Efficient implementation of the fast multipole method

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Abstract
A number of computational techniques are described that reduce the effort related to the continuous fast multipole method, used for the evaluation of Coulomb matrix elements as needed in Hartree-Fock and density functional theories. A new extent definition for Gaussian charge distributions is proposed, as well as a new way of dividing distributions into branches. Also, a new approach for estimating the error caused by truncation of multipole expansions is presented. It is found that the use of dynamically truncated multipole expansions gives a speedup of a factor of 10 in the work required for multipole interactions, compared to the case when all interactions are computed using a fixed multipole expansion order. Results of benchmark calculations on three-dimensional systems are reported, demonstrating the usefulness of our present implementation of the fast multipole method.