In the particle mesh method, just as in standard Ewald summation, the generic interaction potential is separated into two terms φ φ ( r ) = d e f φ φ s r ( r ) + φ φ ℓ ℓ r ( r ) . The basic idea of particle mesh Ewald summation is to replace the direct summation of interaction energies between point particles E TOT = ∑ ∑ i , j φ φ ( r j − − r i ) = E s r + E ℓ ℓ r with two summations, a direct sum E s r of the short-ranged potential in real space E s r = ∑ ∑ i , j φ φ s r ( r j − − r i ) (this is the particle part of particle mesh Ewald) and a summation in Fourier space of the long-ranged part E ℓ ℓ r = ∑ ∑ k Φ Φ ~ ~ ℓ ℓ r ( k ) | ρ ρ ~ ~ ( k ) | 2