title: The Elephant in the Room of Density Functional Theory Calculations.
abstract: Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.
authors.affiliation: Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT - The Arctic University of Norway , N-9037 Tromsø, Norway.
authors.forename: Stig Rune
authors.identifier: http://orcid.org/0000-0002-2175-5723
authors.initials: SR
authors.lastname: Jensen
authors.affiliation: Department of Physics, Universität Basel , Klingelbergstrasse 82, 4056 Basel, Switzerland.
authors.forename: Santanu
authors.initials: S
authors.lastname: Saha
authors.affiliation: Department of Physics, Universität Basel , Klingelbergstrasse 82, 4056 Basel, Switzerland.
authors.forename: José A
authors.initials: JA
authors.lastname: Flores-Livas
authors.affiliation: Department of Mechanical Engineering and Materials Science, Duke University , Durham, North Carolina 27708, United States.
authors.forename: William
authors.initials: W
authors.lastname: Huhn
authors.affiliation: Department of Mechanical Engineering and Materials Science, Duke University , Durham, North Carolina 27708, United States.
authors.forename: Volker
authors.identifier: http://orcid.org/0000-0001-8660-7230
authors.initials: V
authors.lastname: Blum
authors.affiliation: Department of Physics, Universität Basel , Klingelbergstrasse 82, 4056 Basel, Switzerland.
authors.forename: Stefan
authors.initials: S
authors.lastname: Goedecker
authors.affiliation: Centre for Theoretical and Computational Chemistry, Department of Chemistry, UiT - The Arctic University of Norway , N-9037 Tromsø, Norway.
authors.forename: Luca
authors.initials: L
authors.lastname: Frediani