Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice.
The Journal of chemical physics
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Willatt, M. J., Ceriotti, M., & Althorpe, S. (2018). Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice.. The Journal of chemical physics, 148 (10), 102336. https://doi.org/10.1063/1.5004808
Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a ‘planetary’ model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum Boltzmann distribution. Here, we show that, for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface, by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the ‘planet’). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics (TRPMD), allows us to test the planetary model on water (gas-phase, liquid and ice), using the q-TIP4P/F potential surface. The ‘planetary’ fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approxima- tion to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.
External DOI: https://doi.org/10.1063/1.5004808
This record's URL: https://www.repository.cam.ac.uk/handle/1810/273453