Interactions of Substituted Nitroaromatics with Model Graphene

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Article Cite This: ACS Omega 2018, 3, 2773−2785

Interactions of Substituted Nitroaromatics with Model Graphene Systems: Applicability of Hammett Substituent Constants To Predict Binding Energies Mehedi H. Khan,† Danuta Leszczynska,‡ D. Majumdar,*,† Szczepan Roszak,*,§ and Jerzy Leszczynski*,† †

Interdisciplinary Center for Nanotoxicity, Department of Chemistry and Biochemistry, and ‡Department of Civil and Environmental Engineering, Jackson State University, Jackson, Mississippi 39217, United States § Advanced Materials Engineering and Modelling Group, Faculty of Chemistry, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland S Supporting Information *

ABSTRACT: Applicability of Hammett parameters (σm and σp) was tested in extended π-systems in gas phase. Three different model graphene systems, viz. 5,5-graphene (GR), 3B-5,5-graphene (3BGR), and 3-N-5,5-graphene (3NGR), were designed as extended π-systems, and interactions of various nitrobenzene derivatives (mainly m- and p-substituted together with some multiple substitutions) on such platforms were monitored using density functional theory (M06/cc-pVDZ, M06/cc-pVTZ, M06/sp-aug-cc-pVTZ) and Møller−Plesset second-order perturbation (MP2/cc-pV-DZ) theory. Offset face to face (OSFF) stackings were found to be the favored orientations, and reasonable correlations were found between binding energies (ΔEB) and the ∑|σm| values of the substituted nitrobenzenes. It was proposed previously that |σm| contains information about the substituents’ polarizability and controls electrostatic and dispersion interactions. The combination of ∑|σm| and molar refractivity (as ∑Mr) or change in polarizability (Δα: with respect to benzene) of nitrobenzene derivatives generated statistically significant correlation with respect to ΔEB, thereby supporting the hypothesis related to the validity of |σm| correlations. The |σp| parameters also maintain similar correlations for the various p-substituted nitrobenzene derivatives together with several multiply-substituted nitrobenzene derivatives. The correlation properties in such cases are similar to the |σm| cases, and the energy partition analysis for both the situations reveled importance of electrostatic and dispersion contributions in such interactions. The applicability of Hammett parameters was observed previously on the restricted parallel face to face orientation of benzene···substituted benzene systems, and the present results show that such an idea could be used to predict ΔEB values in OSFF orientations, if the scaffolds are designed in such a way that substituted benzene systems cannot escape their π-clouds. aromatics.41 The results were interpreted as support to the proposed domination of the dispersion and electrostatic interactions in such cases. Still the Hammett constants σm or ∑σm for multisubstituted aromatics were not found to be sufficient to predict the arene−arene binding energies. More recently, Watt et al.42 have shown a good correlation between the ΔEB of arene−arene complexes and the ∑|σm| values of the substituted arenes. These studies were carried out under constrained geometric conditions to keep the interacting molecules in strict PFF orientations. Obviously, such an orientation was chosen to maximize π−π (origin of most of the dispersive forces) and electrostatic interactions. The authors also found the contribution of both electrostatic and dispersion energies as important guiding factors to impose

1. INTRODUCTION Noncovalent interactions of aromatics are important in a wide range of chemical and biological processes.1−7 These include enzyme−substrate recognition,4,8 protein structure and function,9−11 DNA/RNA base stacking12 and intercalation,13,14 organic reaction development,15 and organic materials.16−19 Arene−arene interactions play a key role in enzyme−substrate reactions. A significant number of experimental4,20−28 and theoretical investigations29−36 are available in this connection explaining the role of such interactions. High-level theoretical investigation demonstrated that dispersion forces primarily dominate the observed binding,30−39 although the initial studies of Hunter and Sanders40 in this direction indicated the major force of interactions to be electrostatic in origin. Computational study of interactions between benzene and monosubstituted benzenes in parallel face to face (PFF) orientation showed that there exists a correlation of binding energies (ΔEB) with Hammett σm values of monosubstituted © 2018 American Chemical Society

Received: December 3, 2017 Accepted: February 22, 2018 Published: March 8, 2018 2773

DOI: 10.1021/acsomega.7b01912 ACS Omega 2018, 3, 2773−2785

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Figure 1. (A−C) Highest occupied molecular orbitals of the optimized structure (DFT/M06/cc-pVDZ level) of GR, 3BGR, and 3NGR, respectively. (D−F) Molecular electrostatic potential (MEP) pictures of the optimized structures (DFT/M06/cc-pVDZ level) of GR···mnitroaniline, 3BGR···p-nitrophenol, and 3NGR···m-nitrophenol, respectively. The various colored regions on the surfaces are deep blue (highly positive, >0.1 au), light blue (0.05 au), green (0.0 au), and yellow (−0.05 au). The optimized geometries of GR (G), 3BGR (H), and 3NGR (I) (DFT/M06/cc-pVDZ level) are also added for more clarity of the scaffold structures.

should have any correlation with ΔEB. The origin of the idea of using Hammett constants to predict arene−arene attraction was explored in numerous experimental studies.8−10,12 The main assumption here is that such an attraction is largely electrostatic in nature (Hunter and Sanders),40 and a parameter that describes the electronic effects of substituents on benzoic acid

good correlation with the ∑|σm| parameters. The importance of ∑|σm| parameters was also demonstrated by Cormier and Lewis for the interactions of Li+ and Na+ with cyclopentadienyl anions.43 No reasonable explanation exists as to why Hammett constant (σm) and related parameters like ∑σm, and ∑|σm| 2774


