A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [Phys. Rev. Lett. 91, 126402 (2003)]]. It includes van der Waals forces in a seamless fashion. By expansion to second order in a carefully chosen quantity contained in the long-range part of the correlation functional, the nonlocal correlations are expressed in terms of a density-density interaction formula. It contains a relatively simple parametrized kernel, with parameters determined by the local density and its gradient. The proposed functional is applied to rare gas and benzene dimers, where it is shown to give a realistic description.

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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.

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 systematic approach for the construction of a density functional for van der Waals interactions that also accounts for saturation effects is described, i.e. one that is applicable at short distances. A very efficient method to calculate the resulting expressions in the case of flat surfaces, a method leading to an order reduction in computational complexity, is presented. Results for the interaction of two parallel jellium slabs are shown to agree with those of a recent RPA calculation (J.F. Dobson and J. Wang, Phys. Rev. Lett. 82, 2123 1999). The method is easy to use; its input consists of the electron density of the system, and we show that it can be successfully approximated by the electron densities of the interacting fragments. Results for the surface correlation energy of jellium compare very well with those of other studies. The correlation-interaction energy between two parallel jellia is calculated for all separations d, and substantial saturation effects are predicted.

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In a framework for long-range density-functional theory we present a unified full-field treatment of the asymptotic van der Waals interaction for atoms, molecules, surfaces, and other objects. The only input needed consists of the electron densities of the interacting fragments and the static polarizability or the static image plane, which can be easily evaluated in a ground-state density-functional calculation for each fragment. Results for separated atoms, molecules, and for atoms/molecules outside surfaces are in agreement with those of other, more elaborate, calculations.PACS numbers: 71.15. Mb,31.15.Ew,34.50.Dy P(r, ω) =