Phase stability and dense polymorph of the BaCa(CO3)2 barytocalcite carbonate.

The double carbonate BaCa(CO3)2 holds potential as host compound for carbon in the Earth's crust and mantle. Here, we report the crystal structure determination of a high-pressure BaCa(CO3)2 phase characterized by single-crystal X-ray diffraction. This phase, named post-barytocalcite, was obtained at 5.7 GPa and can be described by a monoclinic Pm space group. The barytocalcite to post-baritocalcite phase transition involves a significant discontinuous 1.4% decrease of the unit-cell volume, and the increase of the coordination number of 1/4 and 1/2 of the Ba and Ca atoms, respectively. High-pressure powder X-ray diffraction measurements at room- and high-temperatures using synchrotron radiation and DFT calculations yield the thermal expansion of barytocalcite and, together with single-crystal data, the compressibility and anisotropy of both the low- and high-pressure phases. The calculated enthalpy differences between different BaCa(CO3)2 polymorphs confirm that barytocalcite is the thermodynamically stable phase at ambient conditions and that it undergoes the phase transition to the experimentally observed post-barytocalcite phase. The double carbonate is significantly less stable than a mixture of the CaCO3 and BaCO3 end-members above 10 GPa. The experimental observation of the high-pressure phase up to 15 GPa and 300 ºC suggests that the decomposition into its single carbonate components is kinetically hindered.

Structural, vibrational and electronic properties of α'-Ga2S3 under compression.

We report a joint experimental and theoretical study of the low-pressure phase of α'-Ga2S3 under compression. Theoretical ab initio calculations have been compared to X-ray diffraction and Raman scattering measurements under high pressure carried out up to 17.5 and 16.1 GPa, respectively. In addition, we report Raman scattering measurements of α'-Ga2S3 at high temperature that have allowed us to study its anharmonic properties. To understand better the compression of this compound, we have evaluated the topological properties of the electron density, the electron localization function, and the electronic properties as a function of pressure. As a result, we shed light on the role of the Ga-S bonds, the van der Waals interactions inside the channels of the crystalline structure, and the single and double lone electron pairs of the sulphur atoms in the anisotropic compression of α'-Ga2S3. We found that the structural channels are responsible for the anisotropic properties of α'-Ga2S3 and the A'(6) phonon, known as the breathing mode and associated with these channels, exhibits the highest anharmonic behaviour. Finally, we report calculations of the electronic band structure of α'-Ga2S3 at different pressures and find a nonlinear pressure behaviour of the direct band gap and a pressure-induced direct-to-indirect band gap crossover that is similar to the behaviour previously reported in other ordered-vacancy compounds, including ß-Ga2Se3. The importance of the single and, more specially, the double lone electron pairs of sulphur in the pressure dependence of the topmost valence band of α'-Ga2S3 is stressed.

Controlling the off-center positions of anions through thermodynamics and kinetics in flexible perovskite-like materials.

Due to the network flexibility of their BX3 sub-lattice, a manifold of polymorphs with potential multiferroic applications can be found in perovskite-like ABX3 materials under different pressure and temperature conditions. The potential energy surface of these compounds usually presents equivalent off-center positions of anions connected by low energetic barriers. This feature facilitates a competition between the thermodynamic and kinetic control of the transitions from low to high symmetry structures, and explains the relationship between the rich polymorphism and network flexibility. In the rhombohedral phase of iron trifluoride, our first-principles electronic structure and phonon calculations reveal the factors that determine which of the two scenarios dominates the transition. At the experimentally reported rhombohedral-cubic transition temperature, the calculated fluorine displacements are fast enough to overcome forward and backward a barrier of less than 30 kJ mol-1, leading to an average structure with cubic symmetry. In addition, lattice strain effects observed in epitaxial growth and nanocrystallite experiments involving BX3 compounds are successfully mimicked by computing the phase stability of FeF3 under negative pressures. We predict a transition pressure at -1.8 GPa with a relative volume change around 5%, consistent with a first-order transition from the rhombohedral to the cubic structure. Overall, our study illustrates how, by strain tuning, either a thermodynamic or a kinetic pathway can be selected for this transformation.

Temperature and pressure-induced strains in anhydrous iron trifluoride polymorphs.

