Leapfrog Rotational Algorithms

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Abstract
A new implicit rotational integrator for the orientation of rigid molecules is introduced, and compared with an existing explicit integrator. Both algorithms are categorised as leapfrogs since the quantities saved between time steps are on the on-step orientation and the mid-step angular momentum. Orientations may be expressed in terms of principal axis vectors or, as in the implementations used here, quaternions. Thermostatted versions of the algorithms as well as conventional energy-conserving versions are described. The algorithms are extensively tested in simulations of liquid water, the aim being to study the effect of increased time steps on a range of measured properties. The implicit algorithm is superior to the explicit algorithm, and can be used with time steps up to 3 fs with energy-conserving dynamics. When thermostatted, it may be used with time steps up to at least 6 fs.