A fast adaptive multipole algorithm for calculating screened Coulomb (Yukawa) interactions

The screened Coulomb (Yukawa or Debye-Huckel) potential, Phi = exp(-kappa r )/r, where r is the separation distance and kappa is the Debye-Huckel scree ning parameter, gives a good description of the electrostatic interactions in a variety of biologically and physically important charged systems. it i s well known that the direct calculation of the energy and forces due to a collection of N charged particles involves the pairwise summation of all ch arged particle interactions and exhibits an O(N-2) computational complexity which severely restricts maximum problem size. This has prompted the devel opment of fast summation algorithms that allow the electrostatic energy and forces to be obtained in only O(N log N) operations. To date, however, pra ctically all such implementations have been limited exclusively to pure Cou lombic potentials (kappa = 0), and the central contribution of the present method is to extend this capability to the entire range of the inverse Deby e length, kappa greater than or equal to 0. The basic formulation and compu tational implementation of the spherical modified Bessel function-based mul tipole expansions appropriate for the screened Coulomb kernel are first pre sented. Next, a simple model system consisting of a single source charged p article is studied to show that the maximum electrostatic energy error incu rred by an M-order multipole expansion for the Yukawa potential is bounded above by the error of the equivalent multipole expansion for the Coulombic potential. Finally, timing and accuracy studies are presented for a variety of charged systems including polyelectrolyte chains, random distributions of charges inside a cube, and face-centered-cubic lattice charge configurat ions containing up to 103,823 charges. (C) 1999 Academic Press.