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.

The PM6-FGC Method: Improved Corrections for Amines and Amides

Recently, we reported a new approach to develop pairwise analytical corrections to improve the description of noncovalent interactions, by approximate methods of electronic structures, such as semiempirical quantum mechanical (SQM) methods. In particular, and as a proof of concept, we used the PM6 Hamiltonian and we named the method PM6-FGC, where the FGC acronym, corresponding to Functional Group Corrections, emphasizes the idea that the corrections work for specific functional groups rather than for individual atom pairs. The analytical corrections were derived from fits to B3LYP-D3/def2-TZVP (reference). PM6 interaction energy differences, evaluated for a reduced set of small bimolecular complexes, were chosen as representatives of saturated hydrocarbons, carboxylic, amine and, tentatively, amide functional groups. For the validation, the method was applied to several complexes of well-known databases, as well as to complexes of diglycine and dialanine, assuming the transferability of amine group corrections to amide groups. The PM6-FGC method showed great potential but revealed significant inaccuracies for the description of some interactions involving the –NH₂ group in amines and amides, caused by the inadequate selection of the model compound used to represent these functional groups (an NH₃ molecule). In this work, methylamine and acetamide are used as representatives of amine and amide groups, respectively. This new selection leads to significant improvements in the calculation of noncovalent interactions in the validation set.

New Approach for Correcting Noncovalent Interactions in Semiempirical Quantum Mechanical Methods: The Importance of Multiple-Orientation Sampling

A new approach is presented to improve the performance of semiempirical quantum mechanical (SQM) methods in the description of noncovalent interactions. To show the strategy, the PM6 Hamiltonian was selected, although, in general, the procedure can be applied to other semiempirical Hamiltonians and to different methodologies. A set of small molecules were selected as representative of various functional groups, and intermolecular potential energy curves (IPECs) were evaluated for the most relevant orientations of interacting molecular pairs. Then, analytical corrections to PM6 were derived from fits to B3LYP-D3/def2-TZVP reference–PM6 interaction energy differences. IPECs provided by the B3LYP-D3/def2-TZVP combination of the electronic structure method and basis set were chosen as the reference because they are in excellent agreement with CCSD(T)/aug-cc-pVTZ curves for the studied systems. The resulting method, called PM6-FGC (from functional group corrections), significantly improves the performance of PM6 and shows the importance of including a sufficient number of orientations of the interacting molecules in the reference data set in order to obtain well-balanced descriptions.

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.

Curvature and size effects hinder halogen bonds with extended π systems

The curvature of aromatic systems strengthens the interaction by the concave face while it weakens by the convex one. Parallel structures are favoured over halogen bonded ones.

Endohedral alkali cations promote charge transfer transitions in complexes of C60 with [10]cycloparaphenylenes

The endohedral alkali cations in M⁺@C₆₀⋯[10]CPP complexes boost the near infrared absorption bands associated with charge transfer from the nanoring to the fullerene.

Rational Design of Efficient Environmental Sensors: Ring-Shaped Nanostructures Can Capture Quat Herbicides

The viability of using [n]-cycloparaphenylenes (CPPs) of different sizes to encapsulate diquat (DQ) pesticide molecules has been tested analyzing the origin of the host-guest interactions stabilizing the complex. This analysis provides rational design capabilities to construct ad hoc capturing systems tailored to the desired pollutant. All CPPs considered (n = 7-12) are capable of forming remarkably stable complexes with DQ, though [9]-CPP is the best candidate, where a fine balance is established between the energy penalty due to the deformation + repulsion of the pesticide molecule inside the cavity (larger in smaller CPPs) and the maximization of the favorable dispersion, electrostatic and induction contributions (which also decrease in larger rings). These encouraging results prompted us to evaluate the potential of using Resonance Raman spectroscopy on nanohoop complexes as a tool for DQ sensing. The shifts observed in the vibrational frequencies of DQ upon complexation allow us to determine whether complexation has been achieved. Additionally, a large enhancement of the signals permits a selective identification of the vibrational modes.

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.

