We derive the exchange-correlation potential corresponding to the nonlocal van der Waals density functional [M.

A density functional theory (DFT) that accounts for van der Waals (vdW) interactions in condensed matter, materials physics, chemistry, and biology is reviewed. The insights that led to the construction of the Rutgers-Chalmers van der Waals density functional (vdW-DF) are presented with the aim of giving a historical perspective, while also emphasizing more recent efforts which have sought to improve its accuracy. In addition to technical details, we discuss a range of recent applications that illustrate the necessity of including dispersion interactions in DFT. This review highlights the value of the vdW-DF method as a general-purpose method, not only for dispersion bound systems, but also in densely packed systems where these types of interactions are traditionally thought to be negligible.

Is the plasmon description within the nonlocal correlation of the van der Waals density functional by Dion and coworkers (vdW-DF) robust enough to describe all exchange-correlation components? To address this question, we design an exchange functional based on this plasmon description as well as recent analysis on exchange in the large-s regime. In the regime with reduced gradients s = |∇n|/2nk F (n) smaller than ≈2.5, dominating the nonlocal correlation part of the binding energy, the enhancement factor F x (s) closely resembles the Langreth-Vosko screened exchange. In the s regime beyond, dominated by exchange, F x (s) passes smoothly over to the revised Perdew-Wang-86 form. We term the specific exchange functional LV-PW86r, wheras the full van der Waals functional version emphasizing consistent handling of exchange is termed vdW-DF-cx. Our tests indicate that vdW-DF-cx produces accurate separations and binding energies of the S22 data set of molecular dimers as well as accurate lattice constants and bulk moduli of layered materials and tightly bound solids. These results suggest that the plasmon description within vdW-DF gives a good description of both exchange and correlation effects in the low-to-moderate s regime. Van der Waals forces are essential for the properties of a wide range of materials and physical processes. Interesting examples go far beyond model cases such as noble gas dimers and include examples such as biomolecular matter, many transition-metal oxides, and chalcogenides. Even to fully describe many covalent effects, van der Waals forces are needed. For catalytic processes, it can be necessary to describe how molecules first adsorb on surfaces or within porous matter. In systems where covalent or electrostatic forces are the primary cause of binding, van der Waals forces sometimes tip the balance between competing configurations or even cause stronger chemical binding.The lack of van der Waals forces in the extensively used generalized gradient approximations (GGAs) to density functional theory (DFT) have triggered many attempts to develop the theory beyond GGA in DFT, as well as attempts to extend related electronic-structure methods to include these forces. A conceptually simple and popular approach is to add pair potentials between the ionic centers of the atoms on top of GGA accounts [1]. These pair potentials may be empirical or semiempirical, that is, fitted once and for all on a given data set. Among the most well known formulations are those of Grimme and coworkers [2][3][4]. A more sophisticated method is to explicitly calculate, based on some scheme, the C 6 coefficients in a given system [5][6][7][8]. These kinds of methods remain in the atomic-pair potential paradigm, yet do contain some ability to adjust the dispersion account to the local environment, and they typically reduce the semiempiricism to a single parameter. The TS method by Tkatchenko and Scheffler is a prominent example [9].The adiabatic connection formula (ACF) [10,11] provides a formally exact determination of th...

To understand sparse systems we must account for both strong local atom bonds and weak nonlocal van der Waals forces between atoms separated by empty space. A fully nonlocal functional form [H. Rydberg, B.I. Lundqvist, D.C. Langreth, and M. Dion, Phys. Rev. B 62, 6997 (2000)] of density-functional theory (DFT) is applied here to the layered systems graphite, boron nitride, and molybdenum sulfide to compute bond lengths, binding energies, and compressibilities. These key examples show that the DFT with the generalized-gradient approximation does not apply for calculating properties of sparse matter, while use of the fully nonlocal version appears to be one way to proceed.PACS numbers: 71.15. Mb, 61.50.Lt, 31.15.Ew, Calculations of structure and other properties of sparse systems must account for both strong local atom bonds and weak nonlocal van der Waals (vdW) forces between atoms separated by empty space. Present methods are unable to describe the true interactions of sparse systems, abundant among materials and molecules. Key systems, like graphite, BN, and MoS 2 , have layered structures. While today's standard tool, density-functional theory (DFT), has broad application, the common local (LDA) and semilocal density approximations (GGA) [1,2,3,4] for exchange and correlation, E xc [n], fail to describe the interactions at sparse electron densities. Here we show that the recently proposed density functional [5] with nonlocal correlations, E nl c [n], gives separations, binding energies, and compressibilities of these layered systems in fair agreement with experiment. This planar case bears on the development of vdW density functionals for general geometries [6,7], as do asymptotic vdW functionals [8].Figure 1 with its 'inner surfaces' defines the problem: voids of ultra-low density, across which electrodynamics leads to vdW coupling. This coupling depends on the polarization properties of the layers themselves, and not on small regions of density overlap between the layers, excluding proper account in LDA or GGA. For large interplanar separation d the vdW interaction energy between planes behaves as −c 4 /d 4 , while LDA or GGA necessarily predicts an exponential falloff. Layers rolled up to form two (i) nanotubes with parallel axes a distance l apart interact as −c 5 /l 5 , or (ii) balls (e.g., C 60 ), a distance r apart, as −c 6 /r 6 . If by fluke an LDA or GGA were to give the correct equilibrium for one shape, it would necessarily fail for the others. The simple expedient of adding the standard asymptotic vdW energies as corrections to the correlation energy of LDA or GGA also fails. The true vdW interaction between two close sheets must be (i) substantially stronger (Fig. 1), (ii) seamless, and (iii) saturate as d shrinks (Fig. 2).Like earlier work directly calculating nonlocal correlations between two jellium slabs [9], the vdW density functional (vdW-DF) theory [5] used here exploits assumed planar symmetry. It divides the correlation energy functional into two pieces,, where E nl c [n] is defined to in...

Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed for the nonlocal correlations between electrons and applied to various relevant molecules and materials, including to those layered systems like graphite, boron nitride and molybdenum sulfide, to dimers of benzene, polycyclic aromatic hydrocarbons (PAHs), doped benzene, cytosine and DNA base pairs, to nonbonding forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators. Comparison with results from wavefunction calculations for the smaller systems and with experimental data for the extended ones show the vdW-DF path to be promising. This could have great ramifications.

The nonlocal correlation energy in the van der Waals density functional (vdW-DF) method [Phys. Rev. Lett. 92, 246401 (2004); Phys. Rev. B 76, 125112 (2007); Phys. Rev. B 89, 035412 (2014)] can be interpreted in terms of a coupling of zero-point energies of characteristic modes of semilocal exchange-correlation (xc) holes. These xc holes reflect the internal functional in the framework of the vdW-DF method [Phys. Rev. B 82, 081101 (2010)]. We explore the internal xc hole components, showing that they share properties with those of the generalized-gradient approximation. We use these results to illustrate the nonlocality in the vdW-DF description and analyze the vdW-DF formulation of nonlocal correlation.

ABSTRACT:The details of a density functional that includes van der Waals (vdW) interactions are presented. In particular we give some key steps of the transition from a form for fully planar systems to a procedure for realistic layered compounds that have planar symmetry only on large-distance scales, and which have strong covalent bonds within the layers. It is shown that the random-phase approximation of that original functional can be replaced by an approximation that is exact at large separation between vdW interacting fragments and seamless as the fragments merge. An approximation to the latter which renders the functional easily applicable and which preserves useful accuracy in both limits and in between is given. We report additional data from applications to forms of graphite, boron nitride, and molybdenum sulfide not reported in our previous communication.

A quantitative study of the long-range interaction between single copper adatoms on Cu(111) mediated by the electrons in the two-dimensional surface-state band is presented. The interaction potential was determined by evaluating the distance distribution of two adatoms from a series of scanning tunneling microscopy images taken at temperatures of 9 -21 K. The long-range interaction is oscillatory with a period of half the Fermi wavelength and decays for larger distances d as 1͞d2 . Five potential minima were identified for separations of up to 70 Å. The interaction significantly changes the growth of Cu͞Cu(111) at low temperatures. PACS numbers: 68.35.Fx, 61.16.Ch Surface-state electrons on the close packed surfaces of noble metals form a two-dimensional nearly free electron gas. The scattering of the electrons off point defects and step edges generates standing wave patterns in the electron density, which can be directly observed with the scanning tunneling microscope (STM) [1]. Analysis of the standing wave patterns provides a direct way to determine the surface-state dispersion and the scattering properties of the scatterers [2,3]. The ability of single adatoms to scatter surface electrons can be used to confine electrons in so-called quantum corrals: artificial structures of single adatoms build up by atomic manipulation [4]. The previous studies on standing waves concentrated on the effects caused by the adatom scatterers on the surface electron gas. The twodimensional electron gas itself should, on the other hand, give rise to an interaction between the scatterers.The surface-state mediated interaction is long ranged and oscillatory in nature. The history of indirect interactions mediated by the substrate electrons began with the theoretical works of Grimley [5], and Einstein and Schrieffer [6,7], followed by the experimental works of Tsong [8], and Watanabe and Ehrlich [9], who used field ion microscopy to observe the long-range interaction between single metal adatoms adsorbed on a W(110) surface. The long-range interaction mediated by a two-dimensional electron gas was considered in 1978 by Lau and Kohn [10]. They showed that, in the special case of a partially filled surface-state band, the interaction energy decays very slowly, as 1͞d 2 for large separations and is oscillatory with a periodicity of half of the Fermi wavelength. Only recently a room temperature STM study discussed an indication of such a long-range interaction between strongly bonded sulfur atoms on a Cu(111) surface [11] and a few further qualitative investigations exist [12].Here we report the first detailed quantitative study of a long-range interaction mediated by a two-dimensional nearly free electron gas. We have determined the interaction energy between single Cu adatoms on a Cu(111) surface from extensive measurements of their mutual spatial correlations. Although the interaction is very weak, the very low diffusion barrier (40 meV) [13][14][15] for the adatoms enabled us to probe their interaction energy up to distances of ...