Assessment of Gaussian-3 and Density Functional Theories for a Larger Experimental Test Set

Critical documentation and evaluation of theoretical methods of electronic structure is essential for such methods to become predictive tools for chemical investigation. An approach to this problem is to assemble a large set of good, credible experimental data and systematically comparing them with corresponding results from theoretical models. 

Previously, we have assembled a test set of molecules containing first- and second-row elements in different bonding environments with well established experimental values. Our test set (G2/97) containing 301 energies (enthalpies of formation, ionization potentials, electron affinities, and proton affinities) has been used to assess the reliability of new theoretical models. 

We have now expanded the test set to include 75 new enthalpies of formation for larger molecules. This new test set (G3/99) is used to assess the reliability of Gaussian-3 (G3) theory (an accurate composite theoretical procedure we have presented previously), and three different density functional (DFT) methods. Overall, G3 theory has a mean absolute deviation of 1.07 kcal/mol for the G3/99 test set and does about as well for the new hydrocarbons and substituted hydrocarbons as it does for those in the G2/97 test. 

However, G3 theory has larger deviations for several of the new non-hydrogen systems in the G3/99 test set such as SF sub 6 and PF sub 5. Part of the source of error is traced to the inadequate geometries used in G3 theory for these molecules. The density functional methods assessed in this study, including the hybrid B3LYP method, all have much larger deviations from experiment for the new enthalpies of formation in the expanded test set; the mean absolute deviation more than doubles compared to that for the enthalpies in the G2/97 test set. This is due to a cumulative effect of the errors in the larger molecules in the density functional methods.