Quantum Chemical Methods Research Articles

Conformations of α-cyclodextrin and its role on the stability of inclusion complexes in aqueous solution

α-Cyclodextrin (αCD), a cyclic carbohydrate polymer, presents a wealth of opportunities for drug delivery and various industrial applications. Its high affinity and selectivity in encapsulating target molecules have been well-documented. However, the influence of αCD's conformational variations on its encapsulation capacity remains a promising area for further exploration. This study explores the conformational dynamics of αCD and its relationship with the formation of inclusion complexes (ICs) in aqueous solutions, focusing on understanding the forces driving these dynamics and the formation of stable ICs. Classical molecular dynamics (CMD) demonstrate that αCD solvated in water can adopt two conformations: a truncated cone shape with a suitable cavity for encapsulation and a distorted cone shape with a collapsed cavity. The predominant conformation observed in the CMD trajectory of pristine αCD is the distorted cone. However, under complexation conditions with aliphatic molecules, the guest molecule's size dictates the ICs' stability, forcing αCD to maintain the truncated cone conformation. Quantum chemistry methods and electron density analyses (Quantum Theory of Atoms in Molecules and Non-Covalent Interactions index) support CMD observations by characterizing and quantifying non-covalent interactions. Findings indicate that the shift from the truncated to the distorted cone conformation in αCD is primarily driven by intramolecular non-covalent interactions and the reconfiguration of water molecules surrounding αCD. The ICs' analysis displays a significant correlation between the size of the aliphatic chain and the intensity of intermolecular interactions. The strength of these interactions can effectively disrupt the αCD intramolecular non-covalent interactions that lead to a conformational change and, consequently, the loss of the inclusion complex. In conclusion, although αCD's conformational change can affect encapsulation, guest molecules can manipulate the conformational preference. The systematic analysis of non-covalent interactions offers a way to characterize and quantify these forces, enhancing our ability to understand and predict the stability of inclusion complexes.

Study of the potential energy surface of reactions in a system containing <i>i</i>-propyl and <i>n</i>-propyl radicals

The energy pathways of possible decomposition and isomerization reactions of iso-propyl (i-C3H7) and n-propyl (n-C3H7) radicals have been studied by computational methods of quantum chemistry. B3LYP, M062X, MP2, and CBS-QB3 methods are used to localize stationary points on the potential energy surface of a system containing propyl radicals. A number of intermediate compounds formed during the isomerization and decomposition of propyl radicals have been identified, and information has been obtained on their structure and thermochemical parameters. Based on the results of the research, a diagram of the energy levels of the system under consideration was constructed.

Quantum-accurate machine learning potentials for metal-organic frameworks using temperature driven active learning

Understanding structural flexibility of metal-organic frameworks (MOFs) via molecular dynamics simulations is crucial to design better MOFs. Density functional theory (DFT) and quantum-chemistry methods provide highly accurate molecular dynamics, but the computational overheads limit their use in long time-dependent simulations. In contrast, classical force fields struggle with the description of coordination bonds. Here we develop a DFT-accurate machine-learning spectral neighbor analysis potentials for two representative MOFs. Their structural and vibrational properties are then studied and tightly compared with available experimental data. Most importantly, we demonstrate an active-learning algorithm, based on mapping the relevant internal coordinates, which drastically reduces the number of training data to be computed at the DFT level. Thus, the workflow presented here appears as an efficient strategy for the study of flexible MOFs with DFT accuracy, but at a fraction of the DFT computational cost.

One molecule to couple them all: Toward realistic numbers of molecules in multiscale molecular dynamics simulations of exciton-polaritons.

Collective strong coupling of many molecules to the confined light modes of an optical resonator can influence the photochemistry of these molecules, but the origin of this effect is not yet fully understood. To provide atomistic insights, several approaches have been developed based on quantum chemistry or molecular dynamics methods. However, most of these methods rely on coupling a few molecules (or sometimes only one) to a single cavity mode. To reach the strong coupling regime with such a small number of molecules, much larger vacuum field strengths are employed than in experiments. To keep the vacuum field realistic and avoid potential artefacts, the number of coupled molecules should be significantly increased instead, but that is not always possible due to restrictions on computational hardware and software. To overcome this barrier and model the dynamics of an arbitrarily large ensemble of molecules coupled to realistic cavity fields in atomistic molecular dynamics simulations, we propose to coarse-grain subsets of molecules into one or more effective supermolecules with an enhanced dipole moment and concerted dynamics. To verify the validity of the proposed multiscale model, we performed simulations in which we investigated how the number of molecules that are coupled to the cavity affects excited-state intra-molecular proton transfer, polariton relaxation, and exciton transport.

