Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem

Reaching Quantum Accuracy in Predicting Adsorption Properties for Ethane/Ethene in Zeolitic Imidazolate Framework-8 at Low Pressure Regime

Nanoporous materials in the form of metal-organic frameworks such as zeolitic imidazolate framework-8 (ZIF-8) are promising membrane materials for the separation of hydrocarbon mixtures. To compute the adsorption isotherms in such adsorbents, grand canonical Monte Carlo simulations have proven to be very useful. The quality of these isotherms depends on the accuracy of adsorbate-adsorbent interactions, which are mostly described using force fields owing to their low computational cost. However, force field predictions of adsorption uptake often show discrepancies from experiments at low pressures, providing the need for methods that are more accurate. Hence, in this work, we propose and validate two novel methodologies for the ZIF-8/ethane and ethene systems; a benchmarking methodology to evaluate the performance of any given force field in describing adsorption in the low-pressure regime and a refinement procedure to rescale the parameters of a force field to better describe the host-guest interactions and provide for simulation isotherms with close agreement to experimental isotherms. Both methodologies were developed based on a reference Henry coefficient, computed with the PBE-MBD functional using the importance sampling technique. The force field rankings predicted by the benchmarking methodology involve the comparison of force field derived Henry coefficients with the reference Henry coefficients and ranking the force fields based on the disparities between these Henry coefficients. The ranking from this methodology matches the rankings made based on uptake disparities by comparing force field derived simulation isotherms to experimental isotherms in the low-pressure regime. The force field rescaling methodology was proven to refine even the worst performing force field in UFF/TraPPE. The uptake disparities of UFF/TraPPE improved from 197% and 194% to 11% and 21% for ethane and ethene, respectively. The proposed methodology is applicable to predict adsorption across nanoporous materials and allows for rescaled force fields to reach quantum accuracy without the need for experimental input.

Structure of Graphene Grown on Cu(111): X-Ray Standing Wave Measurement and Density Functional Theory Prediction

We report the quantitative adsorption structure of pristine graphene on Cu(111) determined using the normal incidence x-ray standing wave technique. The experiments constitute an important benchmark reference for the development of density functional theory approximations able to capture long-range dispersion interactions. Electronic structure calculations based on many-body dispersion-inclusive density functional theory are able to accurately predict the absolute measure and variation of adsorption height when the coexistence of multiple moiré superstructures is considered. This provides a structural model consistent with scanning probe microscopy results.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Quantum-mechanical water-flow enhancement through a sub-nanometer carbon nanotube

Experimental observations unambiguously reveal quasi-frictionless water flow through nanometer-scale carbon nanotubes (CNTs). Classical fluid mechanics is deemed unfit to describe this enhanced flow, and recent investigations indicated that quantum mechanics is required to interpret the extremely weak water-CNT friction. In fact, by quantum scattering, water can only release discrete energy upon excitation of electronic and phononic modes in the CNT. Here, we analyze in detail how a traveling water molecule couples to both plasmon and phonon excitations within a sub-nanometer, periodic CNT. We find that the water molecule needs to exceed a minimum speed threshold of ∼50 m/s in order to scatter against CNT electronic and vibrational modes. Below this threshold, scattering is suppressed, as in standard superfluidity mechanisms. The scattering rates, relevant for faster water molecules, are also estimated.

libMBD: A general-purpose package for scalable quantum many-body dispersion calculations

Many-body dispersion (MBD) is a powerful framework to treat van der Waals (vdW) dispersion interactions in density-functional theory and related atomistic modeling methods. Several independent implementations of MBD with varying degree of functionality exist across a number of electronic structure codes, which both limits the current users of those codes and complicates dissemination of new variants of MBD. Here, we develop and document libMBD, a library implementation of MBD that is functionally complete, efficient, easy to integrate with any electronic structure code, and already integrated in FHI-aims, DFTB+, VASP, Q-Chem, CASTEP, and Quantum ESPRESSO. libMBD is written in modern Fortran with bindings to C and Python, uses MPI/ScaLAPACK for parallelization, and implements MBD for both finite and periodic systems, with analytical gradients with respect to all input parameters. The computational cost has asymptotic cubic scaling with system size, and evaluation of gradients only changes the prefactor of the scaling law, with libMBD exhibiting strong scaling up to 256 processor cores. Other MBD properties beyond energy and gradients can be calculated with libMBD, such as the charge-density polarization, first-order Coulomb correction, the dielectric function, or the order-by-order expansion of the energy in the dipole interaction. Calculations on supramolecular complexes with MBD-corrected electronic structure methods and a meta-review of previous applications of MBD demonstrate the broad applicability of the libMBD package to treat vdW interactions.

