General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: theory,...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Time-dependent density functional theory (TD-DFT) is crucial for excited-state calculations.
• Spin-flip (SF) variants of TD-DFT are used for open-shell systems.
• Evaluating functional performance is key for accurate predictions.

Purpose of the Study:

• Implement and evaluate spin-flip (SF) TD-DFT with non-collinear (NC) formalism.
• Assess performance across various functionals (local, GGA, hybrid, range-separated).
• Benchmark accuracy using energy gaps of diradicals and open-shell atoms.

Main Methods:

• Implemented SF-TDDFT within the Tamm-Dancoff approximation and NC formalism.
• Utilized local, generalized gradient approximation (GGA), hybrid, and range-separated functionals.
• Performed benchmark calculations on 41 energy gaps for diradicals and open-shell atoms.

Main Results:

• The Perdew-Burke-Ernzerhof (PBE) family, particularly PBE0 and PBE50, demonstrated consistent high accuracy.
• PBE50 achieved a mean average deviation of 0.090 eV.
• Collinear SF-TDDFT with PBE50 did not enhance accuracy compared to NC variants.

Conclusions:

• PBE-based functionals, especially PBE50, are highly recommended for SF-TDDFT calculations of energy gaps.
• NC-SF-TDDFT and collinear SF-TDDFT show similar accuracy with specific functionals.
• Care must be taken with functionals like LYP or B97 for same-center diradicals due to large errors.