Non-covalent interactions atlas benchmark data sets 4: σ-hole interactions

Manipulating σ-Hole Interactions in Halogenated Additives for High-Performance Organic Solar Cells with 19.8 % Efficiency

The incorporation of volatile solid additives has emerged as an effective strategy for enhancing the performance of organic solar cells (OSCs). However, the influence of the electronic structure of these additives on morphological evolution remains insufficiently understood. Herein, 1,4-Dibromobenzene (DBB) and 1,4-Difluoro-2,5-dibromobenzene (DFBB) are introduced as volatile additives into OSCs. Theoretical calculations indicate that DFBB has a higher electrostatic potential extremum and stronger σ-holes interaction compared to DBB, enabling more robust intermolecular interactions with acceptors. The synergistic halogen interactions between DFBB and the active layer matrix balances the differences in crystallinity between the donor and acceptor during the film formation process, promotes the formation of dense molecular packing and ordered orientation, optimizes the vertical composition distribution, and promotes the formation of domain sizes close to the exciton diffusion distance. Consequently, the PM6 : L8-BO-based device treated with DFBB achieves an efficiency of 19.2 % with a fill factor (FF) of 80.8 %, which is superior to the control and DBB. Further validation across various systems, including PM6 : Y6, PM6 : BTP-eC9, and D18 : L8-BO, highlights similar efficiency enhancements, with the D18 : L8-BO system achieving an outstanding PCE of 19.8 %. This work demonstrates that the modulation of σ-hole interactions in volatile additives can effectively optimize multi-scale morphology for high-performance OSCs.

PM6-ML: The Synergy of Semiempirical Quantum Chemistry and Machine Learning Transformed into a Practical Computational Method

Machine learning (ML) methods offer a promising route to the construction of universal molecular potentials with high accuracy and low computational cost. It is becoming evident that integrating physical principles into these models, or utilizing them in a Δ-ML scheme, significantly enhances their robustness and transferability. This paper introduces PM6-ML, a Δ-ML method that synergizes the semiempirical quantum-mechanical (SQM) method PM6 with a state-of-the-art ML potential applied as a universal correction. The method demonstrates superior performance over standalone SQM and ML approaches and covers a broader chemical space than its predecessors. It is scalable to systems with thousands of atoms, which makes it applicable to large biomolecular systems. Extensive benchmarking confirms PM6-ML's accuracy and robustness. Its practical application is facilitated by a direct interface to MOPAC. The code and parameters are available at https://github.com/Honza-R/mopac-ml.

End-Point Affinity Estimation of Galectin Ligands by Classical and Semiempirical Quantum Mechanical Potentials

The use of quantum mechanical potentials in protein-ligand affinity prediction is becoming increasingly feasible with growing computational power. To move forward, validation of such potentials on real-world challenges is necessary. To this end, we have collated an extensive set of over a thousand galectin inhibitors with known affinities and docked them into galectin-3. The docked poses were then used to systematically evaluate several modern force fields and semiempirical quantum mechanical (SQM) methods up to the tight-binding level under consistent computational workflow. Implicit solvation models available with the tested methods were used to simulate solvation effects. Overall, the best methods in this study achieved a Pearson correlation of 0.7-0.8 between the computed and experimental affinities. There were differences between the tested methods in their ability to rank ligands across the entire ligand set as well as within subsets of structurally similar ligands. A major discrepancy was observed for a subset of ligands that bind to the protein via a halogen bond, which was clearly challenging for all the tested methods. The inclusion of an entropic term calculated by the rigid-rotor-harmonic-oscillator approximation at SQM level slightly worsened correlation with experiment but brought the calculated affinities closer to experimental values. We also found that the success of the prediction strongly depended on the solvation model. Furthermore, we provide an in-depth analysis of the individual energy terms and their effect on the overall prediction accuracy.

