Recently, a number of groups have discovered that the use of Ewald summation leads to greatly improved stability in molecular dynamics simulations of nucleic acids, proteins and membrane bilayers. This presentation will first outline the mathematical development of Ewald summation, discussing what is currently understood about the long-range boundary effects, and about the correct way to treat charged unit cells. Following this, the Particle Mesh Ewald (PME) approach to fast Ewald summation will be introduced, along with suggestions for possible future improvements. Possible artifacts due to the use of Ewald summation in molecular dynamics simulations will be discussed, and finally the treatment of free energy perturbation, in particular the free energy of charging an ion in water, will be discussed in the context of Ewald summation.

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1996-1997 Mathematics in High Performance Computing