Theoretical Study of the Halogen Concentration Effect on the 1,3-Butadiene Polymerization Catalyzed by the Neodymium-Based Ziegler–Natta System

In this work, an attempt is made to theoretically substantiate the experimentally known facts of the influence of halogen concentration on the catalytic properties of the neodymium-based Ziegler–Natta system. Based on the structural and thermochemical data obtained using modern methods of quantum chemistry, the process of the 1,3-butadiene cis-1,4-polymerization under the model active centers of the neodymium Ziegler–Natta catalysts with different contents of chloride ions was studied. Results are presented that explain the increase in the cis-stereospecificity and activity of the polymerization system with an increase in the content of the chloride ions in the neodymium catalytic system. Reasons were established for the decrease in the concentration of active centers relative to the introduced Nd(III) with an excess of chloride ions and the occurrence of the anti-syn isomerization as a source of the formation of the trans-1,4-structures in the cis-1,4-polybutadiene.

Simulation of lithium hydroxide decomposition using deep potential molecular dynamics.

Chemical reactions and vapor-liquid equilibria for molten lithium hydroxide (LiOH) were studied using molecular dynamics simulations and a deep potential (DP) model. The neural network for the model was trained on quantum density functional theory data for a range of conditions. The DP model allows simulations over timescales of hundreds of ns, which provide equilibrium compositions for the systems of interest. Single-phase NPT simulations of the liquid show the decomposition of LiOH into lithium oxide (Li2O) and dissolved water (H2O). These DP results were validated by direct abinitio molecular dynamics simulations that confirmed the accuracy of the model with respect to reaction kinetics and equilibrium properties of the melt. The reactive vapor-liquid behavior of this system was subsequently studied using direct coexistence interfacial DP simulations. Partial pressures of H2O in the vapor are found to be in close agreement with available experimental measurements. By fitting temperature-dependent expressions for the reaction equilibrium and Henry's law constants, the equilibrium composition for any given initial composition and temperature can be quantitatively modeled. For high initial concentrations of Li2O or H2O, mixtures of LiOH + Li2O/H2O are found to undergo phase separation. The present study illustrates how DP-based molecular dynamics simulations can be used for quantitative modeling of multiphase reactive behavior with the accuracy of the underlying abinitio quantum chemical methods.

The Performance of Amino‐ and Hydroxy‐Substituted Benzothiazoles in Inhibiting the Corrosion of Carbon Steel in HCl and the Molecular‐Level Mechanisms

AbstractIn the pickling process and acidizing program for oil wells, the acidic corrosion of metals is a problem that needs to be addressed. Various acid corrosion inhibitors have been studied and used to mitigate the acidic corrosion of carbon steel. In this paper, the corrosion inhibition of 2‐aminobenzothiazole (2 N‐BT), 2‐amino‐4‐hydroxybenzothiazole (2 N4O‐BT), and 2‐amino‐6‐hydroxybenzothiazole (2 N6O‐BT) on carbon steel in 0.5 mol/L HCl was investigated using electrochemical and quantum chemical methods. All three molecules exhibited corrosion inhibition effects. Compared to 2 N‐BT, 2 N4O‐BT and 2 N6O‐BT showed less sensitivity to the environmental conditions and the surface state of the metal. Among them, 0.0010 mol/L 2 N6O‐BT demonstrated the highest and most persistent corrosion inhibition, exhibiting a mixed inhibition mechanism with cathodic inhibition dominance. The adsorption of 2 N6O‐BT on the carbon steel surface was found to be non‐uniform, preferentially adsorbing at certain active sites on the surface, following Freundlich‐Langmuir thermodynamic characteristics. It showed initial strongly adsorbed points and weakly adsorbed regions. With continued adsorption of 2 N6O‐BT, the differences between strongly adsorbed points and weakly adsorbed regions decreased. The introduction of hydroxyl groups, especially in 2 N6O‐BT, extended the negative potential region and enhanced the coordination activity of the molecule, generating the orbital distribution that was advantageous to flat adsorption and the formation of feedback bonds. This provided a molecular structural basis for the excellent corrosion inhibition properties of 2 N6O‐BT.

