An Ewald summation based multipole method

~assuming the simulation box is cubic!, where qi and ri are the charge and position of particle i, L is the size of the simulation box, n5(n1 ,n2 ,n3), and the prime indicates that the i5 j terms are omitted when n50. The Ewald summation method has been widely used to handle the lattice sum in Eq. ~1!. In the method, the above-mentioned conditionally convergent series is written as a sum of a constant E (0) and two rapidly convergent series, the real space sum E (r) and the reciprocal space sum E , E5E ~0 1E ~r 1E ~k , ~2!