The Particle Mesh Ewald (PME) method is an N log N algorithm for efficiently calculating electrostatic energies and forces in large periodic systems. This method combines direct space and reciprocal space Ewald sums, using fast Fourier transforms (FFTs) to evaluate the reciprocal space convolutions. The method is particularly effective for large macromolecular simulations where conventional Ewald summation becomes computationally prohibitive. The PME method involves choosing a parameter β to ensure that only the minimum image terms in the direct space sum are retained, reducing the computational complexity. The reciprocal space sum is then approximated using a multidimensional interpolation approach, inspired by the particle-mesh method. This allows the reciprocal space energy and forces to be expressed as convolutions, which can be efficiently evaluated using FFTs. The resulting algorithm has a computational complexity of O(N log N), making it suitable for large systems. The method is implemented by precomputing the reciprocal space potential and its gradients on a grid of fractional coordinates. These values are then used to interpolate the potential at each point, allowing for efficient calculation of the total electrostatic energy and forces. The accuracy of the PME method is demonstrated through tests on several macromolecular crystals, showing that high precision can be achieved with a modest increase in computational time. The PME method offers several advantages, including high accuracy, ease of implementation into conventional molecular dynamics algorithms, continuity of the potential and its derivatives, and efficiency. It is particularly effective for nonorthogonal unit cells and can handle nonuniform particle distributions with high precision. The method is also memory-efficient, with memory requirements increasing slowly as computational power improves. The PME method is a valuable tool for simulating large macromolecular systems with high accuracy and efficiency.The Particle Mesh Ewald (PME) method is an N log N algorithm for efficiently calculating electrostatic energies and forces in large periodic systems. This method combines direct space and reciprocal space Ewald sums, using fast Fourier transforms (FFTs) to evaluate the reciprocal space convolutions. The method is particularly effective for large macromolecular simulations where conventional Ewald summation becomes computationally prohibitive. The PME method involves choosing a parameter β to ensure that only the minimum image terms in the direct space sum are retained, reducing the computational complexity. The reciprocal space sum is then approximated using a multidimensional interpolation approach, inspired by the particle-mesh method. This allows the reciprocal space energy and forces to be expressed as convolutions, which can be efficiently evaluated using FFTs. The resulting algorithm has a computational complexity of O(N log N), making it suitable for large systems. The method is implemented by precomputing the reciprocal space potential and its gradients on a grid of fractional coordinates. These values are then used to interpolate the potential at each point, allowing for efficient calculation of the total electrostatic energy and forces. The accuracy of the PME method is demonstrated through tests on several macromolecular crystals, showing that high precision can be achieved with a modest increase in computational time. The PME method offers several advantages, including high accuracy, ease of implementation into conventional molecular dynamics algorithms, continuity of the potential and its derivatives, and efficiency. It is particularly effective for nonorthogonal unit cells and can handle nonuniform particle distributions with high precision. The method is also memory-efficient, with memory requirements increasing slowly as computational power improves. The PME method is a valuable tool for simulating large macromolecular systems with high accuracy and efficiency.