Nonlocal Van Der Waals Density Research Articles

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.

Band Gap Alteration of Halide Mixing in Hybrid Perovskites: A First-Principles Study with Statistical Analysis.

Despite numerous studies on the band gap of three-dimensional halide perovskites using the first-principles calculations, there are still significant discrepancies between theoretical and experimental values. Various solutions have been proposed, such as employing a system-specific hybrid functional with varying degrees of exact exchange and explicitly incorporating spin-orbit coupling effects. Our research involved a comprehensive investigation of three typical lead-containing three-dimensional perovskites MAPbI3, MAPbBr3, and MAPbCl3 (MA = CH3NH3). Through a statistical analysis comparing mean absolute error (MAE) with experimental results, we demonstrated that the nonlocal van der Waals (vdW) density functional corrections (i.e., optB86b) yielded the most approximate lattice parameters in comparison to experimental values. Furthermore, based on these lattice parameters, the HSE06 hybrid functional is the optimal estimation of the band gap among all the options. Moreover, we investigated three sets of mixed three-dimensional halide perovskites by varying the halide component. This exploration contributes to the identification of MAPb(Br0.333I0.667)3 and MAPb(Cl0.333I0.667)3 as exhibiting the smallest band gap of 1.315 (1.867) eV and 1.313 (1.885) eV for PBE (HSE06), respectively. These band gaps were determined using the HSE06 method with the optimized lattice by PBE considering the optB86b corrections. The approach employed in this work produced a band gap trend closely aligned with experimental observations, underscoring the importance of adopting a reliable and material-independent computational strategy when screening new halide perovskite materials for optoelectronic applications.

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.

Density functional theory study of NO−H2O coadsorption on Cu(111)

The coadsorption and complex formation of nitric oxide (NO) and water $({\mathrm{H}}_{2}\mathrm{O})$ on Cu(111) are studied theoretically using the nonlocal van der Waals density functional method. The energetics, adsorption geometries, and vibrational properties of several $n\mathrm{NO}\text{\ensuremath{-}}{m\mathrm{H}}_{2}\mathrm{O}$ complexes $(n=1--4$, $m=1--3)$ on Cu(111) are reported, and the relative stabilities of those complexes are compared with their respective NO and ${\mathrm{H}}_{2}\mathrm{O}$ clusters on Cu(111). We find that the mixed $n\mathrm{NO}\text{\ensuremath{-}}{m\mathrm{H}}_{2}\mathrm{O}$ complexes on Cu(111) are more stable than separated NO and ${\mathrm{H}}_{2}\mathrm{O}$ clusters due to the attractive $\mathrm{NO}\text{\ensuremath{-}}{\mathrm{H}}_{2}\mathrm{O}$ and NO-NO interactions on the surface. The attractive $\mathrm{NO}\text{\ensuremath{-}}{\mathrm{H}}_{2}\mathrm{O}$ interaction originates mainly from the hydrogen bonding between ${\mathrm{H}}_{2}\mathrm{O}$ and the negatively charged NO upon adsorption. Moreover, hydrogen bonding also induces an additional back donation process from Cu(111), further strengthening the $\mathrm{NO}\text{\ensuremath{-}}{\mathrm{H}}_{2}\mathrm{O}$ coadsorption. In addition to hydrogen bonding, the NO-NO interaction originating from $2{\ensuremath{\pi}}^{*}$ orbital hybridization further stabilizes the formation of the $4\mathrm{NO}\text{\ensuremath{-}}3{\mathrm{H}}_{2}\mathrm{O}$ complex, which is observed in the experiment. Even though the hydrogen bonding strength in $\mathrm{NO}\text{\ensuremath{-}}{\mathrm{H}}_{2}\mathrm{O}$ complexes is slightly weaker than the one in ${\mathrm{H}}_{2}\mathrm{O}$ clusters, due to the saturation of hydrogen bonding and the NO-NO interaction, NO and ${\mathrm{H}}_{2}\mathrm{O}$ tends to form a mixed $\mathrm{NO}\text{\ensuremath{-}}{\mathrm{H}}_{2}\mathrm{O}$ complex on Cu(111), in agreement with experiment. Our findings shed light on the role of intermolecular interactions between NO and ${\mathrm{H}}_{2}\mathrm{O}$ in the formation of the NO complex, which is important for understanding the reaction of NO in three-way catalysts.

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.

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.

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.

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.

