Van Der Waals Density Functionals Research Articles

Range-separated hybrid van der Waals density functionals to describe Cu[formula omitted]O[formula omitted]-complexes

Dimeric copper centers are commonly used to activate molecular oxygen in enzymatic and heterogeneous catalysis where Cu2 is embedded in porous structures. Here we evaluate the ability of recently developed range-separated hybrid van der Waals density functionals to describe activated O2 in a crystal with the Cu2O2 unit and in a ▪ complex embedded in a chabzite zeolite. The electronic and geometrical structure of the Cu2O2 unit depends sensitively on the exchange–correlation functional and a sufficiently large amount of short-ranged Fock-exchange is needed to describe the experimentally observed Cu2O2 structures.

Studying the adsorption of emerging organic contaminants in zeolites with dispersion-corrected density functional theory calculations: From numbers to recommendations.

Adsorption energies obtained from dispersion-corrected density functional theory (DFT) calculations show a considerable dependence on the choice of exchange-correlation functional and dispersion correction. A number of investigations have employed different approaches to compute adsorption energies of small molecules in zeolites, using reference values from high-level calculations and/or experiments. Such comparative studies are lacking for larger functional organic molecules such as pharmaceuticals or personal care products, despite their potential relevance for applications, e. g., in contaminant removal or drug delivery. The present study aims to fill this gap by comparing adsorption energies and, for selected cases, equilibrium structures of emerging organic contaminants adsorbed in MOR- and FAU-type all-silica zeolites. A total of 13 dispersion-corrected DFT approaches are compared, including methods using a pairwise dispersion correction as well as non-local van der Waals density functionals. While absolute values of adsorption energies vary widely, qualitative trends across the set of zeolite-guest combinations are not strongly dependent on the choice of functional. For selected cluster models, DFT adsorption energies are compared to reference values from coupled cluster (DLPNO-CCSD(T)) calculations. Although all DFT approaches deliver systematically more negative adsorption energies than the coupled cluster reference, this tendency is least pronounced for the rev-vdW-DF2 functional.

Piezoelectric Response of Plastic Ionic Molecular Crystals: Role of Molecular Rotation

Plastic ionic molecular crystals are a novel class of materials that have attracted recent interest due to the discovery of ferroelectric and piezoelectric properties together with an orientationally disordered mesophase with high plasticity. Despite the growing interest, little is known about the mechanisms that underpin their piezoelectric properties. To address this knowledge gap, we use density functional theory calculations with van der Waals density functionals to study the dielectric, piezoelectric, and elastic properties of 11 plastic ionic molecular crystals. The piezoelectric coefficients were found to reach values comparable to inorganic piezoelectrics. Further, some plastic crystals have strikingly large piezoelectric anisotropies. For HQReO4 (quinuclidinium perrhenate) an anisotropy of |d16/d33| = 118 was found, 11 times that of LiNbO3, a phase pure inorganic noted for its anisotropy. Our study links the anisotropy to the rotational motion of the constituent molecules in response to shear stress. The large shear piezoelectric coefficients, yet modest dielectric permittivity, results in coupling coefficients─a measure of its suitability for energy harvesting─with values up to 0.79. Our study points to the engineering of the rotational response of plastic ionic crystals as key to realizing the outstanding functional properties of these compounds.

Band valley modification under strain in monolayer WSe2

We study the band valley modification induced by isotropic strain in monolayer WSe2 using the non-local van der Waals density functionals theory including the spin–orbit coupling effect. The dominant contributions of orbitals to the band extrema, spin splitting, and exciton diversity in monolayer WSe2 are visually displayed. The vertical shift of the d and p partial orbitals of W and Se atoms, respectively, at band edges under strain results in a notable reduction of the bandgap. Under tensile strain, the deformations of the band valleys lead to an additional appearance of optical excitons and the disappearance of momentum excitons. Therefore, the experimental observations of the changes in the radiation spectra such as the redshift of A and B excitons, blueshift of C and D excitons, enhancement of intensity, localization, and symmetrization of the exciton resonances can be explained thoroughly. Under compression, the band valley modification may lead to an additional appearance of momentum excitons and the disappearance of optical excitons. The compression is predicted to cause the blueshift of A and B excitons while it brings the redshift to C and D excitons. An asymmetric broadening and intensity de-enhancement of the exciton resonances are also found when a compression strain is applied. The modification of the band valleys can be explained by the enhancement/reduction of hybridization between orbitals under strain. These results offer new perspectives to comprehend the appearance/disappearance of the excitons in monolayer transition metal dichalcogenide materials upon mechanical perturbation.

