Understanding the Many-Body Basis Set Superposition Error: Beyond Boys and Bernardi

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Fragment-based methods offer linear scaling for accurate energetics, relying on localized many-body interactions.
• Basis set superposition error (BSSE) previously undermined this premise for water clusters, necessitating computationally expensive supersystem basis sets.
• Existing frameworks for BSSE in many-body expansions have differing interpretations of the problem and its solution.

Purpose of the Study:

• To propose a more general framework for addressing basis set superposition error (BSSE) in many-body expansions.
• To reconcile differing interpretations of BSSE frameworks and demonstrate their compatibility.
• To apply the generalized BSSE framework to water clusters and achieve high accuracy benchmarks.

Main Methods:

• Development of a generalized theoretical framework for basis set superposition error (BSSE).
• Analysis of existing BSSE frameworks by Bettens and Mayer/Bakó, identifying them as different normalization conditions.
• Application of the new framework to small water clusters, performing correlated three-body and Hartree-Fock four-body computations.

Main Results:

• The proposed general BSSE framework unifies and clarifies previous interpretations.
• Application to water clusters yields results within ±0.5 kcal mol⁻¹ of coupled cluster complete basis set limits.
• High accuracy is achieved using a correlated three-body computation (quadruple-ζ basis set) and a four-body Hartree-Fock computation (triple-ζ basis set).

Conclusions:

• The generalized BSSE framework provides a robust method for accurate fragment-based calculations.
• It is possible to overcome BSSE limitations in many-body expansions without sacrificing computational efficiency.
• This approach enables high-accuracy energetic predictions for molecular systems like water clusters.