Predicting the Strength of AnionâÏ Interactions of Substituted

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Predicting the Strength of Anion-# Interactions of Substituted Benzenes: the Development of Anion-# Binding Substituent Constants Christina Bagwill, Christa Anderson, Elizabeth Sullivan, Varun Manohara, Prithvi Murthy, Charles C. Kirkpatrick, Apryll M. Stalcup, and Michael Adam Lewis J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06276 • Publication Date (Web): 25 Oct 2016 Downloaded from http://pubs.acs.org on October 28, 2016

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The Journal of Physical Chemistry

Predicting the Strength of Anion-π Interactions of Substituted Benzenes: the Development of Anion-π Binding Substituent Constants Christina Bagwill, 1 Christa Anderson,1 Elizabeth Sullivan, 1 Varun Manohara, 1 Prithvi Murthy, 1

Charles C. Kirkpatrick,1 Apryll Stalcup2 and Michael Lewis*,1

1

Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, MO 63103

2

Irish Separation Science Cluster, National Centre for Sensor Research, Dublin City University,

Glasnevin, Dublin 9, Ireland [email protected] CORRESPONDING AUTHOR FOOTNOTE: Michael Lewis, 314-977-2853 (phone), 314-9772521 (facsimile)

ABSTRACT: A computational study aimed at accurately predicting the strength of the anion-π binding of substituted benzenes is presented.

The anion-π binding energies (Ebind) of 37

substituted benzenes, and the parent benzene, with chloride or bromide were investigated at the MP2(full)/6-311++G** level of theory.

In addition, energy decomposition analysis was

performed on 27 selected chloride-arene complexes via Symmetry Adapted Perturbation Theory (SAPT), using the SAPT2+ approach. Initial efforts aimed to correlate the anion-π Ebind values

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with the sum of the Hammett constants σp (Σσp) or σm (Σσm), as done by others. This proved a decent approach for predicting the binding strength of aromatics with electron-withdrawing substituents. For the Cl–-substituted benzene Ebind values, the correlation with the Σσp and Σσm values of aromatics with electron-withdrawing groups had r2 values of 0.89 and 0.87 respectively. For the Br–-substituted benzene Ebind values, the correlation with the Σσp and Σσm values of aromatics with electron-withdrawing groups had r2 values of 0.90 and 0.87. However, adding aromatics with electron-donating substituents to the investigation caused the correlation to deteriorate. For the Cl–-substituted benzene complexes the correlation between Ebind values and the Hammett constants had r2 = 0.81 for Σσp and r2 = 0.84 for Σσm. For the Br–-substituted benzene complexes, the respective r2 values were 0.71 for Σσp and 0.79 for Σσm.

The

deterioration in correlation upon consideration of substituted benzenes with electron-donating substituents is due to the anion-π binding energies becoming more attractive regardless of what type of substituent is added to the aromatic. A similar trend has been reported for parallel faceto-face substituted benzene-benzene binding. This is certainly counter to what electrostatic arguments would predict for trends in anion-π binding energies, and this discrepancy is further highlighted by the SAPT2+ calculated electrostatic component energies (Eele). The Eele values for the Cl–-substituted benzene anion-π complexes are all more binding than the Eele value for the Cl–-benzene complex, with the exception of chloride-1,3,5-trimethylbenzene. Again, this is a similar trend to what has been reported for parallel face-to-face substituted benzene-benzene binding. A discussion on this surprising result is presented. In addition, an improved approach to predicting the relative anion-π binding strength of substituted benzene is developed using the results of the SAPT2+ calculations.


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Introduction Noncovalent interactions of aromatics have been found to be of great importance in many systems.1

Anion-π interactions are typically termed as energetically favorable noncovalent

interactions of aromatics between an electron deficient, π-acidic, aromatic system and an anion.23

Thus anion-π interactions of aromatics were largely overlooked as they were expected to

exhibit a repulsive interaction between the negatively charged anion and the electron rich area of the aromatic ring.4-6 Still, early experimental work by Chowdhury and Kebarle suggested the existence of anion-π interactions,7 and later computational work showed that the negative end of a dipolar molecule could interact favorably with the π-electron cloud of hexafluorobenzene.8-9 This work was quickly followed by computational studies by Mascal2 and Deya3 demonstrating the possibility of an attractive interaction between anions and the π-electron density of electrondeficient aromatics. Deya and coworkers explored the Cambridge Structural Database (CSD) and found numerous crystallographic structures to experimentally support the existence of anionπ interactions.3 Numerous computational studies of anion-π interactions have been reported.4, 6, 10-21

Experimental work in the area of anion-π interactions of aromatics has demonstrated the existence of such complexes in the solid state,5, 19, 22-23 in solution,5, 24-34 and utility as reaction catalysts.35

Recent focus has turned toward identifying hosts that exhibit specific anion

recognition through aromatic π-electron density, such as tetroxacalix[2]arene[2]triazine,36-38 calix[4]pyrroles,34,

39-42

N6- and N9-decyladenine salts,43-44 1,4,5,8,9,12 hexaazatriphenylene-

hexacarbonitrile (HAT(CN)6),45-47 and transporters.24, 33, 48-54 The (HAT(CN)6) complex reported by Dunbar and coworkers is a neutral π-electron deficient aromatic unit that exhibits multisite interactions, including charge transfer and anion-π type interactions, in solution and the solid


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state.45-46 The novel cyclic and rod-shaped naphthalenediimide transporters developed by Matile and coworkers impressively demonstrate the possibility of lipid bilayer membrane channels that rely on anion-π interactions as the key transport mechanism.33, 48-49 While much has been learned from computational and experimental studies of anion-π interactions of aromatics, many questions remain.

