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...

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.

We develop a proper nonempirical spin-density formalism for the van der Waals density functional (vdW-DF) method. We show that this generalization, termed svdW-DF, is firmly rooted in the single-particle nature of exchange and we test it on a range of spin systems. We investigate in detail the role of spin in the nonlocal-correlation driven adsorption of H2 and CO2 in the linear magnets Mn-MOF74, Fe-MOF74, Co-MOF74, and Ni-MOF74. In all cases, we find that spin plays a significant role during the adsorption process despite the general weakness of the molecular-magnetic responses. The case of CO2 adsorption in Ni-MOF74 is particularly interesting, as the inclusion of spin effects results in an increased attraction, opposite to what the diamagnetic nature of CO2 would suggest. We explain this counter-intuitive result, tracking the behavior to a coincidental hybridization of the O p states with the Ni d states in the down-spin channel. More generally, by providing insight on nonlocal correlation in concert with spin effects, our nonempirical svdW-DF method opens the door for a deeper understanding of weak nonlocal magnetic interactions. The modular building-block nature of metal organic frameworks (MOFs) and their extraordinary affinity for adsorption of small molecules make these nano-porous materials ideal for technologically important applications. MOFs are used, for example, for gas storage and sequestration [1][2][3][4][5], catalysis [6,7], polymerization [8,9], luminescence [10,11], non-linear optics [12], magnetic networks [13], targeted drug delivery [14], multiferroics [15][16][17], and sensing [18][19][20][21]. The design of novel MOFs with improved properties requires insight into the molecule/MOF interaction. The large unit cells and periodic nature of MOFs make density functional theory (DFT) the prospective tool for a theory exploration. However, both the adsorbate molecule and the MOF's metal centers can carry spin, giving rise to complex magnetic interactions and a molecular-spin response. It is thus crucial that DFT can reliably capture van der Waals (vdW) forces-which govern adsorption in MOFs-in concert with spin effects.Concerning the former, the last decade witnessed the development of DFT descriptions for these forces [22]. Here, the vdW-DF versions [23][24][25][26] stand out by being nonempirical exchange-correlation functionals that are systematic and truly nonlocal extensions beyond LDA [27] and GGA [28] in the electron-gas tradition [22,29,30]. Subsequent developments include variants which differ by their choice of the semi-local exchange [31][32][33][34][35] and related nonlocal correlation functionals that rely on optimizing parameters [36][37][38]. The vdW-DF method and relatives have been successfully applied to numerous materials in general [22,29,39], and to smallmolecule adsorption in MOFs in particular [4,5,[40][41][42][43][44][45][46].Concerning the spin effects, however, a systematic description within the vdW-DF framework is still missing. Such effects can play important roles ...

The theoretical description of sparse matter attracts much interest, in particular for those ground-state properties that can be described by density functional theory. One proposed approach, the van der Waals density functional (vdW-DF) method, rests on strong physical foundations and offers simple yet accurate and robust functionals. A very recent functional within this method called vdW-DF-cx [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412 (2014)] stands out in its attempt to use an exchange energy derived from the same plasmon-based theory from which the nonlocal correlation energy was derived. Encouraged by its good performance for solids, layered materials, and aromatic molecules, we apply it to several systems that are characterized by competing interactions. These include the ferroelectric response in PbTiO3, the adsorption of small molecules within metal-organic frameworks, the graphite/diamond phase transition, and the adsorption of an aromatic-molecule on the Ag(111) surface. Our results indicate that vdW-DF-cx is overall well suited to tackle these challenging systems. In addition to being a competitive density functional for sparse matter, the vdW-DF-cx construction presents a more robust general-purpose functional that could be applied to a range of materials problems with a variety of competing interactions.

Molecular crystals are a prototypical class of van der Waals (vdW) bound organic materials with excitedstate properties relevant for optoelectronics applications. Predicting the structure and excited-state properties of molecular crystals presents a challenge for electronic structure theory, as standard approximations to density functional theory (DFT) do not capture long-range vdW dispersion interactions and do not yield excited-state properties. In this work, we use a combination of DFT including vdW forces, using both nonlocal correlation functionals and pairwise correction methods, together with many-body perturbation theory (MBPT) to study the geometry and excited states, respectively, of the entire series of oligoacene crystals, from benzene to hexacene. We find that vdW methods can predict lattice constants within 1% of the experimental measurements, on par with the previously reported accuracy of pairwise approximations for the same systems. We further find that excitation energies are sensitive to geometry, but if optimized geometries are used MBPT can yield excited-state properties within a few tenths of an eV from experiment. We elucidate trends in MBPT-computed charged and neutral excitation energies across the acene series and discuss the role of common approximations used in MBPT.

Using a van der Waals density functional ͑vdW-DF͒ ͓Phys. Rev. Lett. 92, 246401 ͑2004͔͒, we perform ab initio calculations for the adsorption energy of benzene ͑Bz͒ on Cu͑111͒ as a function of lateral position and height. We find that the vdW-DF inclusion of nonlocal correlations ͑responsible for dispersive interactions͒ changes the relative stability of eight binding-position options and increases the binding energy by over an order of magnitude, achieving good agreement with experiment. The admolecules can move almost freely along a honeycomb web of "corridors" passing between fcc and hcp hollow sites via bridge sites. Our diffusion barriers ͑for dilute and two condensed adsorbate phases͒ are consistent with experimental observations. Further vdW-DF calculations suggest that the more compact ͑hexagonal͒ Bz-overlayer phase, with lattice constant a = 6.74 Å, is due to direct Bz-Bz vdW attraction, which extends to ϳ8 Å. We attribute the second, sparser hexagonal Bz phase, with a = 10.24 Å, to indirect electronic interactions mediated by the metallic surface state on Cu͑111͒. To support this claim, we use a formal Harris-functional approach to evaluate nonperturbationally the asymptotic form of this indirect interaction. Thus, we can account well for benzene self-organization on Cu͑111͒.

The adsorption of benzene and C60 on graphene and boron nitride (BN) is studied using density functional theory with the non-local correlation functional vdW-DF. By comparing these systems we can systematically investigate their adsorption nature and differences between the two functional versions vdW-DF1 and vdW-DF2. The bigger size of the C60 molecule makes it bind stronger to the surface than benzene, yet the interface between the molecules and the sheets are similar in nature. The binding separation is more sensitive to the exchange variant used in vdW-DF than to the correlation version. This result is related to the exchange and correlation components of the potential energy curve (PEC). We show that a moderate dipole forms for C60 on graphene, unlike for the other adsorption systems. We find that the corrugation is very sensitive to the variant or version of vdW-DF used, in particular the exchange. Further, we show that this sensitivity arise indirectly through the shift in binding separation caused by changing vdW-DF variant. Based on our results, we suggest a concerted theory-experiment approach to assess the exchange and correlation contributions to physisorption. Using DFT calculations, the corrugation can be linked to the optimal separation, allowing us to extract the exchange-correlation part of the adsorption energy. Molecules with same interfaces to the surface, but different geometries, can in turn cast light on the role of van der Waals forces.