Functional group corrections to the GFN2-xTB and PM6 semiempirical methods for noncovalent interactions in alkanes and alkenes.

Analytical corrections were developed to improve the accuracy of the PM6 and GFN2-xTB semiempirical quantum mechanical methods for the evaluation of noncovalent interaction energies in alkanes and alkenes. We followed the approach of functional group corrections, wherein the atom-atom pair corrections depend on the nature of the interacting functional groups. The training set includes 21 alkane and 13 alkene complexes taken from the Donchev et al.'s database [Sci. Data 8, 55 (2021)], with interaction energies calculated at the CCSD(T)/CBS level, and our own data obtained for medium-size complexes (of 100 and 112 atoms). In general, for the systems included in the training and validation sets, the errors obtained with the PM6-FGC and xTB-FGC methods are within the chemical accuracy.

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.

Curvature and size effects hinder halogen bonds with extended π systems.

Curvature and size effects in halogen interactions with extended aromatic species have been evaluated, employing computational methods, in dimers formed by dihalogens Cl2, Br2 and I2 with both planar (coronene and circumcoronene) and curved (corannulene, sumanene and C60) aromatic systems. The main controlling factor in these interactions is dispersion, so they become stronger as the size of the halogen grows. The nature of the interaction with the halogen changes depending on the curvature and the extension of the aromatic system. As the aromatic species becomes larger, parallel stacked structures are favoured by dispersion increases over halogen bonded ones. Parallel dimers by the concave side are also favoured as the curvature of the aromatic species increases, while the effect is the opposite by the convex side. Overall, halogen bond interactions are not favoured for large planar or curved aromatic systems; only by the convex face of the most curved structures the dispersion contribution decreases enough so as to make halogen bonded structures competitive with parallel stacked ones.

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.

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

[10]cycloparaphenylene ([10]CPP) effectively encapsulates ionic endofullerenes M+C60 (M = Li+, Na+, K+) as revealed by dispersion-corrected density functional theory methods. The interaction between [10]CPP and these fullerenes is dominated by dispersion, though it is stronger than with pristine C60 due to a reinforcement of electrostatic and induction contributions to the stability. The C60 carbon cage effectively shields the cations and distributes the charge among all carbon atoms, so the nature of the endohedral cation has no noticeable effect upon the final stability of the complexes. However, the presence of the cation induces important changes in the absorption spectra of the complexes, and new absorption bands near the infrared region appear. These bands are associated with charge transfer transitions from [10]CPP to the fullerene, suggesting the suitability of these complexes for use in organic photovoltaic devices.

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

Complexes formed by fullerenes C60/C70 and substituted cycloparaphenylenes with the capability of acting as donor/acceptor pairs ([10]CPAq and [10]CPTcaq nanohoops) have been studied using density functional theory methods empirically corrected for dispersion. All nanohoops form stable complexes with fullerenes, with complexation energies amounting to around -32 kcal mol-1 with C60 and reaching between -36 and -39 kcal mol-1 in the case of C70. According to DFT calculations, the rings are too large to appropriately accommodate the fullerene, which moves from the centre of the ring to a side region (in most cases located on the side opposite the anthracene unit). In this way, the rings are deformed (the oval is stretched) in order to better accommodate the fullerene. Anyway, the orientation and position of the fullerenes inside the nanohoop have moderate influence on the stability. The preference for a given structure is the result of the combined effect of larger dispersion energies and smaller energy costs associated with the deformation of the ring. The analysis of the electronic transitions of the different complexes suggests that the presence of the anthracene unit promotes the appearance of intermolecular (nanohoop to fullerene) charge transfer transitions, even though no direct participation of the substituent has been observed.

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.

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.

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

The present work studies the interaction of two extended curved π-systems (corannulene and sumanene) with various cations (sodium, potassium, ammonium, tetramethylammonium, guanidinium and imidazolium). Polyatomic cations are models of groups found in important biomolecules in which cation-π interaction plays a fundamental role. The results indicate an important size effect: with extended π systems and cations of the size of potassium and larger, dispersion is much more important than has been generally recognized for cation-π interactions. In most of the systems studied here, the stability of the cation-π complexes is the result of a balanced combination of electrostatic, induction and dispersion contributions. None of the systems studied here owes its stability to the electrostatic interaction more than 42%. Induction dominates stabilization in complexes with sodium, and in some of the potassium and ammonium complexes. In complexes with large cations and with flat cations dispersion is the major stabilizing contribution and can provide more than 50% of the stabilization energy. This implies that theoretical studies of the cation-π interaction involving large or even medium-size fragments require a level of calculation capable of properly modelling dispersion. The separation between the cation and the π system is another important factor to take into account, especially when the fragments of the cation-π complex are bound (for example, to a protein backbone) and cannot interact at the most favourable distance.

