Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Conventional time-dependent density functional theory (TDDFT) is a powerful tool for calculating electronic excitation energies.
• However, standard TDDFT formulations are limited in their ability to describe transitions involving spin flips.

Purpose of the Study:

• To introduce a generalized formulation of time-dependent density functional theory (TDDFT) incorporating a noncollinear exchange-correlation potential.
• To extend the capabilities of TDDFT to accurately describe spin-flip transitions and excited state spin multiplets.

Main Methods:

• Development of a noncollinear exchange-correlation potential within the TDDFT framework.
• Application of the new TDDFT formulation to analyze the dissociation of H(2) molecules.
• Investigation of multiplet splitting in atomic systems.

Main Results:

• The generalized TDDFT formulation maintains accuracy for non-spin-flip transitions.
• The formulation successfully accounts for spin-flip transitions, enabling the resolution of excited state spin multiplets.
• For closed-shell systems, singlet-triplet excitation energies calculated using the new method match those from ordinary TDDFT.

Conclusions:

• The proposed noncollinear TDDFT formulation offers a more comprehensive approach to studying electronic excitations.
• This method enhances the ability to analyze spin-dependent phenomena in molecular and atomic systems.
• The generalization provides a valuable advancement for computational quantum chemistry and condensed matter physics.