Van Der Waals Density Functionals Research Articles

Benchmarking several van der Waals dispersion approaches for the description of intermolecular interactions.

Seven methods, including three van der Waals density functionals (vdW-DFs) and four different variants of the Tkatchenko-Scheffler (TS) methods, are tested on the A24, L7, and Taylor et al.'s "blind" test sets. It is found that for these systems, the vdW-DFs perform better that the TS methods. In particular, the vdW-DF-cx functional gives binding energies that are the closest to the reference values, while the many-body correction of TS does not always lead to an improvement in the description of molecular systems. In light of these results, several directions for further improvements to describe van der Waals interactions are discussed.

CO2 adsorption on the copper surfaces: van der Waals density functional and TPD studies.

We investigated the adsorption of CO2 on the flat, stepped, and kinked copper surfaces from density functional theory calculations as well as the temperature programmed desorption and X-ray photoelectron spectroscopy. Several exchange-correlation functionals have been considered to characterize CO2 adsorption on the copper surfaces. We used the van der Waals density functionals (vdW-DFs), i.e., the original vdW-DF (vdW-DF1), optB86b-vdW, and rev-vdW-DF2, as well as the Perdew-Burke-Ernzerhof (PBE) with dispersion correction (PBE-D2). We have found that vdW-DF1 and rev-vdW-DF2 functionals slightly underestimate the adsorption energy, while PBE-D2 and optB86b-vdW functionals give better agreement with the experimental estimation for CO2 on Cu(111). The calculated CO2 adsorption energies on the flat, stepped, and kinked Cu surfaces are 20-27 kJ/mol, which are compatible with the general notion of physisorbed species on solid surfaces. Our results provide a useful insight into appropriate vdW functionals for further investigation of related CO2 activation on Cu surfaces such as methanol synthesis and higher alcohol production.

Assessment of two hybrid van der Waals density functionals for covalent and non-covalent binding of molecules.

Two hybrid van der Waals density functionals (vdW-DFs) are developed using 25% Fock exchange with (i) the consistent-exchange vdW-DF-cx functional [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412 (2014)] and (ii) with the vdW-DF2 functional [K. Lee et al., Phys. Rev. B 82, 081101 (2010)]. The ability to describe covalent and non-covalent binding properties of molecules is assessed. For properties related to covalent binding, atomization energies (G2-1 set), molecular reaction energies (G2RC set), and ionization energies (G21IP set) are benchmarked against experimental reference values. We find that hybrid-vdW-DF-cx yields results that are rather similar to those of the standard non-empirical hybrid PBE0 [C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999)], with mean average deviations (MADs) of 4.9 and 5.0 kcal/mol for the G2-1 set, respectively. In this comparison, experimental reference values are used, back corrected by wavefunction-based quantum-chemistry calculations of zero-point energies. Hybrid vdW-DF2 follows somewhat different trends, showing on average significantly larger deviations from the reference energies, with a MAD of 14.5 kcal/mol for the G2-1 set. Non-covalent binding properties of molecules are assessed using the S22 benchmark set of non-covalently bonded dimers and the X40 set of dimers of small halogenated molecules, using wavefunction-based quantum chemistry results as references. For the S22 set, hybrid-vdW-DF-cx performs better than standard vdW-DF-cx for the mostly hydrogen-bonded systems, with MAD dropping from 0.6 to 0.3 kcal/mol, but worse for purely dispersion-bonded systems, with MAD increasing from 0.2 to 0.6 kcal/mol. Hybrid-vdW-DF2 offers a slight improvement over standard vdW-DF2. Similar trends are found for the X40 set, with hybrid-vdW-DF-cx performing particularly well for binding energies involving the strongly polar hydrogen halides, but poorly for systems with tiny binding energies. Our study of the X40 set reveals the potential of mixing Fock exchange with vdW-DF, but also highlights shortcomings of the hybrids constructed here. The solid performance of hybrid-vdW-DF-cx for covalent-bonded systems, as well as the strengths and issues uncovered for non-covalently bonded systems, makes this study a good starting point for developing even more accurate hybrid vdW-DFs.