Van der Waals density functional with corrected C6 coefficients

The non-local van der Waals density functional (vdW-DF) has had tremendous success since its inception in 2004 due to its constraint-based formalism that is rigorously derived from a many-body starting point. However, while vdW-DF can describe binding energies and structures for van der Waals complexes and mixed systems with good accuracy, one long-standing criticism---also since its inception---has been that the $C_6$ coefficients that derive from the vdW-DF framework are largely inaccurate and can be wrong by more than a factor of two. It has long been thought that this failure to describe the $C_6$ coefficients is a conceptual flaw of the underlying plasmon framework used to derive vdW-DF. We prove here that this is not the case and that accurate $C_6$ coefficient can be obtained without sacrificing the accuracy at binding separations from a modified framework that is fully consistent with the constraints and design philosophy of the original vdW-DF formulation. Our design exploits a degree of freedom in the plasmon-dispersion model $\omega_{\mathbf{q}}$, modifying the strength of the long-range van der Waals interaction and the cross-over from long to short separations, with additional parameters tuned_ to reference systems. Testing the new formulation for a range of different systems, we not only confirm the greatly improved description of $C_6$ coefficients, but we also find excellent performance for molecular dimers and other systems. The importance of this development is not necessarily that particular aspects such as $C_6$ coefficients or binding energies are improved, but rather that our finding opens the door for further conceptual developments of an entirely unexplored direction within the exact same constrained-based non-local framework that made vdW-DF so successful in the first place.

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.

Quantum molecular dynamics study on the proton exchange, ionic structures, and transport properties of warm dense hydrogen-deuterium mixtures.

Comprehensive knowledge of physical properties such as equation of state (EOS), proton exchange, dynamic structures, diffusion coefficients, and viscosities of hydrogen-deuterium mixtures with densities from 0.1 to 5g/cm^{3} and temperatures from 1 to 50 kK has been presented via quantum molecular dynamics (QMD) simulations. The existing multi-shock experimental EOS provides an important benchmark to evaluate exchange-correlation functionals. The comparison of simulations with experiments indicates that a nonlocal van der Waals density functional (vdW-DF1) produces excellent results. Fraction analysis of molecules using a weighted integral over pair distribution functions was performed. A dissociation diagram together with a boundary where the proton exchange (H_{2}+D_{2}⇌2HD) occurs was generated, which shows evidence that the HD molecules form as the H_{2} and D_{2} molecules are almost 50% dissociated. The mechanism of proton exchange can be interpreted as a process of dissociation followed by recombination. The ionic structures at extreme conditions were analyzed by the effective coordination number model. High-order cluster, circle, and chain structures can be founded in the strongly coupled warm dense regime. The present QMD diffusion coefficient and viscosity can be used to benchmark two analytical one-component plasma (OCP) models: the Coulomb and Yukawa OCP models.

Effects of Dispersion Corrections and Nonlocality on Density Functional Predictions of Pressure-Induced Polymorphic Transitions of Crystalline Diborane

The role of dispersion interactions in density functional calculations of the relative enthalpies of compressed BH3 polymorphs was investigated using plane-wave and Gaussian basis set codes. Addition of semiempirical atom-pairwise dispersion corrections to generalized gradient approximations (GGAs) was found to have little effect on the relative enthalpies of various boron hydride structures. By contrast, the stability ranking obtained with the nonlocal van der Waals density functional (vdW-DF) of Dion and co-workers was substantially more realistic than the rankings predicted by plain and dispersion-corrected GGAs. Of the functionals tested, only vdW-DF correctly predicts that compressed diborane does not leave the B2H6 motif until at least 20 GPa. This finding serves as direct computational evidence of the thermodynamic stability of molecular B2H6 units in the 0–20 GPa pressure range, an experimental result that until now has been at variance with theoretical predictions.

Structural and electronic properties of MoS2, WS2, and WS2/MoS2 heterostructures encapsulated with hexagonal boron nitride monolayers

In this study, we investigate the structural and electronic properties of MoS2, WS2, and WS2/MoS2 structures encapsulated within hexagonal boron nitride (h-BN) monolayers with first-principles calculations based on density functional theory by using the recently developed non-local van der Waals density functional (rvv10). We find that the heterostructures are thermodynamically stable with the interlayer distance ranging from 3.425 Å to 3.625 Å implying van der Waals type interaction between the layers. Except for the WS2/h-BN heterostructure which exhibits direct band gap character with the value of 1.920 eV at the K point, all proposed heterostructures show indirect band gap behavior from the valence band maximum at the Γ point to the conduction band minimum at the K point with values varying from 0.907 eV to 1.710 eV. More importantly, it is found that h-BN is an excellent candidate for the protection of intrinsic properties of MoS2, WS2, and WS2/MoS2 structures.

Image potential states from the van der Waals density functional.

The image potential state is one of the fundamental surface electronic states and has a great relevance to many surface phenomena, but its accurate description is a great challenge for the semilocal density functional. Here, we use the nonlocal van der Waals density functional to describe the image potential states of graphene, graphite, and carbon nanotubes. We found that although it does not yield the correct image potential outside the surface, the van der Waals density functional improves the description of image potential states because of the nonlocal correlation potential. Our study demonstrates the usefulness of the van der Waals density functional to study the surface electronic properties.

