Nonbonded energy, discontinuities

The discontinuities in the nonbonded energy, and, hence, forces on the atoms, may be addressed by scaling the nonbonded interaction using cubic spline functions (,S). For the classical description of the force field, the nonbonded interaction energy is written as ... 

If a cutoff is abruptly applied at a particular interatomic distance, this discontinuity can cause problems in energy minimization and molecular-dynamics calculations. To avoid this, one can use a cutoff that makes the nonbonded interactions go to zero gradually over a distance of, say, 1 A. This is done using what is called a switching function. 

In this section, we present a detailed discussion of methods relevant to counterion simulations of DNA. Electrostatic interactions dominate all energies involving the DNA and ions. The largest systems simulated to date typically require truncation of nonbonded interaction potentials at around ISA. Abrupt truncation of the potential has the adverse effect of creating an artificial boundary. In an MD simulation, the abrupt truncation produces a discontinuity in force because the first derivative of the interaction potential at the cutoff radius is infinity. Computer programs simply set the forces at the boundary to be zero instead of large values to represent infinity. 

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