A comparison between quantum chemistry and quantum Monte Carlo techniques for the adsorption of water on the (001) LiH surface.

We present a comprehensive benchmark study of the adsorption energy of a single water molecule on the (001) LiH surface using periodic coupled cluster and quantum Monte Carlo theories. We benchmark and compare different implementations of quantum chemical wave function based theories in order to verify the reliability of the predicted adsorption energies and the employed approximations. Furthermore we compare the predicted adsorption energies to those obtained employing widely used van der Waals density-functionals. Our findings show that quantum chemical approaches are becoming a robust and reliable tool for condensed phase electronic structure calculations, providing an additional tool that can also help in potentially improving currently available van der Waals density-functionals.

Erratum: Assessing the accuracy of the van der Waals density functionals for rare-gas and small molecular systems [Phys. Rev. B 91 , 195103 (2015)

Erratum: Assessing the accuracy of the van der Waals density functionals for rare-gas and small molecular systems [Phys. Rev. B <b>91</b> , 195103 (2015)

Desorption dynamics of CO2 from formate decomposition on Cu(111).

We performed ab initio molecular dynamics analysis of formate decomposition to CO2 and H on a Cu(111) surface using van der Waals density functionals. Our analysis shows that the desorbed CO2 has approximately twice larger bending vibrational energy than the translational, rotational, and stretching vibrational energies. Since formate synthesis, the reverse reaction of formate decomposition, has been suggested experimentally to occur via the Eley-Rideal mechanism, our results indicate that the formate synthesis can be enhanced if the bending vibrational mode of CO2 is excited rather than the translational and/or stretching vibrational modes. Detailed information on the energy distribution of desorbed CO2 as a formate decomposition product may provide new insights for improving the catalytic activity of formate synthesis.

Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo

We studied the low-pressure (0–10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo and density functional theory (DFT) methods. We performed diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. Using density functional perturbation theory, we computed the phonon contributions to the free energies. Our DFT enthalpy-pressure phase diagrams indicate that the Pbca and P21/c structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature Pbca to P21/c phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations give 50.6 ± 0.5 kJ/mol for crystalline benzene lattice energy.

Effect of van der Waals interactions on the structural and binding properties of GaSe

The influence of van der Waals interactions on the lattice parameters, band structure, elastic moduli and binding energy of layered GaSe compound has been studied using projector-augmented wave method within density functional theory. We employed the conventional local/semilocal exchange-correlation functionals and recently developed van der Waals functionals which are able to describe dispersion forces. It is found that application of van der Waals density functionals allows to substantially increase the accuracy of calculations of the lattice constants a and c and interlayer distance in GaSe at ambient conditions and under hydrostatic pressure. The pressure dependences of the a-parameter, Ga–Ga, Ga–Se bond lengths and Ga–Ga–Se bond angle are characterized by a relatively low curvature, while c(p) has a distinct downward bowing due to nonlinear shrinking of the interlayer spacing. From the calculated binding energy curves we deduce the interlayer binding energy of GaSe, which is found to be in the range 0.172–0.197eV/layer (14.2–16.2meV/Å2).

Assessing the accuracy of the van der Waals density functionals for rare-gas and small molecular systems

The precise description of chemical bonds with different natures is a prerequisite for an accurate electronic structure method. The van der Waals density functional is a promising approach that meets such a requirement. Nevertheless, the accuracy should be assessed for a variety of materials to test the robustness of the method. We present benchmark calculations for weakly interacting molecular complexes and rare-gas systems as well as covalently bound molecular systems, in order to assess the accuracy and applicability of rev-vdW-DF2, a recently proposed variant [I. Hamada, Phys. Rev. B 89, 121103 (2014)] of the van der Waals density functional. It is shown that although the calculated atomization energies for small molecules are less accurate rev-vdW-DF2 describes the interaction energy curves for the weakly interacting molecules and rare-gas complexes, as well as the bond lengths of diatomic molecules, reasonably well.