Role of Cyclic Ketene Dithioacetals in Free Radical Polymerization of Vinyl Chloride

AbstractThe role of the sulfur analog of cyclic ketene acetals in the synthesis of polyvinyl chloride is examined in this study. In this context, whether 2‐methylene‐1,3‐dithiolane (S‐CKA5), 2‐methylene‐1,3‐dithione (S‐CKA6), and 2‐methylene‐1,3‐dithiepane (S‐CKA7) monomers are involved in the radical polymerization of vinyl chloride through the ring opening reaction is examined by quantum chemical methods. In light of calculations at the M06‐2X/6‐31+G(d) level, it is concluded that, in general, S‐CKAs undergo little or no ring‐opening and form block copolymers, mainly with the homopolymerization of S‐CKAs and their ring‐retaining step. It is determined that S‐CKA7 is the most prone to ring‐opening reaction and inserting dithioate links to the polymer backbone. However, the radical ring‐opening of S‐CKA7 is strongly reversible, as in other S‐CKAs.

Synthesis, Structural, Spectroscopic (NMR, FT-IR and UV-vis), NLO, in silico (ADMET and Molecular Docking) and DFT Investigations of a Flavonol Derivative 2-(4-chlorophenyl)-7-fluoro-3-hydroxy-4H-chromen-4-one

The geometric, spectroscopic and electronic features of the newly synthesized 3-Hydroxy-2-(4-chlorophenyl)-7-fluoro-4H-chromen-4-one have been analyzed using a combination of single crystal XRD, FT-IR, NMR shifts, and UV-Vis. spectroscopic methods both experimentally and theoretically. The molecule has crystallized in orthorhombic space group Pca21 and it has stabilized with C-H···O, O-H···O intra-molecular and O-H···O inter-molecular interactions. The geometric parameters (bond lengths and bond angles), vibrational wavenumbers, 1H and 13C NMR chemical shifts, UV-Vis. electronic transitions, the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital) analyses, NLO (non-linear optical properties) and the MEP (molecular electrostatic potential) surface have been computed by using the DFT/B3LYP quantum chemical method with 6-311++G(d,p) level of theory to compare with the experimental findings. Absorption bands of the molecule have computed around 300 and 360 nm, while observed at 244, 312 and 344 nm in the experimental UV-Vis. spectrum. Moreover, the mean polarizability value of the compound has been calculated 6.47 times greater than urea. The objective of the in silico investigation was to ascertain the biological effect profile of the title compound. The ADMETlab 2.0 web service has been employed to analyze the physicochemical, medicinal chemistry, metabolism, distribution, absorption, excretion and toxicity features of the compound. Its protein kinase CK2 inhibitory activity for the target macromolecule 5M4U has been investigated by means of a molecular docking study to investigate the anti-cancer activity of our flavonol derivative compound.

Solvation and its influence on the electronic structure and pharmacological activity of 2-fluoro-6-trifluromethyl acetophenone

The molecular framework and vibrational spectra of 2′-Fluoro-6′-Trifluoromethyl Acetophenone (MA3) in diverse solvent environments are being studied using quantum chemistry methods like DFT. The structure was successfully optimized using gas phase and solvent phases such as ethanol, diethyl sulfoxide, chloroform, and diethyl ether. Using FT-Raman and FT-IR techniques, both theoretical and experimental scenarios were examined. The IEFPCM model was used to explore the electronic properties, including HOMO-LUMO gaps, UV–Vis spectra, NBO, Mulliken analysis, and MEP, in various solvents. The TD-DFT approach and IEFPCM model were utilized to replicate the UV spectra. The Fukui function helped locate reactive sites and understand chemical interactions. Comprehensive topological analysis using Multiwfn – 3.8 suite integrated RDG, ALIE, ELF, and LOL to identify key binding sites and weak interactions. The molecular docking studies highlighted the compound’s binding affinities with target proteins, showcasing its potential pharmacological applications. This research underscores the critical role of solvation in determining the electronic and structural properties of MA3, paving the way for its application in drug development and other fields.

