Erratum: Van der Waals Density Functional for General Geometries [Phys. Rev. Lett.<b>92</b>, 246401 (2004)]

Dion, Maxime; Rydberg, Henrik; Schröder, Elsebeth; Langreth, David C.; Lundqvist, Bengt I.

doi:10.1103/physrevlett.95.109902

Cited by 1,466 publications

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“…Van der Waals interactions were considered at the vdW-DF level 43,44 with the optB86b 45 exchange functional, which achieves accurate results in calculating structural properties of two dimensional materials 19,20,22,46,47 The authors declare no competing financial interests.…”

Section: Dft Calculationsmentioning

confidence: 99%

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe₂

et al. 2017

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Interlayer rotation and stacking were recently demonstrated as effective strategies for tuning physical properties of various two-dimensional materials. The latter strategy was mostly realized in heterostructures with continuously varied stacking orders, which obscure the revelation of the intrinsic role of a certain stacking order in its physical properties. Here, we introduce inversion-domain-boundaries into molecular-beam-epitaxy grown MoSe2 homobilayers, which induce uncommon fractional lattice translations to their surrounding domains, accounting for the observed diversity of large-area and uniform stacking sequences. Low-symmetry stacking orders were observed using scanning transmission electron microscopy and detailed geometries were identified by density functional theory. A linear relation was also revealed between interlayer distance and stacking energy. These stacking sequences yield various energy alignments between the valence states at the Γ and K points of the Brillouin zone, showing stacking-dependent bandgaps and valence band tail states in the measured scanning tunneling spectroscopy. These results may benefit the design of two-dimensional multilayers with manipulable stacking orders

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Section: Dft Calculationsmentioning

confidence: 99%

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe₂

et al. 2017

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“…Our SIESTA calculations rely on the efficient implementation of vdW-DFs proposed by Romań-Peŕez and Soler. 15 Within the vdW-DF framework, the correlation energy is written as a double integral of the density, 10 where the kernel is a function of n(r) and ▽n(r), and it is expressed in terms of the wavevector q 0 (r) = k F (r)[ε xc 0 (r)/ε x LDA (r)], with k F (r) = [3π 2 n(r)] 1/3 and…”

Section: ■ Computational Detailsmentioning

confidence: 99%

“…10 It is worth mentioning that vdW-PBE has been employed to successfully reproduce structural properties of liquid water. 20 In this case, the vdW-PBE functional led to a better description of the radial distribution function compared to vdW-DF, due to the underestimation of H-bond interaction and a consequent overestimation of the O−O distance by revPBE.…”

Section: ■ Computational Detailsmentioning

confidence: 99%

“…16,17 Within the vdW-DF framework, the exchange and correlation energy is partitioned as with exact exchange. 10 Although past work with this functional led to reasonable results for binding energies for many of the molecules within the S22 set, 19 calculated binding distances were too large compared with experiments. 10,20 More recently, several vdW-DFs have been proposed with different E x GGA and E c nl to improve accuracy.…”

Section: ■ Introductionmentioning

confidence: 99%

“…14 A particularly promising solution, balancing computational efficiency 15 with accuracy, is the nonlocal correlation functional proposed by Dion et al in 2004, 10 often referred to as a van der Waals density functional (vdW-DF), which has been successfully used to describe adsorption of gaseous hydrogen by MOFs. 16,17 Within the vdW-DF framework, the exchange and correlation energy is partitioned as with exact exchange.…”

Section: ■ Introductionmentioning

confidence: 99%

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CO₂ Capture by Metal–Organic Frameworks with van der Waals Density Functionals