An orbital-overlap complement to σ-hole electrostatic potentials

A σ-hole is an electron-deficient region of positive electrostatic potential (ESP) opposite from a half-filled p orbital involved in forming a covalent bond. The σ-hole concept helps rationalize directional noncovalent interactions, known as σ-hole bonds, between covalently bonded group V-VII atoms and electron-pair donors. The magnitude and orientation of σ-holes are correlated with the strength and geometry of halogen bonds. However, ESP computed for isolated σ-holes are not always predictive of interaction energies. For example, the σ-holes of isolated CHFBr2 and isolated CH2FI have identical ESP on the molecule surface, but halogen bonds to these molecules generally have different strengths. Here we show that the compact/diffuse nature of the orbitals involved plays an important role. Our orbital overlap distance quantifies the compact/diffuse nature of the "test orbital" that best overlaps with a systems orbitals at each point. The overlap distance captures the response properties of σ-holes: diffuse σ-holes with large overlap distance are typically "softer" and more polarizable. This aids visualization and interpretation. A linear fit to overlap distance and ESP is predictive of the halogen bond strengths of CH3X and CF3X (X = Cl, Br and I). We suggest that the overlap distance will be a useful partner to ESP for characterizing σ-holes.

Assessing Computational Methods to Calculate the Binding Energies of Dimers of Five-Membered Heterocyclic Molecules

Computational electronic structure methods, including ab initio and density functional theory (DFT), have been assessed in calculating the binding energies of 14 five-membered heterocyclic dimers. The configurations were generated using classical molecular dynamics before optimization at the MP2/aug-cc-pVTZ. Benchmark binding energies are calculated at the CCSD(T)/CBS level of theory. Among the ab initio methods, the DLPNO-CCSD(T)/CBS method has the best performance, reproducing CCSD(T)/CBS with a mean absolute deviation (MAD) of 0.17 kcal/mol. In addition, a schematic CCSD(T)/CBS approach perfectly reproduces the canonical CCSD(T)/CBS with a mean absolute error of 0.08 kcal/mol. Regarding DFT functionals, it has been found that counterpoise corrections have negligible effects on the accuracy of the functionals. Furthermore, including the D3 empirical dispersion considerably enhances the accuracy of the DFT functionals. As a result, outstanding performance is noted for the double hybrid functional B2K-PLYP, with a mean absolute error of 0.25 kcal/mol. In addition to the B2K-PLYP double hybrid functional, M05-D3, B97D, M05-2X-D3, M05-2X, M06-HF, M08-HX, M11, TPSSh-D3, and RSX-0DH-D3(BJ) have MAD values lower than 0.5 kcal/mol. These functionals are recommended for further investigations of five-membered heterocyclic clusters.

Using atomic clustering based on structural and electronic descriptors that consider surrounding environment to evaluate local properties of DFT functionals

We developed a method for evaluating the accuracies of the local properties of DFT functionals in detail using a clustering method based on machine learning and structural/electronic descriptors. We generated 36 clusters consistent with human intuition using 30,436 carbon atoms from the QM9 dataset. The results were used to evaluate 13C NMR chemical shifts calculated using 84 DFT functionals. Carbon atoms were grouped based on their similar environments, reducing errors within these groups. This enables more accurate assessment of the accuracy using a specific DFT functional. Therefore, the present atomic clustering provides more detailed insight into accuracy verification.

Differing Effects of Nonlinearity around the Proton Acceptor on CH··O and NH··O H-Bond Strength within Proteins

The effects of deviations from nonlinearity around the carbonyl proton acceptor of an amide group are assessed by DFT quantum chemical calculations for both CH··O and NH··O H-bonds. The proton donors are the imidazole functional group of His and the indole of Trp, which are paired respectively with N-methylacetamide and acetamide. The displacement of either CH or NH group toward the carbonyl O sp2 lone pairs stabilizes the system and strengthens the H-bond. But the two donor groups differ in their response to a shift out of the amide plane. While the NH··O H-bond is weakened by this displacement, a substantial strengthening is observed when the CH donor is moved out of this plane, in one direction versus the other. This pattern is explained on the basis of simple Coulombic considerations.

