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Efficient molecular quantum dynamics in coordinate and phase space using pruned bases.

H R Larsson1, B Hartke1, D J Tannor2

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|December 3, 2016
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Summary
This summary is machine-generated.

We developed efficient quantum dynamics simulations using projected Weylets. This new method significantly speeds up calculations by intelligently pruning basis functions, especially in coordinate space.

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Area of Science:

  • Quantum Dynamics
  • Computational Chemistry
  • Theoretical Physics

Background:

  • Accurate quantum dynamics simulations are computationally intensive.
  • Basis set localization is crucial for efficient representation of quantum systems.
  • Existing methods like biorthogonal von Neumann basis (PvB) and DVR bases have limitations.

Purpose of the Study:

  • To develop an efficient implementation of dynamically pruned quantum dynamics.
  • To introduce a novel basis set, projected Weylets, combining advantages of PvB and Gaussian wave packets.
  • To benchmark the performance of projected Weylets against existing methods in various dimensions.

Main Methods:

  • Implementation of dynamically pruned quantum dynamics in both coordinate and phase space.
  • Development of projected Weylets by combining biorthogonal von Neumann basis (PvB) and orthogonalized momentum-symmetrized Gaussians (Weylets).
  • Benchmarking using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases for systems up to six dimensions.

Main Results:

  • Coordinate-space localization is the primary factor for efficient pruning in quantum dynamics.
  • Pruned dynamics simulations are significantly faster than unpruned, exact dynamics.
  • Projected Weylets provide a more compact representation than pruned DVR bases for demanding dynamics requiring many basis functions.

Conclusions:

  • Dynamically pruned quantum dynamics offers a substantial speedup for simulations.
  • Projected Weylets represent a powerful new basis set for efficient quantum dynamics.
  • The choice of basis localization (coordinate vs. phase space) impacts pruning efficiency and representation compactness.