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ACS Omega acidity,44 the Hammett constant, should work to model such electronic/electrostatic arene−arene interactions. Several investigations in recent times have, however, found that this assumption is not correct. Watt and co-workers42 carried out detailed analysis in this respect and proposed that the ∑|σm| values contain information that regular Hammett paramers σm and ∑σm are lacking. They concluded that it is probably the dispersion contribution to the overall binding. The hypothesis did originate from the results of multiple regression analysis correlating ΔEB with ∑σm and ∑Mr (Mr: refractivity of molecules) parameters. The correlation was very promising, and because Mr implicitly involves polarizability of molecules, the hypothesis of the involvement of dispersion effect in ∑|σm| was qualitatively substantiated. A recent review by Lewis and co-workers45 summarized the different ideas related to this problem, but their explanations are not yet conclusive and the authors still supported their earlier conclusion.42 The Hammett constant σp had also been found to correlate with ΔEB in arene−arene interactions for multiply-substituted benzene systems. Wheeler and Houk41 suggested that the correlation of σp with ΔEB in such cases relates to the polarization of the π-system of the substituted ring. Subsequent investigations of Watt et al.42 also suggested that ∑σp and ∑Mr (replaced further by lipophilicity parameter ∑π) for substituted benzenes in PFF orientations of the arene−arene systems show similar correlation to ΔEB as discussed for the σm parameter cases, although the correlations were not as good. There are two other orientations in arene−arene interactions, viz. offset face to face (OSFF) and edge to face (ETF). The interacting moieties in OSFF orientations were more stable than the rest of the geometric orientations.36 In the case of benzene−benzene dimers, OSFF and ETF orientations were almost equally stable.29−35 There could be, of course, an infinite number of OSFF and ETF arene−arene dimer orientations. The OSFF orientations can vary by how offset the two arenes are with respect to each other (in an infinite number of directions), and the ETF arene−arene dimer orientations can vary in the angle between the two aromatics and whether the vertical aromatic has an edge, a C atom, or some intermediate orientation, interacting with the horizontal aromatic. So, there is no unique orientation for the most stable benzene··· substituted benzene interactions. The interacting systems (OSFF) were not considered in most of the previous studies of Hammett correlations with ΔEB, as face to face π−π interactions would be lost and Hammett constant correlation might not be that important. There have been, of course, several arene−substituted arene interaction studies in recent times to show the importance of OSFF orientation of the interacting systems in explaining structural aspects of different π−π stackings.46,47 Now, if one changes the scaffold to a larger conjugated π-system like graphene (instead of benzene), the substituted benzene moieties in parallel orientations (either in PFF or OSFF) cannot escape π−π stacking. Thus, the hypotheses of the correlations of Hammett constants with ΔEB could be valid here, regardless of the nature of the parallel orientations of the substituted benzenes against the graphene scaffold. Moreover, it will also be interesting to monitor the effect of doping on the graphene sheet for such interactions. Controlled doping of the single-walled carbon nanotubes by boron atoms does not have marked change in the π-character44 of the system and it is expected to be the same for the graphene sheet also. In the present situation, it will be interesting to see if

such doping has any effect on the Hammett correlations as discussed above. The work presented here addresses the idea of Hammett constants’ (σm, σp, and related parameters) correlation with the ΔEB of various nitrobenzene derivatives on model graphene scaffolds. The nitrobenzene derivatives were chosen because of the availability of the experimental Gibbs free energy of binding of a few of such compounds with the graphene systems in OSFF orientation (discussed in detail in Section 2). These experimental values are useful to calibrate the computed binding energy data. The model graphene system was designed from 5,5-graphene. Singly B- and N-doped graphenes were also designed from this model for further use as scaffolds with graphene-like π-orbital character. The B- and N-doped graphene materials are quite well known,48−50 and previous theoretical studies also showed that they preserve the properties of the pristine graphene materials.50 The singly doped model B- and N-graphenes in the present studies are thus expected to influence the nature of interactions with nitroaromatics (due to the influence of B and N atoms) without disturbing the π-character of the whole system with respect to pristine graphene. The preservation of π−π stacking character was observed in case of interactions between N-doped graphene systems.51,52 The size of the graphene systems was chosen such that the nitrobenzene derivatives retain OSFF orientations during interactions avoiding edge effect. It would be shown that dispersion forces together with electrostatic interactions play important roles in such binding, as was suggested in arene−arene interactions. Although the Hammett σ-parameters of nitrobenzene derivatives show good correlations in terms of ∑|σx| (x: m or p) during their interactions with 5,5-graphene, two variable equations with a combination involving ∑σx (x: m or p) and ∑Mr are found to be more convincing. Moreover, because the parameter Mr involves polarizability, the computed shift of polarizabilities (Δα) of nitrobenzene derivatives (with respect to benzene) in combination with ∑σx (x: m or p) parameter also shows convincing correlation in this respect. Although doped 5,5graphenes show similar interactions to nitrobenzene derivatives, the correlations with Hammett parameters are not as good as the 5,5-graphene cases. Probably, change of electrostatic interactions with respect to pristine graphene system plays a role here. Energy decomposition analysis has been carried out to account for the role of electrostatic and dispersion interactions in such complexes. The results will also show their influence in correlating the binding energies to Hammett σ-parameters.

2. METHODS OF COMPUTATION The model 5,5-graphene (GR) system is shown in Figure 1. The system is designed in such a way that it has a mirror plane with respect to the x-axis. Thus, full optimization of the system does not disturb the overall symmetry (D2h) of this model graphene unit. The edges of the graphene unit are terminated with H-atoms to avoid edge effect during interactions with the chosen nitrobenzene systems. The B- and N-doped model systems were designed by substituting C3 of the central ring (C2v-symmetry), as shown in Figure 1, and we designate them as 3-B-5,5-graphene (3BGR) and 3-N-5,5-graphene (3NGR), respectively. The substituted nitrobenzene dimers (X−C6H4− NO2) were chosen to have X = H, CH3, OCH3, OC2H5, Cl, Br, I, OH, CN, and NH2 substituents at m- and p-positions. Moreover, three compounds with substituents 3-NO2-4-OH, 2775


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Energy partitioning analyses were carried out to estimate the contribution of electrostatic interactions in such complex formations. These were computed using a hybrid variational− perturbational interaction energy decomposition scheme.58 The SCF interaction energy is partitioned into first-order electro(10) static (E(10) el ), Heitler−London exchange (Eex ), and higherHF order delocalization (ΔEdel ) energy terms.

3,5-di-NO2-4-OH, and 3,5-di-NO2-4-CH3 (with respect to the NO2 group of nitrobenzene) were also considered for investigating the interaction properties. The interaction geometries between the GR and substituted nitrobenzene molecules were computed, allowing the systems to relax fully from initial PFF orientation. A similar approach was adopted for the interactions with 3BGR and 3NGR scaffolds. There could be more than one local minimum in such optimizations, but we have located the desired minima through optimizations from different starting parallel OSFF orientations. Geometry optimizations of nitroaromatics, graphene scaffolds, and their complexes were carried out using density functional theory (DFT)53 with M06 functional54 and cc-pVDZ basis set of atoms (cc-pVDZ-PP ECP (effective core potential) basis set was used for iodine). The M06-2X functional54 could have been another choice here, but because both M06 and M06-2X generate similar results for such noncovalent interactions, we have used the M06 functional only. M06-2X was used for the initial calibrations. The minimum-energy structures in the respective cases were confirmed through frequency calculations. These results were used to compute the binding energy (ΔEB), enthalpy (ΔHB°), and Gibbs free energy (ΔGB°) of binding (at 298K) of the complexes. The calculations included counterpoise (CP) and zero-point energy (ZPE) corrections. Calculations of thermodynamic properties were carried out by applying the ideal gas, rigid rotator, and harmonic oscillator approximations.55 The computed ΔEB values (ΔEBs) were further refined using higher-level cc-pVTZ and sp-aug-cc-pVTZ basis sets at the DFT/M06 level. There were convergence problems in using aug-cc-pVTZ basis sets directly in the energy calculations of the GR/3BGR/3NGR···nitrobenzene (and nitrobenzene derivative) complexes (probably because of linear dependence). The higher-angular-momentum diffuse functions (d and f) of the main atoms and the hydrogen diffuse functions were causing such problems, and these diffuse functions were eliminated in the final sp-aug-cc-pVTZ basis sets to achieve energy convergence. In the case of iodine, the cc-pVTZ-PP and spaug-cc-pVDZ-PP ECP basis sets were used for energy calculations. Single-point calculations were carried out on the optimized geometries at the DFT/cc-pVDZ level to estimate the CP corrections. The ZPE and the energies for the individual components were obtained from the frequency analysis of the optimized structures at the DFT/cc-pVDZ level for the computations of ΔE B s. The ΔE B s from all of these computations, and ΔHB° and ΔGB° at the DFT/cc-pVDZ level as well, were further corrected through inclusion of dispersion energy of interactions (ΔEdisp). The magnitude of ΔEdisp was estimated at the DFT/cc-pVTZ level (using optimized geometries from the DFT/cc-pVDZ calculations) through inclusion of Grimme’s empirical dispersion (GD3)56 and obtained as the difference of interaction energies (with CP corrections) with and without the dispersion effects. The computed ΔEdisp values were added to the estimated binding energies. This is a valid approximation as the geometries are the same at all of these basis set levels. We have further estimated the ΔEB (CP- and ZPE-corrected) through single-point Møller−Plesset second-order perturbation (MP2)57 calculations (cc-pVDZ basis sets) using the geometries and ZPE corrections from the DFT/cc-pVDZ results. The results generated a direct estimation of ΔEdisp and used in energy partitioning analysis.

