How important are dispersion interactions to the strength of aromatic stacking interactions in solution?

The effect of tethered bi-naphthyls on visible-light promoted alkene-alkene [2 + 2] cycloadditions

Dispersion interactions are ubiquitous weak interactions that can play a role in many chemical events. Tailor-made catalysts and additives can lead to more selective reactions by properly exploiting dispersion interactions. Although radical-π dispersion interactions are known to have an important stabilizing role, this concept has been so far overlooked in synthetic photochemistry. We recently proved that similar dispersion interactions can play a profound impact on several reactions involving an energy transfer step. We present herein a study on the co-catalytic effect of tethered bi-naphthyl derivatives on the visible-light-promoted alkene-alkene [2 + 2] cycloaddition. A library of tethered bi-naphthyl derivatives was prepared in order to evaluate the impact of the tether on the efficiency of the prototypical [2 + 2] cycloaddition. The best performing additives showed a dramatic effect on the efficiency of the cyclization, and a rationalization of their relative efficiency was carried out through DFT modeling. The best co-catalyst allowed one to isolate desired products in good to excellent yields even employing several challenging substrates. These results offer new tools to devise optimized [2 + 2] photocycloaddition methods and provide valuable information for the design of organic co-catalyst that can boost photochemical reactions by exploiting dispersion interactions.

Direct Through-Space Substituent-π Interactions in Noncovalent Arene-Fullerene Assemblies

The arene-arene interactions between electron-rich and deficient aromatics have been less understood. Herein, we focus on a [60]fullerene π-surface as an electron-deficient aromatics. Using a 1H signal of H2O@C60 as a magnetic probe, the presence of benzene-fullerene interactions was confirmed. To investigate substituent effects on the noncovalent arene-fullerene interactions, NMR titration experiments were carried out using an open-[60]fullerene and a series of substituted benzenes, i. e., PhX (X=NO2, CN, Cl, OMe, H, CH3, and NH2), demonstrating a 1 : 2 stoichiometry with a positive correlation between stabilization energies upon the first association (ΔG1) and Hammet constants (σm). The destabilization of the self-assembled structure for X=OMe with a σ-withdrawing nature clearly showed direct through-space substituent-π interactions describable by the Wheeler-Houk model while the second association was suggested to be considerably perturbed by the secondary effects.

Distinction and Quantification of Noncovalent Dispersive and Hydrophobic Effects

The possibilities of comparing computational results of noncovalent interactions with experimental data are discussed, first with respect to intramolecular interactions. For these a variety of experimental data such as heats of formation, crystal sublimation heats, comparison with energy minimized structures, and spectroscopic data are available, but until now largely have not found widespread application. Early force field and QM/MP2 calculations have already shown that the sublimation heats of hydrocarbons can be predicted with an accuracy of ±1%. Intermolecular interactions in solution or the gas phase are always accompanied by difficult to compute entropic contributions, like all associations between molecules. Experimentally observed T∆S values contribute 10% to 80% of the total ∆G, depending on interaction mechanisms within the complexes, such as, e.g., hydrogen bonding and ion pairing. Free energies ∆G derived from equilibrium measurements in solution allow us to define binding increments ∆∆G, which are additive and transferable to a variety of supramolecular complexes. Data from more than 90 equilibrium measurements of porphyrin receptors in water indicate that small alkanes do not bind to the hydrophobic flat surfaces within a measuring limit of ∆G = ±0.5 kJ/mol, and that 20 functions bearing heteroatoms show associations by dispersive interactions with up to ∆G = 8 kJ/mol, roughly as a function of their polarizability. Aromatic systems display size-dependent affinities ∆G as a linear function of the number of π-electrons.

A density functional theory study on interactions in water-bridged dimeric complexes of lignin

Lignin is the main plant cell wall component responsible for recalcitrance in the process of lignocellulosic biomass conversion into biofuels. The recalcitrance and insolubility of lignin in different reaction media are due in part to the hydrogen bonds and π interactions that hold syringyl (S) and guaiacyl (G) units together and promote the formation of stable water-bridged dimeric complexes (WBDCs): S⋯G and S⋯S, in native lignin. The current understanding of how each type of interaction influences the stability of these complexes within lignin native cell walls is still limited. Here, we found by DFT calculations that hydrogen bonding is more dominant than π-stacking interaction between aromatic rings of WBDCs. Although there is a stronger interaction of hydrogen bonds between subunits and water and higher π-stacking interaction in the S⋯S complex compared to the S⋯G complex, the former complex is less thermodynamically stable than the latter due to the entropic contribution coming from the methoxy substituents in the S-unit. Our results demonstrate that the methoxylation degree of lignin units does not significantly influence the structural geometries of WBDCs; if anything, an enhanced dispersion interaction between ring aromatics results in quasi-sandwich geometries as found in "coiled" lignin structures in the xylem tissue of wood. In the same way as that with ionic liquids, polar solvents can dissolve S-lignin by favorable interactions with the aliphatic hydroxyl group in the α-position as the key site or the aromatic hydroxyl group as the secondary site.

