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  3. Multidimensional Quantum Dynamics With Explicitly Correlated Gaussian Wave Packets Using Rothe's Method.
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  3. Multidimensional Quantum Dynamics With Explicitly Correlated Gaussian Wave Packets Using Rothe's Method.

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Multidimensional quantum dynamics with explicitly correlated Gaussian wave packets using Rothe's method.

Simon Elias Schrader1, Thomas Bondo Pedersen1, Simen Kvaal1

  • 1Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.

The Journal of Chemical Physics
|January 8, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

Rothe's method efficiently solves the time-dependent Schrödinger equation using Explicitly Correlated Gaussian (ECG) functions. This approach enables accurate quantum dynamics and molecular simulations in complex systems and strong fields.

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Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • Rothe's method previously solved the Schrödinger equation for hydrogen atoms in laser fields.
  • Time-dependent Gaussian wave packets were used in prior work.

Purpose of the Study:

  • Generalize Rothe's method for propagating Explicitly Correlated Gaussian (ECG) functions.
  • Apply the method to multidimensional systems like the Hénon-Heiles potential.
  • Demonstrate efficient and accurate quantum dynamics calculations.

Main Methods:

  • Propagating thawed, complex-valued ECGs with dense correlation matrices.
  • Utilizing Rothe's method for time-dependent Schrödinger equation solutions.
  • Applying the method to 2D, 3D, and 4D Hénon-Heiles potentials.

Main Results:

  • Rothe's method successfully propagates arbitrary numbers of ECGs in varying dimensions.
  • Quantitative reproduction of dynamics with a small number of Gaussians (e.g., 30 in 2D).
  • Accurate spectra obtained using compact ECG representations (20 in 2D, 30-40 in 3D/4D).

Conclusions:

  • Rothe's method provides a compact and efficient representation of wave functions.
  • The method facilitates high-quality molecular dynamics beyond the Born-Oppenheimer approximation.
  • Enables accurate simulations in strong fields and complex potentials.