A structural role for tryptophan in proteins, and the ubiquitous Trp Cδ1-H...O=C (backbone) hydrogen bond

Tryptophan is the most prominent amino acid found in proteins, with multiple functional roles. Its side chain is made up of the hydrophobic indole moiety, with two groups that act as donors in hydrogen bonds: the Nϵ-H group, which is a potent donor in canonical hydrogen bonds, and a polarized Cδ1-H group, which is capable of forming weaker, noncanonical hydrogen bonds. Due to adjacent electron-withdrawing moieties, C-H...O hydrogen bonds are ubiquitous in macromolecules, albeit contingent on the polarization of the donor C-H group. Consequently, Cα-H groups (adjacent to the carbonyl and amino groups of flanking peptide bonds), as well as the Cϵ1-H and Cδ2-H groups of histidines (adjacent to imidazole N atoms), are known to serve as donors in hydrogen bonds, for example stabilizing parallel and antiparallel β-sheets. However, the nature and the functional role of interactions involving the Cδ1-H group of the indole ring of tryptophan are not well characterized. Here, data mining of high-resolution (r ≤ 1.5 Å) crystal structures from the Protein Data Bank was performed and ubiquitous close contacts between the Cδ1-H groups of tryptophan and a range of electronegative acceptors were identified, specifically main-chain carbonyl O atoms immediately upstream and downstream in the polypeptide chain. The stereochemical analysis shows that most of the interactions bear all of the hallmarks of proper hydrogen bonds. At the same time, their cohesive nature is confirmed by quantum-chemical calculations, which reveal interaction energies of 1.5-3.0 kcal mol-1, depending on the specific stereochemistry.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Conformational energies of biomolecules in solution: Extending the MPCONF196 benchmark with explicit water molecules

A prerequisite for the computational prediction of molecular properties like conformational energies of biomolecules is a reliable, robust, and computationally affordable method usually selected according to its performance for relevant benchmark sets. However, most of these sets comprise molecules in the gas phase and do not cover interactions with a solvent, even though biomolecules typically occur in aqueous solution. To address this issue, we introduce a with explicit water molecules solvated version of a gas-phase benchmark set containing 196 conformers of 13 peptides and other relevant macrocycles, namely MPCONF196 [J. Řezáč et al., JCTC 2018, 14, 1254-1266], and provide very accurate PNO-LCCSD(T)-F12b/AVQZ' reference values. The novel solvMPCONF196 benchmark set features two additional challenges beyond the description of conformers in the gas phase: conformer-water and water-water interactions. The overall best performing method for this set is the double hybrid revDSDPBEP86-D4/def2-QZVPP yielding conformational energies of almost coupled cluster quality. Furthermore, some (meta-)GGAs and hybrid functionals like B97M-V and ω B97M-D with a large basis set reproduce the coupled cluster reference with an MAD below 1 kcal mol- 1  . If more efficient methods are required, the composite DFT-method r2 SCAN-3c (MAD of 1.2 kcal mol- 1 ) is a good alternative, and when conformational energies of polypeptides or macrocycles with more than 500-1000 atoms are in the focus, the semi-empirical GFN2-xTB or the MMFF94 force field (for very large systems) are recommended.

Types of noncovalent bonds within complexes of thiazole with CF4 and SiF4

The five-membered heteroaromatic thiazole molecule contains a number of electron-rich regions that could attract an electrophile, namely the N and S lone pairs that lie in the molecular plane, and π-system areas above the plane. The possibility of each of these sites engaging in a tetrel bond (TB) with CF4 and SiF4, as well as geometries that encompass a CH⋯F H-bond, was explored via DFT calculations. There are a number of minima that occur in the pairing of thiazole with CF4 that are very close in energy, but these complexes are weakly bound by less than 2 kcal mol-1 and the presence of a true TB is questionable. The inclusion of zero-point vibrational energies alters the energetic ordering, which is further modified when entropic effects are added. The preferred geometry would thus be sensitive to the temperature of an experiment. Replacement of CF4 by SiF4 leaves intact most of the configurations, and their tight energetic clustering, the ordering of which is again altered as the temperature rises. But there is one exception in that by far the most tightly bound complex involves a strong Si⋯N TB between SiF4 and the lone pair of the thiazole N, with an interaction energy of 30 kcal mol-1. Even accounting for its high deformation energy and entropic considerations, this structure remains as clearly the most stable at any temperature.