"Freedom of design" in chemical compound space: towards rational in silico design of molecules with targeted quantum-mechanical properties

The rational design of molecules with targeted quantum-mechanical (QM) properties requires an advanced understanding of the structure-property/property-property relationships (SPR/PPR) that exist across chemical compound space (CCS). In this work, we analyze these fundamental relationships in the sector of CCS spanned by small (primarily organic) molecules using the recently developed QM7-X dataset, a systematic, extensive, and tightly converged collection of 42 QM properties corresponding to ≈4.2M equilibrium and non-equilibrium molecular structures containing up to seven heavy/non-hydrogen atoms (including C, N, O, S, and Cl). By characterizing and enumerating progressively more complex manifolds of molecular property space-the corresponding high-dimensional space defined by the properties of each molecule in this sector of CCS-our analysis reveals that one has a substantial degree of flexibility or "freedom of design" when searching for a single molecule with a desired pair of properties or a set of distinct molecules sharing an array of properties. To explore how this intrinsic flexibility manifests in the molecular design process, we used multi-objective optimization to search for molecules with simultaneously large polarizabilities and HOMO-LUMO gaps; analysis of the resulting Pareto fronts identified non-trivial paths through CCS consisting of sequential structural and/or compositional changes that yield molecules with optimal combinations of these properties.

MBD + C: How to Incorporate Metallic Character into Atom-Based Dispersion Energy Schemes

The dispersion component of the van der Waals interaction in low-dimensional metals is known to exhibit anomalous "Type-C non-additivity" [Int. J. Quantum Chem. 2014, 114, 1157]. This causes dispersion energy behavior at asymptotically large separations that is missed by popular atom-based schemes for dispersion energy calculations. For example, the dispersion interaction energy between parallel metallic nanotubes at separation D falls off asymptotically as approximately D-2, whereas current atom-based schemes predict D-5 asymptotically. To date, it has not been clear whether current atom-based theories also give the dispersion interaction inaccurately at smaller separations for low-dimensional metals. Here, we introduce a new theory that we term "MBD + C". It permits inclusion of Type C effects efficiently within atom-based dispersion energy schemes such as many body dispersion (MBD) and universal MBD (uMBD). This allows us to investigate asymptotic, intermediate, and near-contact regimes with equal accuracy. (The large contact energy of intimate metallic bonding is not primarily governed by dispersion energy and is described well by the semi-local density functional theory.) Here, we apply a simplified version, "nn-MBD + C", of our new theory to calculate the dispersion interaction for three low-dimensional metallic systems: parallel metallic chains of gold atoms, parallel Li-doped graphene sheets, and parallel (4,4) armchair carbon nanotubes. In addition to giving the correct asymptotic behavior, the new theory seamlessly gives the dispersion energy down to near-contact geometry, where it is similar to MBD but can give up to 15% more dispersion energy than current MBD schemes, in the systems studied so far. This percentage increases with separation until nn-MBD + C dominates MBD at asymptotic separations.

Modeling coarse-grained van der Waals interactions using dipole-coupled anisotropic quantum Drude oscillators

The Quantum Drude Oscillator (QDO) model is a promising candidate for accurately calculating the van der Waals (vdW) interaction. Anisotropic QDO models have recently been used to represent quantum fluctuations of molecular fragments rather than that of single atoms. While this model promises accurate calculation of vdW energy, there is significant room for improvements, such as incorporating a proper fragmentation method, higher-order dispersion corrections, and so forth. The present work attempts to gauge dipole-dipole interactions' ability without fragmentation. A suitable anisotropic damping function is also introduced to work with anisotropic QDO. This revised model accurately predicts the binding energies of vdW complexes for most of the systems considered. This work indicates the limit of dipole approximation for an anisotropic QDO-based model.

Generalized Many-Body Dispersion Correction through Random-Phase Approximation for Chemically Accurate Density Functional Theory

We extend our recently proposed Deep Learning-aided many-body dispersion (DNN-MBD) model to quadrupole polarizability (Q) terms using a generalized Random Phase Approximation (RPA) formalism, thus enabling the inclusion of van der Waals contributions beyond dipole. The resulting DNN-MBDQ model only relies on ab initio-derived quantities as the introduced quadrupole polarizabilities are recursively retrieved from dipole ones, in turn modeled via the Tkatchenko-Scheffler method. A transferable and efficient deep-neuronal network (DNN) provides atom-in-molecule volumes, while a single range-separation parameter is used to couple the model to Density Functional Theory (DFT). Since it can be computed at a negligible cost, the DNN-MBDQ approach can be coupled with DFT functionals, such as PBE, PBE0, and B86bPBE (dispersionless). The DNN-MBQ-corrected functionals reach chemical accuracy while exhibiting lower errors compared to their dipole-only counterparts.

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.

The effect of different energy portions on the 2D/3D stability swapping for 13-atom metal clusters

