Yamamoto Takeshi M
Department of Chemistry, Graduate School of Science, Kyoto University, Japan.
J Chem Phys. 2005 Sep 8;123(10):104101. doi: 10.1063/1.2013257.
We first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to different forms of the estimator (e.g., centroid virial). The merit of this procedure is that it allows a finite-difference evaluation of the virial estimator with respect to temperature, which totally avoids the need of higher-order potential derivatives. We apply this procedure to energy and heat-capacity calculations of the (H(2))(22) and Ne(13) clusters at low temperature using the fourth-order Takahashi-Imada [J. Phys. Soc. Jpn. 53, 3765 (1984)] and Suzuki [Phys. Lett. A 201, 425 (1995)] propagators. This type of calculation requires up to third-order potential derivatives if analytical virial estimators are used, but in practice only first-order derivatives suffice by virtue of the finite-difference scheme above. From the application to quantum clusters, we find that the fourth-order propagators do improve upon the primitive approximation, and that the choice of the reference point plays a vital role in reducing the variance of the virial estimator.
我们首先表明，对根据给定参考点定义的涨落坐标进行简单缩放，可在离散路径积分中得到传统的维里估计量，其中参考点的不同选择会导致估计量的不同形式（例如质心维里）。此过程的优点在于它允许对维里估计量进行关于温度的有限差分评估，这完全避免了对高阶势导数的需求。我们使用四阶高桥 - 今田[《日本物理学会杂志》53, 3765 (1984)]和铃木[《物理快报A》201, 425 (1995)]传播子，将此过程应用于低温下(H₂)₂₂和Ne₁₃团簇的能量和热容计算。如果使用解析维里估计量，这种类型的计算需要高达三阶的势导数，但实际上借助上述有限差分方案，仅一阶导数就足够了。通过对量子团簇的应用，我们发现四阶传播子确实比原始近似有所改进，并且参考点的选择在降低维里估计量的方差方面起着至关重要的作用。
