Correlation in quantum chemical calculation and its effect on the uncertainty of theoretically predicted rate coefficients and branching ratios

Abstract

The transition state theory (TST) and RRKM/master equation (ME) method have been well acknowledged in developing combustion models. Uncertainties in input parameters, such as energies and vibrational frequencies which are produced from quantum chemical computations, largely contribute to uncertainties of the theoretically predicted rate coefficients. The potential correlations among these parameters and their effects on the uncertainty of rate coefficients have been investigated in the present work. The correlations in quantum chemical computations on H abstraction, H addition and thermal decomposition reactions, regarding radical sites, molecular types and reaction types are investigated and quantified using Pearson correlation coefficients. The results show that notable correlations exist in energies and imaginary frequencies. The correlation factors are then incorporated into the global uncertainty analysis for two typical TST and RRKM/ME computation systems, i.e., H abstraction reactions of acetaldehyde by the HO2 radical (TST) and the multi-well multi-channel reactions on the C4H7 potential energy surface (RRKM/ME) to unravel the effects of correlation on the uncertainties of rate coefficients and branching ratios. Comparing with the random independent sampling for input parameters, to include correlations among input parameters largely reduces the predicted uncertainties, with the largest reduction of ∼30% for absolute rates and ∼45% for the branching ratio in TST calculations and ∼33% for absolute rates and ∼50% for branching ratios in RRKM/ME calculations. The uncertainty propagation behavior with and without considering the correlation in the input parameters was further uncovered by the sensitivity analysis. In the TST calculation, the uncertainty reduction for absolute rate coefficients solely originates from the reduction of the sampling space, and the uncertainty reduction for the branching ratio originates from both the reduced parameter space and the cancelation of sensitive parameters. In the RRKM/ME calculation, the uncertainty reduction in rate coefficients arises only from reduced sampling space, but the uncertainty reduction in branching ratios is due to both the parameter cancelling effect and correlation.