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While most molecules and solids are spin-unpolarized, most chemically-active atoms are partly spin-polarized. As a result, the errors of the spin-dependence of a density functional are much more troublesome for atomization energies than they are for typical reaction or formation energies. This observation explains why the atomization energy errors of approximate functionals do not correlate with their other errors, and why the errors of atomization energies for a given functional can be radically reduced by fitting the energies of the atoms. We present an illustrative example from the recent nonempirical construction of the SCAN meta-generalized gradient approximation. [ABSTRACT FROM AUTHOR]

In the assessment of density functional approximations for the exchange‐correlation energy, great weight is usually given to the accuracy of molecular atomization energies, or the enthalpies of formation constructed from calculated atomization energies. Here we show that a recent nonempirical functional, the meta‐generalized gradient approximation of Tao, Perdew, Staroverov, and Scuseria, achieves remarkably accurate atomization energies even for the larger organic molecules of the G3‐3 test set. But we also present strong evidence that most of the error of previous nonempirical functionals resides in the energy of the free atom and so cancels out of typical reaction energies. Finally, we suggest that enthalpies of formation calculated without any reference to the free atoms would provide a fairer assessment of the performance of approximate density functionals. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [ABSTRACT FROM AUTHOR]