Stochastic dynamics for molecules with constraints: Brownian dynamics of n-alkanes

Abstract

It is shown how constraints, such as bondlength or bond angle constraints, can be incorporated in the algorithms currently being used in brownian dynamics (BD) simulations of molecular liquids or solutions. The validity of the BD model, in which the stochastic and frictional force fields possess neither time correlations nor space correlations between different atoms of the molecule, is investigated by comparing the BD results with those of molecular dynamics (MD) simulations for liquid n-butane and n-decane. The BD model appears to yield a good approximation to the dynamics of a chain molecule in the liquid state. For butane, solvent packing effects play an important role in the condensed phase. For decane, the equilibrium conformation and dynamics are determined mainly by intramolecular interactions. When analysing the conformational transitions occurring in these molecules, one observes a correlation between consecutive transitions both of one dihedral angle and of two adjacent dihedral angles, due to conservation of angular momentum. Various theories of rate processes are discussed. A Kramers-modified transition state theory appears to produce reliable predictions of transition rates. It turns out to be essential to use the correct normal mode values for the frequency of the motion in the dihedral wells.