Relativistic time-dependent density functional theories.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Relativistic effects are crucial for accurately describing molecular systems with heavy elements.
• Time-dependent density functional theory (TD-DFT) is a powerful tool for studying excited states.
• Existing R-TD-DFT methods face challenges in handling complex electronic structures, especially for open-shell systems.

Purpose of the Study:

• To critically review the foundations, formalisms, technicalities, and practicalities of relativistic time-dependent density functional theories (R-TD-DFT).
• To explore different variants of R-TD-DFT, including four-component (4C) and two-component (X2C) approaches.
• To highlight advancements and potential future developments in the field.

Main Methods:

• Review of four-component (4C) and exact two-component (X2C) R-TD-DFT variants.
• Analysis of a composite two-component variant (sf-X2C-S-TD-DFT-SOC).
• Investigation of the noncollinear exchange-correlation kernel and symmetry adaptation.

Main Results:

• 4C/X2C-TD-DFT can be made symmetry adapted for closed-shell systems, simplifying calculations.
• A novel approach allows solving 4C/X2C-TD-DFT eigenvalue problems similarly to nonrelativistic TD-DFT.
• sf-X2C-S-TD-DFT-SOC successfully accesses spinor excited states for both closed- and open-shell systems.

Conclusions:

• R-TD-DFT methods provide robust frameworks for studying relativistic effects in molecular excited states.
• Symmetry adaptation offers significant computational advantages for specific R-TD-DFT variants.
• Further developments in R-TD-DFT promise enhanced accuracy and applicability to a wider range of systems.