SQM2.20: Semiempirical quantum-mechanical scoring function yields DFT-quality protein-ligand binding affinity predictions in minutes

Accurate estimation of protein-ligand binding affinity is the cornerstone of computer-aided drug design. We present a universal physics-based scoring function, named SQM2.20, addressing key terms of binding free energy using semiempirical quantum-mechanical computational methods. SQM2.20 incorporates the latest methodological advances while remaining computationally efficient even for systems with thousands of atoms. To validate it rigorously, we have compiled and made available the PL-REX benchmark dataset consisting of high-resolution crystal structures and reliable experimental affinities for ten diverse protein targets. Comparative assessments demonstrate that SQM2.20 outperforms other scoring methods and reaches a level of accuracy similar to much more expensive DFT calculations. In the PL-REX dataset, it achieves excellent correlation with experimental data (average R2 = 0.69) and exhibits consistent performance across all targets. In contrast to DFT, SQM2.20 provides affinity predictions in minutes, making it suitable for practical applications in hit identification or lead optimization.

Benchmarking Swaths of Intermolecular Interaction Components with Symmetry-Adapted Perturbation Theory

A benchmark database for interaction energy components of various noncovalent interactions (NCIs) along their dissociation curve is one of the essential needs in theoretical chemistry, especially for the development of force fields and machine-learning methods. We utilize DFT-SAPT or SAPT(DFT) as one of the most accurate methods to generate an extensive stock of the energy components, including dispersion energies extrapolated to the complete basis set limit (CBS). Precise analyses of the created data, and benchmarking the total interaction energies against the best available CCSD(T)/CBS values, reveal different aspects of the methodology and the nature of NCIs. For example, error cancellation effects between the S2 approximation and nonexact xc-potentials occur, and large charge transfer energies in some systems, including heavy atoms, can explain the lower accuracy of DFT-SAPT. This method is perfect for neutral complexes containing light nonmetals, while other systems with heavier atoms should be treated carefully. In the last part, a representative data set for all NCIs is extracted from the original data.

Reliable Dimerization Energies for Modeling of Supramolecular Junctions

Accurate estimates of intermolecular interaction energy, ΔE, are crucial for modeling the properties of organic electronic materials and many other systems. For a diverse set of 50 dimers comprising up to 50 atoms (Set50-50, with 7 of its members being models of single-stacking junctions), benchmark ΔE data were compiled. They were obtained by the focal-point strategy, which involves computations using the canonical variant of the coupled cluster theory with singles, doubles, and perturbative triples [CCSD(T)] performed while applying a large basis set, along with extrapolations of the respective energy components to the complete basis set (CBS) limit. The resulting ΔE data were used to gauge the performance for the Set50-50 of several density-functional theory (DFT)-based approaches, and of one of the localized variants of the CCSD(T) method. This evaluation revealed that (1) the proposed "silver standard" approach, which employs the localized CCSD(T) method and CBS extrapolations, can be expected to provide accuracy better than two kJ/mol for absolute values of ΔE, and (2) from among the DFT techniques, computationally by far the cheapest approach (termed "ωB97X-3c/vDZP" by its authors) performed remarkably well. These findings are directly applicable in cost-effective yet reliable searches of the potential energy surfaces of noncovalent complexes.

Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

Relation between Halogen Bond Strength and IR and NMR Spectroscopic Markers

The relationship between the strength of a halogen bond (XB) and various IR and NMR spectroscopic quantities is assessed through DFT calculations. Three different Lewis acids place a Br or I atom on a phenyl ring; each is paired with a collection of N and O bases of varying electron donor power. The weakest of the XBs display a C-X bond contraction coupled with a blue shift in the associated frequency, whereas the reverse trends occur for the stronger bonds. The best correlations with the XB interaction energy are observed with the NMR shielding of the C atom directly bonded to X and the coupling constants involving the C-X bond and the C-H/F bond that lies ortho to the X substituent, but these correlations are not accurate enough for the quantitative assessment of energy. These correlations tend to improve as the Lewis acid becomes more potent, which makes for a wider range of XB strengths.

Accurate three-body noncovalent interactions: the insights from energy decomposition

An impressive collection of accurate two-body interaction energies for small complexes has been assembled into benchmark databases and used to improve the performance of multiple density functional, semiempirical, and machine learning methods. Similar benchmark data on nonadditive three-body energies in molecular trimers are comparatively scarce, and the existing ones are practically limited to homotrimers. In this work, we present a benchmark dataset of 20 equilibrium noncovalent interaction energies for a small but diverse selection of 10 heteromolecular trimers. The new 3BHET dataset presents complexes that combine different interactions including π-π, anion-π, cation-π, and various motifs of hydrogen and halogen bonding in each trimer. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition of the two- and three-body interaction energies shows that 3BHET consists of electrostatics- and dispersion-dominated complexes. The nonadditive three-body contribution is dominated by induction, but its influence on the overall bonding type in the complex (as exemplified by its position on the ternary diagram) is quite small. We also tested the extended SAPT (XSAPT) approach which is capable of including some nonadditive interactions in clusters of any size. The resulting three-body dispersion term (obtained from the many-body dispersion formalism) is mostly in good agreement with the supermolecular CCSD(T)-MP2 values and the nonadditive induction term is similar to the three-body SAPT(DFT) data, but the overall three-body XSAPT energies are not very accurate as they are missing the first-order exchange terms.

