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Parameterless Stopping Criteria for Recursive Density Matrix Expansions.

Anastasia Kruchinina1, Elias Rudberg1, Emanuel H Rubensson1

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New parameterless stopping criteria for electronic structure calculations automatically detect numerical errors. This avoids manual tolerance setting, improving density matrix construction in recursive polynomial expansions.

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Area of Science:

  • Computational chemistry
  • Electronic structure theory
  • Numerical analysis

Background:

  • Accurate density matrix construction is crucial for electronic structure calculations.
  • Traditional methods rely on user-defined stopping tolerances, which can be difficult to optimize.
  • Recursive polynomial expansions are used for efficient density matrix computation.

Purpose of the Study:

  • To develop and validate parameterless stopping criteria for recursive polynomial expansions.
  • To automate the detection of numerical error dominance in density matrix calculations.
  • To eliminate the need for manual tolerance setting in electronic structure computations.

Main Methods:

  • Convergence-order estimation to predict calculation behavior.
  • Development of automatic stopping criteria based on error detection.
  • Implementation and testing within the Ergo quantum chemistry program.

Main Results:

  • The proposed parameterless criteria effectively identify when numerical errors dominate calculations.
  • These criteria successfully prevent unnecessary iterations that do not improve results.
  • Demonstrated efficacy in both dense and sparse matrix computations.
  • Successful application in large-scale self-consistent field (SCF) calculations.

Conclusions:

  • Parameterless stopping criteria offer a robust and automated approach to density matrix construction.
  • These criteria simplify calculations by removing the need for manual parameter tuning.
  • The method enhances the reliability and efficiency of electronic structure calculations.