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

A comprehensive computational analysis of all possible complexes between the carbon-nanorings, CNRs, [10]CPP and [6]CPPA with the fullerenes C60 and C70, was carried out. The B97-D2 functional together with the def2-TZVP basis set was used through the work, although comparisons with other different functionals (BLYP-D2, B3LYP-D3(BJ), TPSS-D3(BJ), PBE0-D3(BJ) and M06-2X) were also performed. In order to find all the possible rearrangements of the fullerenes inside the CNRs, two methods of different complexities and computational costs were employed. After localization of all minima of interest, the corresponding complexation energies were evaluated, and subsequently, the different minima were compared both from a structural and an energetic point of view. According to our results, the largest complexation energy clearly corresponds to the C70@[10]CPP complex: -53.32 kcal mol-1. This complex shows a structure where each of the ten rings of [10]CPP directly faces a six-membered ring of C70. That is to say, the best possible overlap between the hexagonal rings of C70 and [10]CPP takes place, showing an arrangement that clearly favours the dispersive ππ interaction. To achieve this spatial disposition, C70 is placed fully vertically (its major diameter perpendicular to the plane of the CNR), and undergoes a small displacement of 0.769 Å from the centre of the CNR. With C60, exactly the same interaction pattern is reproduced, and it is indeed the reason for this fullerene to be just inside the CNR, since for C60 the belt formed by the six-membered rings is placed exactly at the centre of the buckyball. Basically due to the smaller dispersion arising for this C60@[10]CPP complex, the complexation energy is somewhat smaller: -49.78 kcal mol-1. All the calculations show that the ability of [6]CPPA as a fullerene receptor is rather smaller than that of [10]CPP (about ten kcal mol-1, regarding complexation energy), both for C60 and C70. This is basically due to the loss of the interaction of four phenyl rings with the fullerenes, not adequately counterbalanced by the weaker interaction with the alkyne bonds.

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

Non-local effects are crucial in order to give an accurate description of substituent effects in extended aromatic systems. As a consequence, the predictions based on the currently accepted through-space picture can lead to large errors in the strength of cationπ interactions, especially for rings furthest from the substituent.

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, 6, 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.

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

Complexes formed by the imidazolium cation and the aromatic amino acids, phenylalanine, tyrosine, tryptophan, and histidine have been studied by using computational methods. Complexation energies estimated at the MP2.X level amount to -123.3, -124.6, -131.5 and -145.5 kJ mol(-1) for Phe, Tyr, Trp and His, respectively. The results obtained for Phe, Tyr and Trp complexes are similar, with the most stable minima corresponding to structures with the imidazolium cation stacked over the rings. The cation forms hydrogen bonds with the amino acid while establishing cationπ contacts with the aromatic rings. Extended structures with the amino acids in zwitterionic form are almost equally stable, though. The interaction is controlled by electrostatics and induction, though the preference for the stacked minima is due to larger contributions from induction and dispersion despite the energy cost of folding the amino acid. His complexes exhibit a totally different behaviour, and no structures displaying cationπ interactions are found among the most stable minima. Most favourable complexes of His show the cation hydrogen bonded to the amino acid in extended zwitterionic form. Overall, Phe, Tyr and Trp complexes can show parallel structures in competition with similarly stable zwitterionic ones, while His only shows zwitterionic minima, with a stability even larger than any of the other aromatic amino acids, though lacking participation of the π cloud in the interaction.

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.

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

A series of buckybowls with different sizes and structures have been tested as potential receptors of fullerenes C60, C70 and C40. Among these bowls are corannulene (C20H10), sumanene (C21H12), pinakene (C28H14), hemifullerene (C30H12), circumtrindene (C36H12), pentaindenocorannulene (C50H20) and bowl-shaped hexabenzocoronene derivatives. An exhaustive study, taking into account different orientations of fullerenes, was performed in order to obtain the most favourable arrangement for interacting with the bowls. Complexes were optimised at the SCC-DFTB-D level and interaction energies were obtained at the B97-D2/TZVP level including BSSE corrections. Comparison with the full B97-D2/TZVP results (optimisation plus interaction energies) suggests that the B97-D2/TZVP//SCC-DFTB-D approach may be a useful screening tool for designing fullerene receptors. Regarding the "catching" ability of the different buckybowls, it can be concluded that the shape of a buckybowl plays a crucial role in its success. Thus, it seems that the addition of flaps at the bowl rim by benzannelation is an effective strategy for enhancing the interaction with fullerenes, providing enough flexibility to extend the contact surface with the fullerene moiety. Accordingly, a bowl-shaped hexabenzocoronene derivative (C72H24) showed the best ability among the buckybowls evaluated for catching the fullerenes C60, C70 and C40; it is noteworthy that, when interacting with C60, the interaction energy is three times that corresponding to the prototypical buckybowl, corannulene. On the contrary, the more rigid and compact is the structure of a buckybowl, the smaller its ability to interact with fullerenes.

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.

Interaction between the guanidinium cation and aromatic amino acids.

The interaction of the guanidinium cation with phenylalanine, tyrosine and tryptophan has been studied using a variety of computational methods. Benchmark values for the interaction have been estimated using the CCSD(T) method extrapolated to the complete basis set limit, indicating that the complexation energy amounts to -123.0, -124.4 and -134.2 kJ mol(-1) for Phe, Tyr and Trp, respectively. Most stable minima correspond to neutral folded amino acids, with the cation interacting simultaneously with the carboxyl oxygen, the amino nitrogen and the aromatic ring. However, complexes with the amino acids as zwitterions are as stable as neutral ones. The final relative stability of the different structures results from a complex balance among different contributions to the complexation energy. Extended neutral structures are favored by larger electrostatic and smaller repulsion contributions, as well as by smaller deformation costs for bringing the amino acid to its final geometry into the complex. Zwitterions show large electrostatic and induction contributions that cancel out the huge deformation cost needed to transfer the proton to the amino group. The presence of the cation···π contact in folded minima introduces larger contributions from induction and dispersion (also as a consequence of the bulky guanidinium cation) that are able to overcome other effects, making folded minima the most stable together with zwitterionic ones.