A systematic way for the cost reduction of density fitting methods

Area of Science:

• Computational chemistry
• Quantum chemistry

Background:

• Density fitting (resolution of identity) is crucial for electron repulsion integrals in quantum chemistry.
• Auxiliary basis sets are essential for density fitting but can be computationally expensive.
• Reducing the size of auxiliary basis sets is key to improving computational efficiency.

Purpose of the Study:

• To develop a novel method for reducing the size of auxiliary basis sets in density fitting.
• To introduce natural auxiliary functions (NAFs) as an efficient alternative to standard fitting functions.
• To assess the impact of NAFs on the computational cost of quantum chemical methods.

Main Methods:

• Singular value decomposition of three-center two-electron integrals.
• Construction of natural auxiliary functions (NAFs) as linear combinations of original fitting functions.
• Systematic truncation of the fitting basis using NAFs.

Main Results:

• NAFs enable systematic truncation of auxiliary basis sets.
• Computational efficiency gains are most significant for iterative methods scaling quadratically with fitting basis size, like direct random phase approximation.
• Potential acceleration of local correlation methods by addressing bottlenecks in three-center Coulomb integrals.

Conclusions:

• Natural auxiliary functions offer a simple and effective approach to reduce auxiliary basis set size.
• This method can lead to significant computational savings in quantum chemistry.
• NAFs show promise for accelerating computationally demanding quantum chemical calculations.