Screened multipole electrostatic interactions at the Debye–Hückel level

We present the multipole Taylor series expansion of the Debye–Hückel potential exp(−R/κ)/R for screened electrostatic interactions, where R is the separation distance and κ is the Debye length. Based on that expansion we derive the expressions for the electrostatic field and interaction energy in the cases of charge–dipole, dipole–dipole, and quadrupole–dipole interactions. The results are compared with a recent expansion of the same potential based on modified spherical Bessel functions [A. Boschitsch, M.O. Fenley, W. Olson, J. Comput. Phys. 151 (1999) 212]. Some examples illustrating the limits of validity of the derived formulae are presented, and their possible applications are discussed.