Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Spectroscopy

Background:

• Linear response time-dependent density functional theory (TDDFT) is crucial for molecular absorption spectra.
• Existing algorithms often face memory and stability limitations.

Purpose of the Study:

• To introduce novel symmetric Lanczos and kernel polynomial methods (KPM) for TDDFT absorption spectra.
• To reformulate the non-Hermitian eigenvalue problem into a self-adjoint product eigenvalue problem.

Main Methods:

• A special symmetric Lanczos algorithm is presented, requiring half the memory of nonsymmetric variants.
• The kernel polynomial method (KPM) offers a low-memory alternative, potentially needing more matrix-vector multiplications.
• Both methods are applied to small and medium-sized molecules.

Main Results:

• The symmetric Lanczos algorithm demonstrates improved numerical stability and reduced memory footprint.
• KPM provides a viable low-memory option, with performance trade-offs discussed.
• Accuracy, computational cost, and storage requirements are analyzed for both approaches.

Conclusions:

• The new symmetric Lanczos algorithm offers significant memory and stability advantages for TDDFT calculations.
• KPM is a valuable low-memory alternative, suitable for specific computational constraints.
• These methods enhance the efficiency and applicability of TDDFT for molecular spectroscopy.