Effects of the Aromatic Substitution Pattern in Cation−π Sandwich

Mar 1, 2013 - A computational study investigating the effects of the aromatic substitution pattern on the structure and binding energies of cation−Ï...
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Effects of the Aromatic Substitution Pattern in Cation−π Sandwich Complexes Selina Wireduaah, Trent M. Parker, and Michael Lewis* Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, Saint Louis, Missouri 63103, United States S Supporting Information *

ABSTRACT: A computational study investigating the effects of the aromatic substitution pattern on the structure and binding energies of cation−π sandwich complexes is reported. The correlation between the binding energies (Ebind) and Hammett substituent constants is approximately the same as what is observed for cation−π half-sandwich complexes. For cation−π sandwich complexes where both aromatics contain substituents the issue of relative conformation is a possible factor in the strength of the binding; however, the work presented here shows the Ebind values are approximately the same regardless of the relative conformation of the two substituted aromatics. Finally, recent computational work has shown conflicting results on whether cation−π sandwich Ebind values (Ebind,S) are approximately equal to twice the respective half-sandwich Ebind values (Ebind,HS), or if cation−π sandwich Ebind,S values are less than double the respective half-sandwich Ebind,HS values. The work presented here shows that for cation−π sandwich complexes involving substituted aromatics the Ebind,S values are less than twice the respective half-sandwich Ebind,HS values, and this is termed nonadditive. The extent to which the cation−π sandwich complexes investigated here are nonadditive is greater for B3LYP calculated values than for MP2 calculated values and for sandwich complexes with electron-donating substituents than those with electron-withdrawing groups. either Li+ or Na+ was stronger than that of the corresponding metal benzene complexes. Most studies of cation−π complexes have focused on the half-sandwich motif (Figure 1a) even though it is estimated that

1. INTRODUCTION The importance of the cation−π interaction has been studied and discussed in numerous biological1 and chemical systems.2 In most computational studies, understanding the strength of the binding energy/enthalpy has been pursued with an aromatic molecule and an alkali3,4 or alkaline earth metal such as Li+, Na+, K+, Mg2+, Be2+, and Ca2+.5,6 In general, a higher binding strength is observed for aromatics with electrondonating substituents and a lower binding strength for aromatics with electron-withdrawing groups,7 while binding strength often decreases with an increase in cation size.5a,8 Furthermore, Du et al. recently suggested that the cation−π interaction involving H+ and Li+ cations may be quite different from the other alkali or alkaline earth metals.9 One of the most important discoveries of the last halfcentury has been organometallic sandwich complexes, with ferrocene being the prototype.10 Ferrocene has two cyclopentadienyl (Cp) anions sandwiching a Fe(II) cation, and although it is not generally considered a cation−π interaction, it does have a cation binding to the π-cloud of an aromatic anion. Cormier and Lewis have studied cation−π interactions of substituted Cp anions with Li+ or Na+ cation,11 and they argued that the complex represented a cation interacting with the πface of an aromatic.11b In experimental and theoretical studies, Ilkhechi et al. also reported on the cation−π binding of Li+, Na+, K+, Rb+, and Cs+ ions with Cp rings, where the Cp rings are also part of ferrocene complexes.12 They noted that the binding of such multiple-decker ferrocene complexes with © 2013 American Chemical Society

Figure 1. (a) Cation−π half-sandwich complex; (b) cation−π sandwich complex. Y+ is the cation, and X represents the aromatic substituents (n = 1−6).

the sandwich complex (Figure 1b), with alkali or alkaline earth metal cations, are at least as abundant in biology.13 For instance, many of the studies that describe the importance of cation−π binding in protein folding, structure, and function are in fact sandwich complexes.14 Cation−π complexes in proteins commonly involve amino acids with side chains that contain quaternary ammonium ions, such as Arg, His, or Lys, interacting with an amino acid containing an aromatic side chain, such as Phe, Tyr, Trp, or His. In addition, it is common for metal cations to bind to the aromatic side chains of Phe, Received: October 1, 2012 Revised: February 28, 2013 Published: March 1, 2013 2598