Various structural configurations of iron trifluoride appear at the nanoscale and macroscopic size, either in the amorphous or crystalline state. The specific atomic organization in these structures crucially alters the performance of FeF3 as an effective cathode in Li-ion batteries. Our detailed first-principles computational simulations examine the structural strains induced by temperature and stress on the four anhydrous polymorphs observed so far in FeF3 at ambient pressure. A wealth of data covering previous experimental results on their equilibrium structures and extending their characterization with new static and isothermal equations of state is provided. We inform on how porous apertures associated with the six-octahedra rings of the HTB and pyrochlore phases are modified under compressive and expansive strains. A quasi-auxetic behavior at low pressures for the ground state rhombohedral phase is detected, which is in concordance with its anomalous structural anisotropy. In contrast with the effect of temperature, this structure undergoes under negative pressure phase transitions to the other three polymorphs, indicating potential conditions where low-density FeF3 could show a better performance in technological applications.

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.

Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems.

The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B-F, Si-Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.

What is "many-body" dispersion and should I worry about it?

Inclusion of dispersion effects in density-functional calculations is now standard practice in computational chemistry. In many dispersion models, the dispersion energy is written as a sum of pairwise atomic interactions consisting of a damped asymptotic expansion from perturbation theory. There has been much recent attention drawn to the importance of "many-body" dispersion effects, which by their name imply limitations with a pairwise atomic expansion. In this perspective, we clarify what is meant by many-body dispersion, as this term has previously referred to two very different physical phenomena, here classified as electronic and atomic many-body effects. Atomic many-body effects refer to the terms in the perturbation-theory expansion of the dispersion energy involving more than two atoms, the leading contribution being the Axilrod-Teller-Muto three-body term. Conversely, electronic many-body effects refer to changes in the dispersion coefficients of the pairwise terms induced by the atomic environment. Regardless of their nature, many-body effects cause pairwise non-additivity in the dispersion energy, such that the dispersion energy of a system does not equal the sum of the dispersion energies of its atomic pairs taken in isolation. A series of examples using the exchange-hole dipole moment (XDM) method are presented to assess the relative importance of electronic and atomic many-body effects on the dispersion energy. Electronic many-body effects can result in variation in the leading-order C6 dispersion coefficients by as much as 50%; hence, their inclusion is critical for good performance of a pairwise asymptotic dispersion correction. Conversely, atomic many-body effects represent less than 1% of the total dispersion energy and are much less significant than higher-order (C8 and C10) pairwise terms. Their importance has been previously overestimated through empirical fitting, where they can offset underlying errors stemming either from neglect of higher-order pairwise terms or from the base density functional.

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.

Gold(i) sulfide: unusual bonding and an unexpected computational challenge in a simple solid.

We report the experimental high-pressure crystal structure and equation of state of gold(i) sulfide (Au2S) determined using diamond-anvil cell synchrotron X-ray diffraction. Our data shows that Au2S has a simple cubic structure with six atoms in the unit cell (four Au in linear, and two S in tetrahedral, coordination), no internal degrees of freedom, and relatively low bulk modulus. Despite its structural simplicity, Au2S displays very unusual chemical bonding. The very similar and relatively high electronegativities of Au and S rule out any significant metallic or ionic character. Using a simple valence bond (Lewis) model, we argue that the Au2S crystal possesses two different types of covalent bonds: dative and shared. These bonds are distributed in such a way that each Au atom engages in one bond of each kind. The multiple arrangements in space of dative and shared bonds are degenerate, and the multiplicity of configurations imparts the system with multireference character, which is highly unusual for an extended solid. The other striking feature of this system is that common computational (DFT) methods fail quite spectacularly to describe it, with 20% and 400% errors in the equilibrium volume and bulk modulus, respectively. We explain this by the poor treatment of static correlation in common density-functional approximations. The fact that the solid is structurally very simple, yet presents unique chemical bonding and is unmodelable using current DFT methods, makes it an interesting case study and a computational challenge.

Quantitative Electron Delocalization in Solids from Maximally Localized Wannier Functions.

Electron delocalization is the quantum-mechanical principle behind chemical concepts such as aromaticity, resonance, and bonding. A common way to measure electron delocalization in the solid state is through the visualization of maximally localized Wannier functions, a method similar to using localized orbitals in molecular quantum chemistry. Although informative, this method can only provide qualitative information and is essentially limited by the arbitrariness in the choice of orbital rotation. Quantitative orbital-independent interatomic delocalization indices can be calculated by integration inside of atomic regions of probability densities obtained from the system's wave function. In particular, Bader's delocalization indices are very informative, but typically expensive to calculate. In this article, we present a fast method to obtain the localization and delocalization indices in a periodic solid under the plane-wave/pseudopotential approximation. The efficiency of the proposed method hinges on the use of grid-based atomic integration techniques and maximally localized Wannier functions. The former enables the rapid calculation of all atomic overlap integrals required in the construction of the delocalization indices. The latter allows discarding the overlaps between maximally localized Wannier functions whose centers are far enough apart. Using the new method, all localization and delocalization indices in solids with dozens of atoms can be calculated in hours on a desktop computer. Illustrative examples are presented and studied: some simple and molecular solids, polymeric nitrogen, intermolecular delocalization in 10 phases of ice, and the self-ionization of ammonia under pressure. This work is an important step toward the quantitative description of chemical bonding in solids under pressure.

