Theory of a systematic computational error in free energy differences.
Theory of a systematic computational error in free energy differences.
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DOI：
10.1103/physrevlett.89.180602
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发表时间：
2002-01
影响因子：
8.6
通讯作者：
D. Zuckerman;T. Woolf
中科院分区：
文献类型：
--
作者：
D. Zuckerman;T. Woolf
系统不准确性是任何非线性平均值的计算估计所固有的，这是由于只有有限数量的数据值N可用。两个状态或系统之间的自由能差（Δ）F是这种平均值的非常重要的例子。以前的工作已经证明，经验，“有限采样误差”可以非常大-许多倍k（B）T-在（德尔塔）F估计简单的分子系统。在这里，我们提出了一个理论描述的不准确性，包括一个样本问题的精确解，精确的渐近行为的1/N大N，一个普遍的法律的识别，和数值例子。该理论依赖于对中心定理和其他极限定理的修正。
Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, N. Free energy differences (Delta)F between two states or systems are critically important examples of such averages. Previous work has demonstrated, empirically, that the "finite-sampling error" can be very large--many times k(B)T--in (Delta)F estimates for simple molecular systems. Here we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of 1/N for large N, the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.