Electron density-based protocol to recover the interacting quantum atoms components of intermolecular binding energy

A new approach for obtaining interacting quantum atoms-defined components of binding energy of intermolecular interactions, which bypasses the use of standard six-dimensional integrals and two-particle reduced density matrix (2-RDM) reconstruction, is proposed. To examine this approach, three datasets calculated within the density functional theory framework using the def2-TZVP basis have been explored. The first two, containing 53 weakly bound bimolecular associates and 13 molecular clusters taken from the crystal, were used in protocol refinement, and the third one containing other 20 bimolecular and three cluster systems served as a validation reference. In addition, to verify the performance of the proposed approach on an exact 2-RDM, calculations within the coupled cluster formalism were performed for part of the first set systems using the cc-pVTZ basis set. The process of optimization of the proposed parametric model is considered, and the role of various energy contributions in the formation of non-covalent interactions is discussed with regard to the obtained trends.

A quantum chemical interaction energy dataset for accurately modeling protein-ligand interactions

Fast and accurate calculation of intermolecular interaction energies is desirable for understanding many chemical and biological processes, including the binding of small molecules to proteins. The Splinter ["Symmetry-adapted perturbation theory (SAPT0) protein-ligand interaction"] dataset has been created to facilitate the development and improvement of methods for performing such calculations. Molecular fragments representing commonly found substructures in proteins and small-molecule ligands were paired into >9000 unique dimers, assembled into numerous configurations using an approach designed to adequately cover the breadth of the dimers' potential energy surfaces while enhancing sampling in favorable regions. ~1.5 million configurations of these dimers were randomly generated, and a structurally diverse subset of these were minimized to obtain an additional ~80 thousand local and global minima. For all >1.6 million configurations, SAPT0 calculations were performed with two basis sets to complete the dataset. It is expected that Splinter will be a useful benchmark dataset for training and testing various methods for the calculation of intermolecular interaction energies.

Enhancement of Halogen Bond Strength by Intramolecular H-Bonds

Quantum calculations study the potential of an intramolecular H-bond between the halogen atom (X) of a halobenzene and a substituent placed ortho to it, to amplify the ability of X to engage in a halogen bond (XB) with a Lewis base. H-bonding substituents NH₂, CH₂CH₂OH, CH₂OH, OH, and COOH were added to halobenzenes (X = Cl, Br, I). The amino group had little effect, but those containing OH increased the CX···N XB energy to a NH₃ nucleophile by about 0.5 kcal/mol; the increment associated with COOH is larger, nearly 2 kcal/mol. These energy increments were approximately doubled if two such H-bonding substituents are present. Combining a pair of ortho COOH groups with an electron-withdrawing NO₂ group in the para position has a particularly large effect, raising the XB energy by about 4 kcal/mol, which can amount to as much as a 4-fold magnification.

Strategies for the Design of PEDOT Analogues Unraveled: the Use of Chalcogen Bonds and σ-Holes

In this theoretical study, we set out to demonstrate the substitution effect of PEDOT analogues on planarity as an intrinsic indicator for electronic performance. We perform a quantum mechanical (DFT) study of PEDOT and analogous model systems and demonstrate the usefulness of the ωB97X-V functional to simulate chalcogen bonds and other noncovalent interactions. We confirm that the chalcogen bond stabilizes the planar conformation and further visualize its presence via the electrostatic potential surface. In comparison to the prevalent B3LYP, we gain 4-fold savings in computational time and simulate model systems of up to a dodecamer. Implications for design of conductive polymers can be drawn from the results, and an example for self-doped polymers is presented where modulation of the strength of the chalcogen bond plays a significant role.

