Table 3.

Computing the reciprocal space electrostatic interactions by Ewald sums in MPH1. The reciprocal space is computed four times. In each of these calculations only a subset of charges is kept on, while the others are set to zero. The resulting potential and forces are then scaled by the switching parameter. In the first calculation only the electrostatic interactions between the “P” particles are kept on and the energy and forces are scaled by λ. Secondly, the electrostatic interactions of “P” and “N” particles are turned on and the resulting energy and forces are scaled by 1−λ. Third only the “M” particles have their charges on and the result is not scaled. Finally, only the charges of the “N” particles are kept on, and the result is scaled by λ. The sum of these four contributions is shown at the bottom of the table. The self-interactions are not scaled, and the external interactions are scaled by 1−λ.

MPH1
#	Type of particle interacting	Scaling	Result
1	P	λ	λU(P)
2	P N	(1−λ)	(1−λ)[U(P)+U(P,N)+U(N)]
3	M	1	U(M)
4	N	λ	λU(N)
OVERALL: U(P) + (1−λ)U(P,N) + U(N) + U(M)