Distance Cut-Off Scheme

The most commonly used approximation cuts-off all pair interactions beyond a certain maximum distance $R_{\mbox{\scriptsize cut}}$. The cut-off is achieved by multiplying the force by a `cut-off'-function, which depends only on the distance and reduces the force to zero in a continous, differentiable, manner. A typical `cut-off'-function assumes the constant value unity up to a distance $R_{\mbox{\scriptsize on}}$, then decreases to zero between $R_{\mbox{\scriptsize on}}$ and $R_{\mbox{\scriptsize cut}}$ and remains zero for all distances greater than $R_{\mbox{\scriptsize cut}}$. As a result, only interactions up to the distance $R_{\mbox{\scriptsize cut}}$ have to be evaluated.

The appropriate choice of $R_{\mbox{\scriptsize cut}}$ is a compromise between accuracy and computing time. On the one hand, the smaller $R_{\mbox{\scriptsize cut}}$ is chosen, the faster the computation will be carried out. On the other hand, a large $R_{\mbox{\scriptsize cut}}$ will reduce the error of the approximation.

The `cut-off', although often employed, cannot be an appropriate approximation for molecular dynamics simulations since a neglect of the Coulomb interaction is believed to cause major rearrangements within the molecule. An improved approximation scheme involves ordering of the long-range interactions according to distance classes [44], as described below. A similar algorithm had been suggested in [37] for short-range forces in Lenard-Jones liquids.