Spin-Orbit-Induced Nonadiabatic Dynamics: An Exact Ω Representation.

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Computational Physics

Background:

• Transforming rovibronic Hamiltonians between ΛS (Hund's case a) and Ω bases is common.
• This transformation aims to simplify calculations by removing spin-orbit coupling (SOC).
• This simplification is often assumed to enable accurate single-state treatments of molecular spectra and dynamics.

Purpose of the Study:

• To investigate the consequences of transforming molecular Hamiltonians to the Ω representation.
• To demonstrate that the apparent removal of SOC generates significant nonadiabatic couplings (NACs).
• To provide accurate conditions and practical guidance for using Ω-based single-state approximations.

Main Methods:

• Analytical derivation using a two-electronic-state model.
• High-accuracy variational benchmarks.
• Implementation of a complete Ω-representation workflow in the Duo software for diatomics.
• Development of diagnostics for single-state pipelines like LEVEL.

Main Results:

• Spin-orbit coupling elimination in the Ω representation necessarily generates sizable nonadiabatic couplings (NACs) from the nuclear kinetic energy operator.
• Neglecting these spin-orbit-induced NACs causes severe errors in calculated rovibronic energies and transition properties.
• Numerical equivalence between Ω and ΛS formulations is achieved under specific conditions, quantified by the study.

Conclusions:

• The simplification offered by Ω-based single-state approximations is only apparent.
• Explicit nonadiabatic terms are required for accurate calculations, even for "forbidden" transitions, when interacting states are not well-separated in the Franck-Condon region.
• The study provides actionable guidance for spectroscopy, photophysics, and kinetics, highlighting the limitations of common single-state approximations.