The complexity of Cu₁₃, Ag₁₃, and Au₁₃ coinage-metal clusters was investigated through their energy contributions via a density functional theory study, considering improvements in the PBE functional, such as van der Waals (vdW) corrections, spin-orbit coupling (SOC), Hubbard term (+U), and their combinations. Investigating two-dimensional (planar 2D) and three-dimensional (distorted 3D, CUB - cuboctahedral, and ICO - icosahedral) configurations, we found that vdW corrections are dominant in modulating the stability swapping between 2D and ICO (3D) for Ag₁₃ (Au₁₃), whereas for Cu₁₃ its role is increasing the relative stability between 2D (least stable) and 3D (most stable), setting ICO as the reference. Among the energy portions that constitute the relative total energy, the dimensionality difference correlates with the magnitude of the relative dispersion energy (large for 2D/ICO and small for 3D/ICO) as the causal factor responsible for an eventual stability swapping. For instance, empirical vdW corrections may favor Ag₁₃ as ICO, while semi empirical ones tend to swap the stability by favoring 2D. The same tendency is observed for Au₁₃, except when SOC is included, which enlarges the stability of 3D over 2D. Energy decomposition analysis combined with the natural orbitals for the chemical valence approach confirmed the correlations between the dimensionality difference and the magnitude of the relative dispersion energies. Our structural analysis protocol was able to capture the local distortion effects (or even their absence) through the quantification of the Hausdorff chirality measure. Here, ICO, CUB, and 2D are achiral configurations for all coinage-metal clusters, whereas Cu₁₃ as 3D presents a slight chirality when vdW correction based on many body dispersion is used, at the same time Ag₁₃ as 3D turned out to be chiral for all calculation protocols as evidence of the role of the chemical composition.

Colossal Enhancement of Atomic Force Response in van der Waals Materials Arising from Many-Body Electronic Correlations

Understanding complex materials at different length scales requires reliably accounting for van der Waals (vdW) interactions, which stem from long-range electronic correlations. While the important role of many-body vdW interactions has been extensively documented for the stability of materials, much less is known about the coupling between vdW interactions and atomic forces. Here we analyze the Hessian force response matrix for a single and two vdW-coupled atomic chains to show that a many-body description of vdW interactions yields atomic force response magnitudes that exceed the expected pairwise decay by 3-5 orders of magnitude for a wide range of separations between perturbed and observed atoms. Similar findings are confirmed for carbon nanotubes, graphene, and delamination of graphene from a silicon substrate previously studied experimentally. This colossal force enhancement suggests implications for phonon spectra, free energies, interfacial adhesion, and collective dynamics in materials with many interacting atoms.

Optical van-der-Waals forces in molecules: from electronic Bethe-Salpeter calculations to the many-body dispersion model

Molecular forces induced by optical excitations are connected to a wide range of phenomena, from chemical bond dissociation to intricate biological processes that underpin vision. Commonly, the description of optical excitations requires the solution of computationally demanding electronic Bethe-Salpeter equation (BSE). However, when studying non-covalent interactions in large-scale systems, more efficient methods are desirable. Here we introduce an effective approach based on coupled quantum Drude oscillators (cQDO) as represented by the many-body dispersion model. We find that the cQDO Hamiltonian yields semi-quantitative agreement with BSE calculations and that both attractive and repulsive optical van der Waals (vdW) forces can be induced by light. These optical-vdW interactions dominate over vdW dispersion in the long-distance regime, showing a complexity that grows with system size. Evidence of highly non-local forces in the human formaldehyde dehydrogenase 1MC5 protein suggests the ability to selectively activate collective molecular vibrations by photoabsorption, in agreement with recent experiments.

The authors devise an efficient quantum approach to address the van der Waals interactions due to photoexcitations by approximating the Bethe-Salpeter equation. Both attractive/repulsive forces can arise, that could couple to collective protein dynamics.

A simple fragment-based method for van der Waals corrections over density functional theory

Modeling intermolecular noncovalent interactions between large molecules remains a challenge for the electron structure theory community due to the high cost. Fragment-based methods usually fare well in reducing the cost...

Assessment of the van der Waals, Hubbard U parameter and spin-orbit coupling corrections on the 2D/3D structures from metal gold congeners clusters

The coinage-metal clusters possess a natural complexity in their theoretical treatment that may be accompanied by inherent shortcomings in the methodological approach. Herein, we performed a scalar-relativistic density functional theory study, considering Perdew, Burke, and Ernzerhof (PBE) with (empirical and semi empirical) van der Waals (vdW), spin-orbit coupling (SOC), +U (Hubbard term), and their combinations, to treat the Cu 13 , Ag 13 , and Au 13 clusters in different structural motifs. The energetic scenario is given by the confirmation of the 3D lowest energy configurations for Cu 13 and Ag 13 within all approaches, while for Au 13 there is a 2D/3D competition, depending on the applied correction. The 2D geometry is 0.43 eV more stable with plain PBE than the 3D one, the SOC, +U, and/or vdW inclusion decreases the overestimated stability of the planar configurations, where the most surprising result is found by the D3 and D3BJ vdW corrections, for which the 3D configuration is 0.29 and 0.11 eV, respectively, more stable than the 2D geometry (with even higher values when SOC and/or +U are added). The D3 dispersion correction represents 7.9% (4.4%) of the total binding energy for the 3D (2D) configuration, (not) being enough to change the sd hybridization and the position of the occupied d -states. Our predictions are in agreement with experimental results and in line with the best results obtained for bulk systems, as well as with hybrid functionals within D3 corrections. The properties description undergoes small corrections with the different approaches, where general trends are maintained, that is, the average bond length is smaller (larger) for lower (higher)-coordinated structures, since a same number of electrons are shared by a smaller (larger) number of bonds, consequently, the bonds are stronger (weaker) and shorter (longer) and the sd hybridization index is larger (smaller). Thus, Au has a distinct behavior in relation to its lighter congeners, with a complex potential energy surface, where in addition to the relevant relativistic effects, correlation and dispersion effects must also be considered.