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Tyr, Trp, and His. For example, unnatural amino acid mutagenesis was recently employed to establish that cation−π binding to the side chain of TrpB is one of the three strongest contact points between the α4β2 receptor and nicotine.15 In this study the aromatic moiety TrpB is complexed to nicotine via a cation−π half-sandwich interaction. Chakravorty et al. studied Cu+/Ag+−Trp44 cation−π interactions at the metal recognition site in WT CusF, and they found the interaction is important in maintaining the delicate balance between protecting Cu+ from oxidation by water molecules and allowing the metal ion to be transferred to the cation efflux pump.16 Furthermore, the cation−π binding in the WT CusF recognition site is a sandwich complex. Using computational techniques, Jiang et al. undertook a study in which they calculated the binding energies of several complexes depicting cation−π sandwich systems, which they termed π−cation−π systems.17 Interestingly, they found that the binding energy of the sandwich complexes was approximately double the binding energy of the corresponding half-sandwich complexes; thus, the sandwich complex binding was additive. More recently, Orabi and Lamoureux reported a computational study that suggested the binding energies of sandwich complexes are nonadditive, which they termed anticooperative.18 Herein the results of a computational study of aromatic− cation−aromatic sandwich complexes (Figure 1b) involving substituted benzenes are reported. Cation−π studies of halfsandwich complexes (Figure 1a) generally show a good correlation between the binding energies and the Hammett constants of the substituted benzenes,11b,19 and this topic will be addressed here for sandwich complexes involving substituted benzenes. Additionally, the issue of relative conformation of the aromatics is important for sandwich complexes involving substituted benzenes, and this issue is also addressed here. Finally, the present study probes the issue of whether the binding energies are additive, as suggested by Jiang et al.,17 or nonadditive, as suggested by Orabi and Lamoureux and as seen in cation−π−π systems.18,20

Figure 2. Sandwich complexes involving substituted aromatics were investigated such that the X substituents were oriented at dihedral angles of (a) 0°, (b) 30°, (c) 60°, (d) 90°, (e) 120°, (f) 150°, and (g) 180°.

aromatics are at a 90° dihedral angle with respect to each other (Figure 2d). Geometry optimizations for all aromatics, half-sandwich complexes, and sandwich complexes were performed at the B3LYP/6-311++G(d,p) level of theory, and the structures were characterized as minima via frequency calculations at the same theoretical level. The absence of imaginary frequencies for almost all structures indicated that the geometries of the aromatics, half-sandwich complexes, and sandwich complexes are potential energy surface (PES) minima. The three exceptions were for F2−30, Cl2−120, and OH2−30. In each case the B3LYP/6-311++G(d,p) optimized geometries had one imaginary frequency; however, the RHF/6-311++G(d,p) optimized geometries did not contain imaginary frequencies suggesting the structures are PES minima. The explanation for the B3LYP/6-311++G(d,p) method giving imaginary frequencies for these structures is likely related to the basis set incompleteness error discussed by Moran et al.22 Single-point energy calculations were performed on all optimized structures at the MP2(full)/6-311++G(d,p) level of theory. E bind,HS(Na +−C6H5X)

2. COMPUTATIONAL METHODS Calculations were performed on Na+−(C6H5X) and (C6H5X)− Na+−(C6H5X) complexes, along with the Na+ cation and the respective C6H5X aromatics, using the Gaussian 09 suite of programs.21 The following substituents were investigated: X = F, Cl, Br, CH3, OH, and NH2. In addition, the parent aromatic benzene (Bz) was also studied. For the half-sandwich complexes, the Na+−Bz complex was investigated, along with the six Na+−(C6H5X) complexes. These complexes are termed Bz, F1, Cl1, Br1, CH31, OH1, and NH21, respectively. For the sandwich complexes, the parent Bz−Na+−Bz complex, the six Bz−Na+−(C6H5X) complexes, and the (C6H5X)−Na+− (C6H5X) complexes were studied. Note, the two aromatics in the (C6H5X)−Na−(C6H5X) sandwich complexes each have the same substituent, and for each of these complexes the issue of relative conformation was investigated by orienting the substituents on opposite aromatics at dihedral angles of 0°, 30°, 60°, 90°, 120°, 150°, and 180°, as shown in Figure 2. The parent sandwich complex is denoted Bz2, and the Bz−Na+− (C6H5X) complexes are named BzF1, BzCl1, BzBr1, BzCH31, BzOH1, and BzNH21. The sandwich complexes with two substituted aromatics are termed X2-##, where the X is the substituent and the ## is the dihedral angle relating the two substituents. For instance, NH22−90 represents the sandwich complex where the amino groups of the two C6H5NH2

