Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

Area of Science:

• Computational Chemistry and Physics
• Materials Science
• Quantum Mechanics

Background:

• Density functional theory (DFT) is a widely used computational method in chemistry and physics.
• Traditional DFT methods can be computationally intensive for certain systems.
• There is a need for efficient and accurate DFT alternatives for small to medium-sized systems.

Purpose of the Study:

• To review recent developments in a Cartesian coordinate grid-based (CCG) pseudopotential Kohn-Sham (KS) DFT framework.
• To validate CCG-DFT as a viable alternative for electronic structure calculations.
• To explore novel numerical approaches for computing exchange-correlation functionals.

Main Methods:

• Development and application of a CCG-based pseudopotential Kohn-Sham DFT framework using the LCAO-MO ansatz.
• Calculation of electric response properties (dipole moment, polarizability, hyperpolarizability).
• Implementation of a purely numerical approach for exact exchange density using Fourier convolution and range-separated Coulomb kernels.
• Application of the adiabatic connection and virial theorems for computing excitation energies.

Main Results:

• CCG-DFT accurately reproduces electric response properties for various systems.
• A novel numerical method efficiently computes exact exchange contributions.
• The approach enables systematic development of hybrid and hyper-functionals.
• Single-particle excitation energies, including optical gaps, are faithfully reproduced for organic chromophores, dyes, PAHs, and charge transfer complexes.

Conclusions:

• The CCG-based DFT framework offers a successful and efficient alternative for electronic structure calculations.
• The developed numerical methods enhance the accuracy and applicability of DFT.
• CCG-DFT demonstrates significant potential for practical applications in diverse electronic systems.