Interfacial Friction Anisotropy in Few-Layer Van der Waals Crystals

Friction anisotropy is one of the important friction behaviors for two-dimensional (2D) van der Waals (vdW) crystals. The effects of normal pressure and thickness on the interfacial friction anisotropy in few-layer graphene, h-BN, and MoSe₂ under constant normal force mode have been extensively investigated by first-principle calculations. The increase of normal pressure and layer number enhances the interfacial friction anisotropy for graphene and h-BN but weakens that for MoSe₂. Such significant deviations in the interfacial friction anisotropy of few-layer graphene, h-BN and MoSe₂ can be mainly attributed to the opposite contributions of electron kinetic energies and electrostatic energies to the sliding energy barriers and different interlayer charge exchanges. Our results deepen the understanding of the influence of external loading and thickness on the friction properties of 2D vdW crystals.

A fresh look at the structure of aromatic thiols on Au surfaces from theory and experiment

A detailed study of the adsorption structure of self-assembled monolayers of 4-nitrothiophenol on the Au(111) surface was performed from a theoretical perspective via first-principles density functional theory calculations and experimentally by Raman and vibrational sum frequency spectroscopy (vSFS) with an emphasis on the molecular orientation. Simulations-including an explicit van der Waals (vdW) description-for different adsorbate structures, namely, for (3×3), (2 × 2), and (3 × 3) surface unit cells, reveal a significant tilting of the molecules toward the surface with decreasing coverage from 75° down to 32° tilt angle. vSFS suggests a tilt angle of 50°, which agrees well with the one calculated for a structure with a coverage of 0.25. Furthermore, calculated vibrational eigenvectors and spectra allowed us to identify characteristic in-plane (NO₂ scissoring) and out-of-plane (C-H wagging) modes and to predict their strength in the spectrum in dependence of the adsorption geometry. We additionally performed calculations for biphenylthiol and terphenylthiol to assess the impact of multiple aromatic rings and found that vdW interactions are significantly increasing with this number, as evidenced by the absorption energy and the molecule adopting a more upright-standing geometry.

Nonradiative Energy Transfer and Selective Charge Transfer in a WS2/(PEA)2PbI4 Heterostructure

van der Waals heterostructures are currently the focus of intense investigation; this is essentially due to the unprecedented flexibility offered by the total relaxation of lattice matching requirements and their new and exotic properties compared to the individual layers. Here, we investigate the hybrid transition-metal dichalcogenide/2D perovskite heterostructure WS₂/(PEA)₂PbI₄ (where PEA stands for phenylethylammonium). We present the first density functional theory (DFT) calculations of a heterostructure ensemble, which reveal a novel band alignment, where direct electron transfer is blocked by the organic spacer of the 2D perovskite. In contrast, the valence band forms a cascade from WS₂ through the PEA to the PbI₄ layer allowing hole transfer. These predictions are supported by optical spectroscopy studies, which provide compelling evidence for both charge transfer and nonradiative transfer of the excitation (energy transfer) between the layers. Our results show that TMD/2D perovskite (where TMD stands for transition-metal dichalcogenides) heterostructures provide a flexible and convenient way to engineer the band alignment.

Many-body van der Waals interactions beyond the dipole approximation

Long-ranged van der Waals (vdW) interactions are most often treated via Lennard-Jones approaches based on the combination of two-body and dipolar approximations. While beyond-dipole interactions and many-body contributions were separately addressed, little is known about their combined effect, especially in large molecules and relevant nanoscale systems. Here, we provide a full many-body description of vdW interactions beyond the dipole approximation, efficiently applicable to large-scale systems. Dipole-quadrupole interactions consistently exhibit large magnitude up to nm-scale separations, while many-body effects lead to system-dependent screening effects, which can reduce vdW interactions by a large fraction. Combined many-body and multipolar terms emerge as an essential ingredient for the reliable description of vdW interactions in molecular and nanoscale systems.

Tunable van der Waals interactions in low-dimensional nanostructures

Non-covalent van der Waals interactions play a major role at the nanoscale, and even a slight change in their asymptotic decay could produce a major impact on surface phenomena, self-assembly of nanomaterials, and biological systems. By a full many-body description of vdW interactions in coupled carbyne-like chains and graphenic structures, here, we demonstrate that both modulus and a range of interfragment forces can be effectively tuned, introducing mechanical strain and doping (or polarizability change). This result contrasts with conventional pairwise vdW predictions, where the two-body approximation essentially fixes the asymptotic decay of interfragment forces. The present results provide viable pathways for detailed experimental control of nanoscale systems that could be exploited both in static geometrical configurations and in dynamical processes.

