Interpolative Separable Density Fitting on Adaptive Real Space Grids

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• The electron repulsion integral (ERI) tensor is crucial for electronic structure calculations.
• Compressing the ERI tensor is essential for computational efficiency.
• Existing methods often struggle with highly localized basis functions.

Purpose of the Study:

• To generalize the interpolative separable density fitting (ISDF) method.
• To incorporate adaptive real space grids for localized basis functions.
• To enable scalable electronic structure simulations for complex systems.

Main Methods:

• Generalization of the ISDF method.
• Employment of a dual-space multilevel kernel-splitting method to solve the Poisson equation.
• Generation of adaptive grids using a high-order accurate procedure.
• Proof that adaptive grids for pair densities can be derived from single-particle basis function grids.

Main Results:

• The ISDF method with adaptive grids achieves comparable compression efficiency for localized basis sets as for uniform grids.
• The number of grid points required for pair densities is a constant factor greater than for single-particle basis functions.
• Demonstrated performance on molecular systems intractable with uniform grids.

Conclusions:

• The developed procedure enables scalable many-body electronic structure simulations with arbitrary smooth basis functions.
• This work paves the way for large-scale simulations of phenomena like core-level excitations.
• The method is effective for systems with all-electron basis sets previously considered intractable.