Optimization Aspects Specific to Force Fields

Because of their utility for very large systems, where their relative speed proves advantageous, force fields present several specific issues with respect to practical geometry optimization that merit discussion. Most of these issues revolve around the scaling behavior 

In practice, even though the use of a cut-off introduces only small disparities in the energy, the discontinuity of these disparities can cause problems for optimizers. A more stable approach is to use a switching function which multiplies the van der Waals interaction and causes it (and possibly its first and second derivatives) to go smoothly to zero at some cut-off distance. This function must, of course, be equal to 1 at short distances. 

In infinite periodic systems, an attractive alternative to the use of a cut-off distance is the Ewald sum technique, first described for chemical systems by York, Darden and Pedersen (1993). By using a reciprocal-space technique to evaluate long-range contributions, the total electrostatic interaction can be calculated to a pre-selected level of accuracy (i.e., the Ewald sum limit is exact) witli a scaling that, in tlie most favorable case (called Particle-mesh Ewald , or PME), is AlogA. Prior to the introduction of Ewald sums, the modeling of polyelectrolytes (e.g., DNA) was rarely successful because of the instabilities introduced 

However, when it comes to reactions where bonds are being made and/or broken, it is clear that, at least for the vast majority of force fields that use polynomial expressions for the bond stretching energy, the normal model is inapplicable. Nevertheless, substantial application of molecular mechanics to such TS structures has been reported, with essentially three different approaches having been adopted. 

This methodology has two chief drawbacks. A philosophical drawback is that movement along the reaction coordinate raises the force-field energy instead of lowering it, which 

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