Exchange-hole Dipole Moment Research Articles

Assessment of the exchange-hole dipole moment dispersion correction for the energy ranking stage of the seventh crystal structure prediction blind test.

The seventh blind test of crystal structure prediction (CSP) methods substantially increased the level of complexity of the target compounds relative to the previous tests organized by the Cambridge Crystallographic Data Centre. In this work, the performance of density-functional methods is assessed using numerical atomic orbitals and the exchange-hole dipole moment dispersion correction (XDM) for the energy-ranking phase of the seventh blind test. Overall, excellent performance was seen for the two rigid molecules (XXVII, XXVIII) and for the organic salt (XXXIII). However, for the agrochemical (XXXI) and pharmaceutical (XXXII) targets, the experimental polymorphs were ranked fairly high in energy amongst the provided candidate structures and inclusion of thermal free-energy corrections from the lattice vibrations was found to be essential for compound XXXI. Based on these results, it is proposed that the importance of vibrational free-energy corrections increases with the number of rotatable bonds.

Modeling Intermolecular Interactions with Exchange-Hole Dipole Moment Dispersion Corrections to Neural Network Potentials.

Neural network potentials (NNPs) are an innovative approach for calculating the potential energy and forces of a chemical system. In principle, these methods are capable of modeling large systems with an accuracy approaching that of a high-level ab initio calculation, but with a much smaller computational cost. Due to their training to density-functional theory (DFT) data and neglect of long-range interactions, some classes of NNPs require an additional term to include London dispersion physics. In this Perspective, we discuss the requirements for a dispersion model for use with an NNP, focusing on the MLXDM (Machine Learned eXchange-Hole Dipole Moment) model developed by our groups. This model is based on the DFT-based XDM dispersion correction, which calculates interatomic dispersion coefficients in terms of atomic moments and polarizabilities, both of which can be approximated effectively using neural networks.

Comparison of Density-Functional Theory Dispersion Corrections for the DES15K Database.

While density-functional theory (DFT) remains one of the most widely used tools in computational chemistry, most functionals fail to properly account for the effects of London dispersion. Hence, there are many popular post-self-consistent methods to add a dispersion correction to the DFT energy. Until now, the most popular methods have never been compared on equal footing due to not being implemented in the same electronic structure packages. In this work, we performed a large-scale benchmarking study, directly comparing the accuracy of the exchange-hole dipole moment (XDM), D3BJ, D4, TS, MBD, and MBD-NL dispersion models when applied to the recent DES15K database of nearly 15,000 molecular complexes at both expanded and compressed geometries. Our study showed similarly good performance for all dispersion methods (except TS) when applied to neutral complexes. However, they all performed worse for ionic complexes, particularly those involving dications of alkaline earth metals, due to systematic overbinding by the base PBE0 density functional. Investigation of the largest outliers also revealed that only the MBD and MBD-NL methods demonstrate surprising errors for complexes involving alkali metal cations at compressed geometries where they tended to significantly overbind. As we would expect minimal dispersion binding for such complexes, we further investigated the origins of these errors for the potential energy curve of a model cation-π complex. Overall, there is little choice between the XDM, D3BJ, D4, MBD, and MBD-NL dispersion methods for most systems. However, the MBD-based methods are not recommended for complexes involving organic species and alkali or alkaline earth metal cations, for example when modeling Li+ intercalation into graphite.

Many-body dispersion in model systems and the sensitivity of self-consistent screening.