Advanced capabilities for materials modelling with Quantum ESPRESSO.

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

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.

Transferable Atom-Centered Potentials for the Correction of Basis Set Incompleteness Errors in Density-Functional Theory.

Recent progress in the accurate calculation of noncovalent interactions has enabled density-functional theory (DFT) to model systems relevant in biological and supramolecular chemistry. The application of DFT methods using atom-centered Gaussian basis sets to large systems is limited by the number of basis functions required to accurately model thermochemistry and, in particular, weak intermolecular interactions. Basis set incompleteness error (BSIE) arising from the use of incomplete basis sets leads to erroneous intermolecular energies, bond dissociation energies, and structures. In this article, we develop a correction for BSIE in DFT calculations using basis set incompleteness potentials (BSIP). BSIPs are atom-based one-electron potentials (ACPs) with the same functional form as effective core potentials (ECP) that are designed to correct the effects of BSIE in properties that are linear mappings of the energy. We present a systematic way of developing general, error-correcting ACPs and apply this technique to generate BSIPs for eight common elements in organic and biological systems (H, C, N, O, F, P, S, and Cl). Two BSIPs were optimized for use with the scaled MINI (MINIs) and MINIs(d) basis sets and were designed to correct for the impacts of BSIE on noncovalent binding energies and intra/intermolecular geometries. BSIPs developed for use with 6-31G*, pc-1, and 6-31+G** basis sets also correct for the effects of BSIE on bond dissociation energies, which enables the study of chemical reactions in very large systems. BSIPs can be used with any density functional in any electronic structure program that implements ECPs. Our BSIPs add very little to the computational cost provided an efficient ECP implementation is used. Our results support the use of BLYP-D3/MINIs-BSIP as a computationally inexpensive and more accurate alternative to other approaches (e.g., B3LYP/6-31G* and BP86/6-31G*) in protein and supramolecular structural studies.

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

Accurate energy ranking is a key facet to the problem of first-principles crystal-structure prediction (CSP) of molecular crystals. This work presents a systematic assessment of B86bPBE-XDM, a semilocal density functional combined with the exchange-hole dipole moment (XDM) dispersion model, for energy ranking using 14 compounds from the first five CSP blind tests. Specifically, the set of crystals studied comprises 11 rigid, planar compounds and 3 co-crystals. The experimental structure was correctly identified as the lowest in lattice energy for 12 of the 14 total crystals. One of the exceptions is 4-hydroxythiophene-2-carbonitrile, for which the experimental structure was correctly identified once a quasi-harmonic estimate of the vibrational free-energy contribution was included, evidencing the occasional importance of thermal corrections for accurate energy ranking. The other exception is an organic salt, where charge-transfer error (also called delocalization error) is expected to cause the base density functional to be unreliable. Provided the choice of base density functional is appropriate and an estimate of temperature effects is used, XDM-corrected density-functional theory is highly reliable for the energetic ranking of competing crystal structures.

4-[(1-Benzyl-1H-1,2,3-triazol-4-yl)meth-oxy]benzene-1,2-dicarbo-nitrile: crystal structure, Hirshfeld surface analysis and energy-minimization calculations.

In the solid state, the title compound, C18H13N5O, adopts a conformation whereby the phenyl ring and meth-oxy-benzene-1,2-dicarbo-nitrile residue (r.m.s. deviation of the 12 non-H atoms = 0.041 Å) lie to opposite sides of the central triazolyl ring, forming dihedral angles of 79.30 (13) and 64.59 (10)°, respectively; the dihedral angle between the outer rings is 14.88 (9)°. This conformation is nearly 7 kcal mol(-1) higher in energy than the energy-minimized structure which has a syn disposition of the outer rings, enabling intra-molecular π-π inter-actions. In the crystal, methyl-ene-C-H⋯N(triazol-yl) and carbo-nitrile-N⋯π(benzene) inter-actions lead to supra-molecular chains along the a axis. Supra-molecular layers in the ab plane arise as the chains are connected by benzene-C-H⋯N(carbo-nitrile) inter-actions; layers stack with no directional inter-actions between them. The specified inter-molecular contacts along with other, weaker contributions to the supra-molecular stabilization are analysed in a Hirshfeld surface analysis.

