The Energetic Origins of Pi-Pi Contacts in Proteins

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

Electrostatic penetration effects stand at the heart of aromatic π interactions

The nature of the interaction in benzene-containing dimers has been analysed by means of Symmetry Adapted Perturbation Theory (SAPT). The total interaction energy and the preference for the dimers to adopt slipped structures are, apparently, consequence of the balance between repulsion and dispersion. However, our results indicate that this only holds when trends are analysed using fixed intermolecular distances. Employing the most favourable separations between rings it turns out that the changes on the total interaction energy are mostly controlled by electrostatics, while repulsion and dispersion cancel each other to a great extent. Most of the electrostatic contribution is accounted for by electrostatic penetration, so a description based on multipoles should not be employed to rationalise the interaction in benzene-containing dimers. The changes on the interaction energy in benzene-containing dimers are steered by electrostatic penetration which, though often overlooked, plays an essential role for the description of aromatic π interactions.

Parallel-stacked aromatic molecules in hydrogen-bonded inorganic frameworks

By precisely constructing molecules and assembling these into well-defined supramolecular structures, novel physical properties and functionalities can be realized, and new areas of the chemical space can be accessed. In both materials science and biology, a deeper understanding of the properties and exploitation of the reversible character of weak bonds and interactions, such as hydrogen bonds and π–π interactions, is anticipated to lead to the development of materials with novel properties and functionalities. We apply the hydrogen-bonded organic frameworks (HOFs) strategy to inorganic materials science using the cubic octamer of orthosilicic acid, [Si₈O₁₂][OH]₈, as a building block, and find that various types of hydrogen-bonded inorganic frameworks (HIFs). We succeed in parallel π-stacking pure benzene, thiophene, selenophene, p-benzoquinone, thiophene·p-benzoquinone, and benzene·p-benzoquinone polymers infinitely. These polymers interact via their π-systems by taking advantage of the flexible pores of the three-dimensional nano-honeycomb HIFs, which consist of periodic wide and narrow segments.

Hydrogen-bonded inorganic frameworks are porous structures that may lead to novel materials with unprecedented properties and functionalities. Here the authors report the solid-state structures of orthosilicic acid-based hydrogen-bonded inorganic frameworks that can encapsulate small unsaturated cyclic molecules such as benzene, which are found stacked in parallel.

Neat, Simple, and Wrong: Debunking Electrostatic Fallacies Regarding Noncovalent Interactions

Multipole moments such as charge, dipole, and quadrupole are often invoked to rationalize intermolecular phenomena, but a low-order multipole expansion is rarely a valid description of electrostatics at the length scales that characterize nonbonded interactions. This is illustrated by examining several common misunderstandings rooted in erroneous electrostatic arguments. First, the notion that steric repulsion originates in Coulomb interactions is easily disproved by dissecting the interaction potential for Ar₂. Second, the Hunter-Sanders model of π-π interactions, which is based on quadrupolar electrostatics, is shown to have no basis in accurate calculations. Third, curved "buckybowls" exhibit unusually large dipole moments, but these are ancillary to the forces that control their intermolecular interactions, as illustrated by two examples involving corannulene. Finally, the assumption that interactions between water and small anions are dictated by the dipole moment of H₂O is shown to be false in the case of binary halide-water complexes. These examples present a compelling case that electrostatic explanations based on low-order multipole moments are very often counterfactual for nonbonded interactions at close range and should not be taken seriously in the absence of additional justification.

The σ-hole⋯σ-hole stacking interaction: An unrecognized type of noncovalent interaction

The σ-hole⋯σ-hole stacking interaction, an unrecognized type of noncovalent interaction, has been found to be present in large quantities in the Cambridge Structural Database. In the σ-hole⋯σ-hole stacking interaction, each of the two interacting σ-holes has the dual electron donor/electron acceptor character; when one σ-hole acts as an electron donor, the other σ-hole acts as an electron acceptor, and vice versa. The σ-hole⋯σ-hole stacking interaction is clearly different from the σ-hole bond in which the charge transfer occurs mainly from the electron donor to the σ-hole. Energy component analysis shows that the σ-hole⋯σ-hole stacking interaction is dominated by the dispersion energy, which is similar to the nature of the aromatic stacking interaction between unsaturated molecules or the σ⋯σ stacking interaction between saturated molecules.

