Accurate Coulomb Potentials for Periodic and Molecular Systems through Density Fitting

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurate evaluation of Coulomb potentials is crucial for electronic structure calculations.
• Existing methods may have limitations in handling diverse system dimensionalities and representations.
• Density fitting schemes offer a computationally efficient alternative for potential evaluation.

Purpose of the Study:

• To introduce a systematically improvable density fitting scheme for Coulomb potential evaluation.
• To develop a method applicable to both periodic and molecular systems.
• To address challenges in evaluating long-range contributions in various dimensionalities.

Main Methods:

• Density partitioning into local contributions expanded by cubic splines.
• Reciprocal space representation of multipole moments for 3D periodic systems.
• Topological extrapolation algorithm for 1D and 2D periodic systems.

Main Results:

• Demonstrated accuracy and numerical robustness of the proposed density fitting scheme.
• Successful application to various periodic and nonperiodic systems.
• Compatibility with both basis set expansions and numerical orbital representations.

Conclusions:

• The developed density fitting scheme provides an accurate and versatile tool for Coulomb potential evaluation.
• The method's systematic improvable nature allows for tailored accuracy.
• It offers a robust and efficient approach for electronic structure calculations in computational chemistry.