Exact Sum-Rule Approach to Polarizability and Asymptotic van der Waals Functionals─Derivation of Exact Single-Particle Benchmarks

Using a sum-rule approach, we develop an exact theoretical framework for polarizability and asymptotic van der Waals correlation energy functionals of small isolated objects. The functionals require only monomer ground-state properties as input. Functional evaluation proceeds via solution of a single position-space differential equation, without the usual summations over excited states or frequency integrations. Explicit functional forms are reported for reference physical systems, including atomic hydrogen and single electrons subject to harmonic confinement, and immersed in a spherical-well potential. A direct comparison to the popular Vydrov-van Voorhis density functional shows that the best performance is obtained when density decay occurs at atomic scales. The adopted sum-rule approach implies general validity of our theory, enabling exact benchmarking of van der Waals density functionals and direct inspection of the subtle long-range correlation effects that constitute a major challenge for approximate (semi)local density functionals.

Improved proton-transfer barriers with van der Waals density functionals: Role of repulsive non-local correlation.

Proton-transfer (PT) between organic complexes is a common and important biochemical process. Unfortunately, PT energy barriers are difficult to accurately predict using density functional theory (DFT); in particular, using the generalized gradient approximation (GGA) tends to underestimate PT barriers. Moreover, PT typically occurs in environments where dispersion forces contribute to the cohesion of the system; thus, a suitable exchange-correlation functional should accurately describe both dispersion forces and PT barriers. This paper provides benchmark results for the PT barriers of several density functionals, including several variants of the van der Waals density functional (vdW-DF). The benchmark set comprises small organic molecules with inter- and intra-molecular PT. The results show that replacing GGA correlation with a fully non-local vdW-DF correlation increases the PT barriers, making it closer to the quantum chemical reference values. In contrast, including non-local correlations with the Vydrov-Voorhis method or dispersion-corrections at the DFT-D3 or the Tkatchenko-Scheffler level has barely any impact on the PT barriers. Hybrid functionals also increase and improve the energies, resulting in an excellent performance of hybrid versions of vdW-DF-cx and vdW-DF2-B86R. For the formic acid dimer PT system, we analyzed the GGA exchange and non-local correlation contributions. The analysis shows that the repulsive part of the non-local correlation kernel plays a key role in the PT energy barriers predicted with vdW-DF.

Linear response calculation with nonlocal van der Waals density functionals

The linear-response approach with the nonlocal van der Waals density functionals is presented, considering three kinds of perturbations: Atomic displacements, uniform electric fields, and strain. The formulas to compute the response with respect to strain are derived for the van der Waals density functionals as well as for the generalized gradient approximation. The linear-response method is implemented within the ultrasoft pseudopotential scheme. The method is applied to weak-coupled layered materials, graphite and ${\mathrm{MoS}}_{2}$. The results support the validity of the derived formulas and demonstrate the utilities of the linear-response method for weak-coupled van der Waals systems.

Hard and soft materials: putting consistent van der Waals density functionals to work

We present the idea and illustrate potential benefits of having a tool chain of closely related regular, unscreened and screened hybrid exchange–correlation (XC) functionals, all within the consistent formulation of the van der Waals density functional (vdW-DF) method (Hyldgaard et al (2020 J. Phys.: Condens. Matter 32 393001)). Use of this chain of nonempirical XC functionals allows us to map when the inclusion of truly nonlocal exchange and of truly nonlocal correlation is important. Here we begin the mapping by addressing hard and soft material challenges: magnetic elements, perovskites, and biomolecular problems. We also predict the structure and polarization for a ferroelectric polymer. To facilitate this work and future broader explorations, we present a stress formulation for spin vdW-DF and illustrate the use of a simple stability-modeling scheme. The modeling supplements density functional theory (DFT) (with a specific XC functional) by asserting whether the finding of a soft mode (an imaginary-frequency vibrational mode, ubiquitous in perovskites and soft matter) implies an actual DFT-based prediction of a low-temperature transformation.

