In this letter we report the error analysis of 59 exchange-correlation functionals in evaluating the structural parameters of small-and medium-sized organic molecules.From this analysis, recently developed double-hybrids, such as xDH-PBE0, emerge as the most reliable methods, while global-hybrids confirm their robustness in reproducing molecular structures. Notably the M06-L density-functional is the only semilocal method reaching an accuracy comparable to hybrids'. A comparison with errors obtained on energetic databases (including thermochemistry, reaction barriers and interaction energies) indicate that most of the functionals have a coherent behavior, showing low (or high) deviations on both energy and structure datasets. Only a few of them are more prone toward one of these two properties.
2The quality of any method rooted in density functional theory (DFT) is (strongly) affected by the choice of the exchange-correlation functional (ECF), which gives the unknown term of the Kohn-Sham energy. If from one side the spreading of DFT in chemistry and physics has encouraged the research of new and better-performing density-functionals, 1 from the other side their validation has become a due step before any routine application. Such a benchmark passes through a careful evaluation (and consequent statistical analysis) of the errors on defined properties and systems sets.Starting from the nineties, a large effort has been made in order to define standard benchmark sets allowing for a meaningful and fair comparison between different ECFs.
2-8Among the properties firstly targeted, atomization energies, ionization potentials and electron affinities 2-4 as well as bond lengths and angles of (mostly) small organic systems received a particular attention. Figure S1 and S2 in the Supporting Information). Both databases are an excellent diagnostic test to discriminate density-functionals in modeling structural parameters of organic systems.In this Letter, we use these two datasets to thoroughly benchmark the accuracy of 59ECFs (reported in Table The references and further details of all the considered computational methods involved in this Letter are given in Table S1 of the Supporting Information.In order to discriminate the accuracy of the selected approaches, we define a criterion based on the matrix containing all the interatomic distances. For each system, we compute the mean absolute deviation (MAD) over the distance matrix of the probed and the reference geometries, and calculate the averaged deviation over the set. Figure 1 reports these statistics for the 63 computational approaches considered in this Letter (see Table S2 and S3 in the Supporting Information for more details).For the CCse21 dataset, the deviations span from 0.002 to 0.016 Å for xDH-PBE0and HF methods, respectively. Within this interval, a smooth transition from high to low accuracy is observed. Apart from the worst performing ECFs like BLYP, B97D, B97D3 or TPSS, most of the methods give a slight increase of the distance matrix deviation (...