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Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice.

Michael J Willatt1, Michele Ceriotti2, Stuart C Althorpe1

  • 1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

The Journal of Chemical Physics
|March 17, 2018
PubMed
Summary

Matsubara dynamics, a quantum method, is approximated by a new "planetary" model. This model accurately predicts vibrational bands in water spectra, offering a practical computational approach.

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Area of Science:

  • Quantum dynamics
  • Computational chemistry
  • Spectroscopy

Background:

  • Matsubara dynamics offers quantum-Boltzmann-conserving classical dynamics but requires approximations due to a phase term.
  • The Feynman-Kleinert (FK) approximation provides a practical route to quantum-Boltzmann distributions.
  • Planetary model dynamics approximates the FK distribution, decoupling centroid motion from harmonic fluctuations.

Purpose of the Study:

  • To evaluate the accuracy of the planetary model dynamics as an approximation to Matsubara trajectories.
  • To simplify the calculation of the FK effective frequency.
  • To test the planetary model's performance on water systems using the q-TIP4P/F potential.

Main Methods:

  • Decoupling the centroid trajectory from locally harmonic Matsubara fluctuations.
  • Approximating the FK effective frequency via direct integration over fluctuations.
  • Utilizing thermostatted ring-polymer molecular dynamics for simulations.

Main Results:

  • The planetary dynamics provides a good approximation to Matsubara trajectories for moderately anharmonic potentials.
  • The FK effective frequency can be directly integrated, avoiding iterative equation solving.
  • Simulations on water (gas, liquid, ice) show good agreement for bend and stretch bands, but poor agreement for rotational/librational bands.

Conclusions:

  • The planetary model offers a computationally efficient approximation for Matsubara dynamics, particularly for vibrational spectra.
  • Motional narrowing by centroid vibrations improves the approximation for bend and stretch bands.
  • Further refinements may be needed for accurate prediction of rotational/librational spectral features.