Reinterpreting π-stacking

The nature of π-π interactions has long been debated. The term "π-stacking" is considered by some to be a misnomer, in part because overlapping π-electron densities are thought to incur steric repulsion, and the physical origins of the widely-encountered "slip-stacked" motif have variously been attributed to either sterics or electrostatics, in competition with dispersion. Here, we use quantum-mechanical energy decomposition analysis to investigate π-π interactions in supramolecular complexes of polycyclic aromatic hydrocarbons, ranging in size up to realistic models of graphene, and for comparison we perform the same analysis on stacked complexes of polycyclic saturated hydrocarbons, which are cyclohexane-based analogues of graphane. Our results help to explain the short-range structure of liquid hydrocarbons that is inferred from neutron scattering, trends in melting-point data, the interlayer separation of graphene sheets, and finally band gaps and observation of molecular plasmons in graphene nanoribbons. Analysis of intermolecular forces demonstrates that aromatic π-π interactions constitute a unique and fundamentally quantum-mechanical form of non-bonded interaction. Not only do stacked π-π architectures enhance dispersion, but quadrupolar electrostatic interactions that may be repulsive at long range are rendered attractive at the intermolecular distances that characterize π-stacking, as a result of charge penetration effects. The planar geometries of aromatic sp² carbon networks lead to attractive interactions that are "served up on a molecular pizza peel", and adoption of slip-stacked geometries minimizes steric (rather than electrostatic) repulsion. The slip-stacked motif therefore emerges not as a defect induced by electrostatic repulsion but rather as a natural outcome of a conformational landscape that is dominated by van der Waals interactions (dispersion plus Pauli repulsion), and is therefore fundamentally quantum-mechanical in its origins. This reinterpretation of the forces responsible for π-stacking has important implications for the manner in which non-bonded interactions are modeled using classical force fields, and for rationalizing the prevalence of the slip-stacked π-π motif in protein crystal structures.

Stacking interactions of resonance-assisted hydrogen-bridged rings and C6-aromatic rings

Stacking interactions between six-membered resonance-assisted hydrogen-bridged (RAHB) rings and C6-aromatic rings were systematically studied by analyzing crystal structures in the Cambridge Structural Database (CSD). The interaction energies were calculated by quantum-chemical methods. Although the interactions are stronger than benzene/benzene stacking interactions (-2.7 kcal mol-1), the strongest calculated RAHB/benzene stacking interaction (-3.7 kcal mol-1) is significantly weaker than the strongest calculated RAHB/RAHB stacking interaction (-4.7 kcal mol-1), but for a particular composition of RAHB rings, RAHB/benzene stacking interactions can be weaker or stronger than the corresponding RAHB/RAHB stacking interactions. They are also weaker than the strongest calculated stacking interaction between five-membered saturated hydrogen-bridged rings and benzene (-4.4 kcal mol-1) and between two five-membered saturated hydrogen-bridged rings (-4.9 kcal mol-1). SAPT energy decomposition analyses show that the strongest attractive term in RAHB/benzene stacking interactions is dispersion, however, it is mostly canceled by a repulsive exchange term; hence the geometries of the most stable structures are determined by an electrostatic term.

Electrostatics does not dictate the slip-stacked arrangement of aromatic π-π interactions

Benzene dimer has long been an archetype for π-stacking. According to the Hunter–Sanders model, quadrupolar electrostatics favors an edge-to-face CH⋯π geometry but competes with London dispersion that favors cofacial π-stacking, with a compromise “slip-stacked” structure emerging as the minimum-energy geometry. This model is based on classical electrostatics, however, and neglects charge penetration. A fully quantum-mechanical analysis, presented here, demonstrates that electrostatics actually exerts very little influence on the conformational landscape of (C₆H₆)₂. Electrostatics also cannot explain the slip-stacked arrangement of C₆H₆⋯C₆F₆, where the sign of the quadrupolar interaction is reversed. Instead, the slip-stacked geometry emerges in both systems due to competition between dispersion and Pauli repulsion, with electrostatics as an ambivalent spectator. This revised interpretation helps to rationalize the persistence of offset π-stacking in larger polycyclic aromatic hydrocarbons and across the highly varied electrostatic environments that characterize π–π interactions in proteins.

