Numerical integration of exchange-correlation energies and potentials using transformed sparse grids

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density-functional theory (DFT) relies on accurate numerical integration for exchange-correlation energies and potentials.
• Conventional DFT methods often employ atom-in-molecule grids, which can limit accuracy and flexibility.
• Developing efficient and accurate integration schemes is crucial for advancing computational chemistry.

Purpose of the Study:

• To introduce a new numerical integration procedure for exchange-correlation calculations in DFT.
• To demonstrate the "proof of principle" of this novel integration scheme.
• To highlight the advantages of a "whole molecule" grid over traditional "atom-in-molecule" grids.

Main Methods:

• The proposed method constructs numerical integration grids using sparse-tensor product grids based on Smolyak's prescription.
• The unit cube grid is transformed to real space using a promolecular density weight function, creating a "whole molecule" grid.
• The scheme was implemented in the DEMON2K DFT program to evaluate exchange-correlation energy density and potential integrals.

Main Results:

• Ground-state energies and molecular geometries were computed with high accuracy.
• The new "whole molecule" grid demonstrated flexibility in adjusting grid point number and distribution.
• The method proved effective in evaluating exchange-correlation integrals within the DEMON2K framework.

Conclusions:

• The proposed numerical integration procedure offers a flexible and accurate alternative for DFT calculations.
• The "whole molecule" grid approach shows potential for basis-set-free computational algorithms.
• This advancement contributes to more efficient and reliable electronic structure calculations.