2012

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We use density functional theory calculations with van der Waals corrections to study the role of dispersive interactions on the structure and binding of CO 2 within two distinct metal−organic frameworks (MOFs): Mg-MOF74 and Ca-BTT. For both classes of MOFs, we report calculations with standard gradient-corrected (PBE) and five van der Waals density functionals (vdW-DFs), also comparing with semiempirical pairwise corrections. The vdW-DFs explored here yield a large spread in CO 2 −MOF binding energies, about 50% (around 20 kJ/ mol), depending on the choice of exchange functional, which is significantly larger than our computed zero-point energies and thermal contributions (around 5 kJ/mol). However, two specific vdW-DFs result in excellent agreement with experiments within a few kilojoules per mole, at a reduced computational cost compared to quantum chemistry or many-body approaches. For Mg-MOF74, PBE underestimates adsorption enthalpies by about 50%, but enthalpies computed with vdW-DF, PBE+D2, and vdW-DF2 (40.5, 38.5, and 37.4 kJ/mol, respectively) compare extremely well with the experimental value of 40 kJ/mol. vdW-DF and vdW-DF2 CO 2 −MOF bond lengths are in the best agreement with experiments, while vdW-C09 x results in the best agreement with lattice parameters. On the basis of the similar behavior of the reduced density gradients around CO 2 for the two MOFs studied, comparable results can be expected for CO 2 adsorption in BTT-type MOFs. Our work demonstrates for this broad class of molecular adsorbate-periodic MOF systems that parameter-free and computationally efficient vdW-DF and vdW-DF2 approaches can predict adsorption enthalpies with chemical accuracy. ■ INTRODUCTIONMetal−organic frameworks (MOFs) are a broad class of threedimensional nanoporous materials that have attracted much attention during the past decade for CO 2 capture from flue gas. 1−6 MOFs consist of metal centers joined by organic molecular "linkers"; there are many possibilities for cation/ linker combinations, and thousands of different MOFs have already been synthesized. 3,5 Understanding mechanisms for CO 2 binding within these frameworks is a fundamental step toward the design of new materials for carbon capture.In order to explore and predict new materials that efficiently capture CO 2 , an accurate quantitative description of both its adsorption energy and geometry is needed. Whereas quantum chemistry methods, such as HF/MP2 or CCSD(T), scale unfavorably with the number of basis functions (N 5 and N 7 ) and are primarily restricted to cluster calculations, density functional theory (DFT) is a very promising framework for studying the mechanism of interaction between CO 2 and extended MOFs. Although DFT is a many-particle framework that includes, in principle, fully nonlocal interactions, its common approximations, such as the local density approximation (LDA) and the generalized gradient approximation (GGA), neglect attractive long-range contributions to van der Waals interactions, so-called London dispersion intera...

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Approximate Density Functionals: Which Should I Choose?

Rappoport

Crawford

Furche

et al. 2005

Encyclopedia of Inorganic Chemistry

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Density functional methods have a long tradition in inorganic and bioinorganic chemistry. We introduce the density functional machinery and give an overview of most popular approximate exchange‐correlation (XC) functionals. We present comparisons of density functionals for energies, structures, and reaction barriers of inorganic and bioinorganic systems, giving guidance on the title question. New development directions and current trends in density functional theory (DFT) are reviewed.

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Erratum: Van der Waals Density Functional for General Geometries [Phys. Rev. Lett.92, 246401 (2004)]

Cited by 1,466 publications

References 0 publications

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe₂

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe₂

CO₂ Capture by Metal–Organic Frameworks with van der Waals Density Functionals

Approximate Density Functionals: Which Should I Choose?

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Erratum: Van der Waals Density Functional for General Geometries [Phys. Rev. Lett.92, 246401 (2004)]

Cited by 1,466 publications

References 0 publications

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe2

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe2

CO2 Capture by Metal–Organic Frameworks with van der Waals Density Functionals

Approximate Density Functionals: Which Should I Choose?

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Product

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Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe₂

Inversion Domain Boundary Induced Stacking and Bandstructure Diversity in Bilayer MoSe₂

CO₂ Capture by Metal–Organic Frameworks with van der Waals Density Functionals