## Abstract

The errors in atomization energies (*AE*) of molecules have long been used to measure the
errors of wavefunction or density functional methods for electronic structure
calculations. In particular, the G3 set of Pople and collaborators (for *sp*-bonded
molecules from the first rows of the periodic table) has become a standard benchmark for
such methods. But the mean absolute error of *AE* tends to increase with increasing number
*N*_{at} of atoms in a molecule. In fact, *AE* is an extensive variable, which
diverges as *N*_{at} →∞. Here, as did Savin and Johnson 2015, we define an
intensive atomization energy, *IAE* = *AE*/*N*_{at} or atomization energy per atom, which
tends to the finite cohesive energy (per atom) of a large cluster or solid (*N*_{at} →∞). We find that the mean absolute error of the G3 molecular *IAE* from
accurate density functionals remains close to 1 kcal/mol as the average molecular
size increases. This makes it possible to estimate in advance the magnitude of the error in
*AE* for a molecule similar to most of those in the G3 set. It also allows us identify the
G3 “outlying molecules”, and to more directly compare the accuracy of a given functional
for different kinds of molecules (such as those containing transition-metal atoms) to that
for G3-type molecules, by removing the otherwise-uncontrolled size factor. Finally, we point
out that the familiar concept of “chemical accuracy” needs to be qualified.

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