Density Functional Geometries and Zero-Point Energies in Ab Initio Thermochemical Treatments of Compounds with First-Row Atoms (H, C, N, O, F)

Density functionals are often used
in ab initio thermochemistry
to provide optimized geometries for single-point evaluations at a
high level and to supply estimates of anharmonic zero-point energies
(ZPEs). Their use is motivated by relatively high accuracy at a modest
computational expense, but a thorough assessment of geometry-related
error seems to be lacking. We have benchmarked 53 density functionals,
focusing on approximations of the first four rungs and on relatively
small basis sets for computational efficiency. Optimized geometries
of 279 neutral first-row molecules (H, C, N, O, F) are judged by energy
penalties relative to the best available geometries, using the composite
model ATOMIC/B5 as energy probe. Only hybrid functionals
provide good accuracy with root-mean-square errors around 0.1 kcal/mol
and maximum errors below 1.0 kcal/mol, but not all of them do. Conspicuously,
first-generation hybrids with few or no empirical parameters tend
to perform better than highly parameterized ones. A number of them
show good accuracy already with small basis sets (6-31G­(d), 6-311G­(d)).
As is standard practice, anharmonic ZPEs are estimated from scaled
harmonic values. Statistics of the latter show less performance variation
among functionals than observed for geometry-related error, but they
also indicate that ZPE error will generally dominate. We have selected
PBE0-D3/6-311G­(d) for the next version of the ATOMIC protocol (ATOMIC-2)
and studied it in more detail. Empirical expressions have been calibrated
to estimate bias corrections and 95% uncertainty intervals for both
geometry-related error and scaled ZPEs.