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Untangling Sources of Error in the Density-Functional Many-Body Expansion.

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The many-body expansion amplifies errors in electronic structure calculations when using standard grids with modern density-functional approximations. This exacerbates delocalization errors, requiring denser grids to mitigate issues in computational chemistry.

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Area of Science:

  • Computational chemistry
  • Electronic structure theory
  • Quantum chemistry

Background:

  • The many-body expansion is a powerful tool for data-driven applications in electronic structure theory, including force field parametrization and machine learning.
  • Modern density-functional approximations (DFAs) are widely used but can be sensitive to numerical approximations.
  • Quadrature grids are essential for numerical integration in electronic structure calculations.

Purpose of the Study:

  • To investigate the impact of quadrature grid errors on the many-body expansion when using modern DFAs.
  • To demonstrate how standard quadrature grids amplify errors and exacerbate delocalization errors in many-body calculations.
  • To explore strategies for mitigating these amplified errors.

Main Methods:

  • Application of the many-body expansion framework.
  • Utilizing modern density-functional approximations, including SCAN, r2SCAN, ωB97X-V, and ωB97M-V.
  • Performing calculations on anion-water clusters.
  • Systematic variation of quadrature grid density.

Main Results:

  • Standard quadrature grids significantly amplify errors when used with the many-body expansion and modern DFAs.
  • Runaway error accumulation was observed with conventional grids, unlike in standard density-functional calculations.
  • Delocalization error is exacerbated, leading to overestimated nonadditive n-body interactions.
  • Employing dense quadrature grids exposes inherent self-interaction errors.

Conclusions:

  • The combination of the many-body expansion and standard quadrature grids with modern DFAs is problematic due to error amplification.
  • Denser quadrature grids are necessary to obtain reliable results and expose underlying errors.
  • Mitigation strategies for self-interaction error can be effectively applied once exposed by dense grids.