Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]

Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias

doi:10.1103/physrevlett.78.1396

Cited by 18,380 publications

(13,111 citation statements)

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“…This includes our own modifications 58 for PIMD 48,59,60 which uses forces computed on-the-fly from the electronic structure calculations. Here we report results using PBE 43 and the DFT-D3 38 exchange-correlation functionals. The latter is a scheme for treating vdW forces in DFT through the inclusion on an additional C 6 /R 6 term, where the C 6 dictates the strength of the binding and R is the distance between pairs of atoms.…”

Section: Methodsmentioning

confidence: 99%

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Cooperative Interplay of van der Waals Forces and Quantum Nuclear Effects on Adsorption: H at Graphene and at Coronene

et al. 2014

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The energetic barriers that atoms and molecules often experience when binding to surfaces are incredibly important to a myriad of chemical and physical processes. However these barriers are difficult to describe accurately with current computer simulation approaches. Two prominent contemporary challenges faced by simulation are the role of van der Waals forces and nuclear quantum effects. Here we examine the widely studied model systems of hydrogen

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Section: Methodsmentioning

confidence: 99%

“…We discuss adsorption at the top site (directly above one carbon atom), since this is where chemisorption occurs, and the physisorption energies at the hollow, bridge and top sites are the same to within a few meV. The total energy profile using the standard Perdew-Burke-Ernzerhof (PBE) functional 43 is shown in Fig. 1.…”

Section: Hydrogen At Graphenementioning

confidence: 99%

Cooperative Interplay of van der Waals Forces and Quantum Nuclear Effects on Adsorption: H at Graphene and at Coronene

et al. 2014

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“…39 The DFT calculations were performed using the CP2K package (CP2K version 2.3.43; CP2K is freely available in http://www.cp2k.org/) with the mixed Gaussian and plane wave formalism 40 and periodic boundary conditions. The exchange and correlation functional used was the revised 41 version of the Perdew-Burke-Ernzerhof (PBE) 42 function. Long-range dispersion interactions were included using the DFT-D3 formalism.…”

Section: Methodsmentioning

confidence: 99%

Dehalogenation and Coupling of a Polycyclic Hydrocarbon on an Atomically Thin Insulator

et al. 2014

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Catalytic activity is of pivotal relevance in enabling efficient and selective synthesis processes.Recently, covalent coupling reactions catalyzed by solid metal surfaces opened the rapidly evolving field of on-surface chemical synthesis. Tailored molecular precursors in conjunction with the catalytic activity of the metal substrate allow the synthesis of novel, technologically highly relevant materials such as atomically precise graphene nanoribbons. However, the reaction path on the metal substrate remains unclear in most cases and the intriguing question is how a specific atomic configuration between reactant and catalyst controls the reaction processes. In this study, we cover the metal substrate with a monolayer of hexagonal boron nitride (h-BN), reducing the reactivity of the metal, and gain unique access to atomistic details during the activation of a polyphenylene precursor by sequential dehalogenation and the subsequent coupling to extended oligomers. We use scanning tunneling microscopy (STM) and density functional theory (DFT) to reveal a reaction site anisotropy, induced by the registry mismatch between the precursor and the nano-structured h-BN monolayer. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 3 An atomically thin layer of insulating h-BN is a structurally analogous counterpart for graphene -a single layer of sp 2 -hybridised carbon atoms 1 -matching the graphene lattice almost perfectly with a small mismatch of approx. 2%. Currently, the fabrication of two-dimensional materials follows two main approaches: i) the bottom-up synthesis by substrate supported chemical vapor deposition (CVD) with suitable precursors and ii) the top-down approach by exfoliation. The assembly of graphene/h-BN heterostructures, leading to novel devices or devices with enhanced performance, usually relies on elaborate, sequential transfer processes of the produced layers. 2 The main obstacles are possible misalignment, introduction of defects and contaminations resulting from transferring layers that are just one atom thick. Only recently, the direct CVD growth of graphene on h-BN was demonstrated, offering superior properties. [3][4][5] However, the growth conditions are harsh (long exposure time, high temperatures, several cycles, etc.). Metal substrates are favored, because of their high catalytic activity, 6 but they have the disadvantage that they strongly alter the properties of the grown layers, which therefore cannot be directly used for electronic device fabrication.A common motif in on-surface chemical reactions is the activation of a precursor, the intermittent complex formed between precursor and substrate, and finally the coupling reaction. 7A long-standing question is the impact of the specific atomic configuration between substrate and reactant on the catalytic efficiency and how does the specific atomic arrangement chan...

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“…DFT provides a rigorous framework to these DFAs and several models have been used to develop functionals based on Local Density and Generalized Gradient Approximations (LDA and GGA, respectively), see for instance references [9][10][11][12][13]. Among others, the model developed by Perdew, Burke and Ernzerhof (PBE) [14] is undoubtedly the most representative functional of such a family, and it clearly shows how interesting numerical performances can be obtained imposing some of the theoretical limits of the ideal functional. As a matter of fact, the PBE functional generally provides results for a large number of properties and systems at least as good as the most-used parameterized approaches, such as BLYP [15,16], and sometimes even better.…”

Section: Theoretical Framework 21 Generalities: Acm and Associated Fmentioning

confidence: 99%

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

Sancho‐García

Adamo

2013

Phys. Chem. Chem. Phys.

109

108

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We review in this Perspective why and how double-hybrid density functionals have become new leading actors in the field of computational chemistry, thanks to the combination of an unprecedented accuracy together with large robustness and reliability. Similarly to their predecessors, the widely employed hybrid density functionals, they are rooted on the Adiabatic Connection Method from which they emerge in a natural way. We present recent achievements concerning applications to chemical systems of the most interest, and current extensions to deal with challenging issues such as non-covalent interactions and excitation energies. These promising methods, despite a slightly higher computational cost than other typical density-based models, are called to play a key role in the near future and can thus pave the way towards new discoveries or advances.2

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Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]

Cited by 18,380 publications

References 0 publications

Cooperative Interplay of van der Waals Forces and Quantum Nuclear Effects on Adsorption: H at Graphene and at Coronene

Cooperative Interplay of van der Waals Forces and Quantum Nuclear Effects on Adsorption: H at Graphene and at Coronene

Dehalogenation and Coupling of a Polycyclic Hydrocarbon on an Atomically Thin Insulator

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

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