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Julian Albert1, Kilian Hader1, Volker Engel1

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This study examines wave packet motion near conical intersections in electron-nuclear systems. It reveals how non-adiabatic transitions and geometrical phases influence dynamics, impacting electronic and nuclear densities.

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Area of Science:

  • Quantum chemistry
  • Molecular dynamics
  • Theoretical physics

Background:

  • The time-dependent Schrödinger equation governs coupled electron-nuclear systems.
  • Conical intersections (CoIns) are critical points where adiabatic potential energy surfaces meet, significantly impacting molecular dynamics.
  • Understanding non-adiabatic transitions is crucial for accurately modeling chemical reactions and molecular processes.

Purpose of the Study:

  • To investigate wave packet dynamics in a model system featuring a conical intersection.
  • To analyze the behavior of nuclear and electronic densities during non-adiabatic transitions.
  • To explore the emergence and detection of geometrical phases in molecular systems.

Main Methods:

  • Numerical solution of the time-dependent Schrödinger equation for a coupled electron-nuclear system.
  • Simulation of wave packet propagation through the conical intersection region.
  • Comparison between exact numerical results and Born-Oppenheimer approximations.

Main Results:

  • Wave packets passing through the CoIn exhibit efficient non-adiabatic transitions, maintaining nuclear Gaussian shape and constant electronic density.
  • In the absence of non-adiabatic transitions, electronic density rotates around the CoIn, revealing a geometrical phase.
  • Wave packet splitting occurs when non-adiabatic transition probabilities are small.

Conclusions:

  • Conical intersections significantly influence electron-nuclear dynamics, leading to non-adiabatic transitions and observable geometrical phases.
  • The study highlights the importance of considering non-adiabatic effects for accurate molecular simulations.
  • Geometrical phases associated with CoIns can be identified through spectral analysis and autocorrelation functions.