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

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 Nat of atoms in a molecule. In fact, AE is an extensive variable, which diverges as Nat →∞. Here, as did Savin and Johnson 2015, we define an intensive atomization energy, IAE = AE/Nat or atomization energy per atom, which tends to the finite cohesive energy (per atom) of a large cluster or solid (Nat →∞). 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