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Energy conserving approximations to the quantum potential: dynamics with linearized quantum force.

Sophya Garashchuk1, Vitaly A Rassolov

  • 1Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA. sgarashc@mail.chem.sc.edu

The Journal of Chemical Physics
|July 23, 2004
PubMed
Summary

This study introduces a novel method for approximating quantum potentials in de Broglie-Bohm quantum dynamics, enabling energy-conserving trajectory propagation. The approach is computationally efficient and accurate for complex chemical reactions and molecular systems.

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Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • The de Broglie-Bohm formulation offers a trajectory-based approach to quantum mechanics.
  • Solving the Schrodinger equation requires accurate treatment of the nonlocal quantum potential.

Purpose of the Study:

  • To develop a new strategy for approximating quantum potentials within the de Broglie-Bohm formulation.
  • To enable energy-conserving and computationally efficient quantum dynamics simulations.

Main Methods:

  • Optimal fitting of approximate quantum potentials to wave function log-derivatives.
  • Utilizing trial functions that lead to linear quantum forces.
  • Analytical solution of the optimization problem using trajectory distribution moments.

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Main Results:

  • The proposed method ensures energy-conserving dynamics for closed systems.
  • Exact time-evolution is achieved for Gaussian wave functions in quadratic potentials.
  • The linear quantum force approximation demonstrates efficiency and accuracy in chemical reaction and photodissociation studies.

Conclusions:

  • The new strategy provides a computationally cheap and accurate method for quantum potential approximation.
  • This approach facilitates efficient calculation of expectation values and phase-dependent quantities.
  • The method is applicable to complex chemical systems, including scattering and photodissociation processes.