HF ΔEHF = Eel(10) + EexHL + ΔEdel

(1)

The MP2 calculations generate an estimation of ΔEdisp, which could be designated as E(2) MP. It includes the dispersion and correlation contributions to the Hartree−Fock components, and is calculated using the supermolecular approach as the difference of MP2 energy corrections of the supermolecule and the monomers (eq 2). (2) (2) EMP = EAB − EA(2) − E B(2)

(2)

The energy terms on the right-hand side of eq 2 represent the difference between the MP2 and Hartree−Fock energies of the supermolecule (AB) and the monomers (A and B). All of the interaction energy terms are calculated consistently in the dimer-centered basis set and are therefore free from the basis set superposition error (BSSE) due to the full counterpoise correction. The contribution of the multipolar electrostatic interactions in the cation−π complexes has been calculated using the distributed atomic multipolar expansion of the charge distributions of monomers.59 The multipolar expansion technique is based on the numerically equivalent spherical harmonic formulations of Stone et al.60,61 The optimized structures at the DFT/B3LYP/cc-pVDZ level were used for such calculations. The results of such energy decomposition calculations are not rigorous and would be valid for interpretation purposes only, as there is an element of arbitrariness in any of such decomposition schemes. All of the computations were carried out using Gaussian 09 code.62 The interaction energy decomposition scheme implemented in the GAMESS code63 was used for energy partitioning analyses and computation of the multipolar components of the total electrostatic interaction energies.64 Molecular graphics have been generated using the GaussView05 software.65

3. RESULTS AND DISCUSSION 3.1. Comparison of the Binding Energies of Nitroaromatics with GR, 3BGR, and 3NGR Scaffolds. The πorbitals of GR, 3BGR, and 3NGR (Figure 1) show that the πnetwork of these systems are capable of holding the nitroaromatics through long-range π−π interactions. The optimized structures of such stackings are available in Figures S1−S4 (Supporting Information), and a general model of such interactions, depicting distance between the two π-systems, is shown in Scheme 1. As expected, all of the optimized structures show OSFF arrangements and the aromatic nitro compounds do not get out of the GR/3BGR/3NGR platforms due their extended π-network. The binding energies (ΔEB, ΔHB°, and ΔGB°) were initially computed (as discussed in Section 2) at the DFT/M06/cc-pVDZ level. The higher basis set (cc-pVTZ and sp-aug-cc-pVTZ) and MP2/cc-pVDZ calculations were carried out to monitor the accuracy of the ΔEB values through higher electron correlation effects. These strategies to compute ΔEB error limits are essential, as the primary objective is to use such results to monitor the validity of Hammett correlation in such interactions. The binding energy values for various 2776


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optimizations with the inclusion of the empirical GD3 function. The results for the GR···p-nitrophenol (DFT/cc-pVDZ level) case is included in Table 2, and the computed binding energies do not differ from those using the approximation as discussed. The Gaussian code actually performs such geometry optimization through the inclusion of GD3 empirical dispersion energy to the nuclear repulsion term in each optimization cycle. Thus, in the case of fully optimized geometry (without dispersion correction), addition of dispersion energy at the final stage is almost equivalent to the full-geometry optimization technique, including dispersion effect, and thus the empirical approach for dispersion correction for binding energies is fully logical. There are not too many experiments to justify the computed binding energies for the present systems. In recent years, experiments have been carried out to estimate adsorption energies (ΔGad) of nitrobenzene, m-dinitrobenzene, and pnitrotoluene on graphene surface.66 The adsorption isotherm was computed using Freundlich and Langmuir techniques. The experimental equilibrium binding constants KF and KL from Freundlich and Langmuir isotherms, respectively, could be used to compute ΔGad values (ΔGads) for these systems. The magnitudes of ΔGads for nitrobenzene, m-nitrobenzene, and pnitrotoluene are −5.3, −5.8, and −5.8 kcal/mol, respectively, using KF (7247.34 ± 228.49 19195.1 ± 752.0, 18645.5 ± 737.6 [(mg/kg)/(mg/L)N; N = 1 here] for the respective cases),66 whereas they are, respectively, −4.2, −5.1, and −5.4 using KL (0.0118 ± 0.00216, 0.0569 ± 0.0128, 0.0939 ± 0.0176 (L/mg) for the respective cases).66 Our computed ΔGB° values (Tables 1 and 2) show that they are not very different from the experiment (−2.6, −3.7, and −5.8 kcal/mol for the respective systems). The exact matching is not possible, as the computed values are in the gas phase. The overestimated CP correction through double-ζ basis set could also contribute to such deviation from experiment. The computed values, of course, maintain the same trend in ΔGB° with respect to the experiment, and the results thus give us confidence that the

Scheme 1. Schematic Representation of the Interacting Distance (d) between Nitrobenzene Derivatives and the Graphene Systems (GR/3BGR/3NGR)a

a

The distance is measured between the center of mass (CM) of the aromatic ring of the nitrobenzene derivatives and the graphene systems. The whole graphene systems were not considered to compute CM. The part over which the aromatic ring of the interacting nitrobenzene derivatives were lying (almost in parallel orientation) was used to compute the CM of the graphene systems.