Interaction energy of Cl2 and Br2 with H2 O: Exchange, dispersion and density the crucial ingredients

Modern Density Functional Theory models are now suitable for many molecular and condensed phase studies. The study of noncovalent interactions, a well-known drawback, is no longer an insurmountable obstacle through design and empirical corrections. However, using empirical corrections as in the DFT-D methods might not be an all-in-one solution. This work uses a simple system, X₂ -H₂ O with X = Cl or Br, with two different interactions, halogen-bonded (XB) and hydrogen-halogen (HX), to investigate the capability of current density functional approximations (DFA) in predicting interaction energies with eight different exchange-correlation functionals. SAPT(DFT) provides, for all the studied cases, better predictions than the widely used supermolecular approach. In addition, the components of the interaction energy suggest where some of the shortcomings originate in each DFA. The analysis of the functionals used confirms that PBE0 and ω-B97X-D have a physically correct behavior. Using SAPT(DFT) and PBE0, and ω-B97X-D, we obtained the interaction energy of Cl₂ and Br₂ inside different clathrate cages and satisfactorily compared with wavefunction results; hence, the lower and upper limits of this value are defined: Cl₂ @5¹² , -5.3 ± 0.3 kcal/mol; Cl₂ @5¹² 6² , -5.5 ± 0.1 kcal/mol; Br₂ @5¹² 6² , -7.6 ± 1.0 kcal/mol; Br₂ @5¹² 6³ , -10.6 ± 1.0 kcal/mol; Br₂ @5¹² 6⁴ , -10.9 ± 0.8 kcal/mol.

Does a halogen bond require positive potential on the acid and negative potential on the base?

It is usually expected that formation of a halogen bond (XB) requires that a region of positive electrostatic potential associated with a σ or π-hole on the Lewis acid will interact with the negative potential of the base, either a lone pair or π-bond region. Quantum calculations of model systems suggest this not to be necessary. The placement of electron-withdrawing substituents on the base can reverse the sign of the potential in its lone pair or π-bond region to positive, and this base can nonetheless engage in a XB with the positive σ-hole of a Lewis acid. The reverse scenario is also possible in certain circumstances, as a negatively charged σ-hole can form a XB with the negative lone pair region of a base. Despite these classical Coulombic repulsions, the overall electrostatic interaction is attractive in these XBs, albeit only weakly so. The strengths of these bonds are surprisingly insensitive to changes in the partner molecule. For example, even a wide range in the depth of the σ-hole of the approaching acid yields only a minimal change in the strength of the XB to a base with a positive potential.

Competition Between the Two σ-Holes in the Formation of a Chalcogen Bond

A chalcogen atom Y contains two separate σ-holes when in a R₁ YR₂ molecular bonding pattern. Quantum chemical calculations consider competition between these two σ-holes to engage in a chalcogen bond (ChB) with a NH₃ base. R groups considered include F, Br, I, and tert-butyl (tBu). Also examined is the situation where the Y lies within a chalcogenazole ring, where its neighbors are C and N. Both electron-withdrawing substituents R₁ and R₂ act cooperatively to deepen the two σ-holes, but the deeper of the two holes consistently lies opposite to the more electron-withdrawing group, and is also favored to form a stronger ChB. The formation of two simultaneous ChBs in a triad requires the Y atom to act as double electron acceptor, and so anti-cooperativity weakens each bond relative to the simple dyad. This effect is such that some of the shallower σ-holes are unable to form a ChB at all when a base occupies the other site.

XDM-corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy

Molecular crystals are important for many applications, including energetic materials, organic semiconductors, and the development and commercialization of pharmaceuticals. The exchange-hole dipole moment (XDM) dispersion model has shown good performance in the calculation of relative and absolute lattice energies of molecular crystals, although it has traditionally been applied in combination with plane-wave/pseudopotential approaches. This has limited XDM to use with semilocal functional approximations, which suffer from delocalization error and poor quality conformational energies, and to systems with a few hundreds of atoms at most due to unfavorable scaling. In this work, we combine XDM with numerical atomic orbitals, which enable the efficient use of XDM-corrected hybrid functionals for molecular crystals. We test the new XDM-corrected functionals for their ability to predict the lattice energies of molecular crystals for the X23 set and 13 ice phases, the latter being a particularly stringent test. A composite approach using a XDM-corrected, 25% hybrid functional based on B86bPBE achieves a mean absolute error of 0.48 kcal mol^-1 per molecule for the X23 set and 0.19 kcal mol^-1 for the total lattice energies of the ice phases, compared to recent diffusion Monte-Carlo data. These results make the new XDM-corrected hybrids not only far more computationally efficient than previous XDM implementations, but also the most accurate density-functional methods for molecular crystal lattice energies to date.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