Advances and Prospects in Understanding London Dispersion Interactions in Molecular Chemistry

London dispersion (LD) interactions are the main contribution of the attractive part of the van der Waals potential. Even though LD effects are the driving force for molecular aggregation and recognition, the role of these omnipresent interactions in structure and reactivity had been largely underappreciated over decades. However, in the recent years considerable efforts have been made to thoroughly study LD interactions and their potential as a chemical design element for structures and catalysis. This was made possible through a fruitful interplay of theory and experiment. This review highlights recent results and advances in utilizing LD interactions as a structural motif to understand and utilize intra- and intermolecularly LD-stabilized systems. Additionally, we focus on the quantification of LD interactions and their fundamental role in chemical reactions.

Probing Non-Covalent Interactions through Molecular Balances: A REG-IQA Study

The interaction energies of two series of molecular balances (1-X with X = H, Me, OMe, NMe2 and 2-Y with Y = H, CN, NO2, OMe, NMe2) designed to probe carbonyl…carbonyl interactions were analysed at the B3LYP/6-311++G(d,p)-D3 level of theory using the energy partitioning method of Interacting Quantum Atoms/Fragments (IQA/IQF). The partitioned energies are analysed by the Relative Energy Gradient (REG) method, which calculates the correlation between these energies and the total energy of a system, thereby explaining the role atoms have in the energetic behaviour of the total system. The traditional "back-of-the-envelope" open and closed conformations of molecular balances do not correspond to those of the lowest energy. Hence, more care needs to be taken when considering which geometries to use for comparison with the experiment. The REG-IQA method shows that the 1-H and 1-OMe balances behave differently to the 1-Me and 1-NMe2 balances because the latter show more prominent electrostatics between carbonyl groups and undergoes a larger dihedral rotation due to the bulkiness of the functional groups. For the 2-Y balance, REG-IQA shows the same behaviour across the series as the 1-H and 1-OMe balances. From an atomistic point of view, the formation of the closed conformer is favoured by polarisation and charge-transfer effects on the amide bond across all balances and is counterbalanced by a de-pyramidalisation of the amide nitrogen. Moreover, focusing on the oxygen of the amide carbonyl and the α-carbon of the remaining carbonyl group, electrostatics have a major role in the formation of the closed conformer, which goes against the well-known n-π* interaction orbital overlap concept. However, REG-IQF shows that exchange-correlation energies overtake electrostatics for all the 2-Y balances when working with fragments around the carbonyl groups, while they act on par with electrostatics for the 1-OMe and 1-NMe2. REG-IQF also shows that exchange-correlation energies in the 2-Y balance are correlated to the inductive electron-donating and -withdrawing trends on aromatic groups. We demonstrate that methods such as REG-IQA/IQF can help with the fine-tuning of molecular balances prior to the experiment and that the energies that govern the probed interactions are highly dependent on the atoms and functional groups involved.

Molecular Wind-Up Meter for the Quantification of London Dispersion Interactions

ConspectusThe experimental quantification of interactions on the molecular level provides the necessary basis for the design of functional materials and chemical processes. The interplay of multiple parameters and the small quantity of individual interactions pose a special challenge for such endeavors. The common method is the use of molecular balances, which can exist in two different states. Thereby, a stabilizing interaction can occur in one of the states, favoring its formation and thus affecting the thermodynamic equilibrium of the system. One challenge is determining the change in this equilibrium since various analytical methods could not be applied to fast-changing equilibria. A new and promising method for quantifying molecular interactions is the use of Molecular Wind-up Meters (MWM) in which the change in kinetics, rather than the effect on thermodynamics, is investigated. An MWM is transformed with an energy input (e.g. irradiation) into a metastable state. Then, the rate of thermal transformation back to the ground state is measured. The strength of interactions present in the metastable state controls the kinetics of the back reactions, allowing direct correlation. The advantage of this approach lies in the high sensitivity (energy differences can be larger by 1 order of magnitude) and, in general, allows the use of a broader range of solvents and analytical methods. An Azobenzene-based MWM has been established as a powerful tool to quantify London dispersion interactions. London dispersion (LD) represents the attractive part of the van der Waals potential. Although neglected in the past due to its weak character, it has been shown that the influence of LD on the structure, stability, and reactivity of matter can be decisive. Especially in larger molecules, its energy contribution increases overproportionately with the number of atoms, which has sparked increasing interest in the use of so-called dispersion energy donors (DED) as a new structural element. Application of the azobenzene-based MWM not only allowed the differentiation of bulkiness, but also systematically addressed the influence of the length of n-alkyl chains. Additionally, the solvent influence on LD was studied. Based on the azobenzene MWM, an increment system has been proposed, allowing a rough estimate of the effect of a specific DED.

Boosting Energy-Transfer Processes via Dispersion Interactions

The generation of open-shell intermediates under mild conditions has opened broad synthetic opportunities during this century. However, these reactive species often require a case specific and tailored tuning of experimental parameters in order to efficiently convert substrates into products. We report a general approach that can overcome these ubiquitous limitations for several visible-light promoted energy-transfer processes. The use of either naphthalene (5-20 equiv.) or simple binaphthyl derivatives (10-30 mol %) greatly increases their efficiency, giving rise to a new strategy for catalysis. The trend is consistent among different media, photocatalysts, light sources and substrates, allowing one to improve existing methods, to more easily optimize conditions for new ones, and, moreover, to disclose otherwise inaccessible reaction pathways.