Organic crystal polymorphism: a benchmark for dispersion corrected mean field electronic structure methods

We analyze the energy landscape of the sixth crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko–Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod–Teller–Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree–Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.

Organic crystal polymorphism: a benchmark for dispersion-corrected mean-field electronic structure methods.

We analyze the energy landscape of the sixth crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko-Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod-Teller-Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree-Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.

Structural and electronic properties of multilayer graphene on monolayer hexagonal boron nitride/nickel (111) interface system: A van der Waals density functional study

The structural and electronic properties of multilayer graphene adsorbed on monolayer hexagonal boron nitride (h-BN)/Ni(111) interface system are investigated using the density functional theory with a recently developed non-local van der Waals density functional (rvv10). The most energetically favourable configuration for a monolayer h-BN/Ni(111) interface is found to be N atom atop the Ni atoms and B atom in fcc site with the interlayer distance of 2.04 Å and adsorption energy of 302 meV/BN. Our results show that increasing graphene layers on a monolayer h-BN/Ni(111) interface leads to a weakening of the interfacial interaction between the monolayer h-BN and Ni(111) surface. The adsorption energy of graphene layers on the h-BN/Ni(111) interface is found to be in the range of the 50–120 meV/C atom as the vertical distance from h-BN to the bottommost graphene layers decreases. With the adsorption of a multilayer graphene on the monolayer h-BN/Ni(111) interface system, the band gap of 0.12 eV and 0.25 eV opening in monolayer graphene and bilayer graphene near the K point is found with an upward shifting of the Fermi level. However, a stacking-sensitive band gap is opened in trilayer graphene. We obtain the band gap of 0.35 eV close to the K point with forming a Mexican hat band structure for ABC-stacked trilayer graphene.

Structural and configurational properties of nanoconfined monolayer ice from first principles.

Understanding the structural tendencies of nanoconfined water is of great interest for nanoscience and biology, where nano/micro-sized objects may be separated by very few layers of water. Here we investigate the properties of ice confined to a quasi-2D monolayer by a featureless, chemically neutral potential, in order to characterize its intrinsic behaviour. We use density-functional theory simulations with a non-local van der Waals density functional. An ab initio random structure search reveals all the energetically competitive monolayer configurations to belong to only two of the previously-identified families, characterized by a square or honeycomb hydrogen-bonding network, respectively. We discuss the modified ice rules needed for each network, and propose a simple point dipole 2D lattice model that successfully explains the energetics of the square configurations. All identified stable phases for both networks are found to be non-polar (but with a topologically non-trivial texture for the square) and, hence, non-ferroelectric, in contrast to previous predictions from a five-site empirical force-field model. Our results are in good agreement with very recently reported experimental observations.

Small-Molecule Adsorption in Open-Site Metal–Organic Frameworks: A Systematic Density Functional Theory Study for Rational Design

Using density functional theory, we systematically compute and investigate the binding enthalpies of 14 different small molecules in a series of isostructural metal–organic frameworks, M-MOF-74, with M = Mg, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn. The small molecules we consider include major flue-gas components, trace gases, and small hydrocarbons, i.e., H2, CO, CO2, H2O, H2S, N2, NH3, SO2, CH4, C2H2, C2H4, C2H6, C3H6, and C3H8. In total, the adsorption energetics of 140 unique systems are presented and discussed. Dispersion interactions are included by employing a nonlocal van der Waals density functional, vdW-DF2. Hubbard U corrections are applied to the localized d electrons of transition metal atoms, and the impact of such corrections is assessed quantitatively. For systems for which measured binding enthalpies have been reported, our calculations lead to excellent overall agreement with experimentally determined structures and isosteric heats of adsorption. For systems that have yet to be realized or characterized, this study provides quantitative predictions, establishes a better understanding of the role of different transition-metal cations in small-molecule binding at open-metal sites, and identifies routes for predicting potential candidates for energy-related gas-separation applications. For example, we predict that Cu-MOF-74 will exhibit selectivity of CO2 over H2O and that Mn-MOF-74 can be used to separate trace flue-gas impurities and toxic gases from gas mixtures.

First Principles Predictions of Van Der Waals Bonded Inorganic Crystal Structures: Test Case, HgCl2

We study the crystals structure and stability of four possible polymorphs of HgCl2 using first principles density functional theory. Mercury (II) halides are a unique class of materials which, depending on the halide species, form in a wide range of crystal structures, ranging from densely packed solids to layered materials and molecular solids. Predicting the groundstate structure of any member of this group from first principles, therefore, requires a general purpose functional that treats van der Waals bonding and covalent/ionic bonding adequately. Here, we demonstrate that the non-local van der Waals density functional paired with the C09 exchange functional meets this bar for HgCl2. In particular, this functional is able to predict the correct groundstate among the structures tested as well as having extremely good agreement with the experimentally known crystal structure. These results highlight the maturity of this functional and open the door to using this method for truly first principles crystal structure predictions.