Investigation of dual inhibition of antibacterial and antiarthritic drug candidates using combined approach including molecular dynamics, docking and quantum chemical methods

Emerging antibiotic resistance in bacteria threatens immune efficacy and increases susceptibility to bone degradation and arthritic disorders. In our current study, we utilized a three-layer in-silico screening approach, employing quantum chemical methods, molecular docking, and molecular dynamic methods to explore the novel drug candidates similar in structure to floroquinolone (ciprofloxacin). We investigated the interaction of novel similar compounds of ciprofloxacin with both a bacterial protein S. aureus TyrRS (1JIJ) and a protein associated with gout arthritis Neutrophil collagenase (3DPE). UTIs and gout are interconnected through the elevation of uric acid levels. We aimed to identify compounds with dual functionality: antibacterial activity against UTIs and antirheumatic properties. Our screening based on several methods, sorted out six promising ligands. Four of these (L1, L2, L3, and L6) demonstrated favorable hydrogen bonding with both proteins and were selected for further analysis. These ligands showed binding affinities of −8.3 to −9.1 kcal/mol with both proteins, indicating strong interaction potential. Notably, L6 exhibited highest binding energies of −9.10 and −9.01 kcal/mol with S. aureus TyrRS and Neutrophil collagenase respectively. Additionally, the pkCSM online database conducted ADMET analysis on all lead ligand suggested that L6 might exhibit the highest intestinal absorption and justified total clearance rate. Moreover, L6 showed a best predicted inhibition constant with both proteins. The average RMSF values for all complex systems, namely L1, L2, L3 and L6 are 0.43 Å, 0.57 Å, 0.55 Å, and 0.51 Å, respectively where the ligand residues show maximum stability. The smaller energy gap of 3.85 eV between the HOMO and LUMO of the optimized molecule L1 and L6 suggests that these are biologically active compound. All the selected four drugs show considerable stabilization energy ranging from 44.78 to 103.87 kcal/mol, which means all four compounds are chemically and physically stable. Overall, this research opens exciting avenues for the development of new therapeutic agents with dual functionalities for antibacterial and antiarthritic drug designing.

Influence of the Fe(II) Spin State on Iron-Ligand Bonds in Heme Model Iron-PorphyrinComplexes with 4, 5 and 6 Ligands.

In this work heme models with four [Fe(II)(P)], five [Fe(II)(P)Im], [Fe(II)(P)(Im)O2] and six ligands [Fe(II)(P)(Im)O2], where P = porphyrin, with different spin states (ms =5, 3 and 1) of the iron atom were investigated using relativistic-corrected quantum chemistry methods (PW6B95-D3-DKH/jorge-TZP-DKH). Dependence of the iron-ligand bond properties on (i) spin state and (ii) number of ligands were analyzed using natural bond orbital analysis, electron density topology, electrostatic potential and electron localization function. It is shown that reversible binding of O2 is possible in case of formation of semicoordination bond between Fe(II) and imidazole. Binding of the fifth and sixth ligand from the energetic and orbital points of view is more favorable for the triplet Fe(II) state. At the same time for the six-coordinated complex [Fe(II)(P)(Im)O2] interconversion of Fe(II) electrons of valent 3d orbital from quintet to triplet and vice versa is possible under thermal fluctuations (energy barriers less than 2 kcal/mol).

Quantum chemistry − guided design of luminescent Triphenylene − based co-crystals: Unveiling heavy atom for enhanced fluorescence lifetime

This study employed quantum chemical methods to predict and synthesize three luminescent cocrystals. Utilizing Triphenylene as the electron donor and 1,2,4,5-tetracyanobenzene (TCNB), 2,3,5,6-tetrafluoroterephthalonitrile (TFP), and 2,3,5,6-tetrachloroterephthalonitrile (TCP) as acceptors, the structures and internal interactions of these cocrystals were analyzed. The predominant interactions observed were charge transfer, hydrogen bonding, and π-π interactions. Notably, the Triphenylene-TCP cocrystal exhibited a significantly extended fluorescence lifetime compared to the other two. Further investigations, employing time-dependent density functional theory (TD-DFT) on Triphenylene-TCP, suggested that intersystem crossing (ISC) and reverse intersystem crossing (RISC) mechanisms contribute to the prolonged fluorescence lifetime. This study offers valuable insights into the design of supramolecular cocrystals to enhance the performance of organic fluorescent materials.

Electric Field Dependence of EPR Hyperfine Coupling Constants.

