Is There Still Room for Parameter Free Double Hybrids? Performances of PBE0-DH and B2PLYP over Extended Benchmark Sets

Bousquet, Diane; Brémond, Éric; Sancho‐García, Juan Carlos; Ciofini, Ilaria; Adamo, Carlo

doi:10.1021/ct400358f

Cited by 39 publications

(36 citation statements)

References 82 publications

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“…Energetic data are taken from the literature. 7,8,32,33 The GMTKN30 and CE345 databases are two extended sets containing 841 and 345 reference relative energies,…”

Section: -8mentioning

confidence: 99%

“…Energetic data are taken from the literature. 7,8,32,33 The GMTKN30 and CE345 databases are two extended sets containing 841 and 345 reference relative energies,respectively, specifically built to analyze the performance of computational methods for main group thermochemistry, kinetics and weak-interactions. In both cases, most of the selected density-functionals cluster on the left down corner of the correlation graphs, and present a deviation of 1.5 to 6.0 kcal mol 1 for energetic, and of 0.003 to 0.008 Å for structural properties.…”

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confidence: 99%

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Benchmarking Density Functionals on Structural Parameters of Small-/Medium-Sized Organic Molecules

Brémond

Savarese

et al. 2016

J. Chem. Theory Comput.

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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 (...

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“…Energetic data are taken from the literature. 7,8,32,33 The GMTKN30 and CE345 databases are two extended sets containing 841 and 345 reference relative energies,…”

Section: -8mentioning

confidence: 99%

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confidence: 99%

Benchmarking Density Functionals on Structural Parameters of Small-/Medium-Sized Organic Molecules

Brémond

Savarese

et al. 2016

J. Chem. Theory Comput.

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171

134

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“…Working along this line, we have developed a number of non-empirical DHs based on the AC theorem, where the a x and a c value directly stems from purely theoretical considerations. 27,29,30 Such functionals are competitive with their parametrized counterparts, 31 and allow to define a whole family of non-empirical functionals which spans over the highest three rungs of the Perdew ladder. 1 The aim of this paper is to illustrate such a contribution to the field of non-empirical DHs through a critical discussion of their performance in the modeling of chemically relevant systems.…”

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confidence: 99%

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

et al. 2016

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ConspectusDensity Functional Theory (DFT) emerged in the last two decades as the most reliable tool the description and prediction of properties of molecular systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing Density Functional Approximations (DFAs).Indeed, the Achilles' heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the '90s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on model. In such a way, a whole family of non-empirical functionals, spanning on the highest rungs of the Perdew's quality scale, is now available and competitive with other -more empirical-DFAs. This is a previous version of the article published in Accounts of Chemical Research. 2016Research. , 49(8): 1503Research. -1513Research. . doi:10.1021 2 Discussion of selected cases, ranging from thermochemistry and reactions to weak interactions and excitations energies, not only show the large range of applicability of non-empirical DFAs, but also underline how increasing the number of theoretical constrains parallel with an improvement of the DFA's numerical performances. This fact further consolidates the strong theoretical framework of non-empirical DFAs.Finally, even if non-empirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all technical enhancements developed for speeding-up post-HartreeFock methods, there is a substantial hope for their near future routine application to the description and prediction of complex chemical systems and reactions.

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“…In our previous investigations, 22,25,26 we tested the relevance of these two models (HYB0 and QIDH) on a large number of ground-and excited-state properties, choosing the PBE parameter-free functional to estimate the density-based energy terms.…”

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Systematic Improvement of Density Functionals through Parameter-Free Hybridization Schemes

Brémond

Savarese

Pérez-Jiménez

et al. 2015

J. Phys. Chem. Lett.

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1: It is suggested here that the ultimate accuracy of DFT methods arises from the type of hybridization scheme followed. This idea can be cast into a mathematical formulation utilizing an integrand connecting the non-interacting and the interacting particle system. We consider two previously developed models for it, dubbed as HYB0 and QIDH, and assess a large number of exchange-correlation functionals against the AE6, G2/148, and S22 reference datasets. An interesting consequence of these hybridization schemes is that the error bars, including the standard deviation, are found to markedly decrease with respect to the pure (non-hybrid) case. This improvement is substantially better than variations due to the underlying density functional used. We thus finally hypothesize about the universal character of the HYB0 and QIDH models.ABSTRACT 2: The hybrid HYB0 and double-hybrid QIDH models, derived previously within the adiabatic connection formalism, are used here with a number of exchange-correlation density functionals to assess their global performance against challenging reference datasets.The systematic improvement observed, on both the average error and the standard deviation over the set of density functionals considered, when this hybridization hierarchy is applied, highlight its robustness and prompted us to speculate about its general applicability. 2Computational chemistry has reached such a degree of maturity and performance that manyelectron properties of systems extending to hundreds of atoms can be predicted with great accuracy. This remark is especially verified for Density Functional Theory (DFT) due to its excellent tradeoff between accuracy and cost, which thus allows for a fine description of covalent and noncovalent electron interactions occurring in biological or chemical systems. Part of this success comes from the steady and step-by-step development of novel density-functionals (DFs), and the special efforts done by the community to overcome some well-known and all-pervasive weaknesses such as the self-interaction error, 1 or the 'soft-or non-binding' behavior of van der Waals' complexes. [2][3][4] Historically, an important breakthrough started in the nineties with the audacious idea to cast semilocal density-functionals (GGA, meta-GGA) into hybrids by combining exact-like and approximate density-based exchange together with a correlation energy functional. [5][6][7][8] Going from the semilocal to the hybrid density-functional approximation enhanced the nonlocal character of the exchange part and succeeded to decrease by a factor of two the errors previously found on covalent or short-range properties. This hybridization mechanism is justified by a rigorous formalism known as the adiabatic connection model: 9where E xc represents the exchange-correlation contribution to the total Kohn-Sham (KS) energy, and W α stands for the exchange-correlation integrand. The coupling-constant integrand, once its conveniently defined, allows for connecting the noninteracting (α = 0) to the f...

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Is There Still Room for Parameter Free Double Hybrids? Performances of PBE0-DH and B2PLYP over Extended Benchmark Sets

Cited by 39 publications

References 82 publications

Benchmarking Density Functionals on Structural Parameters of Small-/Medium-Sized Organic Molecules

Benchmarking Density Functionals on Structural Parameters of Small-/Medium-Sized Organic Molecules

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

Systematic Improvement of Density Functionals through Parameter-Free Hybridization Schemes

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