Next-Generation Nonlocal van der Waals Density Functional.

The fundamental ideas for a nonlocal density functional theory-capable of reliably capturing van der Waals interactions-were already conceived in the 1990s. In 2004, a seminal paper introduced the first practical nonlocal exchange-correlation functional called vdW-DF, which has become widely successful and laid the foundation for much further research. However, since then, the functional form of vdW-DF has remained unchanged. Several successful modifications paired the original functional with different (local) exchange functionals to improve performance, and the successor vdW-DF2 also updated one internal parameter. Bringing together different insights from almost 2 decades of development and testing, we present the next-generation nonlocal correlation functional called vdW-DF3, in which we change the functional form while staying true to the original design philosophy. Although many popular functionals show good performance around the binding separation of van der Waals complexes, they often result in significant errors at larger separations. With vdW-DF3, we address this problem by taking advantage of a recently uncovered and largely unconstrained degree of freedom within the vdW-DF framework that can be constrained through empirical input, making our functional semiempirical. For two different parameterizations, we benchmark vdW-DF3 against a large set of well-studied test cases and compare our results with the most popular functionals, finding good performance in general for a wide array of systems and a significant improvement in accuracy at larger separations. Finally, we discuss the achievable performance within the current vdW-DF framework, the flexibility in functional design offered by vdW-DF3, as well as possible future directions for nonlocal van der Waals density functional theory.

Advanced capabilities for materials modelling with Quantum ESPRESSO.

Quantum EXPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum EXPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.

Spin Signature of Nonlocal Correlation Binding in Metal-Organic Frameworks.

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 H_{2} and CO_{2} 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 CO_{2} 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 CO_{2} would suggest. We explain this counterintuitive 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.

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.

NMR study of small molecule adsorption in MOF-74-Mg.

We calculate the carbon nuclear magnetic resonance (NMR) shielding for CO2 and the hydrogen shieldings for both H2 and H2O inside the metal organic framework MOF-74-Mg. Our ab initio calculations are at the density functional theory level using the van der Waals including density functional vdW-DF. The shieldings are obtained while placing the small molecules throughout the structure, including the calculated adsorption site for various loading scenarios. We then explore relationships between loading, rotational and positional characteristics, and the NMR shieldings for each adsorbate. Our NMR calculations show a change in the shielding depending on adsorbate, position, and loading in a range that is experimentally observable. We further provide a simple model for the energy and the NMR shieldings throughout the cavity of the MOF. By providing this mapping of shielding to position and loading for these adsorbates, we argue that NMR probes could be used to provide additional information about the position at which these small molecules bind within the MOF, as well as the loading of the adsorbed molecule.

Binding interactions in dimers of phenalenyl and closed-shell analogues.

Phenalenyl, an open-shell neutral radical that can form both π-stacked dimers and conducting molecular crystals, has gained attention for its interesting and potentially useful electrical and magnetic properties. The properties of this complex physical system are fairly well understood, making it an ideal testing ground for the newly developed van der Waals density functional (vdW-DF). We invoke a simple approximation, allowing the vdW-DF to be used within spin-polarized density functional theory and test this approximation on the π-stacked phenalenyl dimer. The results indicate that the vdW-DF is capable of qualitatively describing the interaction between two neutral radicals in the π-stacked configuration, producing, in line with experiment, binding distances that are significantly below the sum of the van der Waals radii. This is a nontypical distance range where most other theories fail. We then investigate two hypothetical closed-shell analogues of this dimer, one formed by replacing the central carbon of phenalenyl with a nitrogen atom and the other formed by replacing the central carbon with a boron atom. In these cases, relatively strong interaction energies are obtained at more typical equilibrium distances for van der Waals dimers. The nitrogen-substituted dimer shows an unexpected rotational barrier that is dictated by the electronic kinetic energy within the system. The torsional curve of the boron-substituted dimer also exhibits a rotational barrier, but this is found to disappear when exact exchange is used in place of a local or semilocal exchange functional.

Diffusion of small molecules in metal organic framework materials.