= E(Na +−C6H5X) − [E(Na +) + E(C6H5X)]

(eq 1)

E bind,S(C6H5X−Na +−C6H5X) = [E(C6H5X−Na +−C6H5X)] − [E(Na +) + 2E(C6H5X)]

(eq 2)

E bind,add(C6H5X−Na +−C6H5X) = E bind,S(C6H5X−Na +−C6H5X) − (2E bind,HS(Na +−C6H5X))

(eq 3)

Binding energies (Ebind) for the half-sandwich (Ebind,HS) and sandwich complexes (Ebind,S) were determined via eqs 1 and 2, respectively, for both the B3LYP and MP2(full) calculated energies. The energies of the half-sandwich [E(Na+−C6H5X)] and sandwich [E(C6H5X)−Na+−(C6H5X)] complexes were corrected for basis set superposition error using the counterpoise method of Boys and Bernardi.23 Additivity energies (Ebind,add) were determined via eq 3 for both the B3LYP/6311++G(d,p) and MP2(full)/6-311++G(d,p)//B3LYP/6-311+ +G(d,p) Ebind values. All additivity energies are calculated with respect to the most stable sandwich orientation among the conformations shown in Figure 2. Finally, the Hammett 2599

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Table 2. Correlation Coefficients (r2) for the Correlations of Ebind,HS or Ebind,S Values with σm, σp, or (σm + σp) Valuesa

substituent constants used in the correlations with the Ebind values were taken from standard literature sources.24

3. RESULTS AND DISCUSSION Binding Energies of Cation−π Sandwich Complexes and the Relationship with Hammett Substituent Constants. The B3LYP/6-311++G(d,p) and MP2(full)/6311++G(d,p)//B3LYP/6-311++G(d,p) Ebind values for the half-sandwich and sandwich complexes are presented in Table 1. As noted above, there are numerous examples of the

Ebind,HS MP2 Ebind,HS B3LYP Ebind,S MP2 Ebind,S B3LYP

Bz F1 Cl1 Br1

Bz2 BzF1 BzCl1 BzBr1 BzCH31 BzOH1 BzNH21 F2−0 F2−30 F2−60 F2−90 F2−120 F2−150 F2−180 Cl2−0 Cl2−30 Cl2−60 Cl2−90 Cl2−120 Cl2−150 Cl2−180 Br2−0 Br2−30 Br2−60 Br2−90

Ebind,HS MP2a

Ebind,HS B3LYPb

−21.4 −17.1 −17.9 −18.0 Ebind,S MP2c

−23.2 −18.5 −19.1 −19.5 Ebind,S B3LYPd

−40.3 −36.6 −37.3 −37.4 −41.9 −40.5 −44.6 −32.6 −32.6 −32.8 −32.6 −32.7 −32.6 −32.6 −34.1 −34.1 −34.3 −34.2 −34.2 −34.1 −34.1 −34.3 −34.4 −34.5 −34.6

−40.8 −37.0 −37.3 −37.6 −42.4 −41.1 −45.4 −32.9 −32.9 −33.0 −33.0 −33.0 −33.0 −33.0 −33.4 −33.5 −33.6 −33.7 −33.7 −33.7 −33.7 −34.0 −34.0 −34.2 −34.3

complex

Ebind,HS MP2a

Ebind,HS B3LYPb

CH31 OH1 NH21

−23.2 −21.8 −26.2

−25.1 −23.6 −28.7

Br2−120 Br2−150 Br2−180 CH32−0 CH32−30 CH32−60 CH32−90 CH32−120 CH32−150 CH32−180 OH2−0 OH2−30 OH2−60 OH2−90 OH2−120 OH2−150 OH2−180 NH22−0 NH22−30 NH22−60 NH22−90 NH22−120 NH22−150 NH22−180

Ebind,S MP2c

Ebind,S B3LYPd

−34.5 −34.5 −34.5 −43.6 −43.6 −43.6 −43.6 −43.6 −43.6 −43.6 −41.4 −41.1 −40.9 −40.8 −40.7 −40.7 −40.7 −48.5 −48.6 −48.6 −48.6 −48.6 −48.6 −48.5