The computational study reported here

focuses on determining what forces are important for predicting the relative strength of anion-π interactions of substituted benzenes, and the work reveals some surprising trends related to the aromatic substitution pattern. A large number of substituted benzenes were investigated for their chloride and bromide binding energies, and Symmetry Adapted Perturbation Theory (SAPT) was employed to discern the importance of the component forces to the overall binding, and to inform on what forces are important for predicting the relative binding strength of the interactions. The SAPT calculations show that while electrostatics plays an important role in anion-π interactions, and are an important consideration for predicting the relative strength of the anion-π binding of substituted benzenes, other forces must be considered to accurately predict the relative strength of these noncovalent interactions.

Computational Methods and Theoretical Approach The chloride and bromide binding of mono-, 1,4-di-, 1,3,5-tri-, and 1,2,4,5-tetra-substituted benzenes, along with the parent benzene, were investigated. All substituted aromatics contained only one type of substituent, and thus had the general formula C6H5X, 1,4-C6H4X2, 1,3,5C6H3X3, or 1,2,4,5-C6H2X4. The substituted benzenes studied were mono-, di- and tri-NO2 (1-3), mono-, di-, tri-, and tetra-CN (4 – 7), mono-, di- and tri-COCH3 (8-10), mono-, di-, tri- and tetraF (11 – 14), Cl (15 – 18), Br (19 – 22), I (23 – 26), CH3 (27 – 30), OH (31 – 34), and mono-, di-


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and tri-NH2 (35 – 37); the parent benzene is termed C6H6. The optimized structures of the tetrasubstituted nitro-, acetyl-, and amino-benzenes had one or more of the substituents rotated outof-plane with the aromatic ring. Anion-π interactions with such substituted benzenes would be dramatically affected by sterics, and since the aim of the current study focuses on the binding of an anion with planar substituted aromatics these substituted benzenes were not included here. All substituted aromatics were optimized and characterized via frequency calculations at the MP2(full)/6-311++G** level of theory. For aromatics with iodine substituents, the MIDI-X basis set was employed for I atoms. Negative frequencies were found for aromatics 7-11, 14, 17, 19-22, 30, and 33 due to basis set incompleteness error (BSIE)55. These compounds were reanalyzed using the RHF/6-311++G** level of theory and the absence of imaginary frequencies confirmed they were a minimum on the potential energy surface. Anion-π binding energies (Ebind) were determined by varying the anion-aromatic centroid distance from 2.5-6.0Å and calculating the energy of attraction at each point via the equation Ebind = [E(anion-arene) – (Eanion + Earene)]. The Ebind value was taken as the lowest point on the resulting potential energy surface (PES), and an example PES is shown in Figure 1 for the Cl–tetracyanobenzene complex. The resulting Ebind values were corrected for basis set superposition error (BSSE) using the counterpoise method,56 and all Ebind values in the manuscript are BSSEcorrected unless otherwise noted. The anion-π Ebind values are correlated with the aromatic substituent Hammett parameters.57

All optimization, characterization, and binding energy

calculations were performed using the Gaussian09 suite of programs.58 Symmetry Adapted Perturbation Theory (SAPT) calculations,59 which determine the contribution of electrostatics (Eele), induction (Eind), dispersion (Edisp), and exchange (Eexch) to the overall binding energy (Ebind), were performed using the SAPT2+ method as implemented in the


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Psi4 open-source quantum chemistry program.60-63 Basis sets from the Psi4 library for aug-ccpVDZ and aug-cc-pVDZ-ri were used for the elements H, C, N, F, Cl, and Br. Default basis sets for iodine are not present in the Psi4 distribution. For calculations involving iodine, we installed the all electron double-zeta basis ADZP,64 along with the resolution-of-the-identity basis set ccpVDZ-PP-ri;65 both were downloaded from the EMSL Basis Set Exchange web site.66 Prior to performing calculations with iodine-containing species, we assessed the suitability of our basis set choices in the SAPT2+ calculations by using sets from the same families for bromine. The SAPT2+ component and total energies obtained from the substituted basis sets with brominecontaining molecules were within 1% of the same values obtained with the Psi4 default aug-ccpVDZ and aug-cc-pVDZ-ri sets, and from these favorable results, we proceeded to use the installed basis sets for SAPT2+ calculations that included the element iodine. Unless otherwise noted, the geometries for the SAPT2+ calculations were the lowest energy BSSE corrected MP2(full)/6-311++G** structures.