interactions at the DFT/cc-pVDZ level are shown in Tables 1 and 2 for the m- and p-substituted nitrobenzenes, respectively, together with di- and tri-substituted nitrobenzenes. The ΔEB at higher basis sets and at the MP2/cc-pVDZ level, for the similar cases, are shown in Tables 3 and 4, respectively. The ΔEB’s computed at different levels are more or less similar, although the computed values at higher basis sets and at the MP2 level are slightly lower than those at the DFT/ccpVDZ computations. This could be due to the fixed geometry (from DFT/cc-pVDZ results) used in such calculations. All of these binding energies (DFT levels) are dispersion (ΔEdisp)corrected, as discussed in Section 2. The approximation used in dispersion correction (Section 2) could be justified by computation of binding energies through full-geometry

Table 1. Computed Binding Energies (ΔEB, kcal/mol) and Related Thermodynamic Parameters (ΔHB°, and ΔGB°, kcal/mol) of Various m-Substituted and Several Di- and Tri-Substituted Nitrobenzene Derivatives Interacting with Model (5,5)-Graphene (GR) and its B- and N-Doped Scaffolds (3BGR and 3NGR, Respectively) at the M06/cc-pVDZ Levela,b GR

3BGR

3NGR

substituents

ΔEB

ΔHB°

ΔGB°

ΔEB

ΔHB°

ΔGB°

ΔEB

ΔHB°

ΔGB°

−Hc m-NH2 m-OH m-OCH3 m-OC2H5 m-CH3 m-NO2 m-CN m-Cl m-Br m-I 3-NO2, 4-OH 3,5-di-NO2, 4-OH 3,5-di-NO2, 4-CH3 benzened

−13.4 −17.5 −16.4 −16.2 −17.6 −16.0 −19.1 −17.7 −17.3 −18.1 −19.1 −19.4 −23.4 −23.9 −4.4

−14.6 −17.5 −15.9 −17.2 −17.3 −16.6 −19.2 −17.3 −16.8 −17.9 −19.0 −19.1 −23.8 −23.5 −3.7

−2.7 −3.5 −4.0 −4.7 −3.7 −2.9 −3.7 −5.0 −4.2 −4.1 −6.3 −10.0 −13.5 −16.2 5.0

−14.3 −17.7 −15.8 −18.8 −18.7 −17.1 −19.3 −18.6 −16.9 −18.3 −18.5 −20.3 −23.6 −23.5 −5.1

−14.1 −17.6 −15.7 −18.4 −17.9 −16.9 −18.9 −18.3 −16.4 −16.6 −18.0 −19.7 −24.1 −23.8 −4.5

−1.2 −3.7 −2.1 −5.6 −3.8 −3.8 −5.2 −4.7 −4.0 −4.9 −3.5 −13.2 −14.1 −13.4 6.0

−15.0 −17.6 −15.5 −18.2 −18.1 −17.3 −19.0 −18.6 −16.0 −18.0 −18.7 −19.3 −24.9 −23.9 −5.7

−15.0 −17.4 −15.6 −18.1 −18.2 −17.0 −19.1 −18.4 −16.8 −17.9 −18.1 −18.7 −24.7 −23.8 −4.8

−1.1 −4.3 −0.8 −3.9 −2.9 −3.9 −3.5 −4.5 −3.3 −3.5 −5.7 −11.5 −17.4 −15.4 4.2

Similar values for the interactions with benzene are also included for comparison. bThe ΔEB, ΔHB°, and ΔGB° values are BSSE- and ZPE-corrected. See the text for details. cNitrobenzene. dBenzene interacting with GR/3BGR/3NGR.

a

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Table 2. Computed Binding Energies (ΔEB, kcal/mol) and Related Thermodynamic Parameters (ΔHB° and ΔGB°, kcal/mol) of Various p-Substituted Nitrobenzene Derivatives Interacting with Model (5,5)-Graphene (GR) and Its B- and N-Doped Scaffolds (3BGR and 3NGR, Respectively) at the M06/cc-pVDZ Levela GR substituents p-NH2 p-OH p-OCH3 p-OC2H5 p-CH3 p-NO2 p-CN p-Cl p-Br p-I

3BGR

3NGR

ΔEB

ΔHB°

ΔGB°

ΔEB

ΔHB°

ΔGB°

ΔEB

ΔHB°

ΔGB°

−17.7 −15.9 (−15.8)b −18.4 −19.9 −17.6 −18.1 −15.8 −16.7 −17.2 −19.0

−17.4 −16.0 (−15.9)b −18.2 −19.8 −16.7 −18.1 −17.7 −17.6 −17.1 −18.8

−5.1 −1.4 (−1.2)b −4.9 −6.0 −5.8 −4.0 −7.0 −5.7 −6.6 −5.6

−17.4 −17.9

−16.9 −17.7

−5.2 −4.1

−16.5 −15.6

−16.5 −15.7

−2.6 −0.3

−18.1 −19.4 −17.4 −18.5 −18.9 −17.6 −17.7 −18.2

−18.0 −19.6 −16.5 −18.2 −18.5 −17.1 −17.3 −18.0

−3.9 −4.1 −5.6 −5.5 −5.6 −5.1 −5.7 −4.4

−18.7 −18.8 −19.3 −19.5 −18.4 −16.5 −18.5 −17.7

−18.7 −19.2 −17.8 −19.1 −18.0 −16.1 −17.9 −17.4

−4.2 −2.9 −5.4 −6.7 −5.4 −3.2 −6.3 −6.3

a The ΔEB, ΔHB°, and ΔGB° values are BSSE- and ZPE-corrected. See the text for details. bComputed values using full-geometry optimization using empirical dispersion corrections.

Table 3. Computed Binding Energies (ΔEB, kcal/mol) and Related Thermodynamic Parameters (ΔHB° and ΔGB°, kcal/mol) of Various m-Substituted and Several Di- and Tri-Substituted Nitrobenzene Derivatives Interacting with Model (5,5)-Graphene (GR) and Its B- and N-Doped Scaffolds (3BGR and 3NGR, Respectively) at the M06/cc-pVTZ (TZ), M06/sp-aug-cc-pVTZ (ATZ), and MP2/cc-pVDZ (MP2) Levelsa ΔEB (GR)

a

ΔEB (3BGR)

ΔEB (3NGR)

substituents

TZ

ATZ

MP2

TZ

ATZ

MP2

TZ

ATZ

MP2

−Hb m-NH2 m-OH m-OCH3 m-OC2H5 m-CH3 m-NO2 m-CN m-Cl m-Br m-I 3-NO2, 4-OH 3,5-di-NO2, 4-OH 3,5-di-NO2, 4-CH3

−13.4 −17.6 −16.0 −16.0 −16.9 −15.7 −18.8 −16.8 −16.6 −17.4 −18.4 −18.9 −23.1 −23.4

−13.4 −17.8 −16.1 −16.1 −16.9 −15.7 −18.8 −16.9 −16.7 −17.4 −18.3 −19.0 −24.0 −23.5

