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Updated: Apr 18, 2026

Spatial Separation of Molecular Conformers and Clusters
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Arbitrary order permanent Cartesian multipolar electrostatic interactions.

H A Boateng1, I T Todorov1

  • 1STFC Daresbury Laboratory, Keckwick Lane, Daresbury, Warrington WA4 4AD, United Kingdom.

The Journal of Chemical Physics
|January 24, 2015
PubMed
Summary

This study introduces a generalized Cartesian formulation for electrostatic multipolar interactions, enabling arbitrary order multipole calculations. This advances molecular simulations by improving accuracy and computational efficiency for condensed phase systems.

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Area of Science:

  • Computational Chemistry
  • Molecular Dynamics
  • Physical Chemistry

Background:

  • Advanced classical potential energy surfaces require higher order multipoles beyond fixed point charges for accurate condensed phase simulations.
  • Current methods are limited to dipoles and quadrupoles due to the complexity of electrostatic multipolar expressions.

Purpose of the Study:

  • To generalize the Cartesian formulation of electrostatic multipolar interactions to arbitrary orders.
  • To develop efficient computational methods for including higher order multipoles in molecular simulations.

Main Methods:

  • Derivation of formulas for arbitrary order implementation of the particle mesh Ewald method.
  • Development of a closed-form formula for the stress tensor in reciprocal space.
  • Provision of recurrence relations for common electrostatic potentials.

Main Results:

  • A generalized Cartesian formulation for electrostatic multipolar interactions up to arbitrary order.
  • Efficient calculation of electrostatic interactions and stress tensor in reciprocal space.
  • Computational cost scaling as O(p(3)) for interactions of order p.

Conclusions:

  • The developed method enables the inclusion of arbitrary order multipoles, significantly enhancing simulation accuracy.
  • The approach provides a computationally tractable framework for advanced molecular simulations.
  • This work overcomes limitations in current electrostatic models, paving the way for more precise condensed phase studies.