The elephant in the room of density-functional theory calculations
While basis set convergence sounds straightforward (though time-consuming) it is hard to rule out that underlying assumptions in the design of the basis set influences the results. However, converged basis set DFT results are needed to separate basis set errors from errors due to the functional. Multiwavelets, a systematic and adaptive multiresolution numerical solution of the one-electron problem, is now the basis set that can reach the highest precision.
Together with our collaborators in Norway and U.S.A, we show in our recent paper that LDA, PBE and PBE0 total energies, atomization energies, and dipoles moments for more than 211 molecules that are converged with respect to basis set to μHartree accuracy. Furthermore these numbers were compared to other basis set such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs) and full-potential augmented plane wave (APW) calculations. In the case of atomization energies, a quintuple GTO basis set (aug-cc-pV5Z) is needed to reach a 1 kcal/mol accuracy in both MAE and RMSE. For aug-cc-pVQZ the MAE is below 1 kcal/mol, but the RMSE is about 1.5 kcal/mol. Perhaps more importantly, the maxAE goes from ca 10 to 2-5 kcal/mol on going from quadruple to pentuple basis set. So even aug-cc-pV5Z cannot consistently reach the basis set limit for atomization energies! This research has been just published in J. Phys. Chem. Lett. (link).