Density Functional Theory Investigation of the Contributions of π−π Stacking and Hydrogen Bonding with Water to the Supramolecular Aggregation Interactions of Model Asphaltene Heterocyclic Compounds

Density Functional Theory Investigation of the Contributions of π−π Stacking and Hydrogen Bonding with Water to the Supramolecular Aggregation Interactions of Model Asphaltene Heterocyclic Compounds | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Density Functional Theory Investigation of the Contributions of π−π Stacking and Hydrogen Bonding with Water to the Supramolecular Aggregation Interactions of Model Asphaltene Heterocyclic Compounds Milena D. Lessa, Stanislav R. Stoyanov, José Walkimar M. Carneiro, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3897675/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Apr, 2024 Read the published version in Journal of Molecular Modeling → Version 1 posted 4 You are reading this latest preprint version Abstract A complex supramolecular process involving electrostatic and dispersion interactions, asphaltene aggregation is associated with detrimental petroleum deposition and scaling that pose challenges to petroleum recovery, transportation, and upgrading. The density functional ωB97X-D with a dispersion correction was employed to investigate supramolecular aggregates incorporating heterocycles dimers with 0, 1, 2, and 3 water molecules forming a stabilizing bridge connecting the monomers. The homodimers of seven heterocyclic model compounds, representative of moieties commonly found in asphaltene structures were studied: pyridine, thiophene, furan, isoquinoline, pyrazine, thiazole, and 1,3-oxazole. The contributions of hydrogen bonding involving water bridges spanning between dimers and π−π stacking to the total interaction energy were calculated and analyzed. The distance between the planes of the aromatic rings is correlated with the π-π stacking interaction strength. All the dimerization reactions are exothermic, although not spontaneous. This is mostly modulated by the strength of the hydrogen bond of the water bridge and the π-π stacking interaction. Dimers bridged by two water molecules are more stable than with additional water molecules or without any water molecule in the bridge. Energy decomposition analysis show that the electrostatic and polarization components are the main stabilizing terms for the hydrogen bond interaction in the bridge, contributing with at least 80% of the interaction energy in all dimers. The non-covalent interaction analysis confirms the molecular sites that have the strongest (hydrogen bond) and weak (π-π stacking) attractive interactions. They are concentrated in the water bridge and in the plane between the aromatic rings, respectively. Heterocycles dimers DFT interaction analysis Chemical scaling Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Highlights - The hydrogen bond bridge is as important as the π-π stacking interaction for the heterocycle dimer interaction; - The most stable heterocycles’ water bridge is formed by 2 water molecules linking the dimers; - The electrostatic and polarization components are the main stabilizing terms for the water bridge hydrogen bond interaction; - The NCI plot distribution shows that the hydrogen bond stabilization is stronger than the π-π stacking; Synopsis The supramolecular interactions between heterocyclic aromatic dimers involving water bridges are quantified in terms of energetic and geometric parameters of π-π stacking and hydrogen bonding contributions. The results show an exothermic and non spontaneous aggregation with two water molecules forming inter-dimer bridge, and hydrogen bonding interaction being as important as π-π stacking for adduct stabilization. Introduction In the last decades, the efficient extraction and transport, marine and terrestrial, of crude oil has become an increasing challenge for the petroleum industry, mainly due to organic and inorganic depositions [ 1 , 2 ]. The formation of insoluble aggregates occurs on the surfaces of practically all oil production and transportation systems: in pipelines, reservoirs, containment screens, submerged or surface installations that significantly reduce the recovery of oil [ 3 , 4 ]. This generates a large financial loss for the oil industry that, as preventive or remedial measures, must stop production for cleaning or maintenance to increase the useful life of the equipment and the continuity of oil recovery [ 4 – 6 ]. Asphaltenes, the densest and most polar fraction of petroleum, are considered the main generators of organic deposition in oil production and transportation systems [ 7 , 8 ]. They are a mixture of large molecular weight organic molecules containing polyaromatic chains, side alkyl groups, polar functional groups and heterocycles with O, N and S as heteroatoms [ 9 , 10 ]. Regarding the molecular structure, asphaltenes can be considered as belonging to the continental model, containing a central aromatic moiety with more than 7 fused rings and pendant aliphatic chains, or the archipelago model, formed by smaller aromatic moieties interconnected by bridges of alkyl groups [ 10 , 11 ]. Experimental and computational studies show that these structures exhibit a strong aggregation preference in solution, forming insoluble solids that reduce oil recovery [ 12 – 20 ]. Asphaltene aggregation is also detrimental in the context of spill response in the event of accidental oil spills in water [ 21 , 22 ]. Due to the complex constitution of asphaltenes, the insoluble aggregates are stabilized by dispersive, polarization, and electrostatic interactions, arising mainly from London forces, π-π stacking, exchange-repulsion contributions, hydrogen bonding and dipole-dipole interactions [ 23 – 26 ]. Recently, Hassanzadeh and Abdouss [ 27 ], based on studies using the supramolecular assembly model by Gray et al. [ 28 ] and the nanoaggregate model by Yen–Mullins [ 29 ], have proposed a supramolecular organization model of asphaltene aggregation that combines cooperative binding by acid-base interactions, hydrogen bonding, π-π stacking, and metal coordination, as well as the formation of hydrophobic pockets, porous networks, and host-guest complexes. All these diverse supramolecular interactions are important for the attraction between asphaltene molecules that leads up to generate organic scaling. Based on the supramolecular assembly model [ 28 ], Gray et al. have developed organic molecules that would experimentally simulate the aggregation behavior of asphaltenes [ 30 ]. Figure 1 shows the structure of one of these synthetic asphaltene molecules that contains a bipyridine tethered with ethyl groups to two pyrene moieties. In previous works [ 31 , 32 ] we investigated computationally the interaction between model asphaltene compounds, reported by Gray et al., to rationalize the experimental information that water traces could enhance the aggregation behavior of asphaltenes. We showed that water molecules could interact with the N atoms of the stacked dimers of asphaltene model compounds, such as PBP and its analogs with varied aromatic hydrocarbon groups. The interaction strength comparison between the π-π stacking and hydrogen bond showed that these interactions have almost the same contribution to the stabilization of the nanoaggregate [ 31 , 32 ]. In the present study, we explore the formation of bridges of water molecules spanning between the stacked homodimers of N, O, and S-containing heterocycles and evaluate the enhancement of the supramolecular interaction strength. The heterocycles pyridine, thiophene, isoquinoline and furan were selected due to their presence as moieties in asphaltene structures [ 33 – 38 ]. Additionally, the heterocycles pyrazine, 1,3-oxazole and 1,3-thiazole were included to study aromatic compounds with two heteroatoms. The structures of these compounds are shown in Fig. 2 . The contributions of π-π stacking and hydrogen bonding interaction to the aggregate stabilization were investigated using noncovalent interaction and energy decomposition analysis (EDA). The interaction energy was rationalized in terms of geometric and energetic parameters inherent to the dimers and monomers. Computational Methods The DFT calculations were performed with the ωB97X-D exchange–correlation density functional with a dispersion energy correction [ 39 ]. Several studies have previously shown successful results with the account of the interaction of π-conjugated oligomers [ 40 ], aggregation of asphaltene model compounds [ 32 , 19 ] and the interaction of polycondensed aromatic molecules [ 41 ]. We employed the Def2-SVP basis set for all atoms. This is a Split Valence Double Zeta basis set with polarization functions for all atoms, proposed by Ahlrichs and Weigeng [ 42 ]. All calculations were performed in Gaussian09 [ 43 ]. After full geometry optimization, the second-order force constant matrix was calculated to confirm that the optimized geometry is a genuine minimum on the potential energy surface. The thermodynamic results are important for the computational determination of the enthalpy and Gibbs free energy of the formation of supramolecular aggregates. The basis set superposition error (BSSE) was accounted for by the counterpoise correction procedure [ 44 ]. The B3LYP/Def2-SVP method was employed for the energy decomposition analysis using the GAMESS software [ 45 , 46 ]. The EDA procedure [ 47 – 49 ] decomposes the total interaction energy in five components: electrostatic (E Elec ), polarization (E Pol ), exchange (E Xc ), dispersion (E Disp ), and Pauli repulsion (E Pauli ). The sum of the polarization and exchange terms yields the covalent component of the interaction. Non-covalent interactions between the monomers in the dimer structure and between the monomers and water molecules in the aggregate structure were also analyzed. For this, we used the NCIplot software [ 50 ]. This software calculates the attractive and repulsive interactions present in the system as a function of the electron density and its reduced gradient. Non-covalent interactions are plotted as an isosurface map using Visual Molecular Dynamics [ 51 ]. Results and Discussion Geometry Optimization. The geometries of 28 supramolecular aggregates containing homodimers and water molecules were fully optimized with the ωB97X-D/Def2-SVP method. The optimized structures for the aggregates containing dimers with and without water molecules are shown in Fig. 3 . For pyridine, furan, thiophene and isoquinoline which have one heteroatom, only one water bridge is formed, whereas for the pyrazine, oxazole and thiazole rings that have two heteroatoms, two water bridges are formed, stabilizing the dimer structure. For pyridine, furan, thiophene, isoquinoline, oxazole and thiazole dimers, the bridge can be formed by one, two or three water molecules, with the aromatic moieties retaining almost parallel orientation. For the pyrazine dimer, only bridges with one or two water molecules are formed. The pyrazine aggregate, composed by three water molecules (Pyra 2 (H 2 O) 6 ), upon optimization converges to a structure where only two water molecules are in the bridge with the third water molecule being hydrogen bonded to the water bridge. As pyrazine has two heteroatoms, two water bridges may be formed, making the aggregate more rigid and keeping the interplanar distance short because of the stabilizing effects of the water bridges. The high symmetry of the pyrazine ring strengthens the π-staking interaction and does not allow the aromatic rings to be sufficiently far from each other to accommodate a third water molecule in the bridge. For isoquinoline, both the dimer without any water molecule (Iso 2 ) and the aggregate with three water molecules (Iso 2 (H 2 O) 6 ) have aromatic rings that are