Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• Accurate approximation of two-particle interactions is crucial for electronic structure calculations.
• Existing methods for generating density fitting basis sets can be computationally intensive.
• Developing efficient and robust algorithms for basis set generation is an ongoing challenge.

Purpose of the Study:

• To present a novel algorithm, model-assisted density fitting (MADF), for generating primitive atomic Gaussian density fitting basis sets (DFBSs).
• To enable accurate and robust density fitting (DF) approximation of two-particle interactions in electronic structure calculations.
• To create a versatile DFBS generator applicable across various chemical systems and computational conditions.

Main Methods:

• The MADF algorithm generates DFBSs from contracted Gaussian orbital basis sets (OBS).
• It involves saturating the OBS product space with Gaussian shells, followed by pruning based on energy contributions.
• The model relies on mathematical and physical principles, minimizing control parameters.

Main Results:

• The MADF algorithm produces DFBSs suitable for accurate DF approximation.
• A single set of three parameters controls density fitting error across diverse computational settings (basis cardinal numbers, electron correlation, relativistic effects).
• DF errors in Hartree-Fock and MP2 energies are approximately 20 and 10 μEh per electron, respectively.

Conclusions:

• The MADF algorithm provides an efficient and accurate method for generating DFBSs.
• The generated DFBSs are applicable to a wide range of elements and computational conditions.
• This approach facilitates robust and reliable electronic structure calculations through density fitting.