A Cost Effective Scheme for the Highly Accurate Description of Intermolecular Binding in Large Complexes

There has been a growing interest in quantitative predictions of the intermolecular binding energy of large complexes. One of the most important quantum chemical techniques capable of such predictions is the domain-based local pair natural orbital (DLPNO) scheme for the coupled cluster theory with singles, doubles, and iterative triples [CCSD(T)], whose results are extrapolated to the complete basis set (CBS) limit. Here, the DLPNO-based focal-point method is devised with the aim of obtaining CBS-extrapolated values that are very close to their canonical CCSD(T)/CBS counterparts, and thus may serve for routinely checking a performance of less expensive computational methods, for example, those based on the density-functional theory (DFT). The efficacy of this method is demonstrated for several sets of noncovalent complexes with varying amounts of the electrostatics, induction, and dispersion contributions to binding (as revealed by accurate DFT-based symmetry-adapted perturbation theory (SAPT) calculations). It is shown that when applied to dimeric models of poly(3-hydroxybutyrate) chains in its two polymorphic forms, the DLPNO-CCSD(T) and DFT-SAPT computational schemes agree to within about 2 kJ/mol of an absolute value of the interaction energy. These computational schemes thus should be useful for a reliable description of factors leading to the enthalpic stabilization of extended systems.

Adjusting the balance between hydrogen and chalcogen bonds

A complex is assembled which pairs a carboxyl group of X₁COOH with a 1,2,5-chalcogenadiazole ring containing substituents on its C atoms. The OH of the carboxyl group donates a proton to a N atom of the ring to form a OH⋯N H-bond (HB), while its carbonyl O engages in a Y⋯O chalcogen bond (ChB) with the ring in which Y = S, Se, Te. The ChB is strengthened by enlarging the size of the Y atom from S to Se to Te. Placement of an electron-withdrawing group (EWG) X₁ on the acid strengthens the HB while weakening the ChB; the reverse occurs when EWGs are placed on the ring. By selection of the proper substituents on the two units, it is possible to achieve a near perfect balance between the strengths of these two bonds. These bond strengths are also reflected in the NMR spectroscopic properties of the chemical shielding of the various atoms and the coupling between the nuclei directly involved in each bond.

Properties and Stabilities of Cyclic and Open Chains of Halogen Bonds

Open and cyclic chains from two to eight units of ICl and IF are constructed and examined by density functional theory (DFT) calculations. These chains contain either I···I or I···X halogen bonds (XBs) where X refers to Cl or F. The closed rings are more stable than the open chains due to the presence of an additional XB and enhanced cooperativity. This pattern is true even for most trimers where there is sizable geometric distortion in the rings. I···F rings are generally more stable than the corresponding I···I cycles as the I···F bond is stronger than I···I even in the simple dimer. However, I···I rings are comparable in energy to I···Cl. It is possible to construct I···I rings of at least as large as eight units, which are held together exclusively by XBs. On the other hand, the maximum possible size of I···X rings is 6. Red shifts are observed in the I-X stretching frequency bands, which magnify as the chain, both cyclic and open, grows longer. The NMR chemical shielding of the I atoms increases for I···I chains but diminishes when I···Cl bonds are present.

Reliable prediction of association (free) energies of supramolecular complexes with heavy main group elements – the HS13L benchmark set

We introduce a set of 13 supramolecular complexes featuring diverse non-covalent interactions with heavy main group elements (Zn, As, Se, Te, Br, I), high charges (−2 up to +4), and large systems with up to 266 atoms (HS13L).

Non-Covalent Interactions Atlas Benchmark Data Sets 5: London Dispersion in an Extended Chemical Space

The Non-Covalent Interactions Atlas (www.nciatlas.org) has been extended with two data sets of benchmark interaction energies in complexes dominated by London dispersion. The D1200 data set of equilibrium geometries provides...