In this article, we introduce a simple but reliable method to calculate the electric field dependence of the isotropic hyperfine coupling tensor Aiso for free radicals. This dependence, also referred to as the Bloembergen effect, can be of interest in analyzing EPR experiments for solid-state materials but is rarely studied for isolated radicals in the gaseous phase. The proposed method uses the numerical differentiation of the field-perturbed A tensor and, consequently, as a purely numerical method, does not depend on a quantum chemical method used to determine the hyperfine tensor A. To test the performance of the proposed method, we used a set of 28 systems, including seven organic radicals, the majority of which were taken from a recent benchmark study by Bartlett's group. We employed the well-tested and robust density functional theory (DFT) functional, namely CAM-B3LYP, and the variant of the CCSD method based on local pair natural orbitals, namely DLPNO-CCSD to calculate the Aiso tensor itself, and all first derivatives or Bloembergen effect constants ai(1).

Novel MCRs of Isatins: Green Synthesis and Theoretical Study of Novel Thiazinoazepines

This study examined the utilization of an intricate procedure including isatin, α-haloketones, electron-deficient acetylenic chemicals, ammonium acetate, and isothiocyanates in an aqueous solution at standard room temperature. The objective was to produce new thiazinoazepine compounds with substantial yields. The synthesized thiazinoazepines possess NH functional groups with acidic protons and exhibit significant antioxidant action. The synthesized compounds demonstrated antibacterial efficacy against both Gram-positive and Gram-negative bacteria, as evaluated by the disk diffusion method. Quantum chemical methods based on density functional theory have been employed to improve understanding of reaction mechanisms. The employed methodology for the synthesis of thiazinoazepines offers numerous benefits, such as swift reaction kinetics, exceptional product yield, and uncomplicated product isolation.

A semi-automated quantum-mechanical workflow for the generation of molecular monolayers and aggregates.

Organic electronics (OE) such as organic light-emitting diodes or organic solar cells represent an important and innovative research area to achieve global goals like environmentally friendly energy production. To accelerate OE material discovery, various computational methods are employed. For the initial generation of structures, a molecular cluster approach is employed. Here, we present a semi-automated workflow for the generation of monolayers and aggregates using the GFNn-xTB methods and composite density functional theory (DFT-3c). Furthermore, we present the novel D11A8MERO dye interaction energy benchmark with high-level coupled cluster reference interaction energies for the assessment of efficient quantum chemical and force-field methods. GFN2-xTB performs similar to low-cost DFT, reaching DFT/mGGA accuracy at two orders of magnitude lower computational cost. As an example application, we investigate the influence of the dye aggregate size on the optical and electrical properties and show that at least four molecules in a cluster model are needed for a qualitatively reasonable description.

In silico modelling of radiative efficiencies of anthropogenic greenhouse gases

Radiative efficiency (RE) is a climate metric adopted in international reports on climate change to quantify the greenhouse capacity of gases, and hence to guide decision-making processes and drive transitions in the production and utilization of chemicals in different application fields. Key quantities for the determination of the RE of a gas are the atmospheric irradiance profile and the infrared (IR) absorption cross section spectrum. The latter is usually measured experimentally, even though acquiring high-quality IR spectra can pose severe challenges, sometimes limiting the accuracy or the accessible spectral range. While computational quantum chemistry methods have emerged as valuable tools to simulate IR absorption properties, their application to REs estimation is still limited to the use of the double-harmonic approximation, which presents fundamental limitations. In this work, a cost-effective quantum chemical (QC) workflow including non-empirical anharmonic contributions to spectral properties and an automatic identification of conformer distribution is presented for the accurate evaluation of REs using a range of atmospheric irradiance profiles. Different levels of theory are considered, according to the current state-of-the-art, and the accuracy of the QC RE tool is demonstrated with reference to a number of representative halocarbons widely used in refrigeration, manufacturing, and pharmaceutical fields. The results show that REs can be computed with an average accuracy of 5% using double-hybrid functionals, which overshoot the widely used B3LYP method. Finally, the QC methodology is applied to determine the REs of selected halocarbons for which data is limited, or to address some contradictory results appeared in the literature for some species. The outcomes of this work demonstrate that QC anharmonic IR cross section spectra can be used to estimate REs with an accuracy on par with that of experimental measurements, hence applicable to challenging cases for providing data for policymakers as well for screening purposes when seeking new replacement compounds.

Tuning Electron Transfer Coupling and Exchange Interaction in Bis-triarylamine Radical Cations and Dications by Bridge Electron Density.