in non-parallel planes, whereas the aggregates of isoquinoline with one (Iso 2 (H 2 O) 2 ) or two (Iso 2 (H 2 O) 4 ) water molecules in the bridge have well aligned aromatic planes. The bridge of one or two water molecules forces the aromatic planes to be one above the other. The dimer without water (Iso 2 ) does not exhibit this effect. The aggregate with three water molecules has more degrees of freedom and a longer bridge that causes the distortion of the heterocyclic plane rather than constraining those to a parallel configuration. The thiazole aggregates with one or two water molecules in the bridge exhibit more substantial horizontal displacement than the structures with three water molecules (Thia 2 (H 2 O) 6 ) and the water-free dimer (Thia 2 ). This is related to the interaction of the water molecules with the heteroatom of the aromatic system and the resultant competition between π-π stacking and electrostatic interaction. Moreover, in the aggregates with one (Thia 2 (H 2 O) 2 ) or two (Thia 2 (H 2 O) 4 ) water molecules per bridge as well as in the water-free dimer (Thia 2 ), the heterocycles are in a staggered configuration, i.e., the N and S atoms of one of the monomers are on opposite sides from those in the other monomer. Thus, the water bridges span between different heteroatoms, forming N … H 2 O … S networks, whereas for the bridge containing three water molecules the interaction is with the same heteroatom, forming N … H 2 O … N and S … H 2 O … S hydrogen bonding networks. We also calculated the thiazole aggregates with bridges containing one (Thia 2 (H 2 O) 2 ) and two water molecules (Thia 2 (H 2 O) 4 ) involving the same heteroatom, i.e., N … H 2 O … N and S … H 2 O … S, but these are less stable than the Thia 2 (H 2 O) 2 and Thia 2 (H 2 O) 4 shown in Fig. 3 . As S has a larger atomic radius than N, its orbitals do not align with the one of the other atoms of the aromatic ring and the π-stacking interaction is more effective by the side of the N atom. This is the reason why the aromatic rings are horizontally displaced, as in the dimer without water molecules (Thia 2 ) the S atoms are in positions opposite to each other. In the aggregate containing three water molecules per bridge (Thia 2 (H 2 O) 6 ), the longer bridge allows the water trimer to interact with the same heteroatoms. It was not possible to optimize the aggregate with a water trimer bridge spanning between different heteroatoms. Energy calculation. The stabilization of the dimer structures is due to the π-π stacking and the water bridge hydrogen bond interactions. The π-π stacking interaction between the rings in each dimer structure was accounted for by means of the ASM method (Activation Strain Model). This model, proposed by Fernández and Bickelhaupt [ 52 ], is a computational approach that uses electronic structure calculations to rationalize the factors that control stability in each stationary point along a reaction coordinate. According to the ASM model, the activation energy (E) can be decomposed into two contributions along the reaction coordinate (Eq. 1). The first one is the strain or distortion energy, \(\varDelta {E}_{STRAIN}\) , related to the deformation of the reactants, mainly affected by the rigidity of their molecular structure and by distortion in pendant groups. The second component is the interaction energy, \(\varDelta {E}_{INT},\) between the reactants, related to the binding capacity between the reactants, which, in our case, accounts to the π-π stacking interaction. \(\varDelta E=\varDelta {E}_{STRAIN}+\varDelta {E}_{INT}\) Eq. 1 In general, \(\varDelta {E}_{STRAIN}\) is a positive term, which destabilizes the system and the \(\varDelta {E}_{INT}\) is a negative term, stabilizing the system. The \(\varDelta {E}_{INT}\) can be decomposed into stabilizing electrostatic interaction (Coulomb) between fragments ∆𝑉 𝑒𝑙𝑠𝑡 (z), destabilizing interaction derived from the overlap of filled orbitals ∆𝐸 𝑃𝑎𝑢𝑙𝑖 (z), orbital interaction energy ∆𝐸 𝑜𝑖 (𝑧), responsible for the charge transfer (HOMO-LUMO interactions, for example) and polarization (mixing unoccupied and occupied orbitals in the different fragments), and the interaction due to dispersion forces ∆𝐸 𝑑𝑖𝑠𝑝 (𝑧). These data are presented in the Supplementary Material. Table 1 presents the values of \(\varDelta {E}_{INT}\) between the heteroaromatic ring dimers and the interplanar distance of the structures shown in Figure 3 . The analysis of Table 1 shows that the strongest \(\varDelta {E}_{INT}\) interaction, corresponding to the lowest energy value, are for the aggregates without any water molecule in the structure. The larger freedom or reduced constraints of the π-electronic clouds of the rings that can undergo horizontal displacement enhance π-π stacking interaction. The largest values of \(\varDelta {E}_{INT}\) is for the isoquinoline ring, almost twice the values found for the other rings; it is followed by the pyrazole and pyridine rings. The isoquinoline is the only system with two fused rings, that enhances π-π stacking interaction. Thus, for water-free dimers, \(\varDelta {E}_{INT}\) is modulated by the size of the aromatic system. The structures linked by water molecules are more rigid and constrained, which cannot assume the alignment between the ring planes required to accommodate the electron density for the π-stacking interaction. In all cases, we note that the aggregates containing a bridge of just one water molecule have the smallest (less negative) \(\varDelta {E}_{INT}\) interaction among the water bridged dimers. The bridge formed by only one water molecule makes the system more rigid, restricting the planes from the adequate horizontal displacement for optimal π-stacking interaction. Generally, the aggregates with two water molecules in the bridge have the second lowest \(\varDelta {E}_{INT}\) , followed by the dimers with three water molecules per bridge. The bridges containing two water molecules apparently provide more favorable structural arrangements for the aromatic planes that enhance the π-stacking interaction than the bridges with three water molecules. In Table 1 we also show the interplanar distance in the dimers. For the pyridine and furan dimers, we notice that as the number of water molecules in the bridge increases, the distance becomes larger. This is due to the hydrogen bond interaction between the dimers and the water bridge that is so effective that enhances the distance between the aromatic planes. For the thiophene and pyrazole aggregates with bridges of two water molecules (Thio 2 (H 2 O) 2 and Pyra 2 (H 2 O) 4 ), the interplanar distance is smaller than for the aggregates with bridges of three water molecules. This is attributable to the more effective accommodation of the aromatic electronic cloud overlap between the planes. For the oxazole and isoquinoline aggregates, the dimers with two (Oxa 2 (H 2 O) 2 and Iso 2 (H 2 O) 2 ) and three (Oxa 2 (H 2 O) 3 and Iso 2 (H 2 O) 3 ) water molecules in the bridge have shorter interplanar distances than those with one or without any water molecule in the bridge. For the isoquinoline system, the aromatic planes deviate from parallel to a crossed configuration as the number of water molecules increases, disrupting the π-π stacking interaction; however, the shorter interplanar distance likely partially offsets for the decreased parallel alignment. The thiazole dimer with two water molecules (Thio 2 (H 2 O) 4 ) in the bridge has the longest interplanar distance of all aggregates analyzed. The π-π stacking interaction and dipole-dipole interaction of the S atom with the water molecules in the bridge is not as strong as the hydrogen bonding within the bridge. The enthalpy (ΔH) and Gibbs free energy (ΔG) for the supramolecular aggregation was calculated considering either none or a cluster of 1–3 water molecules ( Equations 2 and 3 ). \({\Delta }H={H}_{complex }-({2H}_{monomer }+{H}_{\left({H}_{2}O\right)x})\) Eq. 2 \({\Delta }G={G}_{complex }-({2G}_{monomer }+{G}_{\left({H}_{2}O\right)}\) x ) Eq. 3 where \({H\left(or G\right)}_{complex }\) is the enthalpy (or Gibbs free energy) of the aggregate with or without water molecules in the bridge, \({H\left(or G\right)}_{monomer }\) is the enthalpy (or Gibbs free energy) of each monomer and \({E}_{{{(H}_{2}O)}_{x}}\) is the enthalpy (or Gibbs free energy) of one ( \(x=1\) ), cluster of two ( \(x=2\) ) or cluster of three ( \(x=3\) ) water molecules. In Table 1 , we show the π-π stacking interaction and thermodynamic results for all the structures shown in Fig. 3 . In the water-free dimers, the ΔH and ΔG are stabilized only due to the π-π stacking interaction between the monomers. In aggregates with the water molecules, in addition to the π-π stacking interaction, the hydrogen bonds also help stabilize the complexes. Table 1 \(\varDelta {E}_{INT}\) (in kcal mol − 1 ), ΔH (in kcal mol − 1 ) and ΔG (in kcal mol − 1 ) for the formation of the aggregates presented in Fig. 3 . The distance ( D ) between the centers of the aromatic rings is in angstrom ( Å ). Values for ΔH and ΔG are corrected by BSSE. \(\varvec{\Delta }{\varvec{E}}_{\varvec{I}\varvec{N}\varvec{T}}\) ΔH* ΔG* D** Pyr 2 -5.53 -2.99 3.79 3.630 Pyr 2 (H 2 O) -4.35 -7.80 10.92 3.707 Pyr 2 (H 2 O) 2 -5.03 -13.15 9.60 3.727 Pyr 2 (H 2 O) 3 -4.55 -10.16 10.41 3.749 Fur 2 -3.95 -1.19 7.55 3.467 Fur 2 (H 2 O) -3.61 -0.18 20.48 3.637 Fur 2 (H 2 O) 2 -3.83 -3.49 20.18 3.700 Fur 2 (H 2 O) 3 -3.81 -0.98 21.26 3.707 Thio 2 -4.21 -1.23 7.99 3.712 Thio 2 (H 2 O) -3.51 -1.30 16.94 3.886 Thio 2 (H 2 O) 2 -3.85 -4.32 16.60 3.785 Thio 2 (H 2 O) 3 -3.52 -1.92 18.39 4.250 Iso 2 -10.75 -7.10 3.71 3.624 Iso 2 (H 2 O) -8.96 -11.76 9.20 3.626 Iso 2 (H 2 O) 2 -10.40 -18.06 7.51 3.537 Iso 2 (H 2 O) 3 -10.51 -15.34 8.38 3.547 Pyra 2 -5.75 -3.63 7.07 3.508 Pyra 2 (H 2 O) 2 -4.08 -12.92 15.36 3.600 Pyra 2 (H 2 O) 4 -5.52 -24.23 13.94 3.448 Pyra 2 (H 2 O) 6 -5.21 -27.28 8.26 3.582 Thia 2 -4.79 -1.81 6.44 3.685 Thia 2 (H 2 O) 2 -2.26 -6.85 21.30 4.810 Thia 2 (H 2 O) 4 -2.71 -19.50 16.26 4.880 Thia 2 (H 2 O) 6 -4.76 -11.14 21.43 3.723 Oxa 2 -4.91 -1.86 7.65 3.437 Oxa 2 (H 2 O) 2 -3.83 -8.40 18.24 3.511 Oxa 2 (H 2 O) 4 -4.84 -19.59 17.59 3.393 Oxa 2 (H 2 O) 6 -4.87 -12.90 19.75 3.380 *ΔH and ΔG values were calculated taking the isolated monomers and one, a cluster of two or a cluster of three water molecules as reference. **The distance shown is the distance between the centers of the aromatic rings. The analysis of Table 1 shows that the aggregations are exothermic (negative ΔH), although not spontaneous (positive ΔG). In general, the aggregates containing two or three water molecules per bridge are the ones that have the smallest values of ΔH, suggesting that the complexes formed with two water molecules are the most stable, followed by those with three water molecules. This result has previously been reported based on the calculation of the aggregation of model asphaltene compounds [ 32 ]. As the ΔH analysis account for both the π-stacking and the hydrogen bond terms, the aggregates with two water molecules per bridge must have the strongest stabilization by hydrogen bonding. The ΔG analysis shows that the structures without any water molecules have the smallest values, although still being positive, in agreement with the experimental report that these molecules do not aggregate spontaneously [ 31 ]. The water bridges increase the distance between the heterocycles, by a maximum of 0.1 Å, weakening the π-π stacking interaction; however, the stabilization of the aggregate seems to be compensated by the hydrogen bonds, since the formation of complexes with two or three water molecules are exothermic. Intermolecular interactions. To examine the non-covalent interactions between the monomers in the dimer structure and between the monomers and water bridges, the NCI