Trouble with the Many-Body Expansion.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The Many-Body Expansion (MBE) is a standard method for approximating energies in large chemical systems.
• Rapid convergence by the four-body term is conventionally assumed for MBE calculations.
• Basis set choice significantly impacts the accuracy of quantum chemical calculations.

Purpose of the Study:

• To investigate the convergence of the Many-Body Expansion (MBE) for large chemical systems using common basis sets.
• To identify the underlying causes of poor MBE convergence.
• To provide recommendations for accurate MBE calculations.

Main Methods:

• Energy calculations on water clusters using various basis sets (e.g., 6-311++G**, aug-cc-pVDZ).
• Systematic analysis of MBE convergence with increasing system size and monomer-monomer separation.
• Examination of molecular orbital (MO) coefficients and basis set superposition effects.

Main Results:

• MBE convergence was found to be poor for moderate-sized basis sets, contrary to conventional wisdom.
• Truncating the MBE at the three-body level yielded deceptively small errors for water clusters.
• Inclusion of higher-order terms (four- and five-body) increased errors, particularly with diffuse basis functions.
• Error per monomer increased with system size, indicating MBE's unsuitability for large systems with these basis sets.
• Poor convergence was also observed for valence-bonded systems.

Conclusions:

• The Many-Body Expansion (MBE) is unreliable for large chemical systems with common, moderate-sized basis sets due to basis set superposition errors.
• Diffuse functions in basis sets exacerbate MBE convergence issues.
• Accurate MBE calculations require using the full-cluster basis set, basis sets without diffuse functions, or high-quality basis sets (e.g., aug-cc-pVTZ).
• Findings have implications for molecular fragmentation methods and computational chemistry best practices.