Contributions of London Dispersion Forces to Solution-Phase Association Processes

ConspectusDespite their ubiquity and early discovery, London dispersion forces are often overlooked. This is due, in part, to the difficulty in assessing their contributions to molecular and polymeric structure, stability, properties, and reactivities. However, recent advances in modeling have revealed that dispersion interactions play an important role in many important chemical and biological processes. Experimental confirmation of their impact in solution has been challenging, leading to controversies about their relative importance.In the course of studying noncovalent interactions using molecular devices, our understanding and appreciation for the importance of dispersion interactions have evolved. This Account follows this intellectual journey by using examples from the literature. The goals are twofold: to describe recent advances in understanding the interaction and to provide guidance to researchers studying weak noncovalent interactions. However, first, the experimental methods for measuring the effects of dispersion interactions and the strategies for isolating their influence are described. These include the design of molecular devices to measure these weak noncovalent interactions and the strategies to disentangle the solvation, solvophobic, and dispersion components of the resulting equilibria.The literature examples are organized around five fundamental questions. (1) Do dispersion interactions have a measurable effect on solution equilibria? (2) To what extent do solvents attenuate or compensate for dispersion interactions? (3) To what extent do the solvation and solvophobic terms influence the dispersion equilibria? (4) Can we predict whether a system will form attractive dispersion or repulsive steric interactions? (5) Can the dispersion term be isolated and interrogated? We were often surprised by the answers to these questions. In each case, we describe how the systems were designed to address these questions and discuss possible interpretations of the results.While dispersion interactions in solution were weak (usually <1 kcal/mol), their influence on complexation and conformational equilibria can be observed and measured. This underscores the significance of these interactions in molecular recognition, coordination chemistry, reaction design, and catalysis. The solvent components of the dispersion equilibria can also be significant. Therefore, the isolation of the dispersion contributions from the solvation and solvophobic effects represents an ongoing challenge. The experimental studies also provide important benchmarks and offer valuable insights to help refine the next generation of computational solvent models.

Dispersion Interactions in Condensed Phases and inside Molecular Containers

ConspectusThe past decade has seen significant progress in the understanding and appreciation of the importance of London dispersion interactions (LDIs) in supramolecular systems and solutions. The Slater-Kirkwood formula relates LDIs to the molecular polarizabilities of the two interacting molecular species (α) and their interaction distance (a dependence of R-6). When advancing arguments related to intermolecular interactions, it is frequently assumed that molecules with larger molecular polarizabilities are more amenable to larger LDIs. However, arguments related to molecular polarizabilities are not always transferable to the condensed phase. In fact, the underlying bulk and molecular polarizabilities of common solvents show opposing trends. The intuitive concept that aromatic molecules are more polarizable than saturated hydrocarbons and that perfluorinated molecules are less polarizable than saturated hydrocarbons applies to the condensed phase only. When treating association phenomena in solution, where LDIs are generally very attenuated, the use of bulk polarizabilities is recommended, which are experimentally accessible through either refractive index measurements or suitable solvatochromic probes. Such probes can also be used to assess polarizabilities inside molecular container compounds, such as cucurbit[n]urils (CBn), cyclodextrins, calixarenes, and hemicarcerands. These macrocyclic cavities can have extreme microenvironments. For example, the inner concave phase of CB7 has been shown to be weakly polarizable, falling in between the gas phase and perfluorohexane; those of β-cyclodextrin and p-sulfonatocalix[4]arene have been found to be similarly polarizable as water and alkanes, respectively, and the inside of hemicarcerands displays a very large bulk polarizability, exceeding that of diiodomethane. CBn compounds are privileged molecular container compounds, which we exemplify in this Account through case studies. (1) CBn macrocycles are prime water-soluble receptors for hydrocarbons, allowing for the reduction of the binding free energies to two components: the hydrophobic effect and dispersion interactions. To understand hydrocarbon binding, we initiated the HYDROPHOBE challenge, which revealed the shortcomings of both quantum-chemical and molecular dynamics approaches. (2) The smallest CBn receptor, CB5, is uniquely suited to bind the entire noble gas series, where hydrophobic effects and dispersion interactions operate in opposite directions. CB5 was revaled to be a unique synthetic receptor for noble gases, with the dominant driving force being the recovery of the cavitation energies for the hydration of noble gases in aqueous solution. Computational methods that encounter challenges in predicting hydrocarbon affinities and trends for CB6 and CB7 perform well for noble gases binding to CB5. (3) The larger homologue, CB8, allows one to set up intermolecular interaction chambers by the encapsulation of a (first) aromatic guest, thereby tuning LDIs inside the receptor cavity. In this manner, CB8 can be modulated to preferentially bind unsaturated and aromatic rather than saturated hydrocarbons, while the unmodified cavities of the smaller macrocycles CB6 and CB7 show selective binding of saturated hydrocarbons. (4) The (charged) host-guest complexes of CBn hosts are sufficiently stable in the gas phase, allowing for the study of the influence of LDIs on inner-phase chemical reactions. These studies are particularly interesting for the theoretical analysis of isolated host-guest LDIs, as experimental and computational data are directly comparable in the gas phase due to the absence of the solvation effect.