Understanding the origin of serrated stacking motifs in planar two-dimensional covalent organic frameworks

Covalent organic frameworks (COFs) have attracted significant attention due to their chemical versatility combined with a significant number of potential applications. Of particular interest are two-dimensional COFs, where the organic building units are linked by covalent bonds within a plane. Most properties of these COFs are determined by the relative arrangement of neighboring layers. These are typically found to be laterally displaced, which, for example, reduces the electronic coupling between the layers. In the present contribution we use dispersion-corrected density-functional theory to elucidate the origin of that displacement, showing that the common notion that the displacement is a consequence of electrostatic repulsions of polar building blocks can be misleading. For the representative case of COF-1 we find that electrostatic and van der Waals interactions would, actually, favor a cofacial arrangement of the layers and that Pauli repulsion is the crucial factor causing the serrated AA-stacking. A more in-depth analysis of the electrostatic contribution reveals that the "classical" Coulomb repulsion between the boroxine building blocks of COF-1 suggested by chemical intuition does exist, but is overcompensated by attractive effects due to charge-penetration in the phenylene units. The situation becomes more involved, when additionally allowing the interlayer distance to relax for each displacement, as then the different distance-dependences of the various types of interactions come into play. The overall behavior calculated for COF-1 is recovered for several additional COFs with differently sized π-systems and topologies, implying that the presented results are of more general relevance.

First-principles calculations of hybrid inorganic-organic interfaces: from state-of-the-art to best practice

The computational characterization of inorganic-organic hybrid interfaces is arguably one of the technically most challenging applications of density functional theory. Due to the fundamentally different electronic properties of the inorganic and the organic components of a hybrid interface, the proper choice of the electronic structure method, of the algorithms to solve these methods, and of the parameters that enter these algorithms is highly non-trivial. In fact, computational choices that work well for one of the components often perform poorly for the other. As a consequence, default settings for one materials class are typically inadequate for the hybrid system, which makes calculations employing such settings inefficient and sometimes even prone to erroneous results. To address this issue, we discuss how to choose appropriate atomistic representations for the system under investigation, we highlight the role of the exchange-correlation functional and the van der Waals correction employed in the calculation and we provide tips and tricks how to efficiently converge the self-consistent field cycle and to obtain accurate geometries. We particularly focus on potentially unexpected pitfalls and the errors they incur. As a summary, we provide a list of best practice rules for interface simulations that should especially serve as a useful starting point for less experienced users and newcomers to the field.

Humidity effect on peeling of monolayer graphene and hexagonal boron nitride

Ambient humidity introduces water adsorption and intercalation at the surfaces and interfaces of low-dimensional materials. Our extensive molecular dynamics (MD) simulations reveal the completely opposite contributions of interfacial water to the peeling of monolayer graphene and hexagonal boron nitride (h-BN) sheets from graphite and BN substrates. For graphene, interfacial water decreases the peeling force, due to lower adhesion at the graphene/water interface. The peeling force of h-BN increases with an increase in the thickness of interfacial water, owing to stronger adhesion at the h-BN/water interface and the detachment of the water layer from the substrates. In this work, a theoretical model considering graphene/water and water/substrate interfacial adhesion energies is established, to predict the peeling forces of graphene and h-BN, which coincides well with the peeling forces predicted by the MD simulations. Our results should provide a deeper insight into the effect of interfacial water, induced by ambient humidity, on mechanical exfoliation and the transfer of two-dimensional van der Waals crystals.

Screening effect of monolayer van der Waals crystals on surface deicing: a molecular simulation study

Our extensive molecular dynamics simulations reveal a significant screening effect of monolayer graphene and hexagonal boron nitride (h-BN) on surface deicing of substrates with different degrees of hydrophilicity, including superhydrophilic (SHP) and superhydrophobic (SHB) substrates. Compared with bare surfaces, graphene and h-BN reduce the interfacial shear strength and the normal detaching strength of ice on an SHP substrate but increase the shear and detaching strengths on hydrophobic and SHB substrates. However, the shear and detaching strengths of ice become approximately unified on all of the surfaces, when interface ice layers melt into liquid water, demonstrating the screening capability from graphene and h-BN that weakens the influence of substrates on ice adhesion. Graphene and h-BN coatings suppress ice premelting on the SHP surface and change the dielectric constant of interface ice or water. This work could deepen our understanding of the role of van der Waals crystals in deicing coating.

Many-Body Dispersion

A broad range of approaches to many-body dispersion are discussed, including empirical approaches with multiple fitted parameters, augmented density functional-based approaches, symmetry adapted perturbation theory, and a supermolecule approach based on coupled cluster theory. Differing definitions of "body" are considered, specifically atom-based vs molecule-based approaches.

Density Functional Model for van der Waals Interactions: Unifying Many-Body Atomic Approaches with Nonlocal Functionals

Noncovalent van der Waals (vdW) interactions are responsible for a wide range of phenomena in matter. Popular density-functional methods that treat vdW interactions use disparate physical models for these intricate forces, and as a result the applicability of these methods is often restricted to a subset of relevant molecules and materials. Aiming towards a general-purpose density functional model of vdW interactions, here we unify two complementary approaches: nonlocal vdW functionals for polarization and interatomic methods for many-body interactions. The developed nonlocal many-body dispersion method (MBD-NL) increases the accuracy and efficiency of existing vdW functionals and is shown to be broadly applicable to molecules, soft and hard materials including ionic and metallic compounds, as well as interfaces between organic molecules and inorganic materials.

