An adaptive treecode for computing nonbonded potential energy in classical molecular systems

A treecode algorithm is presented for rapid computation of the nonbonded potential energy in classical molecular systems. The algorithm treats a general form of pairwise particle interaction with the Coulomb and London dispersion potentials as special cases. The energy is computed as a sum of group–group interactions using a variant of Appel's recursive strategy. Several adaptive techniques are employed to reduce the execution time. These include an adaptive tree with nonuniform rectangular cells, variable order multipole approximation, and a run-time choice between direct summation and multipole approximation for each group–group interaction. The multipole approximation is derived by Taylor expansion in Cartesian coordinates, and the necessary coefficients are computed using a recurrence relation. An error bound is derived and used to select the order of approximation. Test results are presented for a variety of systems.