An improved statistical analysis for predicting the critical temperature and critical density with Gibbs ensemble Monte Carlo simulation

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.