Theoretical Techniques for Determining Precise Thermophysical Properties

Quantum mechanics (QM) calculations, coupled with statistical mechanics (SM), provide a means to obtain thermophysical properties from first principles. Because of the limitations in modern computational resources, many of these properties are obtained for isolated molecules. Despite this limitation, QM is still very useful for thermophysical property generation in an ideal gas reference state where the molecules are isolated.

In this thesis, a combination of quantum mechanics and statistical mechanics calculations is used to generate entropies of aromatic compounds in the ideal gas reference state. This information is necessary for practical calculations such as the determination of the free energy of a reaction involving these compounds and the equilibrium distribution between isomers.

The QM and SM calculation procedure is used to generate entropies of simple aromatic compounds—benzene, toluene, p-xylene, m-xylene and o-xylene— in the ideal gas state from 250 K to 540 K. Having accurate experimental frequencies and entropies for these compounds from literature, we systematically examine how the choice of the QM level of theory impacts the agreement between theory and experiment. The calculated entropies fall within 0.5% of experimentally determined values for these compounds. We acknowledge that given the state of the art of computational quantum mechanics today, all levels of theory require an empirical scaling factor for vibrational frequencies. This empirical scaling factor largely eliminates the advantage in accuracy of more sophisticated levels of theory. Thus we see that our “purely computational” estimates of the entropy still have a fundamental connection to experiment through this single empirical scaling factor.