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Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

Figure 2

Accuracy of the 2-charge practical point charge approximation (PPCA) for charge distributions with a net zero charge.

Accuracy is calculated as the RMS error relative to the exact computation, at a distance of 10 Å () from the center of geometry. RMS error for the 2-charge PPCA (Eq. (18)) is shown as a function of the distance between the two charges of the PPCA . The RMS error for the 2-charge PPCA is compared to that of the point dipole approximation with an optimal center of expansion. (a) Cases where Eq. (23) is true. (b) Cases where Eq. (23) is false. This figure also includes the 2-charge optimal point charge approximation (Eq. (22)) for comparison. Connecting lines are shown to guide the eye.

Figure 2