Parametrization of atomic energies to improve small basis set density functional thermochemistry

Enthalpies of formation predicted with density functional theory and small basis sets can be greatly improved by treating the atomic energies as empirical parameters. When a variety of functionals and small basis sets are used, the root-mean-square error in enthalpies of formation is reduced by a factor of approximately two for the least improved functional/ basis set pair, with significantly larger reductions for other functionals, especially LSDA. When the 3-21G* and 3-21+G* basis sets are used with nonempirical functionals, it is possible to achieve accuracy greater than that of PM3, which was primarily designed to reproduce enthalpies of formation. In addition to decreasing statistical errors, our procedure can also remove qualitative errors in density functional/ basis set pairs that fail for the prediction of enthalpies of formation.