Notes on “Ewald summation of electrostatic multipole interactions up to quadrupolar level” [J. Chem. Phys. 119, 7471 (2003)]

In an article [A. Aguado and P. A. Madden, J. Chem. Phys. 119, 7471 (2003)] published in this journal, Ewald summation expressions were derived for the energy, interatomic forces, pressure tensor, electrostatic field, and electrostatic field gradients in simulation system composed of molecules with charges, induced dipoles, and quadrupoles. In this letter we propose an alternative formulation of the reciprocal space terms generalized to higher multipoles, providing, at the same time, a few important corrections for previously published derivations. The present expressions, more compact than the ones proposed in the original work, provide a straightforward approach to implement an Ewald summation scheme for multipole interactions in codes where a standard Ewald summation is already available. A major result of the present derivation is an increase in the computational efficiency compared to the previous implementation of the several different electrostatic terms.