According to the Hunter–Sanders model, geometries in π–π systems arise from competition between quadrupolar electrostatics (favoring an edge-to-face geometry) and London dispersion (favoring stacking), but this model misrepresents the molecular physics.

The relative position of π-π interacting rings notably changes the nature of the substituent effect

The substituent effect in monosubstituted benzene dimers mostly follows changes on electrostatics mainly controlled by the direct interaction of the substituent and the other phenyl ring, whereas the contribution from the interacting rings is smaller. As the substituent is located further away the two contributions become of similar magnitude, so the global result is a combination of both effects. These trends are confirmed in larger systems containing a contact between phenyl rings; at closer distances the interaction of the substituent and the other ring clearly dominates over changes associated with the substituted ring, but as the substituent is located further away its contribution decreases and the contribution from the ring becomes more relevant. Care should be taken in larger systems because the observed energy change can also be affected by interactions with other regions of the molecule not directly involved in the π-π interaction.

What Is Special about Aromatic-Aromatic Interactions? Significant Attraction at Large Horizontal Displacement

High-level ab initio calculations show that the most stable stacking for benzene-cyclohexane is 17% stronger than that for benzene-benzene. However, as these systems are displaced horizontally the benzene-benzene attraction retains its strength. At a displacement of 5.0 Å, the benzene-benzene attraction is still ∼70% of its maximum strength, while benzene-cyclohexane attraction has fallen to ∼40% of its maximum strength. Alternatively, the radius of attraction (>2.0 kcal/mol) for benzene-benzene is 250% larger than that for benzene-cyclohexane. Thus, at relatively large distances aromatic rings can recognize each other, a phenomenon that helps explain their importance in protein folding and supramolecular structures.

Toward Predictive Molecular Dynamics Simulations of Asphaltenes in Toluene and Heptane

The conventional definition of asphaltenes is based on their solubility in toluene and their insolubility in heptane. We have utilized this definition to study the influence of partial charge parametrization on the aggregation behavior of asphaltenes using classical atomistic molecular dynamics simulations performed on the microsecond time scale. Under consideration here are toluene- and heptane-based systems with different partial charges parametrized using the general AMBER force field (GAFF). Systems with standard GAFF partial charges calculated by the AM1-BCC and HF/6-31G*(RESP) methods were simulated alongside systems without partial charges. The partial charges implemented differ in terms of the resulting electrical negativity of the asphaltene polyaromatic core, with the AM1-BCC method giving the greatest magnitude of the total core charge. Based on our analysis of the molecular relaxation and orientation, and on the aggregation behavior of asphaltenes in toluene and heptane, we proposed to use the partial charges obtained by the AM1-BCC method for the study of asphaltene aggregates. A good agreement with available experimental data was observed on the sizes of the aggregates, their fractal dimensions, and the solvent entrainment for the model asphaltenes in toluene and heptane. From the results obtained, we conclude that for a better predictive ability, simulation parameters must be carefully chosen, with particular attention paid to the partial charges owing to their influence on the electrical negativity of the asphaltene core and on the asphaltenes aggregation.

