@article{Tameling2014:590,
author = "Daniel Tameling and Paul Springer and Paolo Bientinesi and {Ahmed E.} Ismail",
title = "Multilevel Summation for Dispersion: A Linear-Time Algorithm for 1/r^6 Potentials",
journal = "Journal of Chemical Physics",
year = 2014,
volume = 140,
pages = 24105,
month = jan,
doi = "10.1063/1.4857735",
url = "https://arxiv.org/pdf/1308.4005.pdf"
}The multilevel summation (MLS) method was developed to evaluate long-range interactions in molecular dynamics (MD) simulations. MLS was initially introduced for Coulombic potentials; we have extended this method to dispersion interactions. While formally short-ranged, for an accurate calculation of forces and energies in cases such as in interfacial systems, dispersion potentials require long-range methods. Since long-range solvers tend to dominate the time needed to perform MD calculations, increasing their performance is of vital importance. The MLS method offers some significant advantages when compared to mesh-based Ewald methods like the particle-particle particle-mesh and particle mesh Ewald methods. Unlike mesh-based Ewald methods, MLS does not use fast Fourier transforms and is thus not limited by communication and bandwidth concerns. In addition, it scales linearly in the number of particles, as compared to the O(N log N) complexity of the mesh-based Ewald methods. While the structure of the MLS method is invariant for different potentials, every algorithmic step had to be adapted to accommodate the 1/r^6 form of the dispersion interactions. In addition, we have derived error bounds, similar to those obtained by Hardy for the electrostatic MLS. Using a prototype implementation, we can already demonstrate the linear scaling of the MLS method for dispersion, and present results establishing the accuracy and efficiency of the method.