Context-Dependent Significance of London Dispersion

ConspectusLondon forces constitute an attractive component of van der Waals interactions and originate from transient correlated momentary dipoles in adjacent atoms. The in-depth investigation of London dispersion forces poses notable challenges, especially in solution, owing to their inherently weak and competing character. Our objective in this Account is to shed light on the context-dependent significance of London dispersion forces by contrasting our own experimental findings with those from other research endeavors. Specifically, we will explore how factors such as the choice of system and solvent can influence the apparent role of London dispersion forces in molecular recognition processes. We initiate our Account by scrutinizing the Wilcox balance, which has yielded diverse and occasionally contradictory results. Following that, we provide an overview of the role of London dispersion forces and their context-dependent variations, encompassing alkyl-alkyl, halogen-π, alkyl-π, and aromatic stacking interactions.Several experimental investigations have revealed how difficult it is to measure the significance of London dispersion in solution. Indeed, dispersion forces seldom act as the exclusive driving force in molecular recognition processes, and solvation energetics also strongly influence equilibria and kinetics. Molecular balances that bring apolar functional groups into contact have proven to be instrumental in the experimental measurement of dispersion. The intramolecular approach avoids the need to pay the entropic cost of bringing interacting groups into contact, while also enabling solvent screening. Such experimental studies have found dispersion interactions between functional groups to be very weak (<5 kJ mol-1), meaning that they frequently take backstage to electrostatic contributions and solvophobic effects and are readily damped by competitive dispersion interactions with the solvent. By using such approaches, competitive dispersion interactions with the solvent have been shown to be described by the bulk polarizability of the solvent (perfluoroalkanes have the lowest bulk polarizabilities, while carbon disulfide has one of the highest). Dispersion interactions are also strongly distance-dependent, which results in considerable context-dependent outcomes across different investigations. For example, we caution against the risk of attributing the stability of a "more sterically hindered" isomer as arising from intramolecular dispersion forces. The total energy of the system can reveal other contributions to stability, such as nonintuitive minimization of strain elsewhere in the molecule. Indeed, the delicate distance-dependent balance between sterics and London dispersion means that even subtle changes in size and geometry can lead to disparate behavior. Similarly, solvophobic effects also contribute to stabilizing contacts between bulky functional groups, which can be revealed if there is a correlation with the cohesive energy density of the solvent.

Experimental Quantification of Halogen⋅⋅⋅Arene van der Waals Contacts

Crystallographic and computational studies suggest the occurrence of favourable interactions between polarizable arenes and halogen atoms. However, the systematic experimental quantification of halogen⋅⋅⋅arene interactions in solution has been hindered by the large variance in the steric demands of the halogens. Here we have synthesized molecular balances to quantify halogen⋅⋅⋅arene contacts in 17 solvents and solvent mixtures using 1 H NMR spectroscopy. Calculations indicate that favourable halogen⋅⋅⋅arene interactions arise from London dispersion in the gas phase. In contrast, comparison of our experimental measurements with partitioned SAPT0 energies indicate that dispersion is sufficiently attenuated by the solvent that the halogen⋅⋅⋅arene interaction trend was instead aligned with increasing exchange repulsion as the halogen increased in size (ΔGX ⋅⋅⋅Ph =0 to +1.5 kJ mol-1 ). Halogen⋅⋅⋅arene contacts were slightly less disfavoured in solvents with higher solvophobicities and lower polarizabilities, but strikingly, were always less favoured than CH3 ⋅⋅⋅arene contacts (ΔGMe ⋅⋅⋅Ph =0 to -1.4 kJ mol-1 ).

How great is the stabilization of crowded polyphenylbiphenyls by London dispersion?

Decaphenylbiphenyl (1) and 2,2',4,4',6,6'-hexaphenylbiphenyl (2) are bulky molecules expected to be greatly destabilized by steric crowding. Herein, through a combined experimental and computational approach, we evaluate the molecular energetics of crowded biphenyls. This is complemented by the study of phase equilibria for 1 and 2. Compound 1 shows a rich phase behavior, displaying an unusual interconversion between two polymorphs. Surprisingly, the polymorph with distorted molecules of C₁ symmetry is found to have the highest melting point and to be the one that is preferentially formed. The thermodynamic results also indicate that the polymorph displaying the more regular D₂ molecular geometry has larger heat capacity and is probably the more stable at lower temperatures. The melting and sublimation data clearly reveal the weakening of cohesive forces in crowded biphenyls due to the lower molecular surface area. The experimental quantification of the intramolecular interactions in 1 and 2 indicated, using homodesmotic reactions, a molecular stabilization of about 30 kJ mol^-1. We attribute the origin of this stabilization in both compounds to the existence of two parallel-displaced π⋯π interactions between the ortho-phenyl substituents on each side of the central biphenyl. Computational calculations with dispersion-corrected DFT methods underestimate the stabilization in 1, unless the steric crowding is well balanced in a homodesmotic scheme. This work demonstrates that London dispersion forces are important in crowded aromatic systems, making these molecules considerably more stable than previously thought.

