Understanding the many-body expansion for large systems. II. Accuracy considerations

Area of Science:

• Computational Chemistry
• Electronic Structure Theory
• Quantum Chemistry

Background:

• Finite precision in electronic structure calculations can impact accuracy.
• Truncated many-body expansions (MBE) are used to approximate calculations for large systems.
• Assessing the accuracy of MBE methods is crucial for reliable results.

Purpose of the Study:

• To evaluate the accuracy of truncated many-body expansion (MBE) methods.
• To compare MBE accuracy against supersystem calculations and high-quality benchmarks.
• To introduce and assess a generalized many-body expansion (GMBE) with counterpoise correction (GMBCP).

Main Methods:

• Calculations performed on water clusters ((H2O)N=6-55) at the B3LYP/cc-pVDZ level.
• Evaluated standard MBE truncated at two-, three-, and four-body terms.
• Introduced and tested a generalized many-body expansion (GMBE(2)) and its counterpoise corrected version (GMBCP(2)).

Main Results:

• Standard two-body MBE yielded a mean absolute error (MAE) of ~1.0 kcal/mol/monomer.
• Three- and four-body MBE improved accuracy to 0.5 and 0.1 kcal/mol/monomer, respectively.
• GMBE(2) achieved an MAE of ~0.02 kcal/mol/monomer, outperforming standard MBE.
• GMBCP(2) provided good results without relying on error cancellation mechanisms.

Conclusions:

• GMBE(2) and GMBCP(2) offer accurate, stable, and tractable approaches for large system calculations.
• These methods reduce computational cost and mitigate issues like floating-point roundoff errors.
• The GMBE(2)+GMBCP(2) approach, combined with suitable electronic structure methods, is promising for complex systems.