Turbo charging time-dependent density-functional theory with Lanczos chains.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Calculating the full spectrum of molecules and extended systems is computationally intensive.
• Existing methods often require significant resources, limiting applications to smaller systems or requiring approximations.
• Accurate spectral calculations are crucial for understanding material properties and chemical reactions.

Purpose of the Study:

• To develop a new, computationally efficient implementation of time-dependent density-functional theory (TD-DFT).
• To enable the calculation of entire molecular and extended system spectra with a cost comparable to ground-state calculations.
• To provide a method suitable for large systems and advanced basis sets like plane waves and real-space grids.

Main Methods:

• Utilized a superoperator formulation of linearized TD-DFT.
• Represented dynamical polarizability using the resolvent of the Liouvillian superoperator.
• Employed a nonsymmetric Lanczos algorithm for efficient resolvent evaluation, avoiding unoccupied Kohn-Sham orbitals.

Main Results:

• Achieved spectral calculations with numerical effort comparable to single ground-state calculations.
• Demonstrated efficiency for large systems and basis sets (plane waves, real-space grids).
• Successfully computed spectra for benzene, C(60) fullerene, and chlorophyll a.

Conclusions:

• The new TD-DFT implementation significantly reduces the computational cost of spectral calculations.
• The method is highly effective for large systems and complex electronic structure problems.
• This advancement opens possibilities for more detailed studies of molecular and material properties.