Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
J Chem Phys. 2018 Mar 14;148(10):102336. doi: 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 [T. J. H. Hele et al., 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, 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 approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.
松田动力学是一种量子-玻尔兹曼守恒的经典动力学，当真实时间相干性从精确量子刘维尔算子中去除时，它仍然存在[T. J. H. Hele 等人，J. Chem. Phys. 142, 134103 (2015)]；由于相位项，它不能在没有进一步近似的情况下用作实际方法。最近，Smith 等人[J. Chem. Phys. 142, 244112 (2015)]开发了一种“行星”模型动力学，该动力学保留了量子-玻尔兹曼分布的 Feynman-Kleinert (FK) 近似。在这里，我们表明，对于适度的非谐势，行星动力学通过将质心轨迹与局部谐和的松田涨落解耦，给出 FK 势能表面上松田轨迹的良好近似，这些涨落简化为一个无相位的涨落粒子（“行星”）。我们还表明，FK 有效频率可以通过对这些涨落进行直接积分来近似，从而避免了求解迭代方程的需要。这种修改，加上使用恒温环聚合物分子动力学，可以使我们使用 q-TIP4P/F 势能表面在水（气相、液相和冰）上测试行星模型。“行星”涨落对红外光谱中的旋转/振动带给出了较差的近似，但对弯曲和伸缩带给出了较好的近似，其中发现涨落谱线形状由于质心的振动而被运动变窄。