From quantum to continuum mechanics in the delamination of atomically-thin layers from substrates

Anomalous proximity effects have been observed in adhesive systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials. In the latter case, long-range forces are evidenced by measurements of non-vanishing stress that extends up to micrometer separations between graphene and the substrate. State-of-the-art models to describe adhesive properties are unable to explain these experimental observations, instead underestimating the measured stress distance range by 2–3 orders of magnitude. Here, we develop an analytical and numerical variational approach that combines continuum mechanics and elasticity with quantum many-body treatment of van der Waals dispersion interactions. A full relaxation of the coupled adsorbate/substrate geometry leads us to conclude that wavelike atomic deformation is largely responsible for the observed long-range proximity effect. The correct description of this seemingly general phenomenon for thin deformable membranes requires a direct coupling between quantum and continuum mechanics.

The unexpectedly long-ranged interface stress observed in recent delamination experiments is yet to be clarified. Here, the authors develop an analytical approach to show the wavelike atomic deformation as the origin for the observed ultra long-range stress in delamination of graphene from various substrates.

Nonlocal Electronic Correlations in the Cohesive Properties of High-Pressure Hydrogen Solids

High-pressure hydrogen exhibits remarkable phenomena including the insulator-to-metal (IM) transition; however, a complete resolution of its phase diagram is still an elusive goal despite many efforts and much controversy. Theoretical modeling is typically based on density functional theory (DFT) with a mean-field description of electronic correlations, which is known to be rather limited in describing IM transitions. Herein, we show that nonlocal electron correlations play a central role in the relative stability of solid hydrogen phases, and that DFT-correcting for these correlations by the many-body dispersion (MBD) model reaches the accuracy of quantum Monte Carlo (QMC) simulations and predicts the same C2/c-24 → Cmca-12 → Cs(IV) IM transition. In contrast with the conventional assumption that many-body electronic correlations become localized in metallic systems because of exponential screening with interelectronic distance, we find that the anisotropy of the electronic response of hydrogen solids under pressure leads to longer-ranged many-body effects in metallic phases relative to insulating ones. This refines our understanding of phase diagram of hydrogen solids as well as anisotropic many-body correlations.

Quantum mechanics of proteins in explicit water: The role of plasmon-like solute-solvent interactions

Quantum-mechanical van der Waals dispersion interactions play an essential role in intraprotein and protein-water interactions-the two main factors affecting the structure and dynamics of proteins in water. Typically, these interactions are only treated phenomenologically, via pairwise potential terms in classical force fields. Here, we use an explicit quantum-mechanical approach of density-functional tight-binding combined with the many-body dispersion formalism and demonstrate the relevance of many-body van der Waals forces both to protein energetics and to protein-water interactions. In contrast to commonly used pairwise approaches, many-body effects substantially decrease the relative stability of native states in the absence of water. Upon solvation, the protein-water dispersion interaction counteracts this effect and stabilizes native conformations and transition states. These observations arise from the highly delocalized and collective character of the interactions, suggesting a remarkable persistence of electron correlation through aqueous environments and providing the basis for long-range interaction mechanisms in biomolecular systems.

A Linear-Scaling Method for Noncovalent Interactions: An Efficient Combination of Absolutely Localized Molecular Orbitals and a Local Random Phase Approximation Approach

A novel method for the accurate and efficient calculation of interaction energies in weakly bound complexes composed of a large number of molecules is presented. The new ALMO+RPAd method circumvents the prohibitive scaling of coupled cluster singles and doubles while still providing similar accuracy across a diverse range of weakly bound chemical systems. Linear-scaling procedures for the Fock build are given utilizing absolutely localized molecular orbitals (ALMOs), resulting in the a priori exclusion of basis set superposition errors. A bespoke data structure and algorithm using density fitting are described, leading to linear scaling for the storage and computation of the two-electron integrals. Electron correlation is included through a new, linear-scaling pairwise local random phase approximation approach, including exchange interactions, and decomposed into purely dispersive excitations (RPAxd). Collectively, these allow meaningful decomposition of the interaction energy into physically distinct contributions: electrostatic, polarization, charge transfer, and dispersion. Comparison with symmetry-adapted perturbation theory shows good qualitative agreement. Tests on various dimers and the S66 benchmark set demonstrate results within 0.5 kcal mol^-1 of coupled cluster singles and doubles results. On a large cluster of water molecules, we achieve calculations involving over 3500 orbital and 12,000 auxiliary basis functions in under 10 min on a single CPU core.

