Linear response time-dependent density functional theory without unoccupied states: The Kohn-Sham-Sternheimer scheme...

Area of Science:

• Computational physics and chemistry
• Quantum mechanics
• Electronic structure theory

Background:

• The Sternheimer approach provides an efficient method for time-dependent density functional theory (TD-DFT) in the linear response regime.
• Its computational efficiency stems from avoiding explicit calculation of unoccupied orbitals and inherent parallelization capabilities of the Sternheimer equations.

Purpose of the Study:

• To present a comprehensive derivation of the frequency-dependent Sternheimer equations.
• To explore efficient numerical implementation strategies for the Sternheimer approach.
• To demonstrate the applicability of the method for computing electronic excitation properties.

Main Methods:

• Derivation of frequency-dependent Sternheimer equations.
• Numerical implementation of the Sternheimer approach.
• Calculation of photoabsorption spectra for hydrogenated silicon clusters.
• Computation of triplet excitations.

Main Results:

• The Sternheimer approach is computationally efficient due to avoiding unoccupied orbitals and enabling parallelization.
• A complete, self-contained derivation of the frequency-dependent Sternheimer equations is provided.
• For small hydrogenated silicon clusters, Kohn-Sham eigenvalue quality is crucial for accurate photoabsorption spectra.
• Triplet excitations can be efficiently computed using the Sternheimer method.

Conclusions:

• The Sternheimer approach is a computationally advantageous method for TD-DFT linear response calculations.
• The method is well-suited for calculating photoabsorption spectra and triplet excitations.
• Numerical efficiency and accuracy can be achieved through careful implementation and consideration of eigenvalue quality.