Path-integral virial estimator based on the scaling of fluctuation coordinates: application to quantum clusters with fourth-order propagators.
Path-integral virial estimator based on the scaling of fluctuation coordinates: application to quantum clusters with fourth-order propagators.
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DOI：
10.1063/1.2013257
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发表时间：
2005-05
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通讯作者：
Takeshi Yamamoto
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作者：
Takeshi Yamamoto
我们首先表明，根据给定的参考点定义的波动坐标的简单缩放给出了离散路径积分中的传统维里估计，其中参考点的不同选择导致不同形式的估计（例如，质心维里）。这个过程的优点是，它允许一个有限差分评估的维里估计相对于温度，这完全避免了需要高阶潜在的衍生物。我们应用这一程序的能量和热容量的计算的（H（2））（22）和Ne（13）团簇在低温下使用四阶高桥-Imada [J。53，3765（1984）]和Suzuki [Phys. Lett. A 201，425（1995）]传播者。如果使用解析维里估计，这种类型的计算需要高达三阶的潜在导数，但在实践中，凭借上述有限差分格式，只有一阶导数就足够了。从量子团簇的应用中，我们发现，四阶传播子的原始近似的改进，并在减少维里估计的方差的参考点的选择起着至关重要的作用。
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.