plots of the optimized structures of the supramolecular aggregates are presented in Fig. 4 . The isosurface colors vary between green and blue colors. The green color represents a weak favorable non-covalent interaction, such as van der Waals interaction. The blue color represents strong favorable non-covalent interactions, such as conventional hydrogen bonds. Unfavorable and repulsive interactions, represented in red color, are not observed on the isosurfaces of any of the aggregates investigated. The analysis of Fig. 4 shows that the green area corresponds to the π-π stacking interaction between the heteroaromatic rings. The green color indicates that this interaction is weak, as expected for this type of interaction, and the dispersed isosurface shows a delocalized interaction. There is no significant difference in the plotted area for the aggregates with one, two, or three waters in relation to the dimers without water. As isoquinoline is composed by two fused aromatic rings, its π-stacking interaction is more diffuse and is seen with enlarged green area. Light blue areas, representing strong attractive interactions due to hydrogen bonding, are also seen in Fig. 4 . The blue regions represent localized interactions and are not as dispersed as the green ones. Furthermore, as the number of water molecules per bridge increases, the localized interactions shown in blue, corresponding to hydrogen bonds, increase, indicating a stronger bridging interaction, as expected for hydrogen bonding networks. For the interaction between the S atom and the water molecules, in thiophene and thiazole, we could not observe blue areas, indicating weaker dipole-dipole interactions. Energy Decomposition Analysis (EDA). The EDA method decomposes the total interaction energy (E tot ) of supramolecular aggregates into five components: electrostatic, E Elec , (opposite charge attraction), polarization, E Pol , (orbital overlap), exchange, E Xc , (parallel spin stabilization), dispersion, E Disp , (long range interactions) and Pauli repulsion, E Pauli , (electronic repulsion) terms [ 47 – 49 ]. The bond between the dimer (first fragment) and the water bridge (second fragment) was decomposed and analyzed. Table 2 shows the EDA results. Table 2 The EDA components E tot , E Elec , E Pol , E Xc , E Disp and E Pauli in kcal mol − 1 . E Elec E Pol E Xc E Disp E Pauli E Tot Pyr 2 (H 2 O) -16.55 -15.87 -7.94 -6.36 32.99 -13.72 Pyr 2 (H 2 O) 2 -23.16 -22.63 -10.93 -8.79 44.39 -21.11 Pyr 2 (H 2 O) 3 -22.61 -25.41 -11.62 -8.96 46.19 -22.40 Fur 2 (H 2 O) -13.65 -13.98 -9.00 -6.94 37.85 -5.72 Fur 2 (H 2 O) 2 -23.61 -22.57 -15.49 -10.28 60.47 -11.48 Fur 2 (H 2 O) 3 -25.92 -25.41 -17.88 -10.81 67.31 -12.71 Thio 2 (H 2 O) -5.53 -9.15 -2.88 -4.72 16.97 -5.31 Thio 2 (H 2 O) 2 -9.38 -14.22 -4.82 -6.81 25.52 -9.71 Thio 2 (H 2 O) 3 -11.74 -14.94 -5.87 -8.52 32.19 -8.90 Iso 2 (H 2 O) -17.94 -16.47 -8.94 -6.57 36.02 -13.90 Iso 2 (H 2 O) 2 -30.95 -29.23 -18.33 -10.47 67.80 -21.18 Iso 2 (H 2 O) 3 -21.00 -25.24 -9.36 -9.25 41.12 -23.73 Pyra 2 (H 2 O) 2 -22.75 -23.44 -7.76 -10.26 40.00 -24.21 Pyra 2 (H 2 O) 4 -41.07 -40.15 -18.66 -16.94 79.71 -37.11 Pyra 2 (H 2 O) 6 -38.89 -38.92 -17.02 -16.83 75.78 -35.88 Thia 2 (H 2 O) 2 -19.50 -21.94 -9.29 -10.21 44.65 -16.29 Thia 2 (H 2 O) 4 -31.72 -35.84 -15.64 -15.93 70.42 -28.70 Thia 2 (H 2 O) 6 -34.94 -37.34 -18.73 -16.91 80.49 -27.43 Oxa 2 (H 2 O) 2 -16.39 -18.86 -4.37 -8.93 29.54 -19.01 Oxa 2 (H 2 O) 4 -35.35 -34.25 -14.10 -15.47 66.22 -32.95 Oxa 2 (H 2 O) 6 -35.91 -37.39 -14.56 -15.88 67.48 -36.26 The analysis of Table 2 shows a trend that is observed for all the components of the interaction as well as for the total interaction energy. As a general trend, the total interaction energy increases when increasing the number of water molecules in the bridge. However, the incremental difference is much more relevant for the first water molecule than for the second or the third one. For example, the difference in the E tot values for the aggregates with one water molecule per bridge to those with two water molecules per bridge is 9.15 ± 3,55 kcal mol − 1 , whereas the difference for the aggregates with two water molecules per bridge to those with three water molecules per bridge is only 1.05 ± 1.65 kcal mol − 1 . This shows that the aggregates with two and three water molecules are significantly more stabilized than those with only one water molecule per bridge. Also, the energies of aggregates with two or three water molecules in the bridge do not vary substantially. The dispersion term (Table 2 ), accounting for long range interactions, has the smallest variation (standard deviation of 3.68 kcal mol − 1 ). It also changes more strongly from the aggregates with one water molecule per bridge to the ones with two water molecules per bridge than for additional water molecules. The structures with the stronger electrostatic term also have the largest repulsion term (E Pauli ). In Fig. 5 , we present the electrostatic and covalent components of the total interaction energy. In this model, the ionic character of the interaction is accounted for by the E Elec term, which comes mainly from opposite charge attraction sites. The covalent component is due to the sum of the E Pol and E Xc terms and considers the overlap of the atomic orbitals that compose the interaction. We can see for all dimers that the covalent character is almost two times larger than the ionic character, corresponding to a stabilization of -12.54 ± 4.41 kcal mol − 1 . As the pyrazole, thiazole, and pyrazine aggregates have two water bridges, the stabilization per water bridge is the total value divided by two. Considering the stabilization energy per water bridge, the most stable aggregates are those with hydrogen bonds between the heteroatom of the dimer and water of the bridge, i.e., interaction of H of water bridge with the O or N atom of the heterocycle. The S-containing heterocycles thiophene and thiazole with dipole-dipole interaction between the H atom of the water bridge and S atom of the heterocycle have lower stabilization energy. Conclusion We investigated the interaction of the supramolecular aggregation of 7 heterocyclic aromatic compounds as water-free dimers as well as dimers with water bridges bonded to the heteroatoms and spanning between the organic planes. We observed, for most of the aggregates that the interaction is favored by bridges composed of two water molecules. Only for the 1,3-thiazole the favorite bridge has three water molecules, probably due to the softness of the sulfur atom. The π-π stacking interaction analysis showed that the water-free dimers have the strongest interaction, followed by the dimers with two water molecules per bridge. In almost all cases, the π-π stacking interaction strength is modulated by the interplanar distance between the monomers in the dimer structure. The ΔH analysis showed that aggregation is an exothermic process. The most stable aggregate for each heterocycle is the system with two water molecules per bridge. The ΔG analysis showed non spontaneous aggregation processes with the smallest values for the dimer without any water molecule in the bridge. The NCI plot analysis identified strong interaction sites around the water molecules, representing hydrogen bonding interactions, and weak attraction between the planes of the organic molecules, representing the π-stacking interactions. The hydrogen bonds between the dimers and the water bridges were decomposed by using the EDA method. The results indicated that the covalent character (polarization and exchange) of the interaction is almost twice as large as the electrostatic term. We also noticed that with one water molecule in the bridge led to a small stabilization of the aggregate, whereas two or three water molecules in the bridge add a considerable stabilization to the supramolecular system, with the aggregates having two water molecules per bridge being the most stable. Our findings justify the conclusion that the π-π stacking interaction is as important as hydrogen bonding for the stabilization of the dimers bridged by water molecules. Declarations Funding Declaration This work was developed without any funding. Acknowledgments Dr. José Walkimar de M. Carneiro and Dr. Leonardo Moreira da Costa acknowledge FAPERJ (Fundação de Amparo a Pesquisa do Estado do Rio de Janeiro), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico). Dr. Stanislav R. Stoyanov acknowledges the support of the Government of Canada’s Program of Energy Research and Development (PERD). Milena D. Lessa was supported by a research fellowship from the MIDAS INCT. Author Contribution MDL and LMC wrote the main manuscript text. MDL prepared the figures and tables of the article.SRS and JWMC reviewed the manuscript.MDL, LMC, SRS and JWMC discussed all the results and analyzed them. References Kamal, M. S.; Hussein, I.; Mahmoud, M.; Sultan, A. S.; Saad, M. A.; J. Pet. Sci. Eng . 2018 , 171, 127. Barber, M.; Water-Formed Deposits; Elsevier: 2022, 295-306. Bader, M. S. H.; J. Pet. Sci. Eng . 2007 , 55, 93. Olajire, A. A.; J. Pet. Sci. Eng . 2015 , 135, 723. Sheu, E. Y.; Mullins, O. C.; Energy Fuels . 2002 , 16, 74. Wiehe, I. A.; Process Chemistry of Petroleum Macromolecules ; CRC Press: Boca Raton, USA, 2008, 427. Ali, S. I.; Lalji, S. M.; Haneef, J.; Louis, C.; Saboor, A.; Yousaf, N.; J. Pet. Explr. Prod. Technol . 2021 , 11, 3599. 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Chim. Acta . 1977 , 46, 1. Contreras-García, J.; Johnson, E. R.; Keinan, S.; Chaudret, R.; Piquemal, J. P.; Beratan, D. N.; Yang, W.; J. Chem. Theory Comput. 2011 , 7, 625. Humphrey, W.; Dalke, A.; Schulten, K.; J. Mol. Graph . 1996 , 14, 33. Fernández, I.; Bickelhaupt, F. M.; Chem. Soc. Rev . 2014 , 43, 4953. Additional Declarations No competing interests reported. Supplementary Files floatimage1.jpeg Graphical Abstract JMMSupportingInformation.docx Cite Share Download PDF Status: Published Journal Publication published 24 Apr, 2024 Read the published version in Journal of Molecular Modeling → Version 1 posted Editorial decision: Revision requested 02 Feb, 2024 Editor assigned by journal 02 Feb, 2024 Submission checks completed at journal 02 Feb, 2024 First submitted to journal 25 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Lessa","email":"","orcid":"","institution":"Universidade Federal Fluminense","correspondingAuthor":false,"prefix":"","firstName":"Milena","middleName":"D.","lastName":"Lessa","suffix":""},{"id":270698763,"identity":"174058df-57ac-4e35-8031-a53e6f4fe380","order_by":1,"name":"Stanislav R. Stoyanov","email":"","orcid":"","institution":"Natural Resources Canada, Canmet ENERGY Devon","correspondingAuthor":false,"prefix":"","firstName":"Stanislav","middleName":"R.","lastName":"Stoyanov","suffix":""},{"id":270698764,"identity":"ae62cb46-e87f-4224-bf53-a98e147b7eb9","order_by":2,"name":"José Walkimar M. Carneiro","email":"","orcid":"","institution":"Universidade Federal Fluminense","correspondingAuthor":false,"prefix":"","firstName":"José","middleName":"Walkimar M.","lastName":"Carneiro","suffix":""},{"id":270698765,"identity":"7b6fccc5-7192-4b28-962b-2091cfb8adfa","order_by":3,"name":"Leonardo M. Costa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuElEQVRIiWNgGAWjYBACPigtx8aQwMBQYQMiCQA2MJnAYAzWciaNBC2JDcRrETv88OHPH3bpfewJbBIHEhjyzBsIaZFOMzbmSUjObeN5ANZSLHOAoJYcNmmGBObcNokENumPPxgSZxB0GFCL5I+E+nQ2CYjDiNMiwZNwOIEULSC/pB03bON52GxxIEGiWIKQFn7p5IcPf9hUy8u3Jx+8cSDBJo+gFiTA2AAkSNEwCkbBKBgFowAnAADnaTW3XVDmXQAAAABJRU5ErkJggg==","orcid":"","institution":"Universidade Federal Fluminense","correspondingAuthor":true,"prefix":"","firstName":"Leonardo","middleName":"M.","lastName":"Costa","suffix":""}],"badges":[],"createdAt":"2024-01-25 15:44:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3897675/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3897675/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00894-024-05922-3","type":"published","date":"2024-04-24T23:22:11+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":50650059,"identity":"d499c652-abc3-4a23-8603-0eee9064a9af","added_by":"auto","created_at":"2024-02-05 08:47:09","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":15256,"visible":true,"origin":"","legend":"\u003cp\u003eModel structure of 4,4’-bis(2-pyren-1-yl-ethyl)-2,2’-bipyridine (PBP).