Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Molecular Dynamics

Background:

• Trajectory-based Gaussian basis sets are effective for high-dimensional quantum molecular dynamics.
• Existing methods face computational challenges in accurately describing complex systems.

Purpose of the Study:

• Introduce a novel pseudospectral Gaussian-based method.
• Achieve accurate quantum dynamics with efficient real-space sampling.
• Reduce computational cost compared to traditional variational methods.

Main Methods:

• Utilizes time-dependent Gaussian basis functions guided by classical mechanics.
• Employs Dirac delta functions for testing basis sets, reducing integration to function evaluation.
• Requires only O(N) potential energy calculations, significantly less than O(N^2) for variational methods.

Main Results:

• The pseudospectral Gaussian method demonstrates competitive accuracy with full variational calculations.
• Efficiently samples high-dimensional potentials using classical trajectories and small basis sets.
• Outperforms the bra-ket averaged Taylor (BAT) expansion, especially in cases of strong quantum mechanical coherence.

Conclusions:

• The pseudospectral Gaussian method offers variational accuracy with reduced computational cost.
• Enables on-the-fly dynamics simulations by requiring only discrete potential energy evaluations.
• Presents a promising alternative for complex molecular dynamics simulations.