Modelling the octanol-air partition coefficient of aromatic pollutants based on the solvation free energy and the dimer effect

In this study, generalized predictive models were developed to estimate K_OA of four kinds of aromatic pollutants based on the calculated solvation free energy and taking the dimer effect into account. Uncorrected log K_OA values, which were directly estimated from the calculated solvation free energy of individual molecules, underestimated experimental values, and the deviation increased with increasing log K_OA. Dimers were found to greatly affect the apparent K_OA values of these aromatic pollutants, which were driven by π-π interactions. London dispersion and exchange-repulsion terms were identified to be dominant components of the underlying π-π interactions. It is interesting to find that the π-π interactions of polybrominated diphenyl ethers correlate with not only the molecular polarizability but also the size of opposing aromatic surfaces, which leads to a different trend of π-π interactions from other aromatic pollutants. A universal quantitative structure-activity relationship model was developed to estimate the proportion of dimers based on five molecular structural descriptors relevant to the π-π interactions. After calibration with the dimer effect, estimations of log K_OA were consistent with experimental values. Therefore, the dimer effect should be taken into consideration when investigating the partition behavior of aromatic pollutants, and the solvation free energy model could be an alternative method for the prediction of K_OA.

Low-Energy Electron Interactions with Resveratrol and Resorcinol: Anion States and Likely Dissociation Pathways

We report a computational study of the anion states of the resveratrol (RV) and resorcinol (RS) molecules, also investigating dissociative electron attachment (DEA) pathways. RV has well-known beneficial effects in human health, and its antioxidant activity was previously associated with DEA reactions producing H₂. Our calculations indicate a valence bound state (π1*) and four resonances (π2* to π5*) for that system. While the computed thermodynamic thresholds are compatible with DEA reactions producing H₂ at 0 eV, the well-known mechanism involving vibrational Feshbach resonances built on a dipole bound state should not be present in RV. Our results suggest that the shallow π1* valence bound state is expected to account for H₂ elimination, probably involving π1*/σOH* couplings along the vibration dynamics. The RS molecule is also an oxidant and a subunit of RV. Because two close-lying hydroxyl groups are found in the RS moiety, the H₂-elimination reaction in RV should take place at the RS site. Our calculations point out a correspondence between the anion states of RV and RS and even between the thresholds. Nevertheless, the absence of bound anion states in RS, indicated by our calculations, is expected to suppress the H₂-formation channel at 0 eV. One is led to conclude that the ethene and phenol subunits in RV stabilize the π1* state, thus switching on the DEA mechanism producing H₂.

Assessing the Experimental Hydrogen Bonding Energy of the Cyclic Water Dimer Transition State with a Cyclooctatetraene-Based Molecular Balance

We have conducted an experimental and computational study of cyclooctatetraene-1,4/1,6-dimethanol (1,4 and 1,6) as a molecular balance with the goal in mind to determine the otherwise inaccessible hydrogen bonding energy (HBE) of the cyclic water dimer, which constitutes a transition state. The 1,4/1,6 folding equilibrium is governed by an intramolecular hydrogen bond in the folded 1,6-isomer, in which the OH groups adopt a cyclic planar geometry, akin to the structure of the cyclic water dimer transition state. We characterized hydrogen bonding in 1,6 and reference complexes utilizing SAPT2 + (3)δMP2/aug-cc-pVTZ and selected quantum theory of atoms in molecule descriptors at M06-2XD3(0)/ma-def2-TZVPP. Additionally, we computed HBEs at the DLPNO-CCSD(T)/aug-cc-pVQZ level of theory. We find that hydrogen bonding in 1,6 is very similar to the interaction in the C_i symmetric cyclic water dimer TS, both in magnitude and character. We experimentally determined the Gibbs free energy of the folding process (ΔG_eq) in a variety of organic solvents via nuclear magnetic resonance spectroscopy measurements at room temperature. By combining experimentally obtained ΔG_eq values with corrections derived from accurate computational methods, we provide estimates for the HBE of cyclic water dimers and the cyclic water dimer TS, as the most stable cyclic water dimer.

Dissecting Solvent Effects on Hydrogen Bonding

The experimental isolation of H‐bond energetics from the typically dominant influence of the solvent remains challenging. Here we use synthetic molecular balances to quantify amine/amide H‐bonds in competitive solvents. Over 200 conformational free energy differences were determined using 24 H‐bonding balances in 9 solvents spanning a wide polarity range. The correlations between experimental interaction energies and gas‐phase computed energies exhibited wild solvent‐dependent variation. However, excellent correlations were found between the same computed energies and the experimental data following empirical dissection of solvent effects using Hunter's α/β solvation model. In addition to facilitating the direct comparison of experimental and computational data, changes in the fitted donor and acceptor constants reveal the energetics of secondary local interactions such as competing H‐bonds.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Dissection of the Polar and Non-Polar Contributions to Aromatic Stacking Interactions in Solution

Aromatic stacking interactions have been a matter of study and debate due to their crucial role in chemical and biological systems. The strong dependence on orientation and solvent together with the relatively small interaction energies have made evaluation and rationalization a challenge for experimental and theoretical chemists. We have used a supramolecular cage formed by two tris(pyridylmethyl)amines units to build chemical Double Mutant Cycles (DMC) for the experimental measurement of the free energies of π-stacking interactions. Extrapolating the substituent effects to remove the contribution due to electrostatic interactions reveals that there is a substantial contribution to the measured stacking interaction energies which is due to non-polar interactions (-3 to -6 kJ mol-1 ). The perfectly flat nature of the surface of an aromatic ring gives π-stacking an inherent advantage over non-polar interactions with alkyl groups and accounts for the wide-spread prevalence of stacking interactions in Nature.