Faraday-like Screening by Two-Dimensional Nanomaterials: A Scale-Dependent Tunable Effect

The modulation of electric fields by mono- or few-layer two-dimensional (2D) nanomaterials embodies a major challenge through vast technological areas, including 2D nanoscale electronics, ultrathin cable shielding, and nanostructured battery and supercapacitor electrodes. By a quantum-mechanical analysis of Faraday-like electrostatic screening due to diverse 2D nanolayers we demonstrate that electric field screening is triggered by charge response nonlocality. The effective screening factor is not only influenced by average polarizability but further exhibits nontrivial scalings with respect to surface distance: while ideal 2D metallic systems cause complete Faraday-cage screening, semimetallic graphene yields a finite, roughly scale-independent field reduction factor. Conversely, screening by finite-gap MoS₂ appears most effective in the vicinity of the surfaces, gradually vanishing in the long-distance limit because of the intrinsic finiteness of the charge-response length scale. The variability of screening effects and of their scaling laws with respect to accessible physical parameters opens novel pathways for experimental modulation of electric fields, ionic interactions, and adsorption of charged or polar moieties.

(Meta-)stability and Core-Shell Dynamics of Gold Nanoclusters at Finite Temperature

Gold nanoclusters have been the focus of numerous computational studies, but an atomistic understanding of their structural and dynamical properties at finite temperature is far from satisfactory. To address this deficiency, we investigate gold nanoclusters via ab initio molecular dynamics, in a range of sizes where a core-shell morphology is observed. We analyze their structure and dynamics using state-of-the-art techniques, including unsupervised machine-learning nonlinear dimensionality reduction (sketch-map) for describing the similarities and differences among the range of sampled configurations. In the examined temperature range between 300 and 600 K, we find that whereas the gold nanoclusters exhibit continuous structural rearrangement, they are not amorphous. Instead, they clearly show persistent motifs: a cationic core of 1-5 atoms is loosely bound to a shell which typically displays a substructure resulting from the competition between locally spherical versus planar fragments. Besides illuminating the properties of core-shell gold nanoclusters, the present study proposes a set of useful tools for understanding their nature in operando.

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.

Tailoring van der Waals dispersion interactions with external electric charges

van der Waals (vdW) dispersion interactions strongly impact the properties of molecules and materials. Often, the description of vdW interactions should account for the coupling with pervasive electric fields, stemming from membranes, ionic channels, liquids, or nearby charged functional groups. However, this quantum-mechanical effect has been omitted in atomistic simulations, even in widely employed electronic-structure methods. Here, we develop a model and study the effects of an external charge on long-range vdW correlations. We show that a positive external charge stabilizes dispersion interactions, whereas a negative charge has an opposite effect. Our analytical results are benchmarked on a series of (bio)molecular dimers and supported by calculations with high-level correlated quantum-chemical methods, which estimate the induced dispersion to reach up to 35% of intermolecular binding energy (4 kT for amino-acid dimers at room temperature). Our analysis bridges electrostatic and electrodynamic descriptions of intermolecular interactions and may have implications for non-covalent reactions, exfoliation, dissolution, and permeation through biological membranes.

Phonon-Polariton Mediated Thermal Radiation and Heat Transfer among Molecules and Macroscopic Bodies: Nonlocal Electromagnetic Response at Mesoscopic Scales

Thermal radiative phenomena can be strongly influenced by the coupling of phonons and long-range electromagnetic fields at infrared frequencies. Typically employed macroscopic descriptions of thermal fluctuations often ignore atomistic effects that become relevant at nanometric scales, whereas purely microscopic treatments ignore long-range, geometry-dependent electromagnetic effects. We describe a mesoscopic framework for modeling thermal fluctuation phenomena among molecules near macroscopic bodies, conjoining atomistic treatments of electronic and vibrational fluctuations obtained from density functional theory in the former with continuum descriptions of electromagnetic scattering in the latter. The interplay of these effects becomes particularly important at mesoscopic scales, where phonon polaritons can be strongly influenced by the objects' finite sizes, shapes, and nonlocal or many-body response to electromagnetic fluctuations. We show that, even in small but especially in elongated low-dimensional molecules, such effects can modify thermal emission and heat transfer by orders of magnitude and produce qualitatively different behavior compared to predictions based on local, dipolar, or pairwise approximations.

The Impact of Atmosphere on the Local Luminescence Properties of Metal Halide Perovskite Grains

Metal halide perovskites are exceptional candidates for inexpensive yet high-performing optoelectronic devices. Nevertheless, polycrystalline perovskite films are still limited by nonradiative losses due to charge carrier trap states that can be affected by illumination. Here, in situ microphotoluminescence measurements are used to elucidate the impact of light-soaking individual methylammonium lead iodide grains in high-quality polycrystalline films while immersing them with different atmospheric environments. It is shown that emission from each grain depends sensitively on both the environment and the nature of the specific grain, i.e., whether it shows good (bright grain) or poor (dark grain) luminescence properties. It is found that the dark grains show substantial rises in emission, while the bright grain emission is steady when illuminated in the presence of oxygen and/or water molecules. The results are explained using density functional theory calculations, which reveal strong adsorption energies of the molecules to the perovskite surfaces. It is also found that oxygen molecules bind particularly strongly to surface iodide vacancies which, in the presence of photoexcited electrons, lead to efficient passivation of the carrier trap states that arise from these vacancies. The work reveals a unique insight into the nature of nonradiative decay and the impact of atmospheric passivation on the microscale properties of perovskite films.

