Curing basis set overcompleteness with pivoted Cholesky decompositions.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Describing weakly bound electronic states is challenging using traditional atomic orbital basis sets.
• Diffuse basis functions, essential for extended states, introduce linear dependencies, leading to unstable electronic structure calculations.

Purpose of the Study:

• To develop a numerically stable method for pruning overcomplete molecular basis sets.
• To reduce the computational cost of electronic structure calculations without sacrificing accuracy.

Main Methods:

• A pivoted Cholesky decomposition of the overlap matrix is employed to identify and remove redundant basis functions.
• The method generates an optimal low-rank approximation of the original basis set.
• Implementation involves either modifying orthogonalization or creating custom atomic basis sets.

Main Results:

• The pruned basis sets allow for stable and accurate electronic structure calculations, even at the self-consistent field (SCF) level.
• Significant cost reductions were observed, with savings increasing with basis set size (9% for single-ζ, 28% for triple-ζ).
• Accuracy comparable to standard augmented basis sets was achieved.

Conclusions:

• Pivoted Cholesky decomposition offers an efficient and stable approach to basis set optimization for electronic structure calculations.
• This method is particularly beneficial for systems with diffuse functions, such as weakly bound states.
• The technique provides a practical way to achieve high accuracy with reduced computational expense.