London dispersion is a weak, attractive, intermolecular force that occurs due to interactions between instantaneous dipole moments. While individual dispersion contributions are small, they are the dominating attractive force between nonpolar species and determine many properties of interest. Standard semi-local and hybrid methods in density-functional theory do not account for dispersion contributions, so a correction such as the exchange-hole dipole moment (XDM) or many-body dispersion (MBD) models must be added. Recent literature has discussed the importance of many-body effects on dispersion, and attention has turned to which methods accurately capture them. By studying systems of interacting quantum harmonic oscillators from first principles, we directly compare computed dispersion coefficients and energies from XDM and MBD and also study the influence of changing oscillator frequency. Additionally, the 3-body energy contributions for both XDM, via the Axilrod-Teller-Muto term, and MBD, via a random-phase approximation formalism, are calculated and compared. Connections are made to interactions between noble gas atoms as well as to the methane and benzene dimers and to two layered materials, graphite and MoS2. While XDM and MBD give similar results for large separations, some variants of MBD are found to be susceptible to a polarization catastrophe at short range, and the MBD energy calculation is seen to fail in some chemical systems. Additionally, the self-consistent screening formalism used in MBD is shown to be surprisingly sensitive to the choice of input polarizabilities.

A neural network potential with rigorous treatment of long-range dispersion

MLXDM: Machine Learned eXchange-hole Dipole Moment dispersion correction for Neural Network Potentials.

Interplay between London Dispersion, Hubbard U, and Metastable States for Uranium Compounds.

High-throughput computational studies of lanthanide and actinide chemistry with density-functional theory are complicated by the need for Hubbard U corrections, which ensure localization of the f-electrons, but can lead to metastable states. This work presents a systematic investigation of the effects of both Hubbard U value and metastable states on the predicted structural and thermodynamic properties of four uranium compounds central to the field of nuclear fuels: UC, UN, UO2, and UCl3. We also assess the impact of the exchange-hole dipole moment (XDM) dispersion correction on the computed properties. Overall, the choice of Hubbard U value and inclusion of a dispersion correction cause larger variations in the computed geometric properties than result from metastable states. The weak dependence of structure optimization on metastable states should simplify future high-throughput calculations on actinides. Conversely, addition of the dispersion correction is found to offset the repulsion introduced by the Hubbard U term and provides greatly improved agreement with experiment for both cell volumes and heats of formation. The XDM dispersion correction is largely invariant to the chosen U value, making it a robust dispersion correction for actinide systems.

Application of XDM to ionic solids: The importance of dispersion for bulk moduli and crystal geometries.

Dispersion corrections are essential in the description of intermolecular interactions; however, dispersion-corrected functionals must also be transferrable to hard solids. The exchange-hole dipole moment (XDM) model has demonstrated excellent performance for non-covalent interactions. In this article, we examine its ability to describe the relative stability, geometry, and compressibility of simple ionic solids. For the specific cases of the cesium halides, XDM-corrected functionals correctly predict the energy ranking of the B1 and B2 forms, and a dispersion contribution is required to obtain this result. Furthermore, for the lattice constants of the 20 alkali halides, the performance of XDM-corrected functionals is excellent, provided that the base functional's exchange enhancement factor properly captures non-bonded repulsion. The mean absolute errors in lattice constants obtained with B86bPBE-XDM and B86bPBE-25X-XDM are 0.060 Å and 0.039 Å, respectively, suggesting that delocalization error also plays a minor role in these systems. Finally, we considered the calculation of bulk moduli for alkali halides and alkaline-earth oxides. Previous claims in the literature that simple generalized gradient approximations, such as PBE, can reliably predict experimental bulk moduli have benefited from large error cancellations between neglecting both dispersion and vibrational effects. If vibrational effects are taken into account, dispersion-corrected functionals are quite accurate (4 GPa-5 GPa average error), again, if non-bonded repulsion is correctly represented. Careful comparisons of the calculated bulk moduli with experimental data are needed to avoid systematic biases and misleading conclusions.

Exfoliation Energy of Layered Materials by DFT-D: Beware of Dispersion!