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/e55d9975e3009aa2c374dfd0.png"},{"id":50650060,"identity":"ada9ce34-be82-42ea-8992-b571e4d67a6b","added_by":"auto","created_at":"2024-02-05 08:47:09","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":114257,"visible":true,"origin":"","legend":"\u003cp\u003eChemical structures of heterocyclic aromatic model compounds and the respective abbreviations: (I) Pyridine, \u003cstrong\u003ePyr\u003c/strong\u003e, (II) Thiophene, \u003cstrong\u003eThio\u003c/strong\u003e, (III) Furan, \u003cstrong\u003eFur\u003c/strong\u003e, (IV) Isoquinoline, \u003cstrong\u003eIso\u003c/strong\u003e, (V) Pyrazine \u003cstrong\u003ePyra\u003c/strong\u003e, (VI) 1,3-Thiazole, \u003cstrong\u003eThia\u003c/strong\u003e and (VII) 1,3-Oxazole, \u003cstrong\u003eOxa\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/ea06dd84f999786aa6624b37.png"},{"id":50650061,"identity":"5ec9a46a-dc0e-4c1b-85c1-60e60b03136a","added_by":"auto","created_at":"2024-02-05 08:47:09","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":393310,"visible":true,"origin":"","legend":"\u003cp\u003eOptimized geometries of water-free dimers and aggregates containing one, two, or three water molecules per bridge.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/657512e2fd2e108f9286ab4d.png"},{"id":50650065,"identity":"79ff5d1b-d0cf-42cd-903c-b5a67187ef0e","added_by":"auto","created_at":"2024-02-05 08:47:09","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":599725,"visible":true,"origin":"","legend":"\u003cp\u003eOptimized structures of the dimers without water, and with one, two, or three water molecules per bridge, showing the non-covalent interaction obtained with NCIplot.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/2b2aafb9cc7b0099ba69588f.png"},{"id":50650063,"identity":"623f8816-c954-4ec3-8d95-9d0617decf62","added_by":"auto","created_at":"2024-02-05 08:47:09","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":71470,"visible":true,"origin":"","legend":"\u003cp\u003eCovalent component (E\u003csub\u003ePol\u003c/sub\u003e and E\u003csub\u003eXc\u003c/sub\u003e) in orange and electrostatic component (E\u003csub\u003eElec\u003c/sub\u003e) in blue of the total interaction energy based on EDA.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/5f8166d3ec8b0397f9657e62.png"},{"id":55691428,"identity":"aaadec55-c33b-44a2-bd21-0675ad8eb7ce","added_by":"auto","created_at":"2024-05-01 23:22:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2085295,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/9ecaafc2-9fdb-4781-a7b1-7e82c7b0259e.pdf"},{"id":50650471,"identity":"7c6cdec4-d094-4f13-88f7-31d76d6d39e5","added_by":"auto","created_at":"2024-02-05 08:55:09","extension":"jpeg","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":561331,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGraphical Abstract\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/aff4b37d7ff7428cd30ec147.jpeg"},{"id":50650064,"identity":"ecddc0c8-cb5f-47b2-8dd7-4ee7d623b8be","added_by":"auto","created_at":"2024-02-05 08:47:09","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":121160,"visible":true,"origin":"","legend":"","description":"","filename":"JMMSupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-3897675/v1/15aa529d1fdbd202f7d85940.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Density Functional Theory Investigation of the Contributions of π−π Stacking and Hydrogen Bonding with Water to the Supramolecular Aggregation Interactions of Model Asphaltene Heterocyclic Compounds","fulltext":[{"header":"Highlights","content":"\u003cp\u003e- The hydrogen bond bridge is as important as the \u0026pi;-\u0026pi; stacking interaction for the heterocycle dimer interaction;\u003c/p\u003e\n\u003cp\u003e- The most stable heterocycles\u0026rsquo; water bridge is formed by 2 water molecules linking the dimers;\u003c/p\u003e\n\u003cp\u003e- The electrostatic and polarization components are the main stabilizing terms for the water bridge hydrogen bond interaction;\u003c/p\u003e\n\u003cp\u003e- The NCI plot distribution shows that the hydrogen bond stabilization is stronger than the \u0026pi;-\u0026pi;\u0026nbsp;stacking;\u003c/p\u003e\n"},{"header":"Synopsis","content":"\u003cp\u003eThe supramolecular interactions between heterocyclic aromatic dimers involving water bridges are quantified in terms of energetic and geometric parameters of \u0026pi;-\u0026pi; stacking and hydrogen bonding contributions. The results show an exothermic and non spontaneous aggregation with two water molecules forming inter-dimer bridge, and hydrogen bonding interaction being as important as \u0026pi;-\u0026pi; stacking for adduct stabilization.\u003c/p\u003e\n"},{"header":"Introduction","content":"\u003cp\u003eIn the last decades, the efficient extraction and transport, marine and terrestrial, of crude oil has become an increasing challenge for the petroleum industry, mainly due to organic and inorganic depositions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The formation of insoluble aggregates occurs on the surfaces of practically all oil production and transportation systems: in pipelines, reservoirs, containment screens, submerged or surface installations that significantly reduce the recovery of oil [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. This generates a large financial loss for the oil industry that, as preventive or remedial measures, must stop production for cleaning or maintenance to increase the useful life of the equipment and the continuity of oil recovery [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAsphaltenes, the densest and most polar fraction of petroleum, are considered the main generators of organic deposition in oil production and transportation systems [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. They are a mixture of large molecular weight organic molecules containing polyaromatic chains, side alkyl groups, polar functional groups and heterocycles with O, N and S as heteroatoms [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Regarding the molecular structure, asphaltenes can be considered as belonging to the continental model, containing a central aromatic moiety with more than 7 fused rings and pendant aliphatic chains, or the archipelago model, formed by smaller aromatic moieties interconnected by bridges of alkyl groups [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Experimental and computational studies show that these structures exhibit a strong aggregation preference in solution, forming insoluble solids that reduce oil recovery [\u003cspan additionalcitationids=\"CR13 CR14 CR15 CR16 CR17 CR18 CR19\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Asphaltene aggregation is also detrimental in the context of spill response in the event of accidental oil spills in water [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDue to the complex constitution of asphaltenes, the insoluble aggregates are stabilized by dispersive, polarization, and electrostatic interactions, arising mainly from London forces, π-π stacking, exchange-repulsion contributions, hydrogen bonding and dipole-dipole interactions [\u003cspan additionalcitationids=\"CR24 CR25\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Recently, Hassanzadeh and Abdouss [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], based on studies using the supramolecular assembly model by Gray et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] and the nanoaggregate model by Yen\u0026ndash;Mullins [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], have proposed a supramolecular organization model of asphaltene aggregation that combines cooperative binding by acid-base interactions, hydrogen bonding, π-π stacking, and metal coordination, as well as the formation of hydrophobic pockets, porous networks, and host-guest complexes. All these diverse supramolecular interactions are important for the attraction between asphaltene molecules that leads up to generate organic scaling. Based on the supramolecular assembly model [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], Gray et al. have developed organic molecules that would experimentally simulate the aggregation behavior of asphaltenes [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the structure of one of these synthetic asphaltene molecules that contains a bipyridine tethered with ethyl groups to two pyrene moieties.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn previous works [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] we investigated computationally the interaction between model asphaltene compounds, reported by Gray et al., to rationalize the experimental information that water traces could enhance the aggregation behavior of asphaltenes. We showed that water molecules could interact with the N atoms of the stacked dimers of asphaltene model compounds, such as PBP and its analogs with varied aromatic hydrocarbon groups. The interaction strength comparison between the π-π stacking and hydrogen bond showed that these interactions have almost the same contribution to the stabilization of the nanoaggregate [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn the present study, we explore the formation of bridges of water molecules spanning between the stacked homodimers of N, O, and S-containing heterocycles and evaluate the enhancement of the supramolecular interaction strength. The heterocycles pyridine, thiophene, isoquinoline and furan were selected due to their presence as moieties in asphaltene structures [\u003cspan additionalcitationids=\"CR34 CR35 CR36 CR37\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Additionally, the heterocycles pyrazine, 1,3-oxazole and 1,3-thiazole were included to study aromatic compounds with two heteroatoms. The structures of these compounds are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The contributions of π-π stacking and hydrogen bonding interaction to the aggregate stabilization were investigated using noncovalent interaction and energy decomposition analysis (EDA). The interaction energy was rationalized in terms of geometric and energetic parameters inherent to the dimers and monomers.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Computational Methods","content":"\u003cp\u003eThe DFT calculations were performed with the ωB97X-D exchange\u0026ndash;correlation density functional with a dispersion energy correction [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Several studies have previously shown successful results with the account of the interaction of π-conjugated oligomers [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], aggregation of asphaltene model compounds [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] and the interaction of polycondensed aromatic molecules [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. We employed the Def2-SVP basis set for all atoms. This is a Split Valence Double Zeta basis set with polarization functions for all atoms, proposed by Ahlrichs and Weigeng [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. All calculations were performed in Gaussian09 [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. After full geometry optimization, the second-order force constant matrix was calculated to confirm that the optimized geometry is a genuine minimum on the potential energy surface. The thermodynamic results are important for the computational determination of the enthalpy and Gibbs free energy of the formation of supramolecular aggregates. The basis set superposition error (BSSE) was accounted for by the counterpoise correction procedure [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. The B3LYP/Def2-SVP method was employed for the energy decomposition analysis using the GAMESS software [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The EDA procedure [\u003cspan additionalcitationids=\"CR48\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] decomposes the total interaction energy in five components: electrostatic (E\u003csub\u003eElec\u003c/sub\u003e), polarization (E\u003csub\u003ePol\u003c/sub\u003e), exchange (E\u003csub\u003eXc\u003c/sub\u003e), dispersion (E\u003csub\u003eDisp\u003c/sub\u003e), and Pauli repulsion (E\u003csub\u003ePauli\u003c/sub\u003e). The sum of the polarization and exchange terms yields the covalent component of the interaction.