Automatic Generation of Auxiliary Basis Sets in Spherical Representation Using the Cholesky Decomposition

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical chemistry

Background:

• Density fitting techniques often use auxiliary basis sets derived from basis function products.
• Previous work introduced a spherical representation for auxiliary basis sets, removing linear dependencies via Cholesky decomposition.

Purpose of the Study:

• To extend the spherical representation approach for auxiliary basis sets.
• To develop approximations for terms not directly computable with standard integral libraries.

Main Methods:

• Utilizing explicit equations for the product of two spherical harmonics.
• Introducing four approximations for specific terms, computable with standard Gaussian-type orbitals.
• Assessing accuracy in the context of approximate coupled-cluster doubles (aCD) and range-separated hybrid functionals.

Main Results:

• The proposed approximations allow for the computation of previously inaccessible terms in auxiliary basis set construction.
• Accuracy was evaluated for electron repulsion integral matrix reconstruction and single point energies.
• The methods were tested within the framework of optimally tuned range-separated hybrid functionals.

Conclusions:

• The developed approximations provide a viable route to extend density fitting techniques using spherical representations.
• These methods enhance the applicability of advanced electronic structure calculations by enabling the use of standard computational tools.