In this paper, we examine the practical procedure used to obtain the thermophysical properties of various compounds in the ideal gas reference state [1-2]. This procedure uses both quantum mechanics and statistical mechanics to calculate the thermophysical properties. Using ab initio calculations, the electronic structure of the molecule is optimized. Normal vibrational frequencies, energetic barriers to internal rotations and moments of inertia are calculated from the optimized structures using quantum mechanics. Given the current state-of-the-art numerical solutions of the Schrödinger equation, it is necessary to apply an empirical scaling factor to the normal vibrational frequencies computed by ab initio means [3]. Averaged scaling factors over samples of molecules are tabulated for a variety of quantum methods and basis sets [4]. In this paper, we use averaged scale factor over simple aromatic compounds since the studied compounds are all aromatic.

Various contributions to entropy are calculated. The internal rotation modes are distinguished from the vibrational modes by creating movies from each mode's eigenvector. We calculate the relaxed energy barrier for each rotor using quantum mechanics. Taking the empirically scaled frequencies and internal rotations from quantum mechanical calculations, statistical mechanics is used to calculate translational, vibrational, rotational and internal rotation contributions to the entropy. Relative enthalpies are calculated from quantum mechanics and coupling it with entropies yields most of the important thermophysical properties.

We present an evaluation of the combined quantum mechanical and statistical mechanical procedure for generating reference entropies, including refinements from previous work. Additionally, we present new data for phenathrene, methyl phenanthrenes, and dimethyl phenathrenes. Our standard, by which the procedure is evaluated, is a set of highly precise experimental measurements of the reference entropies for these compounds.

Acknowledgements

The authors gratefully acknowledge the financial support of the Office of Fossil Energy of the U.S. Department of Energy (DOE). Through the UT Computational Science Initiative, this research project used resources of the Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the DOE under Contract DE-AC05-00OR22725.

References

1. Kassaee, M. H.; Keffer, D. J.; Steele, W. V., A comparison between entropies of aromatic compounds from quantum mechanical calculations and experiment. Journal of Molecular Structure (Theochem) 2007, 802, 23-34.

2. Kassaee, M. H.; Keffer, D. J.; Steele, W. V., Theoretical Calculation of Thermodynamic Properties of Naphthalene, Methylnaphthalenes and Dimethylnaphthalenes. submitted to J. Chem. Eng. Data, 04/2007.

3. Scott, A. P.; Radom, L., Harmonic Vibrational Frequencies: An Evaluation of Hartree-Fock, Moller-Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors. Journal of Physical Chemistry, 1996 100(41), 16502-16513.

4. NIST, Computational Chemistry Comparison and Benchmark DataBase. 2007, National Institute of Standards and Technology.