Van der Waals interaction in a boron nitride bilayer

We have carried out quantum Monte Carlo (QMC) calculations to study the interlayer interaction in a boron nitride (BN) bilayer. The binding energy, 81 meV/2BN after finite-size corrections, was found to be larger than that obtained by density functional theory (DFT) with local density approximation, and smaller than those using van der Waals density functionals, both by considerable amounts. The QMC calculated interaction beyond the equilibrium interlayer separation was found to have a longer-range behavior than all the available DFT schemes.

Li intercalation in graphite: A van der Waals density-functional study

Modeling layered intercalation compounds from first principles poses a problem, as many of their properties are determined by a subtle balance between van der Waals interactions and chemical or Madelung terms, and a good description of van der Waals interactions is often lacking. Using van der Waals density functionals we study the structures, phonons and energetics of the archetype layered intercalation compound Li-graphite. Intercalation of Li in graphite leads to stable systems with calculated intercalation energies of $-0.2$ to $-0.3$~eV/Li atom, (referred to bulk graphite and Li metal). The fully loaded stage 1 and stage 2 compounds LiC$_6$ and Li$_{1/2}$C$_6$ are stable, corresponding to two-dimensional $\sqrt3\times\sqrt3$ lattices of Li atoms intercalated between two graphene planes. Stage $N>2$ structures are unstable compared to dilute stage 2 compounds with the same concentration. At elevated temperatures dilute stage 2 compounds easily become disordered, but the structure of Li$_{3/16}$C$_6$ is relatively stable, corresponding to a $\sqrt7\times\sqrt7$ in-plane packing of Li atoms. First-principles calculations, along with a Bethe-Peierls model of finite temperature effects, allow for a microscopic description of the observed voltage profiles.

Testing several recent van der Waals density functionals for layered structures.

Six recently developed exchange functionals for pairing with two different versions of van der Waals density functionals (vdW-DF) are tested for weakly bonded solids. The test, using 26 layered weakly bonded compounds, benchmarks the lattice constants against experimental data and the interlayer binding energies against reference data from the random-phase approximation (RPA). The investigated functionals tend to give interlayer binding energies higher than the RPA benchmark, and the overall performance for lattice constants is good. The exchange functionals optB86b and cx13 paired with the original vdW-DF and the B86R functional paired with vdW-DF2 are found to give particularly good results for equilibrium geometries.

Structural and Electronic Properties of Carbon-Nanotube/Graphene Junction: A First-Principles Study

