Introduction to Molecular Dynamics: Theory and Applications in Biomolecular Modeling - Computational Modeling of Biological Systems - page 11

Fig. 3 The periodic boundary conditions. The original simulation box in the center is replicated
throughout space to form an infinite lattice. For clarity, only eight replicas are shown in the figure
into the simulation results if we simply truncate the electrostatic potential at the
cutoff distance. To solve the problem, several methods have been proposed, and
a commonly used method is the Ewald summation [ 5 , 38 ]. The basic idea of the
method is to introduce a neutralizing charge distribution for every point charge in
the system. The resulting electrostatic potential, which decays much faster than r 1 ,
can then be calculated using a cutoff scheme. Of course, we have to calculate the
electrostatic potential of the neutralizing charge distribution and remove it from
the final result. Due to the slowly varying nature of this potential, this part of the
calculation can be performed in the reciprocal space via Fourier transform, where
we can use the cutoff scheme once again.
The application of the Ewald summation requires the periodic boundary con-
ditions (PBC), i.e., the cubic box containing the original simulation system is
replicated throughout space to form an infinite lattice, and atoms leaving the box
from one side will enter from the opposite side (Fig. 3 ). Apart from enabling the
Ewald calculation, the PBC have many advantages. For instance, the surface effect
of a finite-sized system is eliminated, since no atom is on the surface of an infinite
lattice. However, the artificial periodicity introduced by PBC inhibits the occurrence
of long-wavelength fluctuations [ 5 ], and has been found to reduce the magnitude