Intensive Atomization Energy: Re-Thinking a Metric for Electronic Structure Theory Methods

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.