Exchange-Correlation Effects for Noncovalent Interactions in Density Functional Theory.

In this article, we develop an understanding of how errors from exchange-correlation functionals affect the modeling of noncovalent interactions in dispersion-corrected density-functional theory. Computed CCSD(T) reference binding energies for a collection of small-molecule clusters are decomposed via a molecular many-body expansion and are used to benchmark density-functional approximations, including the effect of semilocal approximation, exact-exchange admixture, and range separation. Three sources of error are identified. Repulsion error arises from the choice of semilocal functional approximation. This error affects intermolecular repulsions and is present in all n-body exchange-repulsion energies with a sign that alternates with the order n of the interaction. Delocalization error is independent of the choice of semilocal functional but does depend on the exact exchange fraction. Delocalization error misrepresents the induction energies, leading to overbinding in all induction n-body terms, and underestimates the electrostatic contribution to the 2-body energies. Deformation error affects only monomer relaxation (deformation) energies and behaves similarly to bond-dissociation energy errors. Delocalization and deformation errors affect systems with significant intermolecular orbital interactions (e.g., hydrogen- and halogen-bonded systems), whereas repulsion error is ubiquitous. Many-body errors from the underlying exchange-correlation functional greatly exceed in general the magnitude of the many-body dispersion energy term. A functional built to accurately model noncovalent interactions must contain a dispersion correction, semilocal exchange, and correlation components that minimize the repulsion error independently and must also incorporate exact exchange in such a way that delocalization error is absent.

Predicting Energetics of Supramolecular Systems Using the XDM Dispersion Model.

In this article, we examine the ability of the exchange-hole dipole moment (XDM) model of dispersion to treat large supramolecular systems. We benchmark several XDM-corrected functionals on the S12L set proposed by Grimme, which comprises large dispersion-bound host-guest systems, for which back-corrected experimental and Quantum Monte Carlo (QMC) reference data are available. PBE-XDM coupled with the relatively economical and efficient pc-2-spd basis set gives excellent statistics (mean absolute error (MAE) = 1.5 kcal/mol), below the deviation between experimental and QMC data. When compared only to the (more accurate) QMC results, PBE-XDM/pc-2-spd (MAE = 1.2 kcal/mol) outperforms all other dispersion-corrected DFT results in the literature, including PBE-dDsC/QZ4P (6.2 kcal/mol), PBE-NL/def2-QZVP (4.7 kcal/mol), PBE-D2/def2-QZVP' (3.5 kcal/mol), PBE-D3/def2-QZVP'(2.3 kcal/mol), M06-L/def2-QZVP (1.9 kcal/mol), and PBE-MBD (1.8 kcal/mol), with no significant bias (mean error (ME) = 0.04 kcal/mol). PBE-XDM/pc-2-spd gives binding energies relatively close to the complete basis-set limit and does not necessitate the use of counterpoise corrections, which facilitates its use. The dipole-quadrupole and quadrupole-quadrupole pairwise dispersion terms (C8 and C10) are critical for the correct description of the dimers. XDM-corrected functionals different from PBE that work well for small dimers do not yield good accuracy for the large supramolecular systems in the S12L, presenting errors that scale linearly with the dispersion contribution to the binding energy.

Halogen Bonding from Dispersion-Corrected Density-Functional Theory: The Role of Delocalization Error.

Halogen bonds are formed when a Lewis base interacts with a halogen atom in a different molecule, which acts as an electron acceptor. Due to its charge transfer component, halogen bonding is difficult to model using many common density-functional approximations because they spuriously overstabilize halogen-bonded dimers. It has been suggested that dispersion-corrected density functionals are inadequate to describe halogen bonding. In this work, we show that the exchange-hole dipole moment (XDM) dispersion correction coupled with functionals that minimize delocalization error (for instance, BH&HLYP, but also other half-and-half functionals) accurately model halogen-bonded interactions, with average errors similar to other noncovalent dimers with less charge-transfer effects. The performance of XDM is evaluated for three previously proposed benchmarks (XB18 and XB51 by Kozuch and Martin, and the set proposed by Bauzá et al.) spanning a range of binding energies up to ∼50 kcal/mol. The good performance of BH&HLYP-XDM is comparable to M06-2X, and extends to the "extreme" cases in the Bauzá set. This set contains anionic electron donors where charge transfer occurs even at infinite separation, as well as other charge transfer dimers belonging to the pnictogen and chalcogen bonding classes. We also show that functional delocalization error results in an overly delocalized electron density and exact-exchange hole. We propose intermolecular Bader delocalization indices as an indicator of both the donor-acceptor character of an intermolecular interaction and the delocalization error coming from the underlying functional.