van der Waals forces in density functional theory: a review of the vdW-DF method.

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.

van der Waals density functionals built upon the electron-gas tradition: facing the challenge of competing interactions.

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.

Benchmarking van der Waals density functionals with experimental data: potential-energy curves for H2 molecules on Cu(111), (100) and (110) surfaces.

Detailed physisorption data from experiment for the H(2) molecule on low-index Cu surfaces challenge theory. Recently, density functional theory (DFT) has been developed to account for nonlocal correlation effects, including van der Waals (dispersion) forces. We show that the functional vdW-DF2 gives a potential-energy curve, potential-well energy levels and difference in lateral corrugation promisingly close to the results obtained by resonant elastic backscattering-diffraction experiments. The backscattering barrier is sensitive to the choice of exchange functional approximation. Further, the DFT-D3 and TS-vdW corrections to traditional DFT formulations are also benchmarked, and deviations are analyzed.

Ab initio van der waals interactions in simulations of water alter structure from mainly tetrahedral to high-density-like.

The structure of liquid water at ambient conditions is studied in ab initio molecular dynamics simulations in the NVE ensemble using van der Waals (vdW) density-functional theory, i.e., using the new exchange-correlation functionals optPBE-vdW and vdW-DF2, where the latter has softer nonlocal correlation terms. Inclusion of the more isotropic vdW interactions counteracts highly directional hydrogen bonds, which are enhanced by standard functionals. This brings about a softening of the microscopic structure of water, as seen from the broadening of angular distribution functions and, in particular, from the much lower and broader first peak in the oxygen-oxygen pair-correlation function (PCF) and loss of structure in the outer hydration shells. Inclusion of vdW interactions is shown to shift the balance of resulting structures from open tetrahedral to more close-packed. The resulting O-O PCF shows some resemblance with experiment for high-density water (Soper, A. K. and Ricci, M. A. Phys. Rev. Lett. 2000, 84, 2881), but not directly with experiment for ambient water. Considering the accuracy of the new functionals for interaction energies, we investigate whether the simulation protocol could cause the deviation. An O-O PCF consisting of a linear combination of 70% from vdW-DF2 and 30% from low-density liquid water, as extrapolated from experiments, reproduces near-quantitatively the experimental O-O PCF for ambient water. This suggests the possibility that the new functionals may be reliable and that instead larger-scale simulations in the NPT ensemble, where the density is allowed to fluctuate in accordance with proposals for supercooled water, could resolve the apparent discrepancy with the measured PCF.

Stacking interactions and DNA intercalation.

The relationship between stacking interactions and the intercalation of proflavine and ellipticine within DNA is investigated using a nonempirical van der Waals density functional for the correlation energy. Our results, employing a binary stack model, highlight fundamental, qualitative differences between base-pair-base-pair interactions and that of the stacked intercalator-base-pair system. The most notable result is the paucity of torque, which so distinctively defines the twist of DNA. Surprisingly, this model, when combined with a constraint on the twist of the surrounding base-pair steps to match the observed unwinding of the sugar-phosphate backbone, was sufficient for explaining the experimentally observed proflavine intercalator configuration. Our extensive mapping of the potential energy surface of base-pair-intercalator interactions can provide valuable information for future nonempirical studies of DNA intercalation dynamics.

Density functional for van der Waals forces accounts for hydrogen bond in benchmark set of water hexamers.

A recent extensive study has investigated how various exchange-correlation (XC) functionals treat hydrogen bonds in water hexamers and has shown traditional generalized gradient approximation and hybrid functionals used in density-functional (DF) theory to give the wrong dissociation-energy trend of low-lying isomers and van der Waals (vdW) dispersion forces to give key contributions to the dissociation energy. The question raised whether functionals that incorporate vdW forces implicitly into the XC functional predict the correct lowest-energy structure for the water hexamer and yield accurate total dissociation energy is here answered affirmatively for the vdW-DF [M. Dion et al., Phys. Rev. Lett.92, 246401 (2004)].

Density functional study of the adsorption and van der Waals binding of aromatic and conjugated compounds on the basal plane of MoS(2).

Accurate calculations of adsorption energies of cyclic molecules are of key importance in investigations of, e.g., hydrodesulfurization (HDS) catalysis. The present density functional theory (DFT) study of a set of important reactants, products, and inhibitors in HDS catalysis demonstrates that van der Waals interactions are essential for binding energies on MoS(2) surfaces and that DFT with a recently developed exchange-correlation functional (vdW-DF) accurately calculates the van der Waals energy. Values are calculated for the adsorption energies of butadiene, thiophene, benzothiophene, pyridine, quinoline, benzene, and naphthalene on the basal plane of MoS(2), showing good agreement with available experimental data, and the equilibrium geometry is found as flat at a separation of about 3.5 A for all studied molecules. This adsorption is found to be due to mainly van der Waals interactions. Furthermore, the manifold of adsorption-energy values allows trend analyses to be made, and they are found to have a linear correlation with the number of main atoms.

Stacking interactions and the twist of DNA.

The importance of stacking interactions for the Twist and stability of DNA is investigated using the fully ab initio van der Waals density functional (vdW-DF). Our results highlight the role that binary interactions between adjacent sets of base pairs play in defining the sequence-dependent Twists observed in high-resolution experiments. Furthermore, they demonstrate that additional stability gained by the presence of thymine is due to methyl interactions with neighboring bases, thus adding to our understanding of the mechanisms that contribute to the relative stability of DNA and RNA. Our mapping of the energy required to twist each of the 10 unique base pair steps should provide valuable information for future studies of nucleic acid stability and dynamics. The method introduced will enable the nonempirical theoretical study of significantly larger pieces of DNA or DNA/amino acid complexes than previously possible.

Application of van der Waals density functional to an extended system: adsorption of benzene and naphthalene on graphite.

It is shown that it is now possible to include van der Waals (vdW) interactions via a nonempirical implementation of density functional (DF) theory to describe the correlation energy in electronic structure calculations on infinite systems of no particular symmetry. The vdW-DF theory [Phys. Rev. Lett. 92, 246401 (2004)] is applied to the adsorption of benzene and naphthalene on an infinite sheet of graphite, as well as the binding between two graphite sheets. A comparison with recent thermal-desorption data [Phys. Rev. B 69, 155406 (2004)] shows great promise for the vdW-DF method.