Figure 1. Lowest energy structure of the Cl–-C6H2(CN)4 complex and the uncorrected (blue) and BSSE-corrected (red) MP2(full)/6-311++G** calculated potential energy surfaces that result from varying the anion-aromatic centroid distance.


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Results and Discussion Chloride and Bromide Binding to Substituted Benzenes. The Cl– and Br– Ebind values for C6H6 and substituted aromatics 1 – 37 are collected in Table 1. The approach shown in Figure 1 found anion-π binding minima for most of the complexes; however, no π-binding minimum was found for chloride binding with any of the amino-substituted benzenes (35 – 37). There are weakly binding PES minima for bromide with di- and tri-aminobenzene (36 and 37). Other anion-π binding minima were found to have positive Ebind values, and thus were repulsive. For instance,

Table 1. Chloride and Bromide Binding Energies (Ebind (Cl–) and Ebind (Br–)) and Anion-Arene Centroid Distances (d-Cl–) and (d-Br–) for C6H6 and Substituted Aromatics 1 – 37 Calculated at the MP2(full)/6-311++G** Level of Theory.a Aromatic C6H6 1 (mono-NO2) 2 (di-NO2) 3 (tri-NO2) 4 (mono-CN) 5 (di-CN) 6 (tri-CN) 7 (tetra-CN) 8 (mono-COCH3) 9 (di-COCH3) 10 (tri-COCH3) 11 (mono-F) 12 (di-F) 13 (tri-F) 14 (tetra-F) 15 (mono-Cl) 16 (di-Cl) 17 (tri-Cl) 18 (tetra-Cl) 19 (mono-Br) 20 (di-Br) 21 (tri-Br)

Ebind (Cl–) -0.17b -4.42 -11.88 -18.74 -3.88 -9.76 -16.88 -22.88 -1.36 -5.09 -8.62 0.18 -2.16 -4.56 -7.15 -0.12 -2.53 -4.73 -6.59 -0.18 -3.03 -5.29

d-Cl– – 3.5 3.3 3.2 3.6 3.3 3.2 3.1 3.7 3.5 3.4 3.9 3.6 3.5 3.4 3.8 3.6 3.4 3.3 3.9 3.5 3.4

Ebind (Br–) -0.67b -4.44 -11.46 -18.00 -3.94 -9.48 -16.27 -21.99 -1.60 -5.21 -8.65 -0.07 -2.26 -4.47 -6.85 -0.38 -2.65 -4.93 -6.52 -0.44 -2.92 -5.28

d-Br– – 3.7 3.4 3.3 3.7 3.5 3.4 3.3 3.9 3.6 3.5 4.0 3.8 3.6 3.5 3.9 3.7 3.6 3.5 4.0 3.7 3.5


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22 (tetra-Br) -7.11 3.3 -7.05 3.5 23 (mono-I) -0.59 3.7 -0.84 3.8 24 (di-I) -3.46 3.5 -3.57 3.6 25 (tri-I) -5.96 3.3 -6.02 3.5 26 (tetra-I) -7.57 3.3 -7.57 3.4 27 (mono-CH3) –c – 1.18 4.3 28 (di-CH3) 4.02 3.5 3.81 3.7 29 (tri-CH3) 0.76 3.9 0.27 4.0 30 (tetra-CH3) 0.55 3.9 0.02 3.9 31 (mono-OH) –c – 1.46 4.4 32 (di-OH) 2.35 4.0 2.04 4.0 33 (tri-OH) 1.11 3.9 0.76 4.0 34 (tetra-OH) 0.12 3.7 -0.21 3.8 35 (mono-NH2) –c – –c – 36 (di-NH2) –c – -0.68 4.3 37 (tri-NH2) –c – -1.40 4.3 a Anion-π Ebind values in kcal/mol and corrected for BSSE; anion-arene centroid distances (dCl–) and (d-Br–) in Å. b The C6H6 Ebind values are the only ones in the Table not corrected for BSSE, as there is no MP2(full)/6-311++G** BSSE corrected minimum. c No π-binding minimum.

the BSSE-corrected PES minima for Cl– and Br– binding to 1,4-di-, 1,3,5-tri- and 1,2,4,5-tetramethylbenzene (28-30), and to 1,4 di- and 1,3,5 tri-hydroxybenzene (32 and 33) were repulsive. The chloride binding to 1,2,4,5-tetra-hydroxybenzene (34) also has a repulsive π-binding minimum, although the bromide binding is slightly attractive.