Intramolecular London Dispersion Interactions Do Not Cancel in Solution

We present a comprehensive experimental study of a di-t-butyl-substituted cyclooctatetraene-based molecular balance to measure the effect of 16 different solvents on the equilibrium of folded versus unfolded isomers. In the folded 1,6-isomer, the two t-butyl groups are in close proximity (H···H distance ≈ 2.5 Å), but they are far apart in the unfolded 1,4-isomer (H···H distance ≈ 7 Å). We determined the relative strengths of these noncovalent intramolecular σ-σ interactions via temperature-dependent nuclear magnetic resonance measurements. The origins of the interactions were elucidated with energy decomposition analysis at the density functional and ab initio levels of theory, pinpointing the predominance of London dispersion interactions enthalpically favoring the folded state in any solvent measured.

London Dispersion in Alkane Solvents

The importance of London dispersion interactions in solution is an ongoing debate. Although the significance of dispersion for structure and stability is widely accepted, the degree of its attenuation in solution is still not properly understood. Quantitative evaluations are derived mostly from computations. Experimental data provide guidelines to include London dispersion in solution phase design. Herein, dispersive interactions were examined with an azobenzene probe. Alkyl substituents in meta positions of the azobenzene core were systematically varied and the effect on the half-lives for the thermally induced Z to E isomerization in several alkane solvents was determined. The results show that intramolecular dispersion is only marginally influenced. In solvents with low surface tension, reduced destabilizing solvent-solvent interactions increase the half-life up to 20 %. Specific individual interactions between alkyl chains on the azobenzene and those of the solvent lead to additional fluctuations of the half-lives. These presumably result from structural changes of the conformer ensemble.

The Size-Accelerated Kinetic Resolution of Secondary Alcohols

The factors responsible for the kinetic resolution of alcohols by chiral pyridine derivatives have been elucidated by measurements of relative rates for a set of substrates with systematically growing aromatic side chains using accurate competitive linear regression analysis. Increasing the side chain size from phenyl to pyrenyl results in a rate acceleration of more than 40 for the major enantiomer. Based on this observation a new catalyst with increased steric bulk has been designed that gives enantioselectivity values of up to s=250. Extensive conformational analysis of the relevant transition states indicates that alcohol attack to the more crowded side of the acyl-catalyst intermediate is favoured due to stabilizing CH-π-stacking interactions. Experimental and theoretical results imply that enantioselectivity enhancements result from accelerating the transformation of the major enantiomer through attractive non-covalent interactions (NCIs) rather than retarding the transformation of the minor isomer through repulsive steric forces.

Quantifying Interactions and Solvent Effects Using Molecular Balances and Model Complexes

Where the basic units of molecular chemistry are the bonds within molecules, supramolecular chemistry is based on the interactions that occur between molecules. Understanding the "how" and "why" of the processes that govern molecular self-assembly remains an open challenge to the supramolecular community. While many interactions are readily examined in silico through electronic structure calculations, such insights may not be directly applicable to experimentalists. The practical limitations of computationally accounting for solvation is perhaps the largest bottleneck in this regard, with implicit solvation models failing to comprehensively account for the specific nature of solvent effects and explicit models incurring a prohibitively high computational cost. Since molecular recognition processes usually occur in solution, insight into the nature and effect of solvation is imperative not only for understanding these phenomena but also for the rational design of systems that exploit them.Molecular balances and supramolecular complexes have emerged as useful tools for the experimental dissection of the physicochemical basis of various noncovalent interactions, but they have historically been underexploited as a platform for the evaluation of solvent effects. Contrasting with large biological complexes, smaller synthetic model systems enable combined experimental and computational analyses, often facilitating theoretical analyses that can work in concert with experiment.Our research has focused on the development of supramolecular systems to evaluate the role of solvents in molecular recognition, and further characterize the underlying mechanisms by which molecules associate. In particular, the use of molecular balances has provided a framework to measure the magnitude of solvent effects and to examine the accuracy of solvent models. Such approaches have revealed how solvation can modulate the electronic landscape of a molecule and how competitive solvation and solvent cohesion can provide thermodynamic driving forces for association. Moreover, the use of simple model systems facilitates the interrogation and further dissection of the physicochemical origins of molecular recognition. This tandem experimental/computational approach has married less common computational techniques, like symmetry adapted perturbation theory (SAPT) and natural bonding orbital (NBO) analysis, with experimental observations to elucidate the influence of effects that are difficult to resolve experimentally (e.g., London dispersion and electron delocalization).

