enantioselectivity is observed. Previous minimization methods work for the free molecular case, but fail when molecules are tightly confined.