In this work, we have computed the exfoliation energy (the energy required to separate a single layer from the bulk structure), the interlayer distance, and the thermodynamic state functions for representative layered inorganic minerals such as Brucite, Portlandite, and Kaolinite, while leaving the more classical 2D transition-metal dichalcogenides (like MoS2) for future work. Such materials are interesting for several applications in the field of adsorption and in prebiotic chemistry. Their peculiar features are directly controlled by the exfoliation energy. In materials without cations/anions linking different layers, the interactions keeping the layers together are of weak nature, mainly dispersion London interactions and hydrogen bonds, somehow challenging to deal with computationally. We used Hartree–Fock (HF) and density functional theory (DFT) approaches focusing on the role of dispersion forces using the popular and widespread Grimme’s pairwise dispersion schemes (-D2 and -D3) and, as a reference method, the periodic MP2 approach based on localized orbitals (LMP2). The results are highly dependent on the choice of the scheme adopted to account for dispersion interactions. D2 and D3 schemes combined with either HF or DFT lead to overestimated exfoliation energies (about 2.5 and 1.7 times higher than LMP2 data for Brucite/Portlandite and Kaolinite) and underestimated interlayer distances (by about 3.5% for Brucite/Portlandite). The reason is that D2 and D3 corrections are based on neutral atomic parameters for each chemical element which, instead, behave as cations in the considered layered material (Mg, Ca, and Al), causing overattractive interaction between layers. More sophisticated dispersion corrections methods, like those based on nonlocal vdW functionals, many body dispersion model, and exchange-hole dipole moment not relying on atom-typing, are, in principle, better suited to describe the London interaction of ionic species. Nonetheless, we demonstrate that good results can be achieved also within the simpler D2 and D3 schemes, in agreement with previous literature suggestions, by adopting the dispersion coefficients of the preceding noble gas for the ionic species, leading to energetics in good agreement with LMP2 and structures closer to the experiments.

Asymptotic Pairwise Dispersion Corrections Can Describe Layered Materials Accurately

A recent study by Tawfik et al. [ Phys. Rev. Mater. 2018, 2, 034005] found that few density functionals, none of which are asymptotic pairwise dispersion methods, describe the geometry and binding of layered materials accurately. Here, we show that the exchange-hole dipole moment (XDM) dispersion model attains excellent results for graphite, hexagonal BN, and transition-metal dichalcogenides. Contrary to what has been argued, successful modeling of layered materials does not necessitate meta-GGA exchange, nonlocal correlation functionals, or the inclusion of three-body dispersion terms. Rather, a GGA functional, combined with a simple asymptotic pairwise dispersion correction, can be reliably used, provided that it properly accounts for the geometric dependence of the dispersion coefficients. The overwhelming contribution to the variation of the pairwise dispersion coefficients comes from the immediate vicinity of an atom and is already present for single layers. Longer-range and interlayer effects are examined in detail for graphite.

Analysis of Density-Functional Errors for Noncovalent Interactions between Charged Molecules.

The study of the structure and chemistry of biological systems with density-functional theory requires an accurate description of intermolecular interactions involving charged moieties. While dispersion-corrected functionals accurately model noncovalent interactions in neutral systems, a systematic study of the performance and errors associated with intermolecular interactions between charged fragments is missing. We undertake this study by examining the performance of a series of dispersion-corrected functionals with varying degrees of exact exchange for the side-chain protein interactions from the BioFragment Database (BFDb) of Burns et al. (the SSI set). In general, hybrid functionals with 20-30% exact exchange are accurate across the board, with the lowest mean absolute errors of 0.11 kcal/mol obtained from the 20% exact-exchange BLYP and PW86PBE hybrids coupled with the exchange-hole dipole moment (XDM) dispersion model. In addition, our analysis shows that functionals with higher exact-exchange fractions overestimate the electrostatic contributions to the binding energies, and that GGA functionals overestimate zwitterion binding energies due to delocalization error and overestimated charge transfer. In addition, the (quite large) repulsion in the dications is systematically overestimated by all functionals, and the trends for the monoanionic and dianionic dimers can be successfully explained by appealing to the ability of the underlying GGA to describe Pauli repulsion, as given by its exchange enhancement factor. Going beyond studies of biomolecules, this latter result has important implications for selecting appropriate GGA functionals for applications to ionic solids and layered materials containing anion-anion interactions.