Recently, a junction made of single wall carbon nanotube and a single sheet of graphene has been fabricated on silicon oxide substrate [1]. Their Raman spectroscopy measurements showed an upshift of the radial breathing modes and G peaks of the nanotube attributed to the charge transfer (CT) at the junction. The direction of the CT was determined from the intensity ratio of 2D/G of graphene, decreasing as a function of G Raman shift, which suggest n-doping of graphene due to the presence of nanotube. Their theoretical work, using molecular dynamics simulation, ruled out the strain on carbon nanotube to be the cause of the Raman upshift. In this work, we perform density functional theory calculations, for a model of C(13,7)/graphene junction, as suggested in Ref. [1]. Figure-1 shows the adopted model with 1132 carbon atoms, rendering the conventional first-principles methods that scale as O(N3) impractical. Therefore, we carried out the optimization of the large model using self-consistent density functional tight-binding method (SCC-DFTB), provided within CP2K package [2]. The resulting structure was then used to perform a single point energy calculation within density functional theory (DFT), adopting B97-D functional [3, 4], suitable for non-covalent interactions. The DFT is based on QUICKSTEP [5], which is an order-N method implemented in CP2K. Our preliminary results indicate that the charge transfer for a suspended nanotube/graphene system takes place from graphene to the carbon nanotube. To ascertain these results, we built a small material model consisting of the armchair C(10,10) and graphene junction, and performed calculations with the VASP package using optPBE [6] functional, which also includes the dispersion to account for van der Waals interactions. The results for the small model suggest an n-doping of carbon nanotube. Our findings are in agreement with the work of Cook et al. [7] for a C(8,0) adsorbed on a flat graphene junction. As can be seen, all the theoretical work seem to be in disagreement with the charge transfer direction, suggested in Ref. [1], which may be due to the pristine nature of the models. In this paper we will report on structural and electronic properties of a CNT/graphene junction, for pristine models as well as doped systems with impurities, where charge re-distribution at the junction will be outlined.1. Geraldine L. C. Paulus, et al., Charge Transfer at Junctions of a Single Layer of Graphene and a Metallic Single Walled Carbon Nanotube. Small, 2013. 9: p. 1954.2. CP2K. Available from: http://www.cp2k.org.3. Grimme, S., Semiemperical GGA-type density functional constructed with long-range dispersion correction. J. Comput. Chem., 2006. 27: p. 1787.4. Becke, A.D., Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals. J. Chem. Phys., 1997. 107: p. 8554.5. J. VandeVondele, et al., QUICKSTEP: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. J. Comput. Phys. Commun., 2005. 167: p. 103.6. Klimes, J., D.R. Bowler, and A. Michaelides, Van der Waals density functionals applied to solids. Phys. Rev. B, 2011. 83: p. 195131.7. Brandon G. Cook, William R. French, and a.K. Varga, Electron Transport properties of carbon nanotube-graphene contacts. Appl. Phys. Lett., 2012. 101: p. 153501.

Role of the dispersion force in modeling the interfacial properties of molecule-metal interfaces: adsorption of thiophene on copper surfaces.

We present density functional theory calculations of the geometry, adsorption energy and electronic structure of thiophene adsorbed on Cu(111), Cu(110) and Cu(100) surfaces. Our calculations employ dispersion corrections and self-consistent van der Waals density functionals (vdW-DFs). In terms of speed and accuracy, we find that the dispersion-energy-corrected Revised Perdue-Burke-Enzerhof (RPBE) functional is the “best balanced” method for predicting structural and energetic properties, while vdW-DF is also highly accurate if a proper exchange functional is used. Discrepancies between theory and experiment in molecular geometry can be solved by considering x-ray generated core-holes. However, the discrepancy concerning the adsorption site for thiophene/Cu(100) remains unresolved and requires both further experiments and deeper theoretical analysis. For all the interfaces, the PBE functional reveals a covalent bonding picture which the inclusion of dispersive contributions does not change to a vdW one. Our results provide a comprehensive understanding of the role of dispersive forces in modelling molecule-metal interfaces.

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.

Hydration structure of Na+ and K+ from ab initio molecular dynamics based on modern density functional theory

Molecular dynamics (Born–Oppenheimer) simulations based on density functional theory have been carried out to investigate the solvation structure of monovalent Na+ and K+ cations in water under ambient conditions. Four recently proposed van der Waals (vdW) density functionals (LMKLL, DRSLL, DRSLL-PBE, DRSLL-optB88), the semiempirical vdW method of Grimme (BLYP-D3) and conventional gradient-corrected (GGA-BLYP) density functionals are applied in order to evaluate their accuracy in describing the hydration structure of alkali metal ions. Theoretical results are compared to available experimental data. Our results indicate that addition of corrections accounting for dispersion forces significantly improves the agreement between predicted and measured coordination numbers for both Na+ and K+ cations. Analysis of radial distribution functions brings further support to the notion that the choice of the generalised gradient approximation density functional impacts crucially on the computed structural properties. DRSLL-optB88 and BLYP-D3 provide the best agreement with experiment.

