Aiming for benchmark accuracy with the many-body expansion

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Fragment-based quantum chemistry methods have advanced significantly over the last 15 years.
• These methods approximate large system properties using smaller subsystem calculations, often based on many-body (n-body) expansions.
• Existing methods present a language barrier due to diverse terminology and working equations.

Purpose of the Study:

• To unify diverse fragment-based quantum chemistry methods under a generalized many-body expansion formalism.
• To provide a universal energy formula encompassing traditional n-body cluster expansions and methods for macromolecules.
• To systematically classify and suggest improvements for fragment-based methods.

Main Methods:

• Developed a generalized many-body expansion formalism.
• Classified fragment-based methods based on fragment construction and higher-order interaction approximation.
• Investigated the efficacy of these methods for large systems, aiming for complete-basis CCSD(T) quality.
• Addressed basis-set superposition error using many-body counterpoise corrections and electrostatic embedding.

Main Results:

• Demonstrated that complete-basis CCSD(T) quality energies can be obtained for small clusters with reduced computation time.
• Observed that low-order n-body expansions can sometimes yield good results due to error cancellation.
• Identified erratic behavior of basis sets in larger systems and with high-order expansions.
• Highlighted potential loss-of-precision issues in large systems due to the combinatorial nature of the many-body expansion.

Conclusions:

• The generalized many-body expansion provides a unified framework for classifying and improving fragment-based methods.
• While promising for accuracy and efficiency, the many-body expansion requires careful implementation, especially for large systems.
• Numerical stability and precision loss are significant concerns, indicating that the many-body expansion is not yet a "black-box" method.