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

Ryan P Brady1, Sergei N Yurchenko1

  • 1Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, U.K.

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|April 18, 2026
PubMed
Summary
This summary is machine-generated.

Transforming molecular Hamiltonians to the Ω representation appears to remove spin-orbit coupling (SOC), but it generates significant nonadiabatic couplings (NACs). Neglecting these NACs leads to errors in spectral and dynamical calculations.

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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.