Finally, there is no BSSE-

corrected MP2(full)/6-311++G** minimum for either chloride or bromide binding to benzene. The Ebind values reported in Table 1 for Cl– and Br– binding with C6H6 are the uncorrected MP2(full)/6-311++G** anion-π binding values. It is worth noting the strong anion-substituted benzene binding values (Ebind) of the aromatics with multiple electron-withdrawing groups. For instance, the Cl– and Br– complexes for the diand tri-nitro substituted benzenes (2 and 3) and for the di-, tri- and tetra-cyano substituted benzenes (5, 6 and 7) are all quite binding, with Ebind values ranging from -9.76 to -22.88


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kcal/mol. Although not quite as strong, the anion binding of the tri- and tetra- halo-substituted aromatics are also notable, with Ebind values ranging from -4.5 to -7.5 kcal/mol depending on the halogen. Of course, these are all gas-phase binding values and, for context, the gas-phase Ebind values for the Na+-benzene complex is -28 kcal/mol.67-68

Thus, the most highly electron-

deficient aromatics in Table 1 are competitive with the Na+-benzene complex in terms of gasphase binding strength. The anion-arene ring centroid distances, shown in Table 1 as d-Cl– and d-Br–, varied depending on the nature and number of substituents. Comparing the anion-substituted benzene complexes of the mono-substituted aromatics, the complexes involving highly electron-withdrawing substituents, such as –NO2 and –CN, have shorter d-Cl– and d-Br– values than those with highly electron-donating groups, such as –CH3 and –OH.

For instance, the bromide-nitrobenzene

complex (1) has d-Br– = 3.7 Å, the bromide-chlorobenzene complex (15) has d-Br– = 3.9 Å, and the bromide-phenol complex (31) has d-Br– = 4.4 Å. The same trend holds for the chloride-arene complexes. Similarly, the greater the number of electron-withdrawing substituents, the shorter the d-Cl– and d-Br– values. The difference between the anion-mono-substituted benzene ring centroid distances and the anion-tetra-substituted benzene ring centroid distances is relatively constant regardless of substituent and anion, with ∆d-Cl– and ∆d-Br– values between 0.4 to 0.6 Å. The trends based on the type of substituent, and on the number of electron-withdrawing substituents are readily explained via an electrostatic view of anion-arene binding; the more electron deficient aromatics have stronger Ebind values and shorter d-Cl– and d-Br– values. Surprisingly, and not readily explained via an electrostatic view of anion-arene binding, is the fact that adding additional electron-donating substituents also oftentimes shortens the anionarene ring centroid distance. For instance, the d-Cl– values for the di-, tri-, and tetra-hydroxyl


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complexes 32, 33, and 34 are 4.0, 3.9, and 3.7 Å. While there are a few instances where adding additional electron-donating substituents lengthens the anion-arene ring centroid distance, the most common result from adding additional electron-donating substituents is shorter d-Cl– or dBr– values (Table 1). While this trend is counterintuitive based on electrostatic arguments, a possible explanation may be the effect of charge penetration, as discussed in the next section. Effect of Increasing the Number of Substituents. One of the most surprising results of this study is the general trend showing that increasing the number of substituents always results in a more attractive binding. The results show that independent of whether a substituent is electronwithdrawing or electron-donating, the interaction energy strengthens as the number of substituents increases, as illustrated in Figure 2 for the bromide complexes. As would be predicted from electrostatics, increasing the number of electron-withdrawing substituents results in more binding anion-π Ebind values, and the most binding chloride and bromide π-binding complexes were calculated for the strongly deactivated 1,3,5 trinitrobenzene (3) and 1,2,4,5 tetracyanobenzene (7); the Cl–-arene binding energies for 3 and 7 are -18.74 and -22.88 kcal/mol, respectively. What is counter-intuitive based on a purely electrostatic view of anion-π binding is that for the three substituents that are traditionally viewed as electron-donating in Table 1, CH3, OH, and NH2, adding additional substituents also causes the anion-π complex to be more binding, with two exceptions. For the bromide binding complexes when going from mono- to di-methyl benzene or mono- to di-hydroxyl benzene, the binding energy decreases as shown in Table 1 and Figure 2. In all other cases, a comparison between the less-substituted and moresubstituted aromatic finds the greater the number of electron-donating substituents the more binding the anion-π complex. For instance, the bromide-aniline (35) π-binding complex is


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Figure 2. In almost all cases, increasing the number of substituents increases the Br--π binding strength, regardless of whether the substituents are electron-withdrawing or electron-donating.

repulsive, yet the diamino and triamino benzenes, 36 and 37, have Br– π-binding Ebind values of 0.48 and -1.40 kcal/mol, respectively. The notion that increasing the number of substituents, regardless of their electron-withdrawing or -donating ability, leads to an increase in the noncovalent binding of an aromatic has been reported for substituted benzene-benzene complexes,69-70 and it was determined that this was caused by charge penetration resulting from the monomers being in close contact.71 When the two aromatics are at far distances the interaction of the π-electron clouds is electrostatically repulsive; however, this interaction becomes electrostatically attractive at the close distances of substituted benzene-benzene dimers due to the electrons of one monomer interacting with the nuclei of the other monomer.71 Similarly, it has been shown that substituted benzene-benzene interactions can be understood via direct local interaction between the substituent and the region


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of the adjacent aromatic closest to the substituent.72-73

