Density Functional Theory for Molecular and Periodic Systems Using Density Fitting and Continuous Fast Multipole...

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Kohn-Sham density functional theory (KS-DFT) is a cornerstone for electronic structure calculations.
• Accurate and efficient treatment of both molecular and periodic systems remains a computational challenge.
• Gaussian-type orbitals (GTOs) are widely used basis functions in quantum chemistry.

Purpose of the Study:

• To develop and report an implementation of KS-DFT within the TURBOMOLE program package.
• To enable the simultaneous treatment of molecular and periodic systems of any dimensionality.
• To achieve computational efficiency and favorable scaling for large systems.

Main Methods:

• Utilizes Gaussian-type orbitals (GTOs) as basis functions.
• Employs a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) for the electronic Coulomb term.
• Operates in direct space, partitioning Coulomb interactions into far-field (multipole expansions) and near-field (density fitting) components.

Main Results:

• Demonstrates computational efficiency and favorable scaling behavior approaching O(N) for Kohn-Sham matrix formation.
• Successfully treats molecular and periodic systems, including 3D models with large unit cells (up to 640 atoms).
• The DF-CFMM scheme provides a robust approach for handling Coulomb interactions.

Conclusions:

• The reported KS-DFT implementation offers a unified and efficient approach for diverse chemical systems.
• The DF-CFMM method is key to achieving near-linear scaling computational cost.
• This work advances the capability of computational chemistry for large-scale simulations.