Spin-Orbit Natural Transition Orbitals and Spin-Forbidden Transitions

Area of Science:

• Quantum Chemistry
• Computational Spectroscopy
• Electronic Structure Theory

Background:

• Natural Transition Orbitals (NTOs) are crucial for visualizing and analyzing electronic transitions.
• Analyzing spin-forbidden transitions requires specialized methods to account for spin-orbit coupling.
• Existing methods may not fully elucidate the orbital contributions to intensity in spin-forbidden processes.

Purpose of the Study:

• To introduce and validate complex-valued spin-orbit Natural Transition Orbitals (SO-NTOs).
• To analyze the components responsible for intensity in formally spin-forbidden transitions.
• To partition transition properties, like transition dipole moments, into SO-NTO hole-particle pairs.

Main Methods:

• Implementation within the restricted active space (RAS) self-consistent field framework.
• Treatment of spin-orbit coupling using RAS state interaction.
• Development of complex-valued spin-orbit NTOs for detailed analysis.

Main Results:

• SO-NTOs successfully analyze formally spin-forbidden transitions.
• Contributions to transition intensity from specific occupied and unoccupied orbitals are obtained.
• Demonstrated applications in T2-S1 state mixing in pyrazine, Tb3+ ion transitions, and Ir(ppy)3 phosphorescence.

Conclusions:

• Complex-valued SO-NTOs provide a powerful tool for understanding spin-forbidden transitions.
• The method offers detailed insights into the orbital origins of transition intensities.
• SO-NTOs have broad applicability in computational chemistry and spectroscopy.