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One consequence of this complex

electrostatic attraction is that the correlation between substituted benzene-benzene binding energies and the Hammett constant σm fails when significant numbers of electron-donating substituents are included in the analysis.71 Given that 11 of the 38 substituted benzenes included in this study have electron-donating substituents according to the Hammett σm definition, the correlation between the Ebind values in Table 1 and the Σσm values of the substituted benzenes was investigated. The Correlation between Anion-π Binding Energies and Hammett Substituent Constants. Historically cation-π and π-π interactions have been correlated with Hammett parameters.74 Conversely, very few studies have been published investigating the correlation between Hammett parameters and anion-arene noncovalent binding energies. There has been two studies focusing on anion…C-H interactions11,

75

and two on anion- π interactions.28,

34

Hay and

coworkers reported the results of a computational study where 7 monosubstituted aromatics participated in two distinct anion…C-H interactions, and they found a strong correlation (r2 ≥ 0.99) between the calculated anion-arene binding energies and the σm of the monosubstituted aromatic.11

Ballester and coworkers experimentally investigated the relationship between

Hammett parameters and anion-π binding energies using calix[4]pyrrole systems with monosubstituted aromatics.28 The calix[4]pyrrole system was prepared with 6 different paramonosubstituted aromatics and the anion-π binding energy was measured via NMR spectroscopy. The correlation between the measured anion-π binding energy and the σp value of the substituted aromatics had an r2 value of 0.95; the correlation with σm had r2 = 0.92. More recent work by the Ballester group34 showed the calculated aromatic ESP value was necessary to correlate the experimentally measured solution-phase anion-π binding of a set of 9 substituted


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aromatics including para-monosubstituted, meta-disubstituted, and perfluoro-substituted aromatics and pyridine. The results reported here allow us to determine the correlation between anion-π binding energies and Hammett substituent constants for a larger data set (Table 1).

Since multi-

substituted aromatics were investigated, the anion-π Ebind values were correlated with the sum of the Hammett constants σm (Σσm) and σp (Σσp) for both the Cl–- and Br–-binding energies. Figure 3 shows the correlations for the chloride anion, and the r2 values for the Σσm and Σσp values are 0.84 and 0.81, respectively. The correlations between the Ebind values and the Σσm and Σσp values for the bromide anion are somewhat worse, with r2 values of 0.79 and 0.71, respectively (see the Supporting Information).

Figure 3. Correlations between anion-π binding energies in Table 1 for chloride and the aromatic ∑σm and ∑σp values.

It is noteworthy that the correlations between the anion-π Ebind values and the Σσm and Σσp values are much better when only electron-withdrawing substituents are considered.

The

correlations for the chloride anion are shown in Figure 4 and the r2 values are 0.86 and 0.90 for


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Σσm and Σσp, respectively. Identical results are found for the correlations between the bromide anion Ebind values and the Σσm and Σσp values for the aromatics with electron-withdrawing substituents; the r2 values are 0.86 and 0.90 respectively (see the Supporting Information). Parallel face-to-face substituted benzene-benzene Ebind values also correlate much better with Σσm and Σσp values when only the electron-withdrawing substituents are considered,69 compared to when all substituted benzenes are considered, and the explanation for this is related to the charge penetration posited by Sherrill and coworkers and noted above.71

Figure 4. Correlations between anion-π binding energies in Table 1 for chloride and the aromatic ∑σm and ∑σp values for aromatics with electron-withdrawing substituents.

Ultimately, the correlations between the Ebind values and the Hammett constants for all substituted aromatics are not very good; the best correlation is between the chloride anion-π Ebind values and the Σσm values (Figure 3), with r2 = 0.84. For Σσp the correlation with the chloride anion-π Ebind values is 0.81 (Figure 3). The correlations between the bromide anion-π Ebind values and the Σσm and Σσp values, for all aromatics in Table 1, are r2 = 0.79 and r2 = 0.71 (see Supporting Information), respectively.

Obviously, Hammett constants are not suitable for


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accurately predicting the relative binding energies of anion-π complexes of substituted aromatics.

Thus, SAPT2+ energy decomposition calculations were performed to better

understand anion-π interactions of aromatics, and to develop a parameter that better predicts the relative Ebind values. SAPT Calculations: Predicting Anion-π Binding Requires Substituent Constants that Describe Electrostatics and Induction. SAPT calculations allow the total binding energy of a noncovalent interaction to be decomposed according to the equation Ebind = Eele + Eind + Edisp + Eexch, where Eele, Eind, Edisp, and Eexch are the energies due to electrostatics, induction, dispersion, and exchange. SAPT calculations were performed, using the SAPT2+ approach, for 27 of the 38 Cl–arene complexes from Table 1, and while the goal was to account for the range of electronwithdrawing and electron-donating substituents, attention was also given to the viability of the calculations as SAPT can be a computationally demanding method.