\u003c/p\u003e \u003cp\u003eNon-covalent interactions between the monomers in the dimer structure and between the monomers and water molecules in the aggregate structure were also analyzed. For this, we used the NCIplot software [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. This software calculates the attractive and repulsive interactions present in the system as a function of the electron density and its reduced gradient. Non-covalent interactions are plotted as an isosurface map using Visual Molecular Dynamics [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e].\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003e \u003cb\u003eGeometry Optimization.\u003c/b\u003e The geometries of 28 supramolecular aggregates containing homodimers and water molecules were fully optimized with the ωB97X-D/Def2-SVP method. The optimized structures for the aggregates containing dimers with and without water molecules are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. For pyridine, furan, thiophene and isoquinoline which have one heteroatom, only one water bridge is formed, whereas for the pyrazine, oxazole and thiazole rings that have two heteroatoms, two water bridges are formed, stabilizing the dimer structure.\u003c/p\u003e \u003cp\u003eFor pyridine, furan, thiophene, isoquinoline, oxazole and thiazole dimers, the bridge can be formed by one, two or three water molecules, with the aromatic moieties retaining almost parallel orientation. For the pyrazine dimer, only bridges with one or two water molecules are formed. The pyrazine aggregate, composed by three water molecules (Pyra\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e6\u003c/sub\u003e), upon optimization converges to a structure where only two water molecules are in the bridge with the third water molecule being hydrogen bonded to the water bridge. As pyrazine has two heteroatoms, two water bridges may be formed, making the aggregate more rigid and keeping the interplanar distance short because of the stabilizing effects of the water bridges. The high symmetry of the pyrazine ring strengthens the π-staking interaction and does not allow the aromatic rings to be sufficiently far from each other to accommodate a third water molecule in the bridge.\u003c/p\u003e \u003cp\u003eFor isoquinoline, both the dimer without any water molecule (Iso\u003csub\u003e2\u003c/sub\u003e) and the aggregate with three water molecules (Iso\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e6\u003c/sub\u003e) have aromatic rings that are in non-parallel planes, whereas the aggregates of isoquinoline with one (Iso\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u003c/sub\u003e) or two (Iso\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e4\u003c/sub\u003e) water molecules in the bridge have well aligned aromatic planes. The bridge of one or two water molecules forces the aromatic planes to be one above the other. The dimer without water (Iso\u003csub\u003e2\u003c/sub\u003e) does not exhibit this effect. The aggregate with three water molecules has more degrees of freedom and a longer bridge that causes the distortion of the heterocyclic plane rather than constraining those to a parallel configuration.\u003c/p\u003e \u003cp\u003eThe thiazole aggregates with one or two water molecules in the bridge exhibit more substantial horizontal displacement than the structures with three water molecules (Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e6\u003c/sub\u003e) and the water-free dimer (Thia\u003csub\u003e2\u003c/sub\u003e). This is related to the interaction of the water molecules with the heteroatom of the aromatic system and the resultant competition between π-π stacking and electrostatic interaction. Moreover, in the aggregates with one (Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u003c/sub\u003e) or two (Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e4\u003c/sub\u003e) water molecules per bridge as well as in the water-free dimer (Thia\u003csub\u003e2\u003c/sub\u003e), the heterocycles are in a staggered configuration, i.e., the N and S atoms of one of the monomers are on opposite sides from those in the other monomer. Thus, the water bridges span between different heteroatoms, forming N\u003csup\u003e\u0026hellip;\u003c/sup\u003eH\u003csub\u003e2\u003c/sub\u003eO\u003csup\u003e\u0026hellip;\u003c/sup\u003eS networks, whereas for the bridge containing three water molecules the interaction is with the same heteroatom, forming N\u003csup\u003e\u0026hellip;\u003c/sup\u003eH\u003csub\u003e2\u003c/sub\u003eO\u003csup\u003e\u0026hellip;\u003c/sup\u003eN and S\u003csup\u003e\u0026hellip;\u003c/sup\u003eH\u003csub\u003e2\u003c/sub\u003eO\u003csup\u003e\u0026hellip;\u003c/sup\u003eS hydrogen bonding networks. We also calculated the thiazole aggregates with bridges containing one (Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u003c/sub\u003e) and two water molecules (Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e4\u003c/sub\u003e) involving the same heteroatom, i.e., N\u003csup\u003e\u0026hellip;\u003c/sup\u003eH\u003csub\u003e2\u003c/sub\u003eO\u003csup\u003e\u0026hellip;\u003c/sup\u003eN and S\u003csup\u003e\u0026hellip;\u003c/sup\u003eH\u003csub\u003e2\u003c/sub\u003eO\u003csup\u003e\u0026hellip;\u003c/sup\u003eS, but these are less stable than the Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u003c/sub\u003e and Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e4\u003c/sub\u003e shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. As S has a larger atomic radius than N, its orbitals do not align with the one of the other atoms of the aromatic ring and the π-stacking interaction is more effective by the side of the N atom. This is the reason why the aromatic rings are horizontally displaced, as in the dimer without water molecules (Thia\u003csub\u003e2\u003c/sub\u003e) the S atoms are in positions opposite to each other. In the aggregate containing three water molecules per bridge (Thia\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e6\u003c/sub\u003e), the longer bridge allows the water trimer to interact with the same heteroatoms. It was not possible to optimize the aggregate with a water trimer bridge spanning between different heteroatoms.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eEnergy calculation.\u003c/b\u003e The stabilization of the dimer structures is due to the π-π stacking and the water bridge hydrogen bond interactions. The π-π stacking interaction between the rings in each dimer structure was accounted for by means of the ASM method (Activation Strain Model). This model, proposed by Fern\u0026aacute;ndez and Bickelhaupt [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e], is a computational approach that uses electronic structure calculations to rationalize the factors that control stability in each stationary point along a reaction coordinate. According to the ASM model, the activation energy (E) can be decomposed into two contributions along the reaction coordinate (Eq.\u0026nbsp;1). The first one is the strain or distortion energy, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{STRAIN}\\)\u003c/span\u003e\u003c/span\u003e, related to the deformation of the reactants, mainly affected by the rigidity of their molecular structure and by distortion in pendant groups. The second component is the interaction energy, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT},\\)\u003c/span\u003e\u003c/span\u003e between the reactants, related to the binding capacity between the reactants, which, in our case, accounts to the π-π stacking interaction.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\varDelta E=\\varDelta {E}_{STRAIN}+\\varDelta {E}_{INT}\\)\u003c/span\u003e \u003c/span\u003e \u003cb\u003eEq.\u0026nbsp;1\u003c/b\u003e\u003c/p\u003e \u003cp\u003eIn general, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{STRAIN}\\)\u003c/span\u003e\u003c/span\u003e is a positive term, which destabilizes the system and the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e is a negative term, stabilizing the system. The \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e can be decomposed into stabilizing electrostatic interaction (Coulomb) between fragments ∆\u0026#119881;\u003csub\u003e\u0026#119890;\u0026#119897;\u0026#119904;\u0026#119905;\u003c/sub\u003e(z), destabilizing interaction derived from the overlap of filled orbitals ∆\u0026#119864;\u003csub\u003e\u0026#119875;\u0026#119886;\u0026#119906;\u0026#119897;\u0026#119894;\u003c/sub\u003e(z), orbital interaction energy ∆\u0026#119864;\u003csub\u003e\u0026#119900;\u0026#119894;\u003c/sub\u003e(\u0026#119911;), responsible for the charge transfer (HOMO-LUMO interactions, for example) and polarization (mixing unoccupied and occupied orbitals in the different fragments), and the interaction due to dispersion forces ∆\u0026#119864;\u003csub\u003e\u0026#119889;\u0026#119894;\u0026#119904;\u0026#119901;\u003c/sub\u003e(\u0026#119911;). These data are presented in the Supplementary Material. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e between the heteroaromatic ring dimers and the interplanar distance of the structures shown in Figure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe analysis of Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows that the strongest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e interaction, corresponding to the lowest energy value, are for the aggregates without any water molecule in the structure. The larger freedom or reduced constraints of the π-electronic clouds of the rings that can undergo horizontal displacement enhance π-π stacking interaction. The largest values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e is for the isoquinoline ring, almost twice the values found for the other rings; it is followed by the pyrazole and pyridine rings. The isoquinoline is the only system with two fused rings, that enhances π-π stacking interaction. Thus, for water-free dimers, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e is modulated by the size of the aromatic system.\u003c/p\u003e \u003cp\u003eThe structures linked by water molecules are more rigid and constrained, which cannot assume the alignment between the ring planes required to accommodate the electron density for the π-stacking interaction. In all cases, we note that the aggregates containing a bridge of just one water molecule have the smallest (less negative) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e interaction among the water bridged dimers. The bridge formed by only one water molecule makes the system more rigid, restricting the planes from the adequate horizontal displacement for optimal π-stacking interaction. Generally, the aggregates with two water molecules in the bridge have the second lowest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e, followed by the dimers with three water molecules per bridge. The bridges containing two water molecules apparently provide more favorable structural arrangements for the aromatic planes that enhance the π-stacking interaction than the bridges with three water molecules.