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Landau-Zener type surface hopping algorithms.

Andrey K Belyaev1, Caroline Lasser2, Giulio Trigila2

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Summary
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This study compares two Landau-Zener (LZ) formulas for nonadiabatic transitions in surface hopping algorithms. Both formulas accurately approximate quantum dynamics, showing effective algorithm performance.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Chemical Physics

Background:

  • Surface hopping algorithms are crucial for simulating nonadiabatic dynamics.
  • Landau-Zener (LZ) formulas provide probabilities for nonadiabatic transitions.
  • Accurate calculation of these transitions is essential for understanding molecular dynamics.

Purpose of the Study:

  • To investigate and compare two recent Landau-Zener (LZ) formulas for nonadiabatic transition probabilities.
  • To evaluate the performance of surface hopping algorithms using these LZ formulas.
  • To assess the accuracy of these methods against a reference solution.

Main Methods:

  • Studied a class of surface hopping algorithms.
  • Compared two Landau-Zener (LZ) formulas: one requiring a diabatic representation, the other using adiabatic potential energy surfaces.
  • Performed numerical experiments with deterministic and probabilistic surface hopping.
  • Used a grid-based pseudo-spectral method to solve the Schrödinger equation for reference solutions.

Main Results:

  • Both LZ formulas showed affinity and approximated the reference solution well.
  • Nonadiabatic transitions were found to occur at local minima of the surface gap.
  • Deterministic and probabilistic surface hopping approaches yielded consistent results.
  • Visualizations confirmed the effective dynamics of the investigated algorithms.

Conclusions:

  • The studied surface hopping algorithms, employing both types of LZ formulas, effectively capture nonadiabatic dynamics.
  • The comparison validates the accuracy of the LZ formulas and the employed algorithms against rigorous quantum mechanical calculations.
  • The findings support the use of these algorithms for simulating complex chemical processes.