Table 2 shows the

component energies Eele, Eind, Edisp, and Eexch for the considered Cl–-arene complexes. Correlation of the Eele, Eind, Edisp, and Eexch values to the overall binding energy Ebind yielded r2 coefficients of 0.98, 0.70, 0.75, and 0.84 respectively (see Supporting Information). Thus, while electrostatics does demonstrate the best correlation to the overall binding energy, induction, dispersion, and exchange also correlate to varying degrees. Another important result from Table 2 is that in 22 of the 27 complexes, the energy due to induction (Eind) is the largest contributor to the overall binding energy, not Eele. As a result of Eele correlating best with the overall binding energy, and Eind generally being the largest contributor to the overall binding energy, an anion-π substituent constant, termed Π–, was designed to reflect the importance of electrostatics and induction.


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Table 2. SAPT2+ Calculated Component Energies (Eele, Eexch, Eind, Edisp), in kcal/mol, for Selected Cl–-Substituted Benzene complexes.a Aromatic Eele Eind Edisp Eexch 3.63 -4.82 -3.69 5.38 C6H6 1 (mono-NO2) -3.68 -5.64 -4.47 6.97 2 (di-NO2) -12.90 -7.25 -6.13 11.48 3 (tri-NO2) -20.81 -8.82 -7.34 14.75 4 (mono-CN) -2.59 -5.21 -3.87 5.44 5 (di-CN) -10.77 -6.77 -5.31 9.21 6 (tri-CN3) -19.87 -8.72 -7.13 14.76 7 (tetra-CN4) -27.71 -10.23 -8.47 18.89 8(mono-COCH3) 0.81 -5.02 -3.51 4.24 9 (di-COCH3) -3.35 -6.53 -4.90 7.02 11 (mono-F) 2.32 -3.72 -2.46 2.53 12 (di-F) -1.02 -4.76 -3.69 5.35 13 (tri-F) -4.03 -5.19 -4.25 6.86 15 (mono-Cl) 1.99 -4.38 -2.97 3.29 16 (di-Cl) -0.97 -5.51 -4.02 5.41 17 (tri-Cl) -4.76 -6.93 -5.47 8.90 19 (mono-Br) 2.26 -4.21 -2.64 2.57 20 (di-Br) -1.72 -6.41 -4.49 6.98 21 (tri-Br) -4.62 -7.49 -5.62 9.03 23 (mono-I) 1.13 -5.25 -3.52 4.24 24 (di-I) -2.59 -7.08 -4.93 7.04 25 (tri-I) -7.44 -9.18 -6.81 11.56 28 (di-CH3) 3.16 -6.01 -4.74 6.94 29 (tri-CH3) 4.06 -4.70 -3.01 2.56 32 (di-OH) 3.40 -3.64 -2.30 1.96 33 (tri-OH) 2.45 -5.64 -4.59 6.81 34 (tetra-OH) 2.70 -4.90 -3.58 4.10 a SAPT2+ calculations performed at aug-cc-pVDZ and aug-cc-pVDZ-ri level of theory for all atoms except for I atoms which were calculated with the all electron double-zeta basis ADZP,64 along with the resolution-of-the-identity basis set cc-pVDZ-PP-ri.65

The Π– term was developed for different substituents X using the summation of the electrostatic (Eele) and induction (Eind) energies for the chloride-disubstituted benzene complex (Cl–C6H4X2) and dividing by the summation of the Eele and Eind terms for the parent Cl–C6H6 complex. Since the disubstituted benzene component energies were used this gives the effect for


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Equation 1: Π– = [Σ(Eele + Eind)(Cl–-C6H4X2))/Σ(Eele + Eind)(Cl–-C6H6))]/2

two substituents, and therefore the ratio was divided by 2 to yield the Π– constant for a single substituent. Equation 1 shows how the Π– constant was calculated. While it would have been simpler to calculate the constant using the SAPT component energies for the mono-substituted benzenes – the need to divide the ratio by 2 would have been negated – three of the monosubstituted benzenes, mono-CH3 (27), mono-OH (31), and mono-NH2 (35), do not have a Cl–binding minimum. Thus, a Π– constant could not be calculated for these three substituents using mono-substituted benzenes. The di-CH3 (28) and di-OH (32) analogs have potential energy surface minima for Cl–-binding, and therefore Equation 1 allowed for the calculation of Π– constants for all substituents except NH2, and they are shown in Table 3.

Table 3. Anion-π Substituent Constants Π-.a Substituent П– Substituent H 0.50 Br NO2 8.48 I CN 7.38 CH3 COCH3 4.16 OH F 2.43 NH2 b Cl 2.72 a Anion-π substituted constants, Π–, calculated using Equation 1. b The Π– calculated using Equation 1, but with Br–-complexes and as described in the text.

П– 3.42 4.07 1.20 0.10 0.09 constant was

As shown in Table 1, a Cl–-binding minima for the mono-, di-, or tri-substituted amino aromatics (35, 36, and 37) does not exist. Therefore, the amino Π– substituent constant was calculated using the Br–-binding complexes for the di-OH (32) and di-NH2 (36) aromatics, both of which have potential energy surface minima, and the C6H6 Br–-binding complex.