\u003c/p\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e we also show the interplanar distance in the dimers. For the pyridine and furan dimers, we notice that as the number of water molecules in the bridge increases, the distance becomes larger. This is due to the hydrogen bond interaction between the dimers and the water bridge that is so effective that enhances the distance between the aromatic planes. For the thiophene and pyrazole aggregates with bridges of two water molecules (Thio\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u003c/sub\u003e and Pyra\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e4\u003c/sub\u003e), the interplanar distance is smaller than for the aggregates with bridges of three water molecules. This is attributable to the more effective accommodation of the aromatic electronic cloud overlap between the planes. For the oxazole and isoquinoline aggregates, the dimers with two (Oxa\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u003c/sub\u003e and Iso\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u003c/sub\u003e) and three (Oxa\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e3\u003c/sub\u003e and Iso\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e3\u003c/sub\u003e) water molecules in the bridge have shorter interplanar distances than those with one or without any water molecule in the bridge. For the isoquinoline system, the aromatic planes deviate from parallel to a crossed configuration as the number of water molecules increases, disrupting the π-π stacking interaction; however, the shorter interplanar distance likely partially offsets for the decreased parallel alignment. The thiazole dimer with two water molecules (Thio\u003csub\u003e2\u003c/sub\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e4\u003c/sub\u003e) in the bridge has the longest interplanar distance of all aggregates analyzed. The π-π stacking interaction and dipole-dipole interaction of the S atom with the water molecules in the bridge is not as strong as the hydrogen bonding within the bridge.\u003c/p\u003e \u003cp\u003eThe enthalpy (ΔH) and Gibbs free energy (ΔG) for the supramolecular aggregation was calculated considering either none or a cluster of 1\u0026ndash;3 water molecules (\u003cb\u003eEquations 2\u003c/b\u003e and \u003cb\u003e3\u003c/b\u003e).\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\Delta }H={H}_{complex }-({2H}_{monomer }+{H}_{\\left({H}_{2}O\\right)x})\\)\u003c/span\u003e \u003c/span\u003e \u003cb\u003eEq.\u0026nbsp;2\u003c/b\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\Delta }G={G}_{complex }-({2G}_{monomer }+{G}_{\\left({H}_{2}O\\right)}\\)\u003c/span\u003e \u003c/span\u003e \u003csub\u003ex\u003c/sub\u003e) \u003cb\u003eEq.\u0026nbsp;3\u003c/b\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H\\left(or G\\right)}_{complex }\\)\u003c/span\u003e\u003c/span\u003e is the enthalpy (or Gibbs free energy) of the aggregate with or without water molecules in the bridge, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H\\left(or G\\right)}_{monomer }\\)\u003c/span\u003e\u003c/span\u003e is the enthalpy (or Gibbs free energy) of each monomer and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({E}_{{{(H}_{2}O)}_{x}}\\)\u003c/span\u003e\u003c/span\u003eis the enthalpy (or Gibbs free energy) of one (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(x=1\\)\u003c/span\u003e\u003c/span\u003e), cluster of two (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(x=2\\)\u003c/span\u003e\u003c/span\u003e) or cluster of three (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(x=3\\)\u003c/span\u003e\u003c/span\u003e) water molecules.\u003c/p\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, we show the π-π stacking interaction and thermodynamic results for all the structures shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. In the water-free dimers, the ΔH and ΔG are stabilized only due to the π-π stacking interaction between the monomers. In aggregates with the water molecules, in addition to the π-π stacking interaction, the hydrogen bonds also help stabilize the complexes.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {E}_{INT}\\)\u003c/span\u003e\u003c/span\u003e (in \u003cb\u003ekcal mol\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;\u003c/b\u003e\u0026thinsp;1\u003c/sup\u003e), ΔH (in \u003cb\u003ekcal mol\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;\u003c/b\u003e\u0026thinsp;1\u003c/sup\u003e) and ΔG (in \u003cb\u003ekcal mol\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;\u0026thinsp;1\u003c/b\u003e\u003c/sup\u003e) for the formation of the aggregates presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The distance (\u003cb\u003eD\u003c/b\u003e) between the centers of the aromatic rings is in angstrom (\u003cb\u003e\u0026Aring;\u003c/b\u003e). Values for ΔH and ΔG are corrected by BSSE.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\Delta }{\\varvec{E}}_{\\varvec{I}\\varvec{N}\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eΔH*\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eΔG*\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD**\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyr\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-5.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-2.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.630\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyr\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-7.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.707\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyr\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-5.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-13.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.727\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyr\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-10.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.749\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFur\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.467\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFur\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.637\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFur\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-3.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.700\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFur\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e21.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.707\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThio\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.712\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThio\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.886\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThio\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-4.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.785\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThio\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.250\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIso\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-10.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-7.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.624\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIso\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-8.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-11.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.626\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIso\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-10.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-18.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.537\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIso\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-10.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-15.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.547\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyra\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-5.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-3.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.508\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyra\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-12.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.600\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyra\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-5.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-24.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e13.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.448\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyra\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-5.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-27.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.582\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThia\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.685\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThia\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-2.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-6.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e21.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.810\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThia\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-2.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-19.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.880\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThia\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-11.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e21.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.723\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eOxa\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.437\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eOxa\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-8.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.511\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eOxa\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-19.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.393\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eOxa\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-4.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-12.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e19.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.380\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e*ΔH and ΔG values were calculated taking the isolated monomers and one, a cluster of two or a cluster of three water molecules as reference.\u003c/p\u003e \u003cp\u003e**The distance shown is the distance between the centers of the aromatic rings.\u003c/p\u003e \u003cp\u003eThe analysis of Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows that the aggregations are exothermic (negative ΔH), although not spontaneous (positive ΔG). In general, the aggregates containing two or three water molecules per bridge are the ones that have the smallest values of ΔH, suggesting that the complexes formed with two water molecules are the most stable, followed by those with three water molecules. This result has previously been reported based on the calculation of the aggregation of model asphaltene compounds [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. As the ΔH analysis account for both the π-stacking and the hydrogen bond terms, the aggregates with two water molecules per bridge must have the strongest stabilization by hydrogen bonding. The ΔG analysis shows that the structures without any water molecules have the smallest values, although still being positive, in agreement with the experimental report that these molecules do not aggregate spontaneously [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe water bridges increase the distance between the heterocycles, by a maximum of 0.1 \u0026Aring;, weakening the π-π stacking interaction; however, the stabilization of the aggregate seems to be compensated by the hydrogen bonds, since the formation of complexes with two or three water molecules are exothermic.