Stacking interactions of borazine: important stacking at large horizontal displacements and dihydrogen bonding governed by electrostatic potentials of borazine

Potential energy surfaces of borazine-benzene and borazine-borazine stacking interactions were studied by performing DFT, CCSD(T)/CBS and SAPT calculations. The strongest borazine-benzene stacking was found in a parallel-displaced geometry, with a CCSD(T)/CBS interaction energy of -3.46 kcal mol-1. The strongest borazine-borazine stacking has a sandwich geometry, with a CCSD(T)/CBS interaction energy of -3.57 kcal mol-1. The study showed that borazine forms significant stacking interactions at large horizontal displacements (over 4.5 Å), with energies of -2.20 kcal mol-1 for the borazine-benzene and -1.96 kcal mol-1 for the borazine-borazine system. The strength of interactions and their geometrical preferences can be rationalized by observing the electrostatic potentials of borazine and benzene, which is in agreement with SAPT analysis showing that electrostatics is the most important energy component for borazine stacking. All the interactions found in crystal structures of borazine and related compounds were identified either as potential curve minima or the geometries obtained from their optimizations. We also report a new dihydrogen bonding dimer with a CCSD(T)/CBS interaction energy of -2.37 kcal mol-1, which is encountered in the borazine crystal structures and enables the formation of additional simultaneous interactions that contribute to the overall stability of the crystals.

Strong stacking interactions of metal–chelate rings are caused by substantial electrostatic component

Stacking interactions of metal–chelate rings are strong due to very strong electrostatic energy component.

On the Nature of σ-σ, σ-π, and π-π Stacking in Extended Systems

Stacking interactions have been evaluated, employing computational methods, in dimers formed by analogous aliphatic and aromatic species of increasing size. Changes in stability as the systems become larger are mostly controlled by the balance of increasing repulsion and dispersion contributions, while electrostatics plays a secondary but relevant role. The interaction energy increases as the size of the system grows, but it does much faster in π-π dimers than in σ-π complexes and more remarkably than in σ-σ dimers. The main factor behind the larger stability of aromatic dimers compared to complexes containing aliphatic molecules is related to changes in the properties of the aromatic systems due to electron delocalization leading to larger dispersion contributions. Besides, an extra stabilization in π-π complexes is due to the softening of the repulsive wall in aromatic species that allows the molecules to come closer.

Steric "attraction": not by dispersion alone

Non-covalent interactions between neutral, sterically hindered organic molecules generally involve a strong stabilizing contribution from dispersion forces that in many systems turns the 'steric repulsion' into a 'steric attraction'. In addition to London dispersion, such systems benefit from electrostatic stabilization, which arises from a short-range effect of charge penetration and gets bigger with increasing steric bulk. In the present work, we quantify this contribution for a diverse set of molecular cores, ranging from unsubstituted benzene and cyclohexane to their derivatives carrying tert-butyl, phenyl, cyclohexyl and adamantyl substituents. While the importance of electrostatic interactions in the dimers of sp²-rich (e.g., π-conjugated) cores is well appreciated, less polarizable assemblies of sp³-rich systems with multiple short-range CH···HC contacts between the bulky cyclohexyl and adamantyl moieties are also significantly influenced by electrostatics. Charge penetration is drastically larger in absolute terms for the sp²-rich cores, but still has a non-negligible effect on the sp³-rich dimers, investigated herein, both in terms of their energetics and equilibrium interaction distances. These results emphasize the importance of this electrostatic effect, which has so far been less recognized in aliphatic systems compared to London dispersion, and are therefore likely to have implications for the development of force fields and methods for crystal structure prediction.

Desorption of Benzene, 1,3,5-Trifluorobenzene, and Hexafluorobenzene from a Graphene Surface: The Effect of Lateral Interactions on the Desorption Kinetics

The desorption of benzene, 1,3,5-trifluorobenzene (TFB), and hexafluorobenzene (HFB) from a graphene covered Pt(111) substrate was investigated using temperature-programmed desorption (TPD). All three species have well-resolved monolayer and second-layer desorption peaks. The desorption spectra for submonolayer coverages of benzene and HFB are consistent with first-order desorption kinetics. In contrast, the submonolayer TPD spectra for TFB align on a common leading-edge, which is indicative of zero-order desorption kinetics. The desorption behavior of the three molecules can be correlated with the strength of the quadrupole moments. Calculations (second-order Møller-Plesset perturbation and density functional theory) show that the potential minimum for coplanar TFB dimers is more than a factor of 2 greater than that for either benzene or HFB dimers. The calculations support the interpretation that benzene and HFB are less likely to form the two-dimensional islands that are needed for submonolayer zero-order desorption kinetics.