Reduced-gradient analysis of van der Waals complexes

Different methods to describe dispersion interactions within density functional theory have been developed, which is essential to describe binding in van der Waals complexes. However, several key aspects of such complexes—including binding energies, lattice constants, and binding distances—also depend on the exchange description that is paired with the description of dispersion interactions. This is particularly true for the vdW-DF family of van der Waals density functionals, which has a clear division between truly non-local correlations and semi-local generalized-gradient exchange. Here, we present a systematic analysis of the reduced-gradient values that determine the semi-local exchange for different classes of van der Waals complexes. In particular, we analyze molecular dimers, layered structures, surface adsorption, and molecular crystals. We find that reduced-gradient values of less than ∼1 to ∼1.5—depending on the system—contribute attractively to the exchange binding, while reduced gradients above those values are repulsive. We find that the attractive contributions can be attributed to low-density regions between the constituents with disk-like iso-surfaces. We further identify a mechanism wherein the surface area of these disks decreases through merging with other iso-surfaces and switches the gradient-correction to exchange from attractive to repulsive. This analysis allows us to explain some of the differences in performance of vdW-DF variants and initiates a discussion of desirable features of the exchange enhancement factor. While our analysis is focused on vdW-DF, it also casts light on van der Waals binding in a broader context and can be used to understand why methods perform differently for different classes of van der Waals systems.

First-principles study of benzene and its homologues upon graphene-metal surfaces: Comparison of London dispersion corrections

We perform a comparative theoretical study of benzene and its homologues (toluene, para-xylene, and mesitylene) adsorbed on Cu/Al/Pd(111)-supported graphene using density functional theory (DFT). The long-range attraction is handled by semiempirical dispersion correction method (PBE-D3) and ab initio van der Waals density functionals (vdW-DF2, optB86b-vdW, optB88-vdW, and SCAN-rVV10). Our results show a systematic increase in the adsorption energy of organic molecules on graphene in the presence of underlaying metal substrates. In the case of strong metal-graphene contact, such as Pd(111)-graphene, the adsorption energy of benzene even increases 0.44 eV, which presents suitable platform for filtering harmful molecules such as benzene. Besides, we find out that the dispersion-corrected functionals play a fundamental role in the structure and adsorption energy. Furthermore, the adsorption energy increases linearly with the number of methyl groups on the benzene ring.

Establishing the accuracy of density functional approaches for the description of noncovalent interactions in ionic liquids.

We test a number of dispersion corrected versatile Generalized Gradient Approximation (GGA) and meta-GGA functionals for their ability to predict the interactions of ionic liquids, and show that most can achieve energies within 1 kcal mol-1 of benchmarks. This compares favorably with an accurate dispersion corrected hybrid, ωB97X-V. Our tests also reveal that PBE (Perdew-Burke-Ernzerhof GGA) calculations using the plane-wave projector augmented wave method and Gaussian Type Orbitals (GTOs) differ by less than 0.6 kJ mol-1 for ionic liquids, despite ions being difficult to evaluate in periodic cells - thus revealing that GTO benchmarks may be used also for plane-wave codes. Finally, the relatively high success of explicit van der Waals density functionals, compared to elemental and ionic dispersion models, suggests that improvements are required for low-cost dispersion correction models of ions.

Perspectives on van der Waals Density Functionals: The Case of TiS2.

