Understanding the many-body expansion for large systems. I. Precision considerations

Area of Science:

• Computational quantum chemistry
• Electronic structure theory

Background:

• Low-order n-body expansions offer efficient alternatives to traditional ab initio methods for large systems.
• These methods leverage the parallelizable nature of numerous subsystem calculations.

Purpose of the Study:

• To investigate the impact of finite precision in subsystem calculations on n-body electronic structure methods.
• To assess the reproducibility of total binding energies for large water clusters using different computational implementations.

Main Methods:

• Comparison of two distinct computer implementations of the n-body expansion applied to water clusters up to (H₂O)₄₇.
• Analysis of total binding energies and propagation of errors using a derived closed-form expression for the n-body expansion.

Main Results:

• Subtle differences in implementations are amplified by the combinatorial nature of n-body expansions, particularly for n ⩾ 4.
• Total energies differed by several kcal/mol between implementations, primarily due to Coulomb self-energy corrections in driver-based approaches.
• Four-body and higher-order expansions demonstrated significant sensitivity to numerical thresholds.

Conclusions:

• Script- or driver-based implementations require careful handling of precision, ideally reading binary output or being fully integrated.
• Fully integrated methods avoiding Coulomb self-energy calculations are recommended for reliable results in large systems.
• The practical utility of four-body and higher-order expansions for large systems is questionable due to numerical sensitivity.