Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate calculation of energy gradients is essential for molecular and periodic systems in computational chemistry.
• Existing methods can be computationally expensive, especially for large systems.

Purpose of the Study:

• To report a full implementation of analytical energy gradients within the TURBOMOLE program package.
• To enable efficient gradient calculations for both molecular and periodic systems using Kohn-Sham density functional theory (KS-DFT).

Main Methods:

• Utilized Gaussian-type orbitals as basis functions.
• Combined density fitting (DF) approximation with the continuous fast multipole method (CFMM) for efficient Coulomb energy gradient calculation.
• Extended a hierarchical numerical integration scheme for the exchange-correlation energy gradient.

Main Results:

• Demonstrated computational efficiency and asymptotic O(N) scaling behavior for the implemented energy gradients.
• Successfully tested on various molecular and periodic model systems, including a large hematite unit cell (640 atoms).
• The computational effort for energy gradients was found comparable to Kohn-Sham matrix formation.

Conclusions:

• The developed implementation provides an efficient and scalable method for calculating analytical energy gradients in KS-DFT.
• This advancement is significant for studying complex molecular and periodic systems, facilitating geometry optimizations and reaction pathway analyses.