Dispersion XDM with Hybrid Functionals: Delocalization Error and Halogen Bonding in Molecular Crystals

The accurate calculation of relative lattice energies of molecular crystals is important in polymorph ranking and crystal structure prediction. Delocalization error has been shown to affect calculated intermolecular binding energies in DFT and is similarly expected to affect the lattice energies of some classes of molecular crystals. In this work, we explore the use of dispersion-corrected hybrid functionals in the planewave-pseudopotentials approach to reduce delocalization error. We combine several hybrid functionals with the exchange-hole dipole moment (XDM) model for dispersion and show that they generally outperform GGA functionals in the calculation of both gas-phase binding energies and molecular crystal lattice energies. We apply the resulting XDM-corrected functionals to four halogen-bonded crystals: Cl2, Br2, I2, and ICl. GGA functionals severely overestimate their lattice energies, while hybrid functionals give accurate values. The preference of GGA functionals for monatomic structures in the Br2 and Cl2 crystals is also explained. Finally, we apply a recently developed method to calculate Bader's delocalization indices to examine the extent of intermolecular delocalization in the halogen molecular crystals. It is shown that intermolecular delocalization indices can be used to measure the strength of halogen bonds within the crystal, as well as detect the presence of delocalization error.

Non-Covalent Interactions in Molecular Crystals: Exploring the Accuracy of the Exchange-Hole Dipole Moment Model with Local Orbitals.

We present the first implementation of the exchange-hole dipole moment (XDM) model in combination with a numerical finite-support local orbital method (the SIESTA method) for the modeling of non-covalent interactions in periodic solids. The XDM model is parametrized for both the B86bPBE and PBE functionals using double-ζ- and triple-ζ-quality basis sets (DZP and TZP). The use of finite-support local orbitals is shown to have minimal impact on the computed dispersion coefficients for van der Waals molecular dimers and small molecular solids. However, the quality of the basis set affects the accuracy of calculated dimer binding energies and molecular-crystal lattice energies quite significantly; the size of the counterpoise correction indicates that this is caused by basis-set incompleteness error. In the case of the DZP basis set, its performance for weakly bound gas-phase dimers is similar to that of a double-ζ Gaussian basis set without diffuse functions. The new XDM implementation was tested on graphite and phosphorene exfoliation, and on the X23 benchmark set of molecular-crystal lattice energies. Our results indicate that lattice energies similar to plane-wave calculations can be obtained only if the counterpoise correction is applied. Alternatively, the calculated equilibrium geometries are reasonably close to the plane-wave equivalents, and composite approaches in which a single-point plane-wave calculation is used at the XDM/DZP equilibrium geometry yield good accuracy at a significantly lower computational cost.

The effect of electronic excitation on London dispersion

Atomic and molecular dispersion coefficients can now be calculated routinely using density-functional theory. In this work, we present the first determination of how electronic excitation affects molecular C6 London dispersion coefficients from the exchange-hole dipole moment (XDM) dispersion model. Excited states are typically found to have larger dispersion coefficients than the corresponding ground states, due to their more diffuse electron densities. A particular focus is both intramolecular and intermolecular charge-transfer excitations, which have high absorbance intensities and are important in organic dyes, light-emitting diodes, and photovoltaics. In these classes of molecules, the increase in C6 for the electron-accepting moiety is largely offset by a decrease in C6 for the electron-donating moiety. As a result, the change in dispersion energy for a chromophore interacting with neighbouring molecules in the condensed phase is minimal.

Evaluating the London Dispersion Coefficients of Protein Force Fields Using the Exchange-Hole Dipole Moment Model

London dispersion is one of the fundamental interactions involved in protein folding and dynamics. The popular CHARMM36, Amber ff14sb, and OPLS-AA force fields represent these interactions through the C6/ r6 term of the Lennard-Jones potential, where the C6 parameters are assigned empirically. Here, dispersion coefficients of these three force fields are shown to be roughly 50% larger than values calculated using the quantum mechanically derived exchange-hole dipole moment (XDM) model. The CHARMM36 and Amber OL15 force fields for nucleic acids also exhibit this trend. The hydration energies of the side-chain models were calculated using REMD-TI for the CHARMM36, Amber ff14sb, and OPLS-AA force fields. These force fields predict side-chain hydration energies that are in generally good agreement with the experimental values, which suggests that the total strength of aqueous dispersion interactions is correct, despite C6 coefficients that are considerably larger than XDM predicts. An analytical expression for the dispersion hydration energy using XDM coefficients shows that higher-order dispersion terms (i.e., C8 and C10) account for roughly 37.5% of the hydration energy of methane. This suggests that the C6 dispersion coefficients used in contemporary force fields are elevated to account for the neglected higher-order terms.

