Algorithms for brownian dynamics

A third order algorithm for brownian dynamics (BD) simulations is proposed, which is identical to the powerful molecular dynamics (MD) algorithm due to Verlet in the limit of infinitely small friction coefficient γ. In contrast to most BD algorithms used up till now, the integration time step Δt is not limited by the condition Δt ≪ γ-1. It is shown how constraints, such as bondlength or bond angle constraints, can be incorporated in the computational scheme. For the molecule considered here the proposed BD algorithm is about ten times more efficient than the second order ones that are generally used. The introduction of bondlength constraints saves about a factor of three in computing time, as in the MD case. The application of bond angle constraints is not recommended.