Approaching the complete-basis limit with a truncated many-body expansion

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• High-accuracy electronic structure calculations require large basis sets and complete-basis extrapolation.
• Fragment-based methods are often evaluated with smaller basis sets, potentially limiting accuracy.
• Basis-set superposition error (BSSE) is a known issue in fragment-based calculations.

Purpose of the Study:

• To examine the convergence of two- and three-body energy expansions towards the basis-set limit for water and ion-water clusters.
• To evaluate the effectiveness of various BSSE corrections consistent with truncated many-body expansions.
• To analyze the interplay of errors from different sources in fragment-based calculations.

Main Methods:

• Second-order Møller-Plesset perturbation theory (MP2) calculations were performed.
• Basis-set convergence was studied for two- and three-body energy expansions.
• Several BSSE corrections were applied and analyzed.
• Water clusters and ion-water clusters were used as model systems.

Main Results:

• Fragment-based methods can benefit from error cancellation, where BSSE compensates for basis set incompleteness and neglected higher-order many-body effects.
• An n-body counterpoise correction enables smooth extrapolation to the MP2 basis-set limit.
• A three-body expansion (n=3) provides accurate results using only trimer-sized subsystems.

Conclusions:

• Fragment-based methods, when properly corrected for BSSE and employing a sufficient many-body expansion, can achieve high accuracy.
• The use of an n-body counterpoise correction is crucial for reliable extrapolation to the basis-set limit.
• A three-body expansion offers a practical and accurate approach for electronic structure calculations of molecular clusters.