Fullerene size controls the selective complexation of [11]CPP with pristine and endohedral fullerenes

The ability of the carbon nanoring [11]cycloparaphenylene ([11]CPP) for coordinating fullerenes has been tested using a series of hosts, including the pristine fullerenes C60, C70, C76 and C78, the clusterfullerene Sc3N@C80, monometallic endofullerenes Y@C82 and Tm@C82, and dimetallic endofullerenes Y2@C82 and Lu2@C82. A systematic theoretical study employing dispersion corrected density functional methods has been carried out in order to explore the characteristics of the complexes and the strength of the interaction. Depending on the dimer, complexation energies span from around -36 kcal mol-1 with C60 to -53 kcal mol-1 with the C82 derivatives. Dispersion is the main stabilizing contribution in these dimers, so the molecules arrange to maximize the number of close interatomic contacts. Since most fullerenes can properly fill the cavity of the nanoring the stability of the complexes is pretty similar, with the exception of the smallest fullerenes. The complexes with endohedral fullerenes show similar stabilities in all cases studied, with no noticeable dependence on the nature of the endohedral species. The results obtained suggest that fullerenes larger than C76 could be selectively encapsulated by [11]CPP compared to smaller fullerenes.

Dissecting the concave-convex π-π interaction in corannulene and sumanene dimers: SAPT(DFT) analysis and performance of DFT dispersion-corrected methods

The characteristics of the concave-convex π-π interactions are evaluated in 32 buckybowl dimers formed by corannulene, sumanene, and two substituted sumanenes (with S and CO groups), using symmetry-adapted perturbation theory [SAPT(DFT)] and density functional theory (DFT). According to our results, the main stabilizing contribution is dispersion, followed by electrostatics. Regarding the ability of DFT methods to reproduce the results obtained with the most expensive and rigorous methods, TPSS-D seems to be the best option overall, although its results slightly tend to underestimate the interaction energies and to overestimate the equilibrium distances. The other two tested DFT-D methods, B97-D2 and B3LYP-D, supply rather reasonable results as well. M06-2X, although it is a good option from a geometrical point of view, leads to too weak interactions, with differences with respect to the reference values amounting to about 4 kcal/mol (25% of the total interaction energy). © 2017 Wiley Periodicals, Inc.

Assessment of electronic transitions involving intermolecular charge transfer in complexes formed by fullerenes and donor–acceptor nanohoops

Inserting an anthraquinone or tetracyanoanthraquinone unit in cycloparaphenylene nanohoops facilitates intermolecular electron transfer to a fullerene guest.

A theoretical study of complexes formed between cations and curved aromatic systems: electrostatics does not always control cation–π interaction

Cation–π interactions in curved aromatic systems are not controlled by electrostatics; induction and dispersion dominate in most cases studied.

Comment on "Theoretical studies on a carbonaceous molecular bearing: association thermodynamics and dual-mode rolling dynamics" by H. Isobe, K. Nakamura, S. Hitosugi, S. Sato, H. Tokoyama, H. Yamakado, K. Ohno and H. Kono, Chem. Sci., 2015, , 2746

The LC-BLYP functional accompanied with proper calculations leads to unreliable results for systems governed by π···π interactions. It seems quite clear that a good representation of dispersion interactions is required, so DFT must be supplemented (through the DFT-D formalism or the many-body dispersion method) in order to afford good results.

Carbon-nanorings ([10]CPP and [6]CPPA) as fullerene (C60 and C70) receptors: a comprehensive dispersion-corrected DFT study

The good performance of [10]CPP for catching fullerenes C₆₀ and C₇₀ is made clear. The largest complexation energy corresponds to the C₇₀@[10]CPP complex: −53.32 kcal mol⁻¹ at the B97-D2/def2-TZVP level.

A through-space description of substituent effects leads to inaccurate molecular electrostatic potentials and cation⋯π interactions in extended aromatic systems

The effect of substituents in extended aromatic systems spreads to the whole molecule. Predictions based on the currently accepted through-space model give significant deviations on the strength of cation⋯π interactions.