−12.3 −14.8 −14.2 −14.1 −13.8 −13.7 −16.7 −16.2 −15.3 −15.5 −15.5 −17.1 −20.2 −20.7

−13.7 −17.6 −15.8 −18.3 −18.5 −16.9 −18.9 −18.3 −16.6 −17.6 −18.4 −20.3 −23.6 −23.6

−13.7 −17.0 −15.8 −18.3 −17.7 −16.9 −19.0 −18.3 −16.6 −17.5 −17.9 −20.2 −21.8 −22.1

−9.6 −14.3 −10.9 −14.7 −12.7 −12.0 −16.9 −16.5 −13.1 −15.3 −15.6 −17.4 −19.6 −20.1

−14.8 −17.5 −15.5 −17.9 −17.7 −16.8 −18.6 −17.9 −16.0 −17.1 −17.7 −19.3 −24.9 −23.9

−14.8 −17.7 −15.5 −17.8 −18.3 −16.9 −18.6 −17.9 −15.5 −17.1 −17.6 −18.5 −26.1 −24.2

−12.1 −17.5 −12.2 −14.3 −17.1 −13.5 −17.1 −17.5 −12.3 −15.7 −15.5 −14.6 −21.0 −22.0

The ΔEB, ΔHB°, and ΔGB° values are BSSE- and ZPE-corrected. See the text for details. bNitrobenzene.

Table 4. Computed Binding Energies (ΔEB, kcal/mol) and Related Thermodynamic Parameters (ΔHB° and ΔGB°, kcal/mol) of Various p-Substituted Nitrobenzene Derivatives Interacting with Model (5,5)-Graphene (GR) and Its B- and N-Doped Scaffolds (3BGR and 3NGR, Respectively) at the M06/cc-pVTZ (TZ), M06/sp-aug-cc-pVTZ (ATZ), and MP2/cc-pVDZ (MP2) Levelsa ΔEB (GR)

a

ΔEB (3BGR)

ΔEB (3NGR)

substituents

TZ

ATZ

MP2

TZ

ATZ

MP2

TZ

ATZ

MP2

p-NH2 p-OH p-OCH3 p-OC2H5 p-CH3 p-NO2 p-CN p-Cl p-Br p-I

−17.2 −16.2 −18.0 −19.3 −16.8 −17.9 −14.9 −15.9 −16.4 −18.3

−17.4 −16.3 −18.1 −19.4 −17.0 −17.9 −15.0 −15.9 −16.5 −18.3

−14.8 −14.2 −14.1 −13.8 −13.7 −16.7 −16.2 −15.3 −15.5 −15.5

−17.1 −17.0 −17.9 −19.5 −17.1 −18.2 −18.6 −17.2 −17.1 −17.8

−17.1 −17.4 −17.9 −19.5 −17.1 −18.2 −18.6 −17.2 −16.8 −17.7

−14.3 −10.9 −14.7 −12.7 −12.0 −16.9 −16.5 −13.1 −15.3 −15.6

−16.2 −15.7 −18.4 −18.7 −18.3 −19.9 −18.0 −15.8 −17.3 −17.2

−16.3 −15.7 −18.4 −17.8 −18.2 −20.4 −18.1 −15.7 −17.3 −17.8

−15.5 −12.2 −14.3 −17.1 −13.5 −17.1 −17.5 −12.3 −15.7 −15.5

The ΔEB, ΔHB°, and ΔGB° values are BSSE- and ZPE-corrected. See the text for details.

3.2. Binding Energies and Hammett Correlation. There are several interesting features related to the binding energies of

computed binding energies could be used for Hammett correlation analysis. 2778


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Table 5. Interacting Distances (d, Å)a between GR/3BGR/3NGR and Various m- and p-Substituted and Several Di- and TriSubstituted Nitrobenzene Derivatives for Their Optimized Geometries at the DFT/M06/cc-pVDZ Level of Computations d (GR)

a

substituents

m-

−Hb −NH2 −OH −OCH3 −OC2H5 −CH3 −NO2 −CN −Cl −Br −I 3-NO2, 4-OH 3,5-di-NO2, 4-OH 3,5-di-NO2, 4-CH3

3.34 3.41 3.28 3.46 3.44 3.48 3.30 3.41 3.40 3.44 3.42

p-

d (3BGR) others

m3.38 3.40 3.32 3.44 3.46 3.42 3.47 3.41 3.41 3.49 3.48

3.33 3.40 3.37 3.50 3.36 3.30 3.37 3.36 3.34 3.44 3.33 3.27 3.38

p-

d (3NGR) others

3.34 3.36 3.45 3.46 3.47 3.47 3.35 3.37 3.40 3.52 3.41 3.28 3.39

m-

p-

3.24 3.26 3.22 3.33 3.34 3.36 3.26 3.33 3.37 3.41 3.40

3.24 3.26 3.32 3.33 3.40 3.30 3.32 3.27 3.34 3.45

others

3.34 3.26 3.34

The definition of the distance d is explained in Scheme 1. bNitrobenzene.

Figure 2. Correlations of ΔEB with ∑|σm| (A) and ∑|σp| (B) for the interactions between GR, 3BGR, and 3NGR with various m- and p-substituted and several di- and tri-substituted nitrobenzene derivatives (Tables 1 and 2) at the DFT/M06/cc-pVDZ level. (A) Correlations of GR (blue line and black dots; ΔEB = −4.22∑|σm| − 12.92, n = 14, r = 0.9), 3BGR (red line; ΔEB = −3.85∑|σm| − 13.84, n = 14, r = 0.91), and 3NGR (green line; ΔEB = −4.04∑|σm| − 13.69, n = 14, r = 0.87) (r: correlation coefficient) interacting with m-substituted and other higher substituted nitrobenzene derivatives. (B) Correlations of GR (blue line; ΔEB = −4.26∑|σp| − 11.98, n = 14, r = 0.91), 3BGR (red line; ΔEB = −3.86∑|σp| − 13.45, n = 14, r = 0.91), and 3NGR (green line; ΔEB = −3.92∑|σp| − 12.90, n = 14, r = 0.80) interacting with p-substituted and other higher substituted nitrobenzene derivatives. Similar correlations through M06/cc-pVTZ, M06/sp-aug-cc-pVTZ, and MP2/cc-pVDZ calculations are shown in Figures S6 and S7 (Supporting Information).