Van der Waals density functional study of the energetics of alkali metal intercalation in graphite

We report on the energetics of intercalation of lithium, sodium and potassium in graphite by density functional theory using recently developed van der Waals (vdW) density functionals. First stage intercalation compounds are well described by conventional functionals like GGA, but van der Waals functionals are crucial for higher stage intercalation compounds and graphite, where van der Waals interactions are important. The vdW-optPBE functional gave the best agreement with reported structure and energetics for graphite and LiC6 and was further applied for intercalation of Na and K. The enthalpy of formation of LiC6 and KC8 were found to be −16.4 and −27.5 kJ mol−1 respectively. NaC6 and NaC8 were unstable with positive enthalpies of formation (+20.8 and +19.9 kJ mol−1). The energetics of stacking of graphene and intercalant layers was investigated from first to fifth stage intercalation compounds. Higher stage compounds of Li and K were stable, but with less negative enthalpy of formation with increasing stage order. The higher stage Na compounds possessed positive enthalpy of formation, but lower in magnitude than the energy difference of 0.6 kJ mol−1 between graphite with AB and AA stacking. The abnormal behaviour of the lower stage Na intercalation compounds was rationalized by the lower energy involved in the formation of the chemical bond between carbon Na relative to the corresponding bond with Li or K. The chemical bond between alkali metal and carbon is characterized by charge transfer from the alkali-metal to carbon resulting in ionized alkali-metals. The intercalation induces only a subtle increase in the in-plane C–C bond lengths, with longer C–C bonds in the vicinity of the alkali metals but without breaking the hexagonal symmetry.

Room temperature compressibility and diffusivity of liquid water from first principles

The isothermal compressibility of water is essential to understand its anomalous properties. We compute it by ab initio molecular dynamics simulations of 200 molecules at five densities, using two different van der Waals density functionals. While both functionals predict compressibilities within ~30% of experiment, only one of them accurately reproduces, within the uncertainty of the simulation, the density dependence of the self-diffusion coefficient in the anomalous region. The discrepancies between the two functionals are explained in terms of the low- and high-density structures of the liquid.

Van der Waals density-functional study of 100% hydrogen coverage on bilayer graphene

We investigate all hydrogen configurations that exist in a 1×1 unit cell of bilayer graphene at 100% coverage to find the low energy competing configurations using density functional theory (DFT). Other unique configurations, obtained from a 2×1 supercell, are also investigated. The GGA-PBE functional and four variants of non-local van der Waals density functionals namely, vdW-DF, vdW-DF2, vdW-DF-C09x, and vdW-DF2-C09x are used to account for the exchange correlation effects. Ten unique hydrogen configurations are identified for 1×1 unit cell bilayer graphene, and nine of these structures are found to be energetically stable with three low energy competing configurations. One arrangement found to exist in both 1×1 and 2×1 cell sizes is the most energetically stable configuration of all considered. For some of the configurations identified from the 2×1 supercell, it is found that the effect of hydrogenation results in greatly distorted hexagonal layers resulting in unequal bond distances between the carbon atoms. Also, interaction between the hydrogen-decorated planes greatly affects the energetics of the structures. The vdW-DF-C09x functional is found to predict the shortest interlayer distances for all the configurations, whereas the GGA-PBE functional predicts the largest. For the most energetically favorable configuration, hydrogenation is found to reduce the elastic properties compared with pristine bilayer graphene.

Nonlocal van der Waals functionals: The case of rare-gas dimers and solids

Recently, the nonlocal van der Waals (vdW) density functionals [M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)] have attracted considerable attention due to their good performance for systems where weak interactions are important. Since the physics of dispersion is included in these functionals, they are usually more accurate and show less erratic behavior than the semilocal and hybrid methods. In this work, several variants of the vdW functionals have been tested on rare-gas dimers (from He2 to Kr2) and solids (Ne, Ar, and Kr) and their accuracy compared to standard semilocal approximations, supplemented or not by an atom-pairwise dispersion correction [S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, J. Chem. Phys. 132, 154104 (2010)]. An analysis of the results in terms of energy decomposition is also provided.