Are dispersion corrections accurate outside equilibrium? A case study on benzene

Modern approaches to modelling dispersion forces are becoming increasingly accurate, and can predict accurate binding distances and energies. However, it is possible that these successes reflect a fortuitous cancellation of errors at equilibrium. Thus, in this work we investigate whether a selection of modern dispersion methods agree with benchmark calculations across several potential-energy curves of the benzene dimer to determine if they are capable of describing forces and energies outside equilibrium. We find the exchange-hole dipole moment (XDM) model describes most cases with the highest overall agreement with reference data for energies and forces, with many-body dispersion (MBD) and its fractionally ionic (FI) variant performing essentially as well. Popular approaches, such as Grimme-D and van der Waals density functional approximations (vdW-DFAs) underperform on our tests. The meta-GGA M06-L is surprisingly good for a method without explicit dispersion corrections. Some problems with SCAN+rVV10 are uncovered and briefly discussed.

Effect of a Metal Substrate on Interlayer Interactions in Bilayer Graphene

Bilayer graphene (BLG) has been shown to have advantageous electronic and physical properties relative to single-layer graphene and is a model system for probing the tribology of graphene-based lubricants. However, few studies have investigated how metal substrates affect interlayer interactions, as quantified by the exfoliation energy and the sliding barrier of the upper graphene layer. In this work, we present a study of adsorbed BLG on several transition-metal surfaces using density-functional theory incorporating the exchange-hole dipole moment dispersion model. Our results show that physisorption of BLG on a surface does not significantly perturb the interlayer interactions, exfoliation, or sliding. Conversely, chemisorption of BLG increases the exfoliation energy and decreases the sliding barriers because of stronger dispersion contributions from the metal substrate. Changes in translational and rotational orientations massively impact the sliding friction for Ni group metals that can facilitate bot...

Evaluating Force-Field London Dispersion Coefficients Using the Exchange-Hole Dipole Moment Model

London dispersion interactions play an integral role in materials science and biophysics. Force fields for atomistic molecular simulations typically represent dispersion interactions by the 12-6 Lennard-Jones potential using empirically determined parameters. These parameters are generally underdetermined, and there is no straightforward way to test if they are physically realistic. Alternatively, the exchange-hole dipole moment (XDM) model from density-functional theory predicts atomic and molecular London dispersion coefficients from first principles, providing an innovative strategy to validate the dispersion terms of molecular-mechanical force fields. In this work, the XDM model was used to obtain the London dispersion coefficients of 88 organic molecules relevant to biochemistry and pharmaceutical chemistry and the values compared with those derived from the Lennard-Jones parameters of the CGenFF, GAFF, OPLS, and Drude polarizable force fields. The molecular dispersion coefficients for the CGenFF, GAFF, and OPLS models are systematically higher than the XDM-calculated values by a factor of roughly 1.5, likely due to neglect of higher order dispersion terms and premature truncation of the dispersion-energy summation. The XDM dispersion coefficients span a large range for some molecular-mechanical atom types, suggesting an unrecognized source of error in force-field models, which assume that atoms of the same type have the same dispersion interactions. Agreement with the XDM dispersion coefficients is even poorer for the Drude polarizable force field. Popular water models were also examined, and TIP3P was found to have dispersion coefficients similar to the experimental and XDM references, although other models employ anomalously high values. Finally, XDM-derived dispersion coefficients were used to parametrize molecular-mechanical force fields for five liquids-benzene, toluene, cyclohexane, n-pentane, and n-hexane-which resulted in improved accuracy in the computed enthalpies of vaporization despite only having to evaluate a much smaller section of the parameter space.