for the nitrobenzene···GR/3BGR/3NGR interactions. The computed ΔEBs for the various disubstituted nitroaromatics (Tables 1−4) further show that it increases with various m- and p-substituents depending on their electron redistribution effect on the aromatic ring, although the changes of distance (Table 5) between the interacting systems are not very significant. These distances were measured as the distance between the center of mass of the aromatic rings of the nitroaromatics and the GR/3BGR/3NGR scaffold, as shown in Scheme 1. With further increase of substituents in the nitroaromatics (Tables 1−4), there are further increment in the ΔEB values. These trends were also observed previously by several authors in the

aromatic nitro compounds on GR, 3BGR, and 3NGR. The binding energies for o- and p-substituted nitroaromatics cases are more or less similar on all of these scaffolds. The ΔEB values of the nitroaromatics are much higher than the interactions of benzene with GR, BGR, and NGR. These values are available in Table 1, and it should be noted that the positive ΔGB° values predict the benzene···GR/BGR/NGR interactions to be relatively unstable. The general trend is that the ΔEBs (ΔHB° and ΔGB° values as well) increase with the increase of the number of substituents in the nitroaromatic ring. It should be noted that regardless of the ortho or meta orientation of the group X in the nitroaromatics, ΔEB is always greater than that 2779


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This is a linear relation between ΔGB° and σ. Because ΔG = ΔH − TΔS (H: enthalpy and S: entropy), one can generate similar relation between ΔHB° and σ (eq 5).

case of benzene···substituted benzene dimers.41,42 The molecular electrostatic potential (MEP) maps for three representative cases are shown in Figure 1. Figure S5 (Supporting Information) shows the MEP maps of several more of such interactions together with the corresponding nitroaromatic components. The pictures show that the individual MEPs of the nitroaromatics do not show any significant change with respect to the composite system. This particular feature indicates that these π−π interactions are mostly dominated by dispersion and the electrostatic contributions for stabilizing effect. It is customary to plot ΔEBs against Hammett σ-parameters44 to investigate the validity of Hammett correlation in cases of π−π stacking. Several authors did such analysis for the benzenesubstituted benzene interactions, and a brief account of the validity of ∑|σm| parameters instead of ∑σm was given in Introduction in relation to the previous findings.42 In the present cases also, the plots of ΔEBs versus ∑σm and ∑σp parameters (Table S1) do not produce decent linear correlations, although the correlations between ΔEB and ∑σm are somewhat better than those of the corresponding ∑σp cases (Figure S6, Supporting Information). These types of correlations could be partly successful if only electronwithdrawing monosubstituted cases are considered, as was done by Houk and Wheeler in their earlier studies on benzene···substituted benzene dimers.41 Because in the present investigations we are studying only the cases of aromatic nitroderivatives, the consideration of such specific features is out of scope here. The plots of ΔEBs versus ∑|σm| (Table S1) for the nitroaromatics produce reasonably good linear correlations for all of the interacting dimers of nitroaromatics with GR/ 3BGR/3NGR (r: correlation coefficient > 0.92 for all three scaffolds). ΔEBs at various levels, viz. DFT/M06 (cc-pVDZ, ccpVTZ, and sp-aug-cc-pVTZ basis sets) and MP2/cc-pVDZ, show more or less similar correlations. Only the correlations through DFT/M06/cc-pVDZ calculations are shown here (Figure 2), and the others are documented in the Supporting Information (Figure S7). This policy is also adopted for the other analysis throughout the manuscript (considering the total amount of analyzed data). The plots of ΔEBs versus ∑|σp| (Table S1) for the nitroaromatics are not as impressive as the ∑|σm| cases, but they still show reasonable correlation in the present molecular domain (Figure 2, cc-pVTZ). The best r value in most of the cases is >0.9. The linear correlation is slightly weaker for these nitrobenzene interactions with 3NGR. The results of such correlation using other basis sets and MP2/ cc-pVDZ are shown in Figure S8 (Supporting Information), and they also indicate that linear correlation exits in such cases. The Hammett equation44 usually predicts a linear correlation of ΔGB° against the σ-parameters from the relation

log

KB =σ K0

ΔHB° = ΔH0° − RTσ

We have neglected the difference (TΔSB − TΔS0), as it is too small. The plots of ∑|σm| parameters of nitrobenzene derivatives versus ΔGB°/ΔHB° generate linear correlations, which are shown in Figure S9 (Supporting Information) as predicted in eqs 4 and 5. Linear correlations were observed for all of the three scaffolds, viz. GR, 3BGR, and 3NGR. Similar correlations were also observed with respect to the ∑|σp| parameters (Figure S9, Supporting Information). The ΔG0°/ ΔH0° terms in eqs 4 and 5 are absorbed in the correlation equations in the intercept parameters and the prefactor term of σ. Because ΔHB and ΔEB are more or less similar, the use of ΔEB to monitor the validity of Hammett correlation is justified. One can compare the strength of such Hammett correlations from the slopes of the linear correlations (called ρ values) as shown in the caption of Figure 2. If ρ > 1, it could be interpreted as a measure of strong Hammett correlation (following the original interpretation of ρ as reaction constant for the reactions of various m- and p-substituted benzene derivatives).67 The slopes of Hammett correlations of ΔEBs versus both ∑|σm| (slopes for GR: 4.22, 3BGR: 3.85, 3NGR: 4.04) and ∑|σp| (slopes for GR: 4.26, 3BGR: 3.86, 3NGR: 3.92) are available in Figure 2. According to the concept of ρ, the Hammett correlation is quite strong in such cases and the strengths are more or less equivalent, although correlations in the case of GR are always slightly stronger. Such analysis could be extended for other correlations also (as presented in Figures S7−S9, Supporting Information). The comparison of such ρ values with arene···arene interactions is not straightforward, as a few results are available with σm correlation only. Wheeler and Houk41 presented the correlation equation between the interaction energies and σm values of benzene···substituted benzene complexes. The computed ρ value for this case is 2.72, which indicated a strong correlation comparable to our cases. The logic behind the use of ∑|σm|/∑|σp| parameters in such correlations has been discussed earlier (Introduction section), and it was proposed that these parameters might take into account the contribution of electrostatic interactions because ∑σm/∑σp parameters together with ∑Mr (Mr: molecular refractivity) correlate jointly with ΔEB. Because Mr implicitly contains molecular polarizability α through the relation Mr = 4/ 3(πNα) (N: Avogadro number), the contribution of electrostatic interactions was indirectly predicted through such correlations. In the present cases, we have found that ΔEB could be satisfactorily correlated with the ∑|σm|/∑|σp| and ∑Mr values of various nitroaromatics68 (Table S2) through multiple correlations, as shown below (eqs 6−11). GR···nitroaromatics (M06/cc-pVDZ)

(3)

ΔE B = −2.53 ∑ σm − 0.22 ∑ M r − 11.58 n = 14,

where KB should be taken as the binding constant for the interactions between the graphene (and doped graphene) and the substituted aromatic system (substituted nitrobenzenes for our specific cases) and K0 is the same constant for any reference system. From eq 3, one can easily show by multiplying both sides with RT (R: universal gas constant, T: absolute temperature) that ΔG B° = ΔG0° − RTσ

(5)

r = 0.96, F = 68.81

(6)

