AN IMPROVED LEAP-FROG ROTATIONAL ALGORITHM

A new implicit leap-frog algorithm for the integration of rigid body r otational motion is presented. Orientations are represented by quatern ions and the algorithm is compared with three existing leap-frog integ rators, by solving the classical equations of motion for a (H2O)(20) c luster. We find that the present scheme exhibits superior energy conse rvation properties, especially for integration times of about 10 ps or longer. Contrary to previous algorithms, the present one behaves as a true Verlet integrator, where the degree of energy conservation is in dependent of the length of the trajectory. The method is similar to th e implicit scheme proposed by D. Fincham (1992, Molec. Simulation, 8, 165), with the difference that self-consistent quaternions, as well as their time derivatives, are obtained by iteration at the mid-timestep instead of after the complete timestep. A slight modification of eith er the explicit or the implicit leap-frog rotational algorithm in exis ting molecular dynamics programs may thus lead to significant improvem ents of energy conservation, as long as this property is not dominated by other sources such as errors due to potential truncation. It is de monstrated that the present algorithm can be used with timesteps as la rge as 4 fs in water simulations, and still produce stable trajectorie s of 10 ns duration.