Exchange-Hole Dipole Dispersion Model for Accurate Energy Ranking in Molecular Crystal Structure Prediction II: Nonplanar Molecules.

The crystal structure prediction (CSP) of a given compound from its molecular diagram is a fundamental challenge in computational chemistry with implications in relevant technological fields. A key component of CSP is the method to calculate the lattice energy of a crystal, which allows the ranking of candidate structures. This work is the second part of our investigation to assess the potential of the exchange-hole dipole moment (XDM) dispersion model for crystal structure prediction. In this article, we study the relatively large, nonplanar, mostly flexible molecules in the first five blind tests held by the Cambridge Crystallographic Data Centre. Four of the seven experimental structures are predicted as the energy minimum, and thermal effects are demonstrated to have a large impact on the ranking of at least another compound. As in the first part of this series, delocalization error affects the results for a single crystal (compound X), in this case by detrimentally overstabilizing the π-conjugated conformation of the monomer. Overall, B86bPBE-XDM correctly predicts 16 of the 21 compounds in the five blind tests, a result similar to the one obtained using the best CSP method available to date (dispersion-corrected PW91 by Neumann et al.). Perhaps more importantly, the systems for which B86bPBE-XDM fails to predict the experimental structure as the energy minimum are mostly the same as with Neumann's method, which suggests that similar difficulties (absence of vibrational free energy corrections, delocalization error,...) are not limited to B86bPBE-XDM but affect GGA-based DFT-methods in general. Our work confirms B86bPBE-XDM as an excellent option for crystal energy ranking in CSP and offers a guide to identify crystals (organic salts, conjugated flexible systems) where difficulties may appear.

Adsorption of graphene to metal (111) surfaces using the exchange-hole dipole moment model

Graphene has a unique electronic structure and excellent tribological properties. A promising method for graphene production involves depositing vaporized carbon on metal substrates, which can also be used to modify graphene's electronic structure through charge transfer. In this work, graphene adsorption on the (111) surface of seven metals (Al, Cu, Ag, Au, Ni, Pd, and Pt) is investigated computationally using density-functional theory with the exchange-hole dipole moment (XDM) dispersion correction. Two distinct graphene-metal orientations, corresponding to 0∘ and 30∘ relative rotation of the graphene layer, are considered to investigate how lattice mismatch affects adsorption. Our results reproduce reference data from the random-phase approximation more closely than other dispersion-corrected density functionals, confirming that XDM is an excellent method for surface chemistry. The rotational orientation of graphene is found to strongly affect its interaction with the substrate. There is an energetic drive for graphene to align with the metal lattice, particularly for Pd and Pt, which causes the formation of multiple Moiré patterns, in agreement with experimental observations.

Adsorption of graphene to nickel (111) using the exchange-hole dipole moment model

Graphene is a promising material for a number of technological applications due to its unique electronic properties. It can be mass produced by depositing carbon atoms on metal scaffolds, such as nickel. This work presents a detailed study of graphene adsorption on the nickel (111) surface using the exchange-hole dipole moment (XDM) dispersion correction. XDM is shown to accurately model graphene-nickel interactions, providing adsorption energies in excellent agreement with available experimental data and with RPA calculations. All six graphene-nickel orientations studied present a physisorption energy minimum, but only three exhibit chemisorption. The physisorption and chemisorption minima are close in energy, and are separated by a barrier of ∼1 kJ/mol per carbon. The relative strength of the chemisorption and physisorption interactions is found to depend heavily on the nickel lattice constant. Thermal expansion stabilizes chemisorption relative to physisorption. The pairwise dispersion coefficients depend strongly on the graphene-nickel distance, and their variation is determined by the exchange-hole dipole moments. If this dependence of the dispersion coefficients with the environment is properly captured, a pairwise dispersion correction (like XDM) is suitable to model surface adsorption.