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Tunneling in two-dimensional systems using a higher-order Herman-Kluk approximation.

Gili Hochman1, Kenneth G Kay

  • 1Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel.

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Semiclassical corrections enhance the Herman-Kluk approximation for describing quantum tunneling in two-dimensional systems. This improvement requires only a moderate number of classical trajectories, overcoming previous limitations.

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Area of Science:

  • Quantum mechanics
  • Chemical physics
  • Computational chemistry

Background:

  • The Herman-Kluk (HK) semiclassical approximation is a widely used method for calculating reaction rates and tunneling probabilities.
  • A known limitation of the HK method is its inaccuracy in describing tunneling between classically allowed regions.
  • Previous work demonstrated that semiclassical corrections improve HK tunneling for one-dimensional systems.

Purpose of the Study:

  • To evaluate the effectiveness of semiclassical corrections in improving the HK approximation for tunneling in two-dimensional systems.
  • To assess the computational feasibility of applying these corrections.

Main Methods:

  • Application of the lowest-order semiclassical correction to the Herman-Kluk approximation.
  • Numerical calculations for tunneling across barriers in two-dimensional systems.
  • Analysis of computational convergence and trajectory requirements.

Main Results:

  • The lowest-order semiclassical correction significantly improves the accuracy of the HK approximation for two-dimensional tunneling.
  • Numerical convergence was achieved without significant difficulties.
  • The calculations required a moderate number of real classical trajectories.

Conclusions:

  • Semiclassical corrections offer a substantial improvement to the Herman-Kluk approximation for describing tunneling in two-dimensional systems.
  • The enhanced method is computationally tractable, requiring a manageable number of trajectories.
  • This approach provides a more reliable description of quantum tunneling phenomena in complex systems.