Evaluation of Uncertainty of Ideal-Gas Entropy and Heat Capacity Calculations by Density Functional Theory (DFT) for Molecules Containing Symmetrical Internal Rotors

The uncertainty of thermophysical data is indispensable information when reporting both experimental and calculated values. In this paper, we present an evaluation of the uncertainty of the ideal-gas entropy and heat capacity calculations by density functional theory (DFT) for molecules containing symmetrical internal rotors. The rigid-rotor harmonic oscillator (RRHO) and one-dimensional hindered rotor (1-DHR) models are compared as well as the effect of the scale factors employed. The calculations of the standard ideal-gas entropy (Sg0) are performed for a selected set of 33 molecules for which reliable reference data were found in the literature. The RRHO model provides Sg0 with the absolute average percentage deviations (σr) about 2 % from the reference data. Scaling the frequencies does not lead to any improvement when using the RRHO model. A significant improvement is achieved when the 1-DHR model and scale factors for low and high frequencies are applied simultaneously (σr less than 0.3 %). The ideal-gas heat capacity (Cpg0) calculations were tested on a set of 72 molecules. The RRHO model yields Cpg0 values with σr up to 3 % at 300 K and 1 % at 1000 K while using the 1-DHR model coupled with a pair of scale factors lowers σr to less than 1.5 % and 0.5 % at 300 K and 1000 K, respectively.