The


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SAPT2+ calculated Eele and Eind values for the Br– complex of 32 are 2.67 and -3.55 kcal/mol, respectively. The Eele and Eind values for the Br– complex of 36 are 2.26 and -3.07 kcal/mol, respectively. For C6H6 the values are Eele: 3.07 kcal/mol and Eind: -3.93 kcal/mol. Using these values to calculate Π– constants using Equation 1, except using Br–-complexes, gives values of 0.51 for OH and 0.47 for NH2. As shown in Table 3, the calculated OH constant when using Cl– -binding complexes is 0.10. Therefore, the NH2 Π– constant was normalized using the 0.10:0.51 ratio for the OH Π– constants calculated using chloride-binding complexes and bromide-binding complexes, respectively. This yields a Π– constant for NH2 of 0.09. To determine how well the Π– values (Table 3) performed at predicting the anion-π binding energies of substituted benzenes, the Ebind for chloride and bromide in Table 1 were correlated with the Π– values in Table 3, and the results are shown in Figure 5. Of course, Table 1 includes both mono- and multi-substituted benzenes, and for the multi-substituted aromatics the sum of the Π– values was used, just as the sum of the Hammett parameters were used in Figure 3. For both the chloride and bromide anion-π binding the correlation with the Π– values was excellent

Figure 5. Correlations between anion-π binding energies in Table 1 and the aromatic ΣΠ– values for Cl– binding complexes (left graph) and for Br–-binding complexes (right graph).


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with r2 values of 0.95 and 0.94, respectively.

This is a significant improvement over the

correlation with the Hammett parameters (Figure 3 and Supporting Information).

It is

noteworthy that the Π– constants were developed from SAPT calculations performed using a different theoretical level and a different basis set than what was used to calculate the Ebind values in Table 1. This suggests the Π– constants are not dependent on the theoretical level or basis set.

Furthermore, the Π– values were calculated primarily from chloride-substituted

benzene Ebind values, yet they perform equally well in correlating the Ebind value of the bromidesubstituted benzene complexes. This suggests they are not dependent on the anion. To further examine whether the results reported here are dependent on the theoretical method we calculated the chloride-substituted benzene Ebind values for complexes 1 (mono-NO2), 2 (diNO2), 5 (di-CN), 17 (tri-Cl), 20 (di-Br), 28 (di-CH3), 30 (tetra-CH3), and 32 (di-OH) at the M052X-D3/6-311++G** level of theory. These 8 complexes were chosen from Table 1 to cover the range of electron-withdrawing and -donating substituents and the range of substitution pattern in the broader set of complexes. The calculated Ebind values for these complexes at the M05-2XD3/6-311++G** level of theory are provided in Table 4, along with the corresponding MP2(full)/6-311++G** Ebind values from Table 1.

While the M05-2X-D3 Ebind values are

always slightly more binding than the MP2(full) Ebind values, the important comparison for the work reported here is with the difference in Ebind values. ∆Ebind values were calculated by comparing the Ebind of complexes 2, 5, 17, 20, 28, 30, and 32 to the Ebind of complex 1; ∆Ebind = Ebind (substituted benzene) – Ebind (1 (mono-NO2)). The ∆Ebind values are collected in Table 4 for both the MP2(full)/6-311++G** and M05-2X-D3/6-311++G** levels of theory, and the numbers are extraordinarily close. The mean average deviation between the two sets of ∆Ebind values is


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only 0.8 kcal/mol, and the ranks for the two sets of ∆Ebind values are identical. This gives us great confidence the reported results are not dependent on the level of theory.

Table 4. Comparison of MP2(full) and M05-2X-D3 calculated Chloride-Substituted Benzene Ebind values.a Complex

MP2(full)/6-311++G** Ebindb Rankd ∆Ebindc

M05-2X-D3/6-311++G**– Ebind Rankd ∆Ebindc -6.67 – –

1 (mono-4.42 – – NO2) 2 (di-NO2) -11.88 -7.46 1 -15.32 -8.65 5 (di-CN) -9.76 -5.34 2 -12.39 -5.72 17 (tri-Cl) -4.73 -0.31 3 -7.04 -0.37 20 (di-br) -3.03 1.39 4 -4.51 2.16 28 (di-CH3) 4.02 8.44 7 0.88 7.56 30 (tetra-CH3) 0.55 4.97 5 0.05 6.72 32 (di-OH) 2.35 6.77 6 0.51 7.18 a The 6-311++G** basis set was used for calculations at both theoretical levels. taken from Table 1. c ∆Ebind = Ebind (substituted benzene) – Ebind (1 (mono-NO2)). ∆Ebind values from most binding (Rank of 1) to least binding (Rank of 7).

