UMRSF-TDDFT: Unrestricted Mixed-Reference Spin-Flip-TDDFT

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Traditional Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) methods often fail for systems with degeneracies or bond dissociation.
• Spin-Flip TDDFT (SF-TDDFT) variants have been developed but can suffer from issues like spin contamination.

Purpose of the Study:

• To develop and validate an unrestricted version of Mixed-Reference Spin-Flip TDDFT (UMRSF-TDDFT).
• To introduce a new molecular orbital reordering scheme and a method for estimating ⟨S²⟩ expectation values.
• To assess the performance of UMRSF-TDDFT on systems where conventional methods falter.

Main Methods:

• Development of Unrestricted Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (UMRSF-TDDFT).
• Incorporation of unrestricted Kohn-Sham (UKS) orbitals and a novel molecular orbital reordering scheme.
• Benchmarking against challenging chemical systems, including Be atom, HF bond breaking, and Jahn-Teller distortion in TMM.

Main Results:

• UMRSF-TDDFT accurately recovers degenerate states for the Be atom, with energies slightly reduced due to UKS flexibility.
• UMRSF-TDDFT correctly describes bond breaking in HF, unlike U-SF-TDDFT which misses a crucial configuration.
• UMRSF-TDDFT shows a greater reduction in singlet-triplet energy difference for TMM compared to U-SF-TDDFT, attributed to orbital relaxations rather than spin contamination.

Conclusions:

• The unrestricted nature of UKS orbitals in UMRSF-TDDFT allows for greater spatial orbital relaxation, leading to lower total energies.
• UMRSF-TDDFT provides a practical and accurate quantum chemical theory, complementing existing restricted open-shell variants.
• This new method enhances the ability to address complex quantum systems where standard theories are insufficient.