The article presents a method called Particle Mesh Ewald (PME) for evaluating electrostatic energies and forces in large periodic systems. The PME method is based on the interpolation of reciprocal space Ewald sums and the use of fast Fourier transforms to evaluate the resulting convolutions. The authors introduce a technique that reduces the computational complexity from \(N^2\) to \(N \log(N)\), making it efficient for large macromolecular systems. The method involves choosing a sufficiently large value of \(\beta\) to negligible the long-range interactions, and then approximating the reciprocal space sum using piecewise interpolation. The approximate reciprocal energy and forces are expressed as convolutions, which can be efficiently computed using FFTs. The method is shown to be accurate and efficient, with reasonable relative accuracy (about \(2 \times 10^{-4}\) rms force error) achievable with a modest increase in computational time. The PME method is implemented into the AMBER3.0 molecular dynamics code and tested on several macromolecular crystals, demonstrating its effectiveness and potential for high-precision simulations.The article presents a method called Particle Mesh Ewald (PME) for evaluating electrostatic energies and forces in large periodic systems. The PME method is based on the interpolation of reciprocal space Ewald sums and the use of fast Fourier transforms to evaluate the resulting convolutions. The authors introduce a technique that reduces the computational complexity from \(N^2\) to \(N \log(N)\), making it efficient for large macromolecular systems. The method involves choosing a sufficiently large value of \(\beta\) to negligible the long-range interactions, and then approximating the reciprocal space sum using piecewise interpolation. The approximate reciprocal energy and forces are expressed as convolutions, which can be efficiently computed using FFTs. The method is shown to be accurate and efficient, with reasonable relative accuracy (about \(2 \times 10^{-4}\) rms force error) achievable with a modest increase in computational time. The PME method is implemented into the AMBER3.0 molecular dynamics code and tested on several macromolecular crystals, demonstrating its effectiveness and potential for high-precision simulations.