\u003c/p\u003e \u003cp\u003e \u003cb\u003eIntermolecular interactions.\u003c/b\u003e To examine the non-covalent interactions between the monomers in the dimer structure and between the monomers and water bridges, the NCI plots of the optimized structures of the supramolecular aggregates are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The isosurface colors vary between green and blue colors. The green color represents a weak favorable non-covalent interaction, such as van der Waals interaction. The blue color represents strong favorable non-covalent interactions, such as conventional hydrogen bonds. Unfavorable and repulsive interactions, represented in red color, are not observed on the isosurfaces of any of the aggregates investigated.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe analysis of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows that the green area corresponds to the π-π stacking interaction between the heteroaromatic rings. The green color indicates that this interaction is weak, as expected for this type of interaction, and the dispersed isosurface shows a delocalized interaction. There is no significant difference in the plotted area for the aggregates with one, two, or three waters in relation to the dimers without water. As isoquinoline is composed by two fused aromatic rings, its π-stacking interaction is more diffuse and is seen with enlarged green area. Light blue areas, representing strong attractive interactions due to hydrogen bonding, are also seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The blue regions represent localized interactions and are not as dispersed as the green ones. Furthermore, as the number of water molecules per bridge increases, the localized interactions shown in blue, corresponding to hydrogen bonds, increase, indicating a stronger bridging interaction, as expected for hydrogen bonding networks. For the interaction between the S atom and the water molecules, in thiophene and thiazole, we could not observe blue areas, indicating weaker dipole-dipole interactions.\u003c/p\u003e \u003cp\u003e \u003cb\u003eEnergy Decomposition Analysis (EDA).\u003c/b\u003e The EDA method decomposes the total interaction energy (E\u003csub\u003etot\u003c/sub\u003e) of supramolecular aggregates into five components: electrostatic, E\u003csub\u003eElec\u003c/sub\u003e, (opposite charge attraction), polarization, E\u003csub\u003ePol\u003c/sub\u003e, (orbital overlap), exchange, E\u003csub\u003eXc\u003c/sub\u003e, (parallel spin stabilization), dispersion, E\u003csub\u003eDisp\u003c/sub\u003e, (long range interactions) and Pauli repulsion, E\u003csub\u003ePauli\u003c/sub\u003e, (electronic repulsion) terms [\u003cspan additionalcitationids=\"CR48\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. The bond between the dimer (first fragment) and the water bridge (second fragment) was decomposed and analyzed. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the EDA results.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe EDA components E\u003csub\u003etot\u003c/sub\u003e, E\u003csub\u003eElec\u003c/sub\u003e, E\u003csub\u003ePol\u003c/sub\u003e, E\u003csub\u003eXc\u003c/sub\u003e, E\u003csub\u003eDisp\u003c/sub\u003e and E\u003csub\u003ePauli\u003c/sub\u003e in \u003cb\u003ekcal mol\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;\u003c/b\u003e\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eE\u003csub\u003eElec\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eE\u003csub\u003ePol\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eE\u003csub\u003eXc\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eE\u003csub\u003eDisp\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eE\u003csub\u003ePauli\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eE\u003csub\u003eTot\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyr\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-16.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-15.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-7.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-6.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e32.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-13.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyr\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-23.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-22.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-10.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-8.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e44.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-21.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyr\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-22.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-25.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-11.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-8.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e46.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-22.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFur\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-13.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-13.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-9.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-6.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e37.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-5.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFur\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-23.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-22.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-15.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-10.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e60.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-11.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFur\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-25.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-25.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-17.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-10.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e67.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-12.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThio\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-5.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-9.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-2.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-4.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e16.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-5.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThio\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-9.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-14.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-4.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-6.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e25.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-9.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThio\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-11.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-14.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-5.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-8.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e32.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-8.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIso\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-17.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-16.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-8.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-6.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e36.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-13.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIso\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-30.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-29.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-18.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-10.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e67.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-21.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIso\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-21.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-25.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-9.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-9.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e41.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-23.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyra\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-22.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-23.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-7.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-10.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e40.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-24.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyra\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-41.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-40.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-18.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-16.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e79.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-37.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePyra\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-38.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-38.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-17.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-16.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e75.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-35.88\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThia\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-19.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-21.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-9.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-10.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e44.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-16.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThia\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-31.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-35.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-15.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-15.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e70.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-28.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThia\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-34.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-37.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-18.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-16.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e80.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-27.43\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eOxa\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-16.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-18.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-4.