Fullerene recognition with molecular tweezers made up of efficient buckybowls: a dispersion-corrected DFT study

In 2007, Sygula and co-workers introduced a novel type of molecular tweezers with buckybowl pincers that have attracted the substantial interest of researchers due to their ideal architecture for recognizing fullerenes by concave-convex π∙∙∙π interactions (A. Sygula et al., J. Am. Chem. Soc., 2007, 129, 3842). Although in recent years some modifications have been performed on these original molecular tweezers to improve their ability for catching fullerenes, very few improvements were achieved to date. For that reason, in the present work a series of molecular tweezers have been devised and their supramolecular complexes with C60 studied at the B97-D2/TZVP//SCC-DFTB-D and B97-D2/TZVP levels. Three different strategies have been tested: (1) changing the corannulene pincers to other buckybowls, (2) replacing the tetrabenzocyclooctatetraene tether by a buckybowl, and (3) adding methyl groups on the molecular tweezers. According to the results, all the three approaches are effective, in such a way that a combination of the three strategies results in buckycatchers with complexation energies (with C60) up to 2.6 times larger than that of the original buckycatcher, reaching almost -100 kcal mol(-1). The B97-D2/TZVP//SCC-DFTB-D approach can be a rapid screening tool for testing new molecular tweezers. However, since this approach does not reproduce correctly the deformation energy and this energy represents an important contribution to the total complexation energy of complexes, subsequent higher-level re-optimization is compulsory to achieve reliable results (the full B97-D2/TZVP level is used herein). This re-optimization could be superfluous when quite rigid buckycatchers are studied.

A theoretical study of ternary indole-cation-anion complexes

The simultaneous interactions of an anion and a cation with a π system were investigated by MP2 and M06-2X theoretical calculations. Indole was chosen as a model π system for its relevance in biological environments. Two different orientations of the anion, interacting with the N-H and with the C-H groups of indole, were considered. The four cations (Na(+), NH4(+), C(NH2)3(+) and N(CH3)4(+)) and the four anions (Cl(-), NO3(-), HCOO(-) and BF4(-)) included in the study are of biological interest. The total interaction energy of the ternary complexes was calculated and separated into its two- and three-body components and all of them are further divided into their electrostatic, exchange, repulsion, polarization and dispersion contributions using the local molecular orbital-energy decomposition analysis (LMO-EDA) methodology. The binding energy of the indole-cation-anion complexes depends on both ions, with the cation having the strongest effect. The intense cation-anion attraction determines the geometric and energetic features in all ternary complexes. These structures, with both ions on the same side of the π system, show an anti-cooperative interaction. However, the interaction is not only determined by electrostatics, but also the polarization contribution is important. Specific interactions like the one established between the anion and the N-H group of indole or the proton transfer between an acidic cation and a basic anion play a significant role in the energetics and the structure of particular complexes. The presence of the polar solvent as modelled with the polarizable continuum model (PCM) does not seem to have a significant effect on the geometry of the ternary complexes, but drastically weakens the interaction energy. Also, the strength of the interaction is reduced at a faster rate when the anion is pushed away, compared to the results obtained in the gas phase. The combination of PCM with the addition of one water molecule indicates that the PCM method properly reproduces the main energetic and geometrical changes, even at the quantitative level, but the explicit hydration allows refining the solvent effect and detecting cases that do not follow the general trend.

Tailoring buckybowls for fullerene recognition. A dispersion-corrected DFT study

The shape of a buckybowl plays a fundamental role in the enhancement of fullerene recognition. Compounds whose structure possesses flaps at the rim of the bowl show an enhanced ability.

On the interaction between the imidazolium cation and aromatic amino acids. A computational study

Phe, Tyr and Trp form parallel complexes with cation⋯π interactions. His complexes are the strongest, but without making contact with the aromatic cloud.