The van der Waals interaction is of foundational importance for a wide variety of physical systems. In particular, van der Waals forces lie at the heart of potential device technologies that may be realized from the functional organization of layered two-dimensional (2D) nanomaterials. For intermediate to large-scale applications modeling, van der Waals density functionals have become the de facto choice for first-principles calculations. In particular, the vdW-DF family of functionals have provided a systematic approach to this theoretically challenging problem. While much progress has been made, there remains room for improvement in the microscopic description of vdW forces from these density functionals. In this work, we compute benchmark results for the binding energy and the electronic density response to binding in TiS2 via accurate diffusion quantum Monte Carlo calculations. We compare these benchmark data to results obtained from local, semilocal, and van der Waals functionals. In particular, we gauge the quality of the original vdW-DF/vdW-DF2 functionals, as well as updated variants such as vdW-DF-C09, vdW-DF-optB88, vdW-DF-optB86b, and vdW-DF2-B86R. We find a close relationship between the accuracy of predicted interlayer separation distances and binding energies for TiS2, with the vdW-DF-optB88 functional performing very well in terms of both quantities. In general, the more recently developed functionals are systematic improvements over older ones. However, when considering the response of the electron density to binding, we find that local-density approximation (LDA) and PBEsol generally outperform the vdW-DF functionals in describing the interlayer charge accumulation with vdW-DF-C09 variants performing the best overall.

Assessment of approaches for dispersive forces employing semihydrogenated graphene as a case study

We study two interchange layer systems, (i) free standing semihydrogenated graphene, and (ii) semihydrogenated graphene on the Nickel (111) surface, to assess various density-functional-theory based computational schemes incorporating van der Waals forces. These various van der Waals methods range from semi-empirical force-field-like corrections, through non-local van der Waals density functionals, up to functionals involving exact exchange and the random phase approximation for correlation. Generally, all computational schemes lead to a similar qualitative picture of hydrogen-layer physisorption and chemisorption to graphene. The largest discrepancies between the approaches emerge for the energetics of the investigated systems. Our studies shed light on the physical mechanisms of graphene hydrogenation both in vacuum and in the proximity of a metallic surface. In particular, it is revealed that the adsorption of hydrogen atoms affects the nature of the bonding between graphene and the Ni(111) surface, from weak to strong semi-covalent bonding. On the other hand, it turns out that the adsorption of a hydrogen layer to graphene is stronger in the presence of the metallic surface.

A comparative investigation of penta-graphene and Pt single atom@penta-graphene in H2 and O2 detection: DFT study with assessment of the van der Waals density functionals

The gas-adsorption behaviors of O2 and H2 on penta-graphene (PG) and Pt single atom@penta-graphene (Pt-PG) were investigated using density functional theory calculations. To illustrate the importance of the van der Waals (vdW) interactions, in addition to popular local density approximation (LDA) and semilocal Perdew-Burke-Ernzerhof generalized gradient approximation (GGA-PBEsol) functionals, two non-local (vdW-DF2 and rev-vdW-DF2) functionals were investigated through the correlation between energetic, structural, and electronic properties. On the surface of the PG (band gap 2.3 eV), O2 was strongly physisorbed, which reduced the O2/PG band gap to ~0.75 eV and created a p-type semiconductor. The H2 was very weakly physisorbed without any changes in the band gap. On the semimetal Pt-PG (zero band gap), the H2 and O2 were strongly chemisorbed which was dissociative for H2. H2 adsorption opens a band gap of 1.45 eV, making the H2/Pt-PG system a semiconductor. But the O2/Pt-PG system remains semimetal. The PG can be used for the detection of O2 but not for H2. The presence of the Pt atoms allows the Pt-PG system to detect the H2 very well. LDA is suggested for investigating H2 adsorption on both the PG and Pt-PG systems, but the non-local vdWs must be used for the O2 adsorption study.

Electronic structure of dense solid oxygen from insulator to metal investigated with X-ray Raman scattering

Electronic structures of dense solid oxygen have been investigated up to 140 GPa with oxygen K-edge X-ray Raman scattering spectroscopy with the help of ab initio calculations based on density functional theory with semilocal metageneralized gradient approximation and nonlocal van der Waals density functionals. The present study demonstrates that the transition energies (Pi*, Sigma*, and the continuum) increase with compression, and the slopes of the pressure dependences then change at 94 GPa. The change in the slopes indicates that the electronic structure changes at the metallic transition. The change in the Pi* and Sigma* bands implies metallic characteristics of dense solid oxygen not only in the crystal a-b plane but also parallel to the c axis. The pressure evolution of the spectra also changes at ∼40 GPa. The experimental results are qualitatively reproduced in the calculations, indicating that dense solid oxygen transforms from insulator to metal via the semimetallic transition.