The influence of the electron density of a bridge connecting two redox centers on both the intervalence hole transfer and the magnetic superexchange was investigated in a series of bridged bis-triarylamine mono- and dications. In this series, the bridge was 2,7-fluorenyl, where the bridge electron density was modified by substituents at the 9-position. For the mixed-valence monocations, the observation of both an intervalence charge transfer (IVCT) band and an absorption band associated with an electron transfer from the bridging fluorene to the triarylamine radical cation centers allowed determination of the electron transfer couplings in the framework of the three-state generalized Mulliken-Hush theory. Comparison of the derived couplings with those obtained from a classical two-state approach demonstrates an enhancement of the electronic coupling which increases with decreasing bridge state energy. For the dicationic diradical counterparts, the singlet-triplet gap (exchange interaction) was determined both experimentally and by quantum chemical methods. Hereby, an increase of antiferromagnetic coupling with a lowering of the bridge state energy by electron donating substituents was observed. Analysis of the involved molecular orbitals suggests that the ferromagnetic coupling is inversely proportional to the square of the bridge energy, which is also supported by the experimental findings. This influence of the bridge state energy on both types of interactions, electron transfer and magnetic exchange, provides a design guideline for fine-tuning the properties of electronically coupled organic redox dyads by variation of the bridge electron density.

Sulfur isotopic fractionation during hydrolysis of carbonyl sulfide

Carbonyl Sulfide (OCS) is the most abundant sulfur-containing gas in the atmosphere, and it is used as a proxy for terrestrial gross primary productivity (GPP). Oceans are the major source of OCS to the atmosphere, produced by photochemical and “dark” reactions. Hydrolysis to H2S and CO2 is the major removal process of OCS from the ocean's surface. Measuring the sulfur isotope values (δ34S) and the isotopic fractionation (ε) associated with these major OCS sources and sinks could decrease the uncertainties in its fluxes. In the current study, we aim to determine the ε during the hydrolysis process of OCS (εh). We used a purge and trap system coupled to a GC/MC-ICPMS to measure δ34S values during hydrolysis under different temperatures (4–40 °C), salinities (0.2–40 g/L), and pH (4–9), representing various natural environmental conditions. In addition, we use the quantum chemical method to calculate the equilibrium εh and compare it to the empirical results. Our results for the low salinity (S =0.2 g/L; pH 8.0) water show a temperature dependency of the εh from −3.9 ‰ ± 0.2 ‰ (4 °C,) to −2.2 ± 0.6 ‰ (40 °C). The higher fractionation at low temperatures has implication for ice-core data interpretation. However, in natural seawater at 4°C and 22 °C (S = 40 g/L, pH 8.2) there was no such temperature dependency and the εh averaged −2.6 ± 0.3 ‰. Thus, it seems that salinity cancels the temperature effect close to the freezing temperature of water. Varying the pH between 4 and 9 (at 22 °C) did not result in any εh trend. Ab-initio calculations suggest that OCS hydrolysis is not controlled by equilibrium. The εh values we report will aid in quantifying the impact of OCS's hydrolysis on the observable sulfur isotopic signature of OCS in oceanic and in freshwater environments. This in turn will facilitate more accurate mass-balance calculations for the OCS budget from the ocean to the atmosphere.

Quantification of Anisotropy in Exchange and Dispersion Interactions: A Simple Model for Physics-Based Force Fields.

In some compounds, exchange repulsion is orientation dependent. However, in contrast to quantum chemical methods that treat exchange explicitly, empirical models assume exchange to be spherically symmetric, yielding an average description only. Here we quantify the anisotropy of exchange and dispersion energy for hydrogen halides and water by probing these compounds with a helium atom using the symmetry-adapted perturbation theory (SAPT). The exchange interaction is reduced by up to 33% due to the σ-hole in hydrogen iodide, depending on the location of the probe. We demonstrate how this anisotropy can be modeled in empirical force fields either using an angle-dependent potential or by introducing virtual sites, reducing the error in the empirical model by a factor of 5 compared to isotropic atoms. Lone-pairs on water, positioned close to perpendicular to the plane of the molecule, on a line with the oxygen atom, and, surprisingly, σ-holes on water both modulate the exchange interaction strongly. Both lone-pairs and σ-holes can be modeled by virtual sites, leading to an 80% reduced error.