N-Arylimide Molecular Balances: A Comprehensive Platform for Studying Aromatic Interactions in Solution

Noncovalent interactions of aromatic surfaces play a key role in many biological processes and in determining the properties and utility of synthetic materials, sensors, and catalysts. However, the study of aromatic interactions has been challenging because these interactions are usually very weak and their trends are modulated by many factors such as structural, electronic, steric, and solvent effects. Recently, N-arylimide molecular balances have emerged as highly versatile and effective platforms for studying aromatic interactions in solution. These molecular balances can accurately measure weak noncovalent interactions in solution via their influence on the folded-unfolded conformational equilibrium. The structure (i.e., size, shape, π-conjugation, and substitution) and nature (i.e., element, charge, and polarity) of the π-surfaces and interacting groups can be readily varied, enabling the study of a wide range of aromatic interactions. These include aromatic stacking, heterocyclic aromatic stacking, and alkyl-π, chalcogen-π, silver-π, halogen-π, substituent-π, and solvent-π interactions. The ability to measure a diverse array of aromatic interactions within a single model system provides a unique perspective and insights as the interaction energies, stability trends, and solvent effects for different types of interactions can be directly compared. Some broad conclusions that have emerged from this comprehensive analysis include: (1) The strongest aromatic interactions involve groups with positive charges such as pyridinium and metal ions which interact with the electrostatically negative π-face of the aromatic surface via cation-π or metal-π interactions. Attractive electrostatic interactions can also form between aromatic surfaces and groups with partial positive charges. (2) Electrostatic interactions involving aromatic surfaces can be switched from repulsive to attractive using electron-withdrawing substituents or heterocycles. These electrostatic trends appear to span many types of aromatic interactions involving a polar group interacting with a π-surface such as halogen-π, chalcogen-π, and carbonyl-π. (3) Nonpolar groups form weak but measurable stabilizing interactions with aromatic surfaces in organic solvents due to favorable dispersion and/or solvophobic effects. A good predictor of the interaction strength is provided by the change in solvent-accessible surface area. (4) Solvent effects modulate the aromatic interactions in the forms of solvophobic effects and competitive solvation, which can be modeled using solvent cohesion density and specific solvent-solute interactions.

Do weak interactions affect the biological behavior of DNA? A DFT study of CpG island-like chains

The origin, stability, and contribution to the formation of noncovalent interactions, such as hydrogen bonds and π - π stacking, have been already widely discussed. However, there are few discussions about the relevance of these weak interactions in DNA performance. In this work, we seek to shed light on the effect of hydrogen bonds and π - π stacking interactions on the biological behavior of DNA through the description of these intermolecular forces in CpG island-like (GC-rich) chains. Furthermore, we made some comparisons with TATA box-like (TA-rich) chains in order to describe hydrogen bond and π - π stacking interactions as a function of the DNA sequence. For hydrogen bonds, we found that there is not a significant effect related to the number of base pairs. Whereas for π - π stacking interactions, the energy tended to decrease as the number of base pairs increased. We observed anticooperative effects for both hydrogen bonds and π - π stacking interactions. These results are in contrast with those of TATA box-like chains since cooperative and additive effects were found for both hydrogen bonds and π - π stacking, respectively. Based on the chemical hardness and density of states, we can conclude that proteins may interact easier with GC-rich chains. We conclude that regardless of the chain length, a protein could interact more easily with these genomics regions because the π - π stacking energies did not increase as a function of the number of base pairs, making, for the first time, a first approximation of the influence of noncovalent interaction on DNA behavior. We did all this work by means of DFT framework included in the DMol³ code (M06-L/DNP). Graphical Abstract Cartoon representation of how nocovalent interactions affect the interaction of DNA with a protein, i.e., how hydrogen bond and π - π stacking interactions influence the biological behavior of DNA.

Measurement of Solvation Ability of Solvents by Porphyrin-Based Solvation/Desolvation Indicators

A new solvent scale, solvation ability (SA), was developed to arrange solvents in the order of their SA for large π-conjugated compounds. The SA of a solvent was determined in a binary solvent system of an assessed solvent and a standard "good" solvent (GS) or "poor" solvent (PS), chloroform or methylcyclohexane, respectively, in the presence of two types of solvation/desolvation indicators, 1Zn₂ and 2Zn₂ . The latter comprises bis(imidazolylporphyrinatozinc) linked via a 1,3-butadiynylene moiety having linear alkyl and hydrophilic side chains, respectively. GSs and PSs give extended (E-) and stacked (S-) supramolecular polymers of the indicators, respectively. SA values are defined as vol % of the standard solvent added to an assessed solvent to give the balance point where comparable amounts of E- and S-polymers of the indicators coexist. GSs and PSs have positive and negative signs, respectively. In this study, the SA of 25 solvents was determined. The SA values with indicator 1Zn₂ were as follows: ethyl acetate (-81), hexane (-66), toluene (-50), cyclohexane (-47), CCl₄ (-25), chloroform (50), and nitrobenzene (79).

Prediction of octanol-air partition coefficients for PCBs at different ambient temperatures based on the solvation free energy and the dimer ratio

Temperature-dependent octanol-air partition coefficients (K_OA) are of great importance in assessing the environmental behavior and fate of persistent organic pollutants including polychlorinated biphenyls (PCBs). Due to the tremendous amounts of time, effort and cost needed for the experimental determination of K_OA, it is desirable to develop a rapid and precise predictive method to estimate K_OA just based on molecular structure. In the present study, a predictive model for log K_OA of PCBs at ambient temperatures was developed based on the thermodynamic relationship between K_OA and the solvation free energy from air to octanol (ΔG_OA). For the calculation of ΔG_OA of PCBs, the optimal combination of theoretical method and basis-set was identified to be HF/MIDI!6D for both geometry optimization and energy calculation. Dimer formation could affect the partition behavior and promote the apparent K_OA values of PCBs. After taking the effect of dimer formation into account, the goodness-of-fit, predictive ability, and robustness of the predictive model were significantly improved. Apparent log K_OA values of PCBs at different ambient temperatures ranging from 283.15 to 303.15 K were predicted. Compared with other reported models, the model developed in the present study had not only comparable goodness-of-fit and predictive ability, but also a universal application domain and the relative independency of experimental data. Therefore, the solvation free energy method could be a promising method for the prediction of K_OA.