Thermodynamics of graphite intercalation binary alloys of Li-Na, Na-K, and Li-K from van der Waals density functionals

Graphite may store lithium or potassium, but not sodium, in its interlayer space under ambient conditions. It is, however, unclear whether binary alkali alloys of Li-Na, Li-K, and Na-K may substitute pure Li or K to form binary alkali alloy-graphite intercalation compounds. We investigate thermodynamics of the binary alloy-graphite intercalation compounds using density functional theory with van der Waals density functionals. We find Li-rich co-intercalation compounds and K-rich ones are associated with negative formation energies, and the Na-K alloy has the broadest domain of co-intercalation (approximately up to 36% Na). Because of convexity of the formation-energy functions, these compounds are metastable and tend to decompose even when formation energies are negative. Na metal is among the decomposition products. Binary Li-K alloys in graphite form segregated phases of LiC6 and KC8, and this allows one to fabricate Li-K mixed-ion batteries using graphite anodes, whereas Li-Na and Na-K alloys are thermodynamically unfavorable. The study highlights the importance of convexity of formation-energy functions in thermodynamics of alloy-graphite intercalation compounds.

Dispersion Energy from Local Polarizability Density.

A simple nonlocal functional for calculation of dispersion energies is proposed. Compared to a similar formula used earlier, we introduced a regularization to remove its singularities and used a dynamic polarizability density similar to those in the so-called van der Waals density functionals. The performance of the new functional is tested on dispersion energies for a set of representative dimers, and it is found that it is significantly more accurate than published nonlocal functionals.

Van der Waals density functional study of formic acid adsorption and decomposition on Cu(111).

We present a density functional theory study on the adsorption and decomposition mechanisms of monomeric formic acid (HCOOH) on a Cu(111) surface. We used Perdew-Burke-Ernzerhof (PBE) functional, PBE with dispersion correction (PBE-D2), and van der Waals density functionals (vdW-DFs). We found that the adsorption energy of HCOOH by using the PBE functional is smaller than the experimental value, while the PBE-D2 and vdW-DFs give better agreement with experimental results. The activation energies of decomposition calculated by using PBE-D2 and vdW-DFs are lower compared with desorption energies, seemingly in contradiction with experimental findings at room temperature, in which no decomposition of HCOOH on Cu(111) is observed when the surface is exposed to the gas phase HCOOH. We performed the reaction rate analysis based on the first-principles calculations for desorption and decomposition processes to clarify this contradiction. We found that the desorption of monomeric HCOOH is faster than that of its decomposition rate at room temperature because of a much larger pre-exponential factor. Thus, no decomposition of monomeric HCOOH should take place at room temperature. Our analysis revealed the competition between desorption and decomposition processes of HCOOH.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations.

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

Application of van der Waals density functionals to two dimensional systems based on a mixed basis approach

A van der Waals (vdW) density functional was implemented with the charge density obtained by the mixed basis approach previously developed for studying two dimensional systems, in which the vdW interaction plays an important role. The basis functions here are taken to be the localized B-splines for the finite non-periodic dimension and plane waves for the two periodic directions. This approach will reduce the size of the basis set, especially for large systems, and therefore is computationally efficient for the diagonalization of the Kohn–Sham Hamiltonian. The nonlocal vdW correlation was treated appropriately according to the layered geometry structure. We applied the present algorithm to calculate the binding energy for graphene and hexagonal boron nitride and the results are consistent with data reported earlier. We also found that, due to the relatively weak vdW interaction, the charge density obtained self-consistently for the whole bilayer system is not significantly different from the simple addition of those for the two individual monolayer systems, except when the interlayer separation is close enough that the strong electron-repulsion dominates. This finding suggests an efficient way to calculate the vdW interaction for large complex systems involving Moiré pattern configurations.