First-principles stability ranking of molecular crystal polymorphs with the DFT+MBD approach

The ability to accurately calculate the relative stabilities of numerous polymorphs of a given molecular crystal is crucial for the success of any molecular crystal structure prediction (CSP) approach. We have recently presented a hierarchical CSP procedure based on van-der-Waals-inclusive density functional theory [Hoja et al., 2018, arXiv:1803.07503], which yields excellent stability rankings for molecular crystals involving rigid molecules, salts, co-crystals, and highly polymorphic drug-like molecules. This approach includes many-body dispersion effects, exact exchange, as well as vibrational free energies. Here, we discuss in detail the impact of these effects on the obtained stability rankings. In addition, we assess the impact of the approximations used in our hierarchical procedure. We show that our procedure is generally robust to 1-2 kJ mol-1 for the systems in the latest CSP blind test but vibrational free energies for crystals involving flexible molecules would benefit from directly including many-body dispersion interactions. In addition, we also discuss the effect of temperature on the structure of molecular crystals and a simple but effective method for estimating anharmonic effects.

Unifying Microscopic and Continuum Treatments of van der Waals and Casimir Interactions

We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e., between molecules and structured surfaces with features on the scale of molecular sizes, in which case the finite sizes, complex shapes, and resulting nonlocal electronic excitations of molecules are strongly influenced by electromagnetic retardation and wave effects that depend crucially on the shapes of surrounding macroscopic bodies. We show that these effects together can modify vdW interaction energies and forces, as well as molecular shapes deformed by vdW interactions, by orders of magnitude compared to previous treatments based on Casimir-Polder, nonretarded, or pairwise approximations, which are valid only at macroscopically large or atomic-scale separations or in dilute insulating media, respectively.

Fast oxygen diffusion and iodide defects mediate oxygen-induced degradation of perovskite solar cells

Methylammonium lead halide perovskites are attracting intense interest as promising materials for next-generation solar cells, but serious issues related to long-term stability need to be addressed. Perovskite films based on CH₃NH₃PbI₃ undergo rapid degradation when exposed to oxygen and light. Here, we report mechanistic insights into this oxygen-induced photodegradation from a range of experimental and computational techniques. We find fast oxygen diffusion into CH₃NH₃PbI₃ films is accompanied by photo-induced formation of highly reactive superoxide species. Perovskite films composed of small crystallites show higher yields of superoxide and lower stability. Ab initio simulations indicate that iodide vacancies are the preferred sites in mediating the photo-induced formation of superoxide species from oxygen. Thin-film passivation with iodide salts is shown to enhance film and device stability. The understanding of degradation phenomena gained from this study is important for the future design and optimization of stable perovskite solar cells.

Determining the degradation pathways in lead halide perovskites is key to its development as a viable solar technology. Aristidou et al. identify iodide vacancies as the preferred sites in mediating the photo-induced formation of superoxide species from intercalated oxygen.

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

Noncovalent van der Waals (vdW) or dispersion forces are ubiquitous in nature and influence the structure, stability, dynamics, and function of molecules and materials throughout chemistry, biology, physics, and materials science. These forces are quantum mechanical in origin and arise from electrostatic interactions between fluctuations in the electronic charge density. Here, we explore the conceptual and mathematical ingredients required for an exact treatment of vdW interactions, and present a systematic and unified framework for classifying the current first-principles vdW methods based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem (namely the Rutgers-Chalmers vdW-DF, Vydrov-Van Voorhis (VV), exchange-hole dipole moment (XDM), Tkatchenko-Scheffler (TS), many-body dispersion (MBD), and random-phase approximation (RPA) approaches). Particular attention is paid to the intriguing nature of many-body vdW interactions, whose fundamental relevance has recently been highlighted in several landmark experiments. The performance of these models in predicting binding energetics as well as structural, electronic, and thermodynamic properties is connected with the theoretical concepts and provides a numerical summary of the state-of-the-art in the field. We conclude with a roadmap of the conceptual, methodological, practical, and numerical challenges that remain in obtaining a universally applicable and truly predictive vdW method for realistic molecular systems and materials.

Anharmonic and Quantum Fluctuations in Molecular Crystals: A First-Principles Study of the Stability of Paracetamol

Molecular crystals often exist in multiple competing polymorphs, showing significantly different physicochemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful form, a real challenge due to the combinatorial search space, and the complex interplay of subtle effects that work together to determine the relative stability of different structures. Here we take a comprehensive approach based on different flavors of thermodynamic integration in order to estimate all contributions to the free energies of these systems with density-functional theory, including the oft-neglected anharmonic contributions and nuclear quantum effects. We take the two main stable forms of paracetamol as a paradigmatic example. We find that anharmonic contributions, different descriptions of van der Waals interactions, and nuclear quantum effects all matter to quantitatively determine the stability of different phases. Our analysis highlights the many challenges inherent in the development of a quantitative and predictive framework to model molecular crystals. However, it also indicates which of the components of the free energy can benefit from a cancellation of errors that can redeem the predictive power of approximate models, and suggests simple steps that could be taken to improve the reliability of ab initio crystal structure prediction.