Exploring London Dispersion and Solvent Interactions at Alkyl-Alkyl Interfaces Using Azobenzene Switches

Interactions on the molecular level control structure as well as function. Especially interfaces between innocent alkyl groups are hardly studied although they are of great importance in larger systems. Herein, London dispersion in conjunction with solvent interactions between linear alkyl chains was examined with an azobenzene-based experimental setup. Alkyl chains in all meta positions of the azobenzene core were systematically elongated, and the change in rate for the thermally induced Z→E isomerization in n-decane was determined. The stability of the Z-isomer increased with longer chains and reached a maximum for n-butyl groups. Further elongation led to faster isomerization. The origin of the intramolecular interactions was elaborated by various techniques, including 1 H NOESY NMR spectroscopy. The results indicate that there are additional long-range interactions between n-alkyl chains with the opposite phenyl core in the Z-state. These interactions are most likely dominated by attractive London dispersion. This work provides rare insight into the stabilizing contributions of highly flexible groups in an intra- as well as an intermolecular setting.

Preferential binding of unsaturated hydrocarbons in aryl-bisimidazolium·cucurbit[8]uril complexes furbishes evidence for small-molecule π-π interactions

Whilst cucurbit[n]urils (CBn) have been utilized in gas encapsulation, only the smaller CBn (n = 5 and 6) have utility given their small cavity size. In this work, we demonstrate that the large cavity of CB8 can be tailored for gaseous and volatile hydrocarbon encapsulation by restricting its internal cavity size with auxiliary aryl-bisimidazolium (Bis, aryl = phenyl, naphthyl, and biphenyl) guests. The binding constants for light hydrocarbons (C ≤ 4) are similar to those measured with CB6, while larger values are obtained with Bis·CB8 for larger guests. A clear propensity for higher affinities of alkenes relative to alkanes is observed, most pronounced with the largest delocalized naphthalene residue in the auxiliary Bis guest, which provides unique evidence for sizable small-molecule π-π interactions.

Study of the Wilcox torsion balance in solution for a Tröger's base derivative with hexyl-and heptyl substituents using a combined molecular mechanics and quantum chemistry approach

The folding equilibrium of the Wilcox torsion balance in solution has been studied using a molecular mechanics method for sampling the conformational space and semi-empirical and density-functional quantum chemistry methods for characterizing the relative stabilities of various solute-solvent clusters extracted with the aid of the MD-quench technique from the different simulations that were performed. The role of the solvent environment has been analyzed by choosing four solvents of different polarities, namely water, acetone, tetrachloromethane, and n-hexane. In all cases, it is found that the attractive intramolecular interactions in folded conformations are strongly compensated by the increase of the solute-solvent interaction energies when the molecule unfolds. The latter can be well explained by the larger number of solvent molecules that can bind to the Wilcox molecule when in an unfolded conformation. The results of this work therefore support the experimental results of Yang et al. (Nature Chem 5:1006, 2013) that the folding free energy of the Wilcox balance is strongly reduced in solution as compared to the gas phase.

Supramolecular cage encapsulation as a versatile tool for the experimental quantification of aromatic stacking interactions

The widespread presence of aromatic stacking interactions in chemical and biological systems, combined with their relatively small energetic contribution, have led to a plethora of theoretical and experimental studies for their quantification and rationalization. Typically, π-π aromatic interactions are studied as a function of substituents to gather information about the interaction mechanism. While experiments suggest that aromatic interactions are dominated by local electrostatic contacts between π-electron density and CH groups, theoretical work has raised the possibility that direct electrostatic interactions between local dipoles of the substituents may play a role. We describe a supramolecular cage that binds two aromatic carboxylates in a stacked geometry such that the aromatic substituents are remote in space. Chemical Double Mutant Cycles (DMCs) were used to measure fifteen different aromatic stacking interactions as a function of substituent (NMe2, OMe, Me, Cl and NO2). When both aromatic rings have electron-withdrawing nitro substituents, the interaction is attractive (-2.8 kJ mol-1) due to reduced π-electron repulsion. When both aromatic rings have electron-donating di-methylamino substituents, the interaction is repulsive (+2.0 kJ mol-1) due to increased π-electron repulsion. The results show that aromatic stacking interactions are dominated by short range electrostatic contacts rather than substituent dipole interactions.

Study of through-space substituent–π interactions using N-phenylimide molecular balances

Substituent–π interactions associated with aromatic stacking interactions were experimentally measured using a small N-phenylimide molecular balance model system.

Quantification of noncovalent interactions – promises and problems

Quantification of noncovalent interactions is the key for the understanding of binding mechanisms, of biological systems, for the design of drugs, their delivery and for the design of receptors for separations, sensors, actuators, or smart materials.