Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Real-time time-dependent density functional theory (RT-TDDFT) is a powerful method for simulating molecular electronic dynamics.
• Accurate and efficient implementations are crucial for studying complex molecular systems.

Purpose of the Study:

• To report an implementation of RT-TDDFT within the TURBOMOLE program package.
• To benchmark the performance of this new implementation for various molecular systems.
• To compare RT-TDDFT results with established methods like linear response TDDFT and coupled cluster.

Main Methods:

• Utilized Gaussian-type orbitals as basis functions.
• Employed second and fourth order Magnus propagators with self-consistent field and predictor-corrector time integration schemes.
• Combined density fitting approximation and the continuous fast multipole method for Coulomb contribution calculation.

Main Results:

• Performance was benchmarked on molecular systems of varying sizes and dimensionalities.
• For linear alkane chains, density matrix propagation time was comparable to Kohn-Sham (KS) matrix construction.
• For larger 2D and 3D molecules (up to ~5,000 basis functions), KS matrix evaluation dominated computational effort.
• Maximum time step was evaluated for molecules of different polarities.

Conclusions:

• The developed RT-TDDFT implementation provides an efficient tool for calculating photoabsorption spectra.
• Computational cost is sensitive to molecular dimensionality, with KS matrix evaluation being the bottleneck for larger systems.
• The results show good agreement with other theoretical methods, validating the implementation.