Ab initio simulations are combined with in situ infrared spectroscopy to unveil the molecular transport of H2, CO2, and H2O in the metal organic framework MOF-74-Mg. Our study uncovers--at the atomistic level--the major factors governing the transport mechanism of these small molecules. In particular, we identify four key diffusion mechanisms and calculate the corresponding diffusion barriers, which are nicely confirmed by time-resolved infrared experiments. We also answer a long-standing question about the existence of secondary adsorption sites for the guest molecules, and we show how those sites affect the macroscopic diffusion properties. Our findings are important to gain a fundamental understanding of the diffusion processes in these nanoporous materials, with direct implications for the usability of MOFs in gas sequestration and storage applications.

A theoretical study of the hydrogen-storage potential of (H2)4CH4 in metal organic framework materials and carbon nanotubes.

The hydrogen-methane compound (H(2))(4)CH(4)-or for short H4M-is one of the most promising hydrogen-storage materials. This van der Waals compound is extremely rich in molecular hydrogen: 33.3 mass%, not including the hydrogen bound in CH(4); including it, we reach even 50.2 mass%. Unfortunately, H4M is not stable under ambient pressure and temperature, requiring either low temperature or high pressure. In this paper, we investigate the properties and structure of the molecular and crystalline forms of H4M, using ab initio methods based on van der Waals DFT (vdW-DF). We further investigate the possibility of creating the pressures required to stabilize H4M through external agents such as metal organic framework (MOF) materials and carbon nanotubes, with very encouraging results. In particular, we find that certain MOFs can create considerable pressure for H4M in their cavities, but not enough to stabilize it at room temperature, and moderate cooling is still necessary. On the other hand, we find that all the investigated carbon nanotubes can create the high pressures required for H4M to be stable at room temperature, with direct implications for new and exciting hydrogen-storage applications.

Structural evolution of amino acid crystals under stress from a non-empirical density functional.

Use of the non-local correlation functional vdW-DF (from 'van der Waals density functional'; Dion M et al 2004 Phys. Rev. Lett. 92 246401) has become a popular approach for including van der Waals interactions within density functional theory. In this work, we extend the vdW-DF theory and derive the corresponding stress tensor in a fashion similar to the LDA and GGA approach, which allows for a straightforward implementation in any electronic structure code. We then apply our methodology to investigate the structural evolution of amino acid crystals of glycine and l-alanine under pressure up to 10 GPa-with and without van der Waals interactions-and find that for an accurate description of intermolecular interactions and phase transitions in these systems, the inclusion of van der Waals interactions is crucial. For glycine, calculations including the vdW-DF (vdW-DF-c09x) functional are found to systematically overestimate (underestimate) the crystal lattice parameters, yet the stability ordering of the different polymorphs is determined accurately, at variance with the GGA case. In the case of l-alanine, our vdW-DF results agree with recent experiments that question the phase transition reported for this crystal at 2.3 GPa, as the a and c cell parameters happen to become equal but no phase transition is observed.

Role of van der Waals interaction in forming molecule-metal junctions: flat organic molecules on the Au(111) surface.

The self-assembly of flat organic molecules on metal surfaces is controlled, apart from the kinetic factors, by the interplay between the molecule-molecule and molecule-surface interactions. These are typically calculated using standard density functional theory within the generalized gradient approximation, which significantly underestimates nonlocal correlations, i.e. van der Waals (vdW) contributions, and thus affects interactions between molecules and the metal surface in the junction. In this paper we address this question systematically for the Au(111) surface and a number of popular flat organic molecules which form directional hydrogen bonds with each other. This is done using the recently developed first-principles vdW-DF method which takes into account the nonlocal nature of electron correlation [M. Dion et al., Phys. Rev. Lett. 2004, 92, 246401]. We report here a systematic study of such systems involving completely self-consistent vdW-DF calculations with full geometry relaxation. We find that the hydrogen bonding between the molecules is only insignificantly affected by the vdW contribution, both in the gas phase and on the gold surface. However, the adsorption energies of these molecules on the surface increase dramatically as compared with the ordinary density functional (within the generalized gradient approximation, GGA) calculations, in agreement with available experimental data and previous calculations performed within approximate or semiempirical models, and this is entirely due to the vdW contribution which provides the main binding mechanism. We also stress the importance of self-consistency in calculating the binding energy by the vdW-DF method since the results of non-self-consistent calculations in some cases may be off by up to 20%. Our calculations still support the usually made assumption of the molecule-surface interaction changing little laterally suggesting that single molecules and their small clusters should be quite mobile at room temperature on the surface. These findings support a gas-phase modeling for some flat metal surfaces, such as Au(111), and flat molecules, at least as a first approximation.

