Pseudospectral time-dependent density functional theory.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Time-Dependent Density Functional Theory (TDDFT) is a key method for calculating electronic excitation energies.
• Conventional TDDFT algorithms face scaling challenges with increasing system size.
• The Tamm-Dancoff Approximation (TDA) is a common simplification of TDDFT.

Purpose of the Study:

• To implement a pseudospectral approach within TDA-TDDFT for efficient calculation of excitation energies.
• To investigate the use of sparse grids in pseudospectral TDDFT.
• To assess the computational speed and accuracy of the new method.

Main Methods:

• Implementation of TDDFT within the TDA using a pseudospectral approach.
• Evaluation of two-electron repulsion integrals via a split representation (spectral basis and physical grid).
• Application of exceptionally sparse grids for excitation energy calculations.

Main Results:

• The pseudospectral TDA-TDDFT method significantly reduces computational cost.
• The method achieves speedups of up to ten times compared to conventional algorithms for hybrid functionals.
• Chemical accuracy is maintained despite the use of sparse grids and reduced computational effort.

Conclusions:

• The pseudospectral approximation offers a computationally efficient route for TDA-TDDFT.
• This approach enables faster and accurate calculation of excitation energies, particularly for larger systems.
• The findings suggest broader applicability of pseudospectral methods in electronic structure theory.