1 2 3 4 7 5 6 b Ebind values d Rank of the

Conclusions Anion-π binding energies, Ebind, were calculated for a large number of substituted aromatics, with both the chloride and bromide anion. As expected, increasing the number of electron withdrawing groups on the aromatic resulted in a more binding anion-π complex. Unexpectedly, this was also largely the case when the number of electron-donating groups was increased. This is very similar to work reported for face-to-face arene-arene complexes involving substituted benzenes, which Sherrill explained as resulting from charge penetration,71 and Wheeler has suggested is a result of direct local interaction between the substituent on one aromatic and the region of the adjacent aromatic closest to the substituent.72-73 This has led to Iverson suggesting


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the terms “π-stacking” and “π-π interactions” are obsolete,76 and the results here suggest the term anion-π may not accurately reflect the interaction of an anion interacting with the face of an aromatic. Although previous studies suggested Hammett constants correlated very well with anion-arene Ebind values, the current study employs a much larger number of substituted aromatics than previously investigated, and the correlations with the Hammett constants σm and σp are not strong. SAPT energy decomposition calculations were performed on 27 of the Cl–substituted aromatic complexes and this showed the importance of electrostatics and induction in the overall binding energy: the energy due to electrostatics (Eele) correlated best with the overall Ebind values, and for most complexes the energy due to induction (Eind) was the largest overall contributor to Ebind. An anion-π parameter, Π–, was developed using the Eele and Eind values for each substituent, and an excellent correlation was found between the anion-arene Ebind values for chloride- and bromide-substituted benzene complexes and the Π– substituent constants. The Π– substituent constant offers an improved parameter for correlating, and predicting, the relative strength of anion-π binding.

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59. Jeziorski, B.; Moszynski, R.; Szalewicz, K. Perturbation theory approach to intermolecular potential energy surfaces of van der Waals complexes. Chem. Rev. (Washington, D. C.) 1994, 94, 1887-930. 60. Hohenstein, E. G.; Sherrill, C. D. Density fitting of intramonomer correlation effects in symmetry-adapted perturbation theory. Journal of Chemical Physics 2010, 133, 014101. 61. Hohenstein, E. G.; Sherrill, C. D. Efficient evaluation of triple excitations in symmetryadapted perturbation theory via MP2 natural orbitals. Journal of Chemical Physics 2010, 133, 104107. 62. Hohenstein, E. G.; Sherrill, C. D. Wavefunction methods for noncovalent interactions. WIREs: Compututational Molecular Science 2012, 2, 304-326. 63. Turney, J. M., et al. Psi4: An open-source ab initio electronic structure program. WIREs: Compututational Molecular Science 2012, 2, 556. 64. de Oliveira, P. J. P.; Barros, C. L.; Jorge, F. E.; Canal Neto, A.; Campos, M. Augmented Gaussian basis set of double zeta valence quality for the atoms Rb and Y-Xe: application in DFT calculations of molecular electric properties. Journal of Molecular Structure THEOCHEM 2010, 948, 43-46. 65. Hattig, C., Auxiliary basis sets for RI-MP2 calculations. TURBOMOLE basis set library 6.0, 2009; Vol. 1. 66. https://bse.pnl.gov/bse/portal 67. Mahadevi, A. S.; Sastry, G. N. Cation-π interaction: its role and relevance in chemistry, biology, and material science. Chem. Rev. (Washington, DC, U. S.) 2013, 113, 2100-2138. 68. Ma, J. C.; Dougherty, D. A. The cation-π interaction. Chemical Reviews 1997, 97, 13031324. 69. Watt, M.; Hardebeck, L. K. E.; Kirkpatrick, C. C.; Lewis, M. Face-to-face arene-arene binding energies: dominated by dispersion but predicted by electrostatic and dispersion/polarizability substituent constants. Journal of the American Chemical Society 2011, 133, 3854-3862. 70. Sinnokrot, M. O.; Sherrill, C. D. Highly accurate coupled cluster potential energy curves for the benzene dimer: sandwich, T-shaped, and parallel-displaced configurations. J. Phys. Chem. A 2004, 108, 10200-10207. 71. Hohenstein, E. G.; Duan, J.; Sherrill, C. D. Origin of the surprising enhancement of electrostatic energies by electron-donating substituents in substituted sandwich benzene dimers. J. Am. Chem. Soc. 2011, 133, 13244-13247. 72. Wheeler, S. E. Local nature of substituent effects in stacking interactions. J. Am. Chem. Soc. 2011, 133, 10262-10274. 73. Wheeler, S. E. Understanding substituent effects in noncovalent interactions involving aromatic rings. Accounts of Chemical Research 2013. 74. Lewis, M.; Bagwill, C.; Hardebeck, L. K. E.; Wireduaah, S. The use of Hammett constants to understand the non-covalent binding of aromatics Computational and Structural Biotechnology Journal [Online], 2012. 75. Tresca, B. W.; Hansen, R. J.; Chau, C. V.; Hay, B. P.; Zakharov, L. N.; Haley, M. M.; Johnson, D. W. Substituent effects in CH hydrogen bond interactions: linear free energy relationships and influence of anions. J. Am. Chem. Soc. 2015, 137, 14959-14967. 76. Martinez, C. R.; Iverson, B. L. Rethinking the term "pi-stacking". Chem. Sci. 2012, 3, 21912201.


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TOC Graphic

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Π = [Σ(Eele + Eind)(Cl -C6H4X2))/Σ(Eele + Eind)(Cl -C6H6))]/2


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Predicting the Strength of AnionâÏ Interactions of Substituted

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Predicting the Strength of AnionâÏ Interactions of Substituted