ΔE B = −0.87 ∑ σp − 0.37 ∑ M r − 12.60 n = 14, r = 0.96, F = 61.22

(4)

(7)

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ΔE B = −2.54 ∑ σm − 0.15Δα − 10.80 n = 14, r = 0.94, F = 40.79

(8)

ΔE B = −1.13 ∑ σp − 0.16Δα − 12.04 n = 14,

ΔE B = −0.43 ∑ σp − 0.26 ∑ M r − 13.68 n = 14, r = 0.94, F = 39.78

r = 0.92, F = 31.90

(9)

ΔE B = −2.00 ∑ σm − 0.24 ∑ M r − 12.11 n = 14, (10)

ΔE B = −0.43 ∑ σp − 0.26 ∑ M r − 13.68 n = 14, r = 0.94, F = 39.78

(11)

The F statistics in the above correlations show that correlations are significant and most satisfactory for the GR···nitroaromatics interactions. The deviations observed in the 3BGR and 3NGR could be attributed to the slight deviations of these scaffolds from ideal π-characters, but still the correlations are significant. The correlations using other basis sets (cc-pVTZ and sp-aug-ccpVTZ) and MP2/cc-pVDZ are shown in Table S3 (Supporting Information). It should be noted that all of the M06 level correlations are more or less similar. The correlations at the MP2/cc-pVDZ level are somewhat weaker, but still show that the correlations at the M06 level are validated in such analysis. The somewhat weaker correlations at the MP2 level are not unexpected, as the geometry of the complexes was not optimized at this level. The implicit contribution of α in Mr has further prompted us to investigate the direct effect of this parameter (as Δα with respect to benzene) in such correlations. The parameter α is directly available in quantum chemical calculations in isotropic form [α = 1/3(αxx + αyy + αzz)], and is an experimentally observable quantity. Moreover, because Δα represents the effect of electronic redistribution due to substitution of various functional groups in benzene, correlation with Δα will directly indicate the role of electrostatic and dispersion contributions in the present interactions. The correlation presented below (eqs 12−17) shows that ΔEB correlates satisfactorily with ∑|σm|/ ∑|σp| and Δα (Table S2). GR···nitroaromatics (M06/cc-pVDZ) ΔE B = −3.27 ∑ σm − 0.12Δα − 10.54 n = 14, r = 0.94, F = 43.60

(12)

ΔE B = −0.08 ∑ σp − 0.23Δα − 10.24 n = 14, r = 0.94, F = 45.19

(13)

3BGR···nitroaromatics (M06/cc-pVDZ) ΔE B = −1.86 ∑ σm − 0.16Δα − 11.44 n = 14, r = 0.95, F = 54.64

(14)

ΔE B = −1.13 ∑ σp − 0.16Δα − 12.04 n = 14, r = 0.92, F = 31.90

(17)

Table S4 (Supporting Information) contains correlations using other basis sets (cc-pVTZ and sp-aug-cc-pVTZ) at M06 and MP2 (cc-pVDZ) levels. The correlations in most of the cases are impressive (r > 0.9), although in a few cases, the MP2 results are not as good as the M06 cases. The situation is similar to that of ∑|σm|/∑|σp|, ∑Mr multiple correlations with ΔEB. Although the parameters, viz. r and F statistics, show impressive correlations, reproducibility of ΔEB from the above correlations need to be further tested. Figures S10−S13 (Supporting Information) show the correlations of ΔEB with the predicted ΔEB from the multiple correlation equations, as discussed above. The linear correlations using various basis sets and techniques (M06 and MP2) are quite satisfactory in our present molecular domain. The MP2 calculations in some cases (mostly in p-substituted compounds) have shown slightly weaker correlations (r < 0.9, Figures S10−S13). These deviations were mostly observed during interactions of such compounds with 3BGR and 3NGR. Previously, lipophilicity parameter π (instead of Mr) was tried as ∑π in the correlation analysis of benzene···substituted benzene interactions.42 We did not take into account such correlations, as we are only studying the gasphase situations. 3.3. Energy Decomposition Calculations. The success of ∑σm/∑σp, Mr/Δα parameters correlating ΔEB’s in the multiple correlations eqs 6−17, shows that the contribution of the dispersion of electrostatic interactions is important in such correlations and also generates the logic behind the intrinsic contributions of such interaction terms in the correlations of ΔEB’s with ∑|σm|/∑|σp|. Such correlations also generate further need to quantitatively analyze the contributions of various interactions terms in such complex formation. Tables S5 and S6 (Supporting Information) show the interaction energy components for m- and p-substituted nitrobenzenes, respectively (together with derivatives with multiple substituents) at the Hartree−Fock (HF) level, as discussed in eq 1, and the contribution of the dispersion interactions (ΔEdisp) ( E(2) MP2 in eq 2). As it could be seen from Tables S5 and S6, the total interactions are repulsive at the HF level. The attractive HF electrostatic (E(10) el ) and delocalization (ΔEdel ) are offset by the repulsive Heitler−London exchange term (EHL ex ). The main stabilization arises from the contribution of the ΔEdisp term, which is actually contribution from dispersion and higher-order correlations with the HF components. Figure 3 represents a bar chart representation of the contributions of the attractive E(10) and ΔEdisp terms in the el interactions between GR/3BGR/3NGR and the various msubstituted nitrobenzenes as well as the derivatives with multiple substituents (as shown in Table S5). Although ΔEdisp shows substantial contribution in stabilization of the complexes in MP2 calculations, E(10) also plays an important el role here. This is evident from the magnitude of the repulsive HL HF EHL ex term in such calculations. If the ΔEdisp, Eex , and ΔEdel terms are added, the total stabilization coming out through such contributions becomes almost equal to the contribution from E(10) el . Figure 3 also contains the contribution of empirical ΔEdisp term in the DFT calculations. These contributions are much

3NGR···nitroaromatics (M06/cc-pVDZ)

r = 0.95, F = 46.94

(16)

(15)

