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

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.