Linear scaling density matrix real time TDDFT: Propagator unitarity and matrix truncation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Standard time dependent density functional theory (TDDFT) formulations face computational limitations for very large systems.
• Orbital-based propagation in TDDFT can be computationally intensive, restricting the size of systems that can be studied.
• Developing efficient methods to calculate optical responses is crucial for understanding material properties.

Purpose of the Study:

• To present a real-time, density matrix based TDDFT implementation for efficient optical response calculations.
• To investigate the impact of spatial cutoff radii and matrix truncation on computational efficiency and accuracy.
• To explore the linear scaling potential of this TDDFT approach for large-scale systems.

Main Methods:

• Implementation of real-time TDDFT using density matrix propagation.
• Application of spatial cutoff radii to sparse matrices for computational workload reduction.
• Analysis of basis set size and matrix truncation effects on propagator unitarity and optical spectra.

Main Results:

• The density matrix based TDDFT method provides direct access to optical responses of large systems.
• Spatial cutoff radii and matrix truncation significantly reduce computational cost, enabling linear scaling.
• Benchmark tests validate the accuracy of the method, showing its applicability to complex systems.

Conclusions:

• Density matrix based TDDFT with spatial truncation offers a computationally feasible route to study optical properties of large systems.
• The method achieves linear scaling with system size when appropriate density matrix truncation is applied.
• Understanding the interplay between basis set size, truncation range, and accuracy is key to reliable predictions.