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.

A density functional for sparse matter.

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.

A density functional theory study of the benzene-water complex.

The intermolecular interaction of the benzene-water complex is calculated using real-space pseudopotential density functional theory utilizing a van der Waals density functional. Our results for the intermolecular potential energy surface clearly show a stable configuration with the water molecule standing above or below the benzene with one or both of the H atoms pointing toward the benzene plane, as predicted by previous studies. However, when the water molecule is pulled outside the perimeter of the ring, the configuration of the complex becomes unstable, with the water molecule attaching in a saddle point configuration to the rim of the benzene with its O atom adjacent to a benzene H. We find that this structural change is connected to a change in interaction from H (water)/pi cloud (benzene) to O (water)/H (benzene). We compare our results for the ground-state structure with results from experiments and quantum-chemical calculations.

An application of the van der Waals density functional: Hydrogen bonding and stacking interactions between nucleobases.

We apply the van der Waals density functional (vdW-DF) to study hydrogen bonding and stacking interactions between nucleobases. The excellent agreement of our results with high level quantum chemical calculations highlights the value of the vdW-DF for first-principles investigations of biologically important molecules. Our results suggest that, in the case of hydrogen-bonded nucleobase pairs, dispersion interactions reduce the cost of propeller twists while having a negligible effect on buckling. Furthermore, the efficient scaling of DFT methods allowed for the easy optimization of separation distance between nucleobase stacks, indicating enhancements in the interaction energy of up to 3 kcalmol over previous fixed distance calculations. We anticipate that these results are significant for extending the vdW-DF method to model larger vdW complexes and biological molecules.

Interaction energies of monosubstituted benzene dimers via nonlocal density functional theory.

We present density functional calculations for the interaction energy of monosubstituted benzene dimers. Our approach utilizes a recently developed fully nonlocal correlation energy functional, which has been applied to the pure benzene dimer and several other systems with promising results. The interaction energy as a function of monomer distance was calculated for four different substituents in a sandwich and two T-shaped configurations. In addition, we considered two methods for dealing with exchange, namely, using the revPBE generalized gradient functional as well as full Hartree-Fock. Our results are compared with other methods, such as Moller-Plesset and coupled-cluster calculations, thereby suggesting the usefulness of our approach. Since our density functional based method is considerably faster than other standard methods, it provides a computationally inexpensive alternative, which is of particular interest for larger systems where standard calculations are too expensive or infeasible.

Orbital magnetization in periodic insulators.

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulklike Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.

Orbital magnetization in extended systems.

While the orbital magnetic dipole moment of any finite sample is well-defined, it becomes ill-defined in the thermodynamic limit as a result of the unboundedness of the position operator. Effects due to surface currents and to bulk magnetization are not easily disentangled. The corresponding electrical problem, where surface charges and bulk polarization appear as entangled, was solved about a decade ago by the modern theory of polarization, based on a Berry phase. We follow a similar path here, making progress toward a bulk expression for the orbital magnetization in an insulator represented by a lattice-periodic Hamiltonian with broken time-reversal symmetry. We therefore limit ourselves to the case where the macroscopic (i.e. cell-averaged) magnetic field vanishes. We derive an expression for the contribution to the magnetization arising from the circulating currents internal to the bulk Wannier functions, and then transform to obtain a Brillouin zone integral involving the occupied Bloch orbitals. A version suitable for practical implementation in discretized reciprocal space is also derived, and the gauge invariance of both versions is explicitly shown. However, tests on a tight-binding model indicate the presence of additional edge currents, and it remains to be determined whether these can be related to the bulk band structure.

Pressure-induced hole doping of the Hg-based cuprate superconductors.

We investigate the electronic structure and the hole content in the copper-oxygen planes of Hg-based high T(c) cuprates for one to four CuO2 layers and hydrostatic pressures up to 15 GPa. We find that with the pressure-induced additional number of holes of the order of 0.05e the density of states at the Fermi level changes by approximately a factor of 2. At the same time, the saddle point is moved to the Fermi level accompanied by an enhanced k(z) dispersion. This finding explains the pressure behavior of T(c) and leads to the conclusion that the applicability of the van Hove scenario is restricted. By comparison with experiment, we estimate the coupling constant to be of the order of 1, ruling out the weak coupling limit.