Automatic Generation of Even-Tempered Auxiliary Basis Sets with Shared Exponents for Density Fitting

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density fitting (DF) is crucial for accelerating electronic structure calculations.
• Accurate auxiliary basis sets are essential for reliable DF results.
• Existing methods for generating auxiliary basis sets can be cumbersome.

Purpose of the Study:

• To develop a new algorithm for automatic generation of auxiliary basis sets.
• To create efficient and accurate auxiliary basis sets for density fitting.
• To assess the performance of the generated basis sets across various elements and molecules.

Main Methods:

• An algorithm generating even-tempered primitive Hermite Gaussian auxiliary basis sets (GEN-X2, GEN-X3, GEN-X4).
• Basis sets span the product space of the orbital basis set for each element.
• Testing accuracy with DZVP, 6-31G**, and def2-TZVPP orbital basis sets for elements H-Kr.

Main Results:

• Achieved density fitting errors below 1 kcal/mol for all tested systems.
• GEN-X2 sufficient for DF PBE, while GEN-X3/GEN-X4 needed for DF Hartree-Fock with heavier elements.
• Demonstrated computational efficiency via large zeolite calculations.

Conclusions:

• The GEN-Xn algorithm provides accurate and efficient auxiliary basis sets for density fitting.
• The generated sets meet theoretical variational bounds for Coulomb and Fock fitting.
• These basis sets significantly enhance the computational feasibility of quantum chemical methods.