Enhanced enthalpies of formation from density functional theory through molecular reference states

Accurate prediction of enthalpy of formation is an important goal for theoretical methods. As such, the ability of a density functional to accurately predict enthalpies of formation for a wide variety of compounds is often used as a critical test of its efficacy. These enthalpies are typically calculated by modeling formation reactions from the isolated atoms that make up the molecule. However, the enthalpy of formation can be calculated from any valid reference state, e.g., as in isodesmic reactions, and using different reference states can alter the accuracy of prediction. We have had excellent results using a single molecular reference state per element, namely C(60) for carbon and the diatomic standard reference states for hydrogen, nitrogen, oxygen, and fluorine. This molecular reference scheme can be viewed as a better measure of the upper limit of accuracy of a density functional/basis set pair, as it leads to generally more accurate predictions than are possible using atomic energies. For example, LSDA's unsigned average error drops from 158.8 to 11.6 kcal/mol, and PBE's error improves to 5.1 kcal/mol from 35.8 kcal/mol with the 6-311G(2df,2p) basis set. This scheme also makes small basis sets far more accurate, indicates that a revision of the relative thermochemical accuracy of functionals may be required, and can remove qualitative failures for some functional/basis set pairs.