Ewald summation schemes

Thus, for both the ionic and the dipolar systems, the actual use of the rigorously derived Ewald summation for slab systems loads to a substantial increase in computer time. One way of dealing with this problem would be to employ precalculated tables [252] for potential energies (and forces) on a three-dimensional spatial grid amended by a suitable interpolation scheme. Another strategy is to employ approximate methods such as the one presented in the subsequent Section 6.3.2. 

Because implicit solvent simulations are typically open, non-periodic systems, electrostatic interactions are calculated according to standard cutoff schemes that do not scale as well to large system sizes as the more efficient Ewald summation method [11,12] that is routinely used in explicit solvent simulations. 

The treatment of boundary conditions can be incorporated in the EMM scheme easily. Periodic boundary conditions as well as Dirichlet, Neumann, and mixed conditions can be accounted for. The EMM approach has been shown to be more efficient than the Ewald summation method (see the next... 

In the simulation of liquids it is usual to consider a computational box with periodic boundary conditions. For the calculation of static crystal energies and forces, this box is naturally a unit cell, but more advantage of symmetry can be taken by limiting the attention to the asymmetric unit only. However, to simulate dynamic properties it may be necessary to use a computational box that comprises a number of unit cells. Calculation of free energies is, as always, difficult but there are a few approaches that are not applicable to the liquid state. A possible complication, not encountered in liquids, is that the unit cell may have a net dipole moment. In that case one must note that calculations with a simple cut-off scheme do not produce the same result as Ewald summations. 

A large number of crystal and NMR structures are available for DNA double-.stranded helices in the environment dependent A-, B-, or Z-forms. Since the first study reported by Levitt in 1983, several MD studies have been conducted on various DNA sequences. As the number of MD simulations increa.sed with available computational means, simulations under in vacuo conditions as well as those using various truncation schemes for the evaluation of the long-range electrostatic interactions have revealed their limits (.see Methodology). New methods, based on the Ewald summation procedure, have been developed and applied to the simulation of nucleic acid duplexes in the crystal phase and in aqueous solution. We will, in the following, report mostly on studies incorporating such advances. Previous work is reviewed in Refs. 2, 4-6, and 8. 

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