Perturbation Theory Treatment of Spin-Orbit Coupling. III: Coupled Perturbed Method for Solids

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Spin-orbit coupling (SOC) is crucial for understanding electronic properties of heavy elements.
• Accurate theoretical treatment of SOC in extended systems remains computationally challenging.
• Previous noncanonical coupled-perturbed Kohn-Sham density functional theory (KS-DFT)/Hartree-Fock (HF) methods were limited to finite systems.

Purpose of the Study:

• To generalize a noncanonical coupled-perturbed KS-DFT/HF treatment for spin-orbit coupling to infinite periodic systems.
• To implement and validate the extended method for calculating electronic properties of materials.
• To assess the accuracy of the perturbation theory approach for various properties and systems.

Main Methods:

• Generalization of coupled-perturbed KS-DFT/HF to periodic systems using a scalar-relativistic approach as the zeroth-order approximation.
• Derivation of explicit expressions for total energy through third-order (satisfying the 2N+1 rule) and second-order corrections to wave functions and properties.
• Implementation within the Crystal program and application to tungsten dichalcogenide hexagonal bilayers (WSe2, WTe2, WPo2, WLv2).

Main Results:

• The method accurately reproduces total energies, electronic band structures, and spin-current density variables for periodic systems.
• Third-order energy corrections (E(3)) consistently improve agreement with reference two-component self-consistent field (2c-SCF) calculations.
• Differences in electronic band structures compared to 2c-SCF were minimal, even for challenging 7p elements, and electron densities showed minor core-region deviations.

Conclusions:

• The generalized coupled-perturbed KS-DFT/HF method provides an accurate and efficient approach for studying spin-orbit coupling in periodic systems.
• The perturbation theory approach is robust, with third-order energy corrections significantly enhancing accuracy.
• The developed method is suitable for investigating electronic properties of materials containing heavy elements, including relativistic effects.