Messerly Richard A, Rowley Richard L, Knotts Thomas A, Wilding W Vincent
Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA.
J Chem Phys. 2015 Sep 14;143(10):104101. doi: 10.1063/1.4928865.
A rigorous statistical analysis is presented for Gibbs ensemble Monte Carlo simulations. This analysis reduces the uncertainty in the critical point estimate when compared with traditional methods found in the literature. Two different improvements are recommended due to the following results. First, the traditional propagation of error approach for estimating the standard deviations used in regression improperly weighs the terms in the objective function due to the inherent interdependence of the vapor and liquid densities. For this reason, an error model is developed to predict the standard deviations. Second, and most importantly, a rigorous algorithm for nonlinear regression is compared to the traditional approach of linearizing the equations and propagating the error in the slope and the intercept. The traditional regression approach can yield nonphysical confidence intervals for the critical constants. By contrast, the rigorous algorithm restricts the confidence regions to values that are physically sensible. To demonstrate the effect of these conclusions, a case study is performed to enhance the reliability of molecular simulations to resolve the n-alkane family trend for the critical temperature and critical density.
本文针对吉布斯系综蒙特卡罗模拟进行了严格的统计分析。与文献中传统方法相比，该分析降低了临界点估计的不确定性。基于以下结果，推荐了两种不同的改进方法。首先，由于汽相和液相密度存在内在相互依存关系，传统的误差传播方法在估计回归中使用的标准差时，对目标函数中的项进行了不当加权。因此，开发了一个误差模型来预测标准差。其次，也是最重要的一点，将一种严格的非线性回归算法与将方程线性化并传播斜率和截距误差的传统方法进行了比较。传统回归方法可能会得出临界常数的非物理置信区间。相比之下，严格算法将置信区域限制在物理上合理的值范围内。为了证明这些结论的效果，进行了一个案例研究，以提高分子模拟的可靠性，从而解析正构烷烃系列的临界温度和临界密度趋势。