Effect of stepwise microhydration on the guanidinium···π interaction

The characteristics of the interaction of microhydrated guanidinium cation with the aromatic moieties present in the aromatic amino acids side chains have been studied by means of computational methods. The most stable minima found for non-hydrated complexes correspond in all cases to structures with guanidinium oriented toward the ring and interacting by means of N-H···π hydrogen bonds. The interaction becomes stronger when going from benzene (-14 kcal mol⁻¹) to phenol (-17 kcal mol⁻¹) to indole (-21 kcal mol⁻¹). These complexes are held together mainly by electrostatics, but with important contributions from induction and dispersion. The presence of a small number of water molecules significantly affects the characteristics of the complexes. Hydrogen bonds formed by water with the cation, another water molecule, or the aromatic units become more and more similar in intensity as water molecules are included in the complex, leading to a great variety of minima with similar stability but showing very different structural patterns. The behavior is similar with the three aromatic units, the differences in stability mainly being a consequence of the different strength of the cation···π contact.

Ring-annelated corannulenes as fullerene receptors. A DFT-D study

Ring-annelated corannulenes behave as better C₆₀/C₇₀ receptor than corannulene C₂₀H₁₀. The interaction is dominated by dispersion, with CH⋯π interactions playing a very important role.

A MP2 and DFT study of the influence of complexation on the aromatic character of phosphole

This work is focused in three topical subjects: intermolecular interactions, metal ions, and aromaticity. A comprehensive MP2/6-31 + G and B3LYP/6-31 + G study of the influence of cation-π interactions on the aromatic character of phosphole was conducted. For this purpose, the structures of complexes were optimized at both theoretical level and different magnetic properties were evaluated. The main conclusion is the increase of the aromatic character of the phosphole when complexes with Li(+), Be(2+), and Al(3+) are formed.

Study of the interaction between water and hydrogen sulfide with polycyclic aromatic hydrocarbons

A computational study has been carried out for determining the characteristics of the interaction between one water and hydrogen sulfide molecule with a series of polycyclic aromatic hydrocarbons of increasing size, namely, benzene, anthracene, triphenylene, coronene, circumcoronene, and dicircumcoronene. Potential energy curves were calculated for structures where H(2)X (X=O,S) molecule is located over the central six-membered ring with its hydrogen atoms pointing toward to (mode A) or away from (mode B) the hydrocarbon. The accuracy of different methods has been tested against the results of coupled cluster calculations extrapolated to basis set limit for the smaller hydrocarbons. The spin component scaled MP2 (SCS-MP2) method and a density functional theory method empirically corrected for dispersion (DFT-D) reproduce fairly well the results of high level calculations and therefore were employed for studying the larger systems, though DFT-D seems to underestimate the interaction in hydrogen sulfide clusters. Water complexes in mode A have interaction energies that hardly change with the size of the hydrocarbon due to compensation between the increase in the correlation contribution to the interaction energy and the increase in the repulsive character of the Hartree-Fock energy. For all the other clusters studied, there is a continuous increase in the intensity of the interaction as the size of the hydrocarbon increases, suggesting already converged values for circumcoronene. The interaction energy for water clusters extrapolated to an infinite number of carbon atoms amounts to -13.0 and -15.8 kJ/mol with SCS-MP2 and DFT-D, respectively. Hydrogen sulfide interacts more strongly than water with the hydrocarbons studied, leading to a limiting value of -21.7 kJ/mol with the SCS-MP2 method. Also, complexes in mode B are less stable than the corresponding A structures, with interaction energies amounting to -8.2 and -18.2 kJ/mol for water and hydrogen sulfide, respectively. The DFT-D calculations give values of -16.2 and -9.3 kJ/mol for hydrogen sulfide complexes in modes A and B, less negative than those predicted by the SCS-MP2 method, probably indicating problems with sulfur dispersion parameters.

Density functional theory study of ruthenium (II)-catalyzed [2+2+2] cycloaddition of 1,6-diynes with tricarbonyl compounds

Density functional theory has been employed to study the mechanism of the [2+2+2] ruthenium(II)-catalyzed cycloaddition between 1,6-diynes and tricarbonyl compounds, proposing a viable multistep-pathway according with that was previously suggested, but clarifying some aspects. This process is compared with the one-step reaction in absence of catalyst.