复合量子化学方法中的不确定性预测

中文摘要 AI 辅助

在这项工作中，我们考虑了通过使用复合量子化学方案进行理论计算所得结果的不确定性估计问题。复合方案的每个组成部分都带有其自身的个体不确定性，这主要源于计算中所用基组的有限大小。实际感兴趣的是总不确定性，即所有组成部分之和的不确定性。我们首先表明，将每个组成部分视为统计上不相关变量的传统误差传播规则在实践中并不合理。为了解决这个问题，我们提出了一种估计复合方案总不确定性的方法，该方法不依赖于各组成部分相互独立的假设。该方法被表述为一系列具有不同起始值的随机游走，这些起始值代表复合方案中每个组成部分的不确定性。该方法首先应用于水二聚体和氮分子的两个示例复合方案，以说明其最显著的特征并允许进行更深入的分析。接下来，该方法在S66数据集的更大一组相互作用能上进行了测试，该数据集具有可信的参考数据，并且可以明确地评估误差。结果表明，该方法能够在给定应用所需的任意预定置信水平下提供可靠且合理紧凑的不确定性估计。虽然本文的重点是复合方案，但我们相信这一总体思路在计算化学和物理学中可以更广泛地发挥作用。

英文摘要

In this work, we consider the problem of uncertainty estimation of the results obtained through theoretical calculations using a composite quantum chemistry scheme. Each component of the composite scheme carries its own individual uncertainty, originating principally from a finite size of the basis set used in the calculations. Of practical interest is the total uncertainty, i.e. the uncertainty of the sum of all components. We first show that the conventional error propagation rules that treat each component as a statistically uncorrelated variable are not well-justified in practice. To remedy this, we propose a method of estimating the total uncertainty of the composite scheme which does not rely on the assumption that the components are independent. It is formulated as a series of random walks with different starting values that represent the uncertainty of each component of the composite scheme. This method is first applied to two example composite schemes for the water dimer and the nitrogen molecule that illustrate its most salient features and allow for a deeper analysis. Next, the method is tested for a larger set of interaction energies from the S66 dataset for which trustworthy reference data are available and the error can be assessed unambiguously. It is shown that the method provides reliable and reasonably tight uncertainty estimates at an arbitrary predefined confidence level required in a given application. While the focus of the paper is on composite schemes, we believe that the general idea can be useful more broadly in computational chemistry and physics.

发表机构

• University of Warsaw, Faculty of Chemistry（华沙大学化学系）

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