A comparison of geometric parameters from PBE-based doubly hybrid density functionals PBE0-DH, PBE0-2, and xDH-PBE0

Su, Neil Qiang; Adamo, Carlo; Xu, Xin

doi:10.1063/1.4827024

Cited by 32 publications

(30 citation statements)

References 97 publications

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“…Also, with only two exceptions, the combination of these methods with dispersion‐corrections has not yet been investigated. Studies involving geometries, atomization energies, barrier heights and also an analysis of parts of the GMTKN30 test set (all without dispersion corrections) have revealed that these methods are definitely better than the underlying B3‐LYP and PBE0 hybrids, but a closer inspection of the results shows that the more empirical B2‐PLYP, B2GP‐PLYP, PWPB95, and the DSD functionals seem to be overall more robust and accurate . Nevertheless, the herein reviewed derivation is of academic value and helps emphasizing the theoretical justification for double‐hybrid functionals.…”

Section: Further Developmentsmentioning

confidence: 87%

Double‐hybrid density functionals

Goerigk

Grimme

2014

WIREs Comput Mol Sci

344

406

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Double‐hybrid density functionals (DHDFs) are reviewed in this study. In DHDFs parts of conventional density functional theory (DFT) exchange and correlation are replaced by contributions from nonlocal Fock‐exchange and second‐order perturbative correlation. The latter portion is based on the well‐known MP2 wave‐function approach in which, however, Kohn–Sham orbitals are used to calculate its contribution. First, related methods preceding this idea are reviewed, followed by a thorough discussion of the first modern double‐hybrid B2‐PLYP. Parallels and differences between B2‐PLYP and its various successors are then outlined. This discussion is rounded off with representative thermochemical examples demonstrating that DHDFs belong to the most robust and accurate DFT approaches currently available. This analysis also presents hitherto unpublished results for recently developed DHDFs. Finally, how double‐hybrids can be combined with linear‐response time‐dependent DFT is also outlined and the value of this approach for electronically excited states is shown. WIREs Comput Mol Sci 2014, 4:576–600. doi: 10.1002/wcms.1193 This article is categorized under: Electronic Structure Theory > Density Functional Theory

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Section: Further Developmentsmentioning

confidence: 87%

Double‐hybrid density functionals

Goerigk

Grimme

2014

WIREs Comput Mol Sci

344

406

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“…However, for the last term, we need the so‐called U matrix to allow orbital mixing upon perturbation, which can only be obtained by solving coupled‐perturbed (CP)‐KS equations via the Z‐vector method . For an xDH functional, attention has been paid to its nonvariational nature that energy is evaluated with a DH functional based on orbitals and density from the other SCF functional, giving rise to extra terms as compared to the standard theories . Hence for response properties calculated by xDH functionals, perturbation on energy from the DH functional is related to the relaxation of orbitals from the SCF functional by solving the CP‐KS equations …”

Section: The Xyg3 Type Of Doubly Hybrid Functionalsmentioning

confidence: 99%

“…In the followed sections, we will discuss the theoretical background of the DH functionals, briefly reviewing the adiabatic connection (AC) formalism, coordinate scaling relations, and Görling–Levy (GL) perturbation theory . General performance of the DH functionals will then be summarized, not only for energies, but also for structures. In particular, we will present the fractional charge behaviors of the DH functionals, examining the SIEs, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps, providing a theoretical rationale for the observed good performance of the xDH functionals.…”

Section: Introductionmentioning

confidence: 99%

The XYG3 type of doubly hybrid density functionals

2016

WIREs Comput Mol Sci

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Doubly hybrid (DH) functionals have emerged as a new class of density functional approximations (DFAs), which not only have a nonlocal orbital-dependent component in the exchange part, but also incorporate the information of unoccupied orbitals in the correlation part, being at the top rung of Perdew's view of Jacob's ladder in DFAs. This review article focuses on the XYG3 type of DH (xDH) functionals, which use a low rung functional to perform the self-consistent-field calculation to generate orbitals and densities, with which a top rung DH functional is used for final energy evaluation. We will discuss the theoretical background of the xDH functionals, briefly reviewing the adiabatic connection formalism, coordinate scaling relations, and Görling-Levy perturbation theory. General performance of the xDH functionals will be presented for both energies and structures. In particular, we will present the fractional charge behaviors of the xDH functionals, examining the self-interaction errors, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps. This provides a theoretical rationale for the observed good performance of the xDH functionals.

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“…However some exceptions can be found in the literature, 18-20 mainly concerning specific cases, like transition state structures, [21][22][23] weakly bound interacting complexes, 24,25 conjugated polymers 26 or H-bonds. 27 Most of these latter studies showed that…”

Section: -8mentioning

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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179

134

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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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A comparison of geometric parameters from PBE-based doubly hybrid density functionals PBE0-DH, PBE0-2, and xDH-PBE0

Cited by 32 publications

References 97 publications

Double‐hybrid density functionals

Double‐hybrid density functionals

The XYG3 type of doubly hybrid density functionals

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

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