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smaller than ΔEdisp in MP2 calculations (E(2) MP2). This is quite obvious from the fact that the DFT calculations already include electron correlation effects to show some stabilization of the complexes. The empirical ΔEdisp here is only the unaccounted dispersion effect in such calculations. This effect (empirical ΔEdisp) actually makes the ΔEB values in DFT calculations more or less similar with respect to the MP2 results (Tables 1−4), although the MP2 values are somewhat lower. Interaction energy components for the p-substituted nitrobenzenes are shown in Table S6 (Supporting Information). Similar to the cases for m-substituted compounds, the psubstituted nitrobenzene derivatives also show that the interactions with GR, 3BGR, and 3NGR are mostly due to E(10) and ΔEdisp contributions. el The symmetry-adapted perturbation theory (SAPT) analysis69 of the interactions between benzene and substituted benzenes at the DFT level42 indicated that the sum of the energy components ΔEdisp + ΔEex + ΔEind (ΔEex: exchange component; ΔEind: induction component) is more or less constant for such interactions. The ΔEex in SAPT and the EHL ex component in our present study are more or less similar, but the ΔEind and ΔEHF del components are not totally similar. is associated with the relaxation of electron Although ΔEHF del densities of monomers upon interaction restrained by the Pauli principle,58,59 (charge delocalization together with chargetransfer interactions), ΔEind is associated with the interactions associated with interactions arising from the charges due to the deformation of the monomer units. Hence, ΔEdisp + EHL ex + ΔEHF del is not constant and varies depending on the associated (10) charge-transfer terms in ΔEHF term increases the del . The Eel binding for both the strong electron-withdrawing and electrondonating substituents and makes almost equal contribution HF with respect to ΔEdisp + EHL ex + ΔEdel (Tables S5 and S6). Thus, ∑σm (or ∑σp) together with ∑Mr or Δα terms is needed to predict ΔEB in the present cases. This observation also concurs with the results of previous SAPT analysis on the benzene··· substituted benzene interactions.42 It is to be remembered that these results hold for the gasphase cases. Because our computed ΔGB° have close resemblance with several experimental results for molecules adsorbed on graphene (as discussed earlier), the propositions for the correlations, as suggested, could also hold for condensed phase. No comments could be made regarding the solvent effect as the GR systems chosen do not have any solubility information. Thus, the proposition of Cockfroft and Hunter regarding70 the absolute dominance of the electrostatic term (in benzene···substituted benzene interactions) cannot be tested here. But it is obvious that E(10) el is one of the dominating factors term has some more in stabilizing such interactions. The E(10) el features in such interactions, and it was also the primary observation of Hunter and Sanders40 in relation to the benzene···substituted benzene interactions. Our analysis showed that the stabilizing effects in E(10) are mostly coming el from charge−charge interactions. But the dipole−dipole, dipole−quadruple, and quadruple−quadruple terms also have contributions. The contribution of the other contributing terms are not very significant. Because the nitrobenzene derivatives chosen for such interactions mostly have appreciable dipole moments (Table S2) and polarizabilities, these contributions of higher-order electrostatic terms in E(10) are justified. The el exceptions in the present cases are p-dinitrobenzene, pcyanonitrobenzene, and a few other nitrobenzene derivatives with multiple substitutions, where the dipole moment is either

Figure 3. Bar chart graphs comparing the contributions of E(10) and el ΔEdisp in GR (A)/3BGR (B)/3NGR (C) interactions with various msubstituted and several di- and tri-substituted nitrobenzene derivatives (Table 1) through energy decomposition analysis. The red and blue bars, respectively, represent ΔEdisp (MP2) and E(10) el contributions. The empirical dispersion contributions at the M06/cc-pVDZ level (green bars) are also included for comparison. The magnitudes of these parameters with other decomposition energy components are available in Table S5 (Supporting Information). The nitrobenzene derivatives (a−n) are same in all of the three panels and are in the same order (from the top) as in Table 1. The results for p- and higher nitrobenzene derivatives are available in the Supporting Information (Table S6). 2782


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zero or very low (Table S2). In such cases, the contribution of component is also low (Tables S5 and S6). The the E(10) el charge−charge and dipole−quadruple terms mostly contribute component. to the stabilizing E(10) el

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.7b01912. Complete reference of Gaussian 09 code; Tables S1−S6; Figures S1−S14 (PDF)

4. CONCLUSIONS We have investigated the applicability of Hammett parameters in extended π-systems, where geometry restrictions were not needed. Three different model graphene systems, viz. GR, 3BGR, and 3NGR, were designed as extended π-systems, and interactions of various nitroaromatics were monitored using M06/cc-pVDZ, M06/cc-pVTZ, M06/sp-aug-cc-pVTZ, and MP2/cc-pVDZ levels of calculation. The applicability of Hammett substituent constants (σm or σp) to predict binding energies for π−π interactions has been investigated previously on various benzene···m- and p-substituted benzene complexes. There were several viewpoints regarding the validity of such an approach, but later it was shown that the sum of the absolute values of σm (∑|σm|) did reasonably good job in such prediction. The ∑σp parameters also did show similar linear correlations to ΔEB, although such correlations were weaker with respect to ∑|σm| parameters. The ∑|σm| parameters were assumed to contain the effect of dispersion (or polarizability) as these parameters together with ∑Mr parameters showed good correlations with ΔEB. The geometry of the complexes in such studies were restricted to PFF orientation to enforce π−π interactions for the applicability of the Hammett parameters. The optimized structures (M06/cc-pVDZ level), in our present investigation, showed these structures to be in OSFF orientation, but because of the extended π-systems of GR, 3BGR, and 3NGR, the nitroaromatics were always experiencing π−π interactions. The ΔEB in all of the three different interactions showed good correlations with ∑|σm| and ∑|σp| parameters. Moreover, the convincing multiple regression analysis using ∑σm and ∑σp and Mr and Δα showed that, like benzene···substituted benzene cases, these interactions have contributions from dispersion and electrostatic components. The energy decomposition analysis for the interactions showed that electrostatic interactions together with ΔEdisp are important factors in such interactions. The E(10) el components in such interactions have almost equal stabilizing contribution HF with respect to the ΔEdisp + EHL ex + ΔEdel interaction energy components, and this contribution varies depending on the always shows ∑|σm| and ∑|σp| values. Furthermore, E(10) el stabilizing effect regardless of the nature of substituents of the terms nitrobenzene derivatives. A further analysis of the E(10) el indicated the contributions of the dipole−dipole, dipole− quadruple, and quadruple−quadruple terms in shaping up the total electrostatic contributions in such interactions and thereby giving some physical background to the importance of ∑Mr and Δα multiple regression equations to predict ΔEBs. Most of these observations are more or less similar to the conclusions of the previous investigations on benzene···substituted benzene systems, which indicates the applicability of Hammett correlation constants to predict ΔEB in OSFF orientations, if scaffolds are designed in such a way that substituted benzene systems cannot escape their π-cloud. The present observations are valid in a limited domain of molecules, and a much wider range of benzene derivatives are to be investigated to achieve a general validity of such hypothesis.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (D.M.). *E-mail: [email protected] (S.R.). *E-mail: [email protected] (J.L.). ORCID

Jerzy Leszczynski: 0000-0001-5290-6136 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by NSF-CREST (Award No. 154774) and NSF-EPSCoR R-II (Award No. OIA-1632899). The authors acknowledge the Mississippi Center for Supercomputing Research and the Wroclaw Centre for Networking and Supercomputing for providing generous computer time. S.R. acknowledges the financial support by a statutory activity subsidy from Polish Ministry of Science and Technology of Higher Education for the Faculty of Chemistry of Wroclaw University of Technology.

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REFERENCES

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Interactions of Substituted Nitroaromatics with Model Graphene

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