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-8.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e29.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-19.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eOxa\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-35.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-34.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-14.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-15.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e66.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-32.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eOxa\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e(H\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eO)\u003c/b\u003e\u003csub\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-35.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-37.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-14.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e-15.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e67.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-36.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe analysis of Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows a trend that is observed for all the components of the interaction as well as for the total interaction energy. As a general trend, the total interaction energy increases when increasing the number of water molecules in the bridge. However, the incremental difference is much more relevant for the first water molecule than for the second or the third one. For example, the difference in the E\u003csub\u003etot\u003c/sub\u003e values for the aggregates with one water molecule per bridge to those with two water molecules per bridge is 9.15\u0026thinsp;\u0026plusmn;\u0026thinsp;3,55 kcal mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, whereas the difference for the aggregates with two water molecules per bridge to those with three water molecules per bridge is only 1.05\u0026thinsp;\u0026plusmn;\u0026thinsp;1.65 kcal mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. This shows that the aggregates with two and three water molecules are significantly more stabilized than those with only one water molecule per bridge. Also, the energies of aggregates with two or three water molecules in the bridge do not vary substantially.\u003c/p\u003e \u003cp\u003eThe dispersion term (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), accounting for long range interactions, has the smallest variation (standard deviation of 3.68 kcal mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e). It also changes more strongly from the aggregates with one water molecule per bridge to the ones with two water molecules per bridge than for additional water molecules. The structures with the stronger electrostatic term also have the largest repulsion term (E\u003csub\u003ePauli\u003c/sub\u003e).\u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, we present the electrostatic and covalent components of the total interaction energy. In this model, the ionic character of the interaction is accounted for by the E\u003csub\u003eElec\u003c/sub\u003e term, which comes mainly from opposite charge attraction sites. The covalent component is due to the sum of the E\u003csub\u003ePol\u003c/sub\u003e and E\u003csub\u003eXc\u003c/sub\u003e terms and considers the overlap of the atomic orbitals that compose the interaction. We can see for all dimers that the covalent character is almost two times larger than the ionic character, corresponding to a stabilization of -12.54\u0026thinsp;\u0026plusmn;\u0026thinsp;4.41 kcal mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. As the pyrazole, thiazole, and pyrazine aggregates have two water bridges, the stabilization per water bridge is the total value divided by two. Considering the stabilization energy per water bridge, the most stable aggregates are those with hydrogen bonds between the heteroatom of the dimer and water of the bridge, i.e., interaction of H of water bridge with the O or N atom of the heterocycle. The S-containing heterocycles thiophene and thiazole with dipole-dipole interaction between the H atom of the water bridge and S atom of the heterocycle have lower stabilization energy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eWe investigated the interaction of the supramolecular aggregation of 7 heterocyclic aromatic compounds as water-free dimers as well as dimers with water bridges bonded to the heteroatoms and spanning between the organic planes. We observed, for most of the aggregates that the interaction is favored by bridges composed of two water molecules. Only for the 1,3-thiazole the favorite bridge has three water molecules, probably due to the softness of the sulfur atom. The π-π stacking interaction analysis showed that the water-free dimers have the strongest interaction, followed by the dimers with two water molecules per bridge. In almost all cases, the π-π stacking interaction strength is modulated by the interplanar distance between the monomers in the dimer structure. The ΔH analysis showed that aggregation is an exothermic process. The most stable aggregate for each heterocycle is the system with two water molecules per bridge. The ΔG analysis showed non spontaneous aggregation processes with the smallest values for the dimer without any water molecule in the bridge. The NCI plot analysis identified strong interaction sites around the water molecules, representing hydrogen bonding interactions, and weak attraction between the planes of the organic molecules, representing the π-stacking interactions. The hydrogen bonds between the dimers and the water bridges were decomposed by using the EDA method. The results indicated that the covalent character (polarization and exchange) of the interaction is almost twice as large as the electrostatic term. We also noticed that with one water molecule in the bridge led to a small stabilization of the aggregate, whereas two or three water molecules in the bridge add a considerable stabilization to the supramolecular system, with the aggregates having two water molecules per bridge being the most stable. Our findings justify the conclusion that the π-π stacking interaction is as important as hydrogen bonding for the stabilization of the dimers bridged by water molecules.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eFunding Declaration\u003c/p\u003e\n\u003cp\u003eThis work was developed without any funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDr. Jos\u0026eacute; Walkimar de M. Carneiro and Dr. Leonardo Moreira da Costa acknowledge FAPERJ (Funda\u0026ccedil;\u0026atilde;o de Amparo a Pesquisa do Estado do Rio de Janeiro), CNPq (Conselho Nacional de Desenvolvimento Cient\u0026iacute;fico e Tecnol\u0026oacute;gico). Dr. Stanislav R. Stoyanov acknowledges the support of the Government of Canada\u0026rsquo;s Program of Energy Research and Development (PERD). Milena D. Lessa was supported by a research fellowship from the MIDAS INCT.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eMDL and LMC wrote the main manuscript text. MDL prepared the figures and tables of the article.SRS and JWMC reviewed the manuscript.MDL, LMC, SRS and JWMC discussed all the results and analyzed them.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKamal, M. S.; Hussein, I.; Mahmoud, M.; Sultan, A. S.; Saad, M. A.; \u003cbr\u003e\u003cem\u003eJ. Pet. Sci. 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Rev\u003c/em\u003e. \u003cstrong\u003e2014\u003c/strong\u003e, 43, 4953.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-molecular-modeling","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmmo","sideBox":"Learn more about [Journal of Molecular Modeling](https://www.springer.com/journal/894)","snPcode":"894","submissionUrl":"https://submission.nature.com/new-submission/894/3","title":"Journal of Molecular Modeling","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Heterocycles dimers, DFT, interaction analysis, Chemical scaling","lastPublishedDoi":"10.21203/rs.3.rs-3897675/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3897675/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA complex supramolecular process involving electrostatic and dispersion interactions, asphaltene aggregation is associated with detrimental petroleum deposition and scaling that pose challenges to petroleum recovery, transportation, and upgrading. The density functional ωB97X-D with a dispersion correction was employed to investigate supramolecular aggregates incorporating heterocycles dimers with 0, 1, 2, and 3 water molecules forming a stabilizing bridge connecting the monomers. The homodimers of seven heterocyclic model compounds, representative of moieties commonly found in asphaltene structures were studied: pyridine, thiophene, furan, isoquinoline, pyrazine, thiazole, and 1,3-oxazole. The contributions of hydrogen bonding involving water bridges spanning between dimers and π−π stacking to the total interaction energy were calculated and analyzed. The distance between the planes of the aromatic rings is correlated with the π-π stacking interaction strength. All the dimerization reactions are exothermic, although not spontaneous. This is mostly modulated by the strength of the hydrogen bond of the water bridge and the π-π stacking interaction. Dimers bridged by two water molecules are more stable than with additional water molecules or without any water molecule in the bridge. Energy decomposition analysis show that the electrostatic and polarization components are the main stabilizing terms for the hydrogen bond interaction in the bridge, contributing with at least 80% of the interaction energy in all dimers. The non-covalent interaction analysis confirms the molecular sites that have the strongest (hydrogen bond) and weak (π-π stacking) attractive interactions. They are concentrated in the water bridge and in the plane between the aromatic rings, respectively.\u003c/p\u003e","manuscriptTitle":"Density Functional Theory Investigation of the Contributions of π−π Stacking and Hydrogen Bonding with Water to the Supramolecular Aggregation Interactions of Model Asphaltene Heterocyclic Compounds","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-05 08:47:04","doi":"10.21203/rs.3.rs-3897675/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-02-02T16:33:47+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-02T16:33:32+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-02-02T11:22:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Molecular Modeling","date":"2024-01-25T15:34:57+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-molecular-modeling","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmmo","sideBox":"Learn more about [Journal of Molecular Modeling](https://www.springer.com/journal/894)","snPcode":"894","submissionUrl":"https://submission.nature.com/new-submission/894/3","title":"Journal of Molecular Modeling","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"cb55adef-6e3f-412c-ad53-af28f29f47cd","owner":[],"postedDate":"February 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-05-01T23:22:11+00:00","versionOfRecord":{"articleIdentity":"rs-3897675","link":"https://doi.org/10.1007/s00894-024-05922-3","journal":{"identity":"journal-of-molecular-modeling","isVorOnly":false,"title":"Journal of Molecular Modeling"},"publishedOn":"2024-04-24 23:22:11","publishedOnDateReadable":"April 24th, 2024"},"versionCreatedAt":"2024-02-05 08:47:04","video":"","vorDoi":"10.1007/s00894-024-05922-3","vorDoiUrl":"https://doi.org/10.1007/s00894-024-05922-3","workflowStages":[]},"version":"v1","identity":"rs-3897675","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3897675","identity":"rs-3897675","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}