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Multilevel summation for dispersion: a linear-time algorithm for r(-6) potentials.

Daniel Tameling1, Paul Springer1, Paolo Bientinesi1

  • 1AICES Graduate School, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany.

The Journal of Chemical Physics
|January 21, 2014
PubMed
Summary
This summary is machine-generated.

The multilevel summation (MLS) method now efficiently calculates dispersion interactions in simulations. This advancement offers linear scaling and avoids limitations of mesh-based methods for complex systems.

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Area of Science:

  • Computational chemistry
  • Molecular dynamics simulations
  • Statistical mechanics

Background:

  • Accurate simulation of interfacial and inhomogeneous systems requires long-range methods for dispersion interactions.
  • Existing methods like particle-particle particle-mesh and smooth particle mesh Ewald have limitations.
  • The multilevel summation (MLS) method was previously developed for Coulombic interactions.

Purpose of the Study:

  • To extend the multilevel summation (MLS) method to accurately handle dispersion interactions.
  • To adapt the MLS algorithm for the r(-6) form of dispersion potentials.
  • To derive error bounds for the dispersion MLS method.

Main Methods:

  • Extension of the multilevel summation (MLS) algorithm.
  • Adaptation of algorithmic steps for r(-6) dispersion interactions.
  • Derivation of error bounds for the dispersion MLS.

Main Results:

  • Demonstrated linear scaling of the MLS method for dispersion interactions via a prototype implementation.
  • Established the accuracy and efficiency of the extended MLS method.
  • MLS method avoids fast Fourier transforms, mitigating communication and bandwidth concerns.

Conclusions:

  • The extended MLS method provides an accurate and efficient approach for calculating dispersion interactions.
  • MLS offers significant advantages over mesh-based methods, including linear scaling and independence from FFTs.
  • This work enables more robust simulations of complex molecular systems.