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Testing Lennard-Jones clusters for optimality.

Michael K-H Kiessling1

  • 1Department of Mathematics Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854, USA.

The Journal of Chemical Physics
|July 6, 2023
PubMed
Summary
This summary is machine-generated.

A new necessary condition for optimality is introduced for cluster energies. This simple test helps identify non-optimal configurations, improving the reliability of published cluster energy data.

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Area of Science:

  • Computational physics
  • Chemical physics
  • Materials science

Background:

  • Determining optimal cluster configurations and energies is crucial for understanding material properties.
  • Existing methods for calculating cluster energies can be computationally intensive and may yield non-optimal results.
  • Newton's third law (action-reaction) governs inter-monomer interactions in clusters.

Purpose of the Study:

  • To introduce a simple, necessary condition for verifying the optimality of computed cluster energies.
  • To provide a practical test for identifying non-optimal energy values in cluster databases.
  • To enhance the reliability of published data on lowest average pair energies of clusters.

Main Methods:

  • Formulation of a necessary condition for optimality based on pair forces satisfying Newton's third law.
  • Application of this condition to a comprehensive dataset of Lennard-Jones cluster energies (2 ≤ N ≤ 1610).
  • Empirical validation of the condition by testing publicly available cluster data.

Main Results:

  • A simple, necessary condition for optimality was successfully derived and applied.
  • The test identified a non-optimal energy value for a 447-particle Lennard-Jones cluster.
  • The condition is computationally inexpensive to implement in optimization search algorithms.

Conclusions:

  • The proposed necessary condition is a useful tool for filtering non-optimal cluster energy data.
  • Implementing this test can increase confidence in the optimality of published cluster energies.
  • This method offers a straightforward way to improve the quality of scientific data in this field.