Force-shifted truncation

Computing the interatomic forces is the most time-consuming part in an MD simulation. The use of a cutoff radius is a standard trick of the trade that reduces computational cost by neglecting interactions between atoms separated by a distance larger than the specified cutoff. As described earlier, this truncation results in a discontinuity of both the potential and the force at the cutoff distance, but the drawback thus entailed can be avoided by implementation of either the shifted-force potential or a taper function. 

This is a spherically truncated and shifted potential, known as STS, which is the potential corresponding to the truncated force. The fact that MC and MD are, in fact, carried out with different potentials is the origin of the observed differences between the density profiles. The STS potential is shallower than the ST potential, and this gives rise to a lower density in the centre of the film. MD can be carried out with an ST potential, if the following modified force scheme is used. 

The zero-th order term is removed by a suitable shift of the origin, the first-order term is zero because the forces (5V/dxi)Q vanish at equilibrium, the second-order term defines a quadratic harmonic potential. In most cases of chemical interest the expansion is truncated at the second order. The analysis of the higher-order terms is outside the scope of our discussion. The truncation at the second order implies that the restoring forces are assumed to be linear with the infinitessimal displacements from the equilibrium position. 

The small changes to the force and potential energy, resulting from the change to a shifted force potential function, provide improved accuracy eind stcibility in computer simulations, with negligible changes to structure and time correlation functions, at short to moderate times, calculated from the usual truncated potential. Corrections to calculated thermodynamic properties to account for modifications to the potential can be calculated by a perturbation method similar to that used for the long tail corrections. This matter will be discussed in detail in a separate paper. 

Figure 1. Potential energy u (solid lines) and force F (dashed lines) as a function of site-site distance r for truncated (a) and shifted-force (h) potential functions. The modified force in (h) is formed by shifting the force-distance curve in (a) upward a distance H, equal to the magnitude of the discontinuity at r = r,.. The modified potential energy in (h) is then defined by Equations 1 and 2.

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