−34.3 −34.3 −34.3 −44.0 −43.9 −43.9 −43.9 −43.9 −43.9 −43.9 −40.1 −41.4 −41.4 −41.4 −41.3 −41.3 −41.4 −49.7 −49.8 −49.8 −49.8 −49.8 −49.8 −49.8

σp

(σm + σp)

r2 = 0.81 r2 = 0.82 Σσp

r2 = 0.94 r2 = 0.94 Σ(σm + σp)

r2 = 0.90 r2 = 0.92

r2 = 0.80 r2 = 0.81

r2 = 0.93 r2 = 0.95

a

The correlations with the sandwich complex binding energies are with the Σσm, Σσp, and Σ(σm + σp) values, where the Hammett constants for the substituents on the two aromatics are summed. The most binding Ebind,S values were used for the correlations.

Table 1. B3LYP/6-311++G(d,p) and MP2(full)/6-311+ +G(d,p)//B3LYP/6-311++G(d,p) Calculated Ebind Values (kcal/mol) for the Na+-Substituted Benzene Half-Sandwich and Sandwich Cation−π Complexes complex

σm r2 = 0.92 r2 = 0.91 Σσm

value of 0.81 or 0.82. The results in Table 2 are similar to those of Jiang et al. who showed that the (σm + σp) values correlated very well with the cation−π binding enthalpies of half-sandwich complexes involving aniline, toluene, phenol, benzene, fluorobenzene, 1,4-difluorobenzene, and 1,3,5-trifluorobenzene.19c Of course, Jiang et al. used Σ(σm + σp) values since two multisubstituted aromatics were investigated.19c The same trends were observed for the correlations between the sandwich complex binding energies (Ebind,S) and the Σσm, Σσp, or Σ(σm + σp) values. The sum of the Hammett constants on the two aromatics in the sandwich complexes was used to investigate the correlations with the Ebind,S values. The r2 values for the correlations are shown in Table 2, and the best correlations were found for the Σ(σm + σp) values with r2 = 0.93 or 0.95. The correlations with the Σσm values were almost as strong, with r2 values of 0.90 or 0.92, and the correlations with the Σσp values were comparatively poor (r2 = 0.80 or 0.81). Of note, for the sandwich complexes where both aromatics contain a substituent, the most binding Ebind,S values of the seven conformations were used to determine the correlations. This was different depending on the substituents; for instance, the most binding B3LYP/6-311++G(d,p) Ebind,S value for the sandwich complex with two fluorobenzenes has the F atoms at dihedral angles of 60−180° with respect to each other (Figure 2c−g), while the most stable sandwich complexes with two chlorobenzenes has the Cl atoms at angles of 90−180°. A further analysis of Table 1 shows that the most stable conformers of the sandwich complexes where both aromatics contain a substituent also differ depending on the theoretical method. Still, as discussed below, there is little difference between the binding energies of sandwich complexes with different conformations (Figure 2a−g), and the correlation coefficients in Table 2 for the sandwich complexes are largely independent of conformation. Effects of Relative Conformations of Substituted Benzenes in Cation−π Sandwich Complexes. As illustrated in Figure 2, sandwich complexes where both aromatics contain a substituent can have varying relative conformations. The initial hypothesis was that there would be significant variability in the binding energies (Ebind,S values) for these conformations. The rationale for expecting a significant difference in the Ebind,S values of the conformers in Figure 2 was because of the dipole−dipole interactions of the aromatics. Having the dipole moments parallel-aligned, as would be the case for Figure 2a conformers, would be repulsive in terms of electrostatics. Conversely, the dipole antiparallel-aligned conformers (Figure 2g) would be attractive due to electrostatics. Thus, the expectation, based on electrostatics, was that the Figure 2a conformers would have the least binding Ebind,S

a

Calculated from the MP2(full)/6-311++G(d,p)//B3LYP/6-311+ +G(d,p) energies using eq 1. bCalculated from the B3LYP/6-311+ +G(d,p) energies using eq 1. cCalculated from the MP2(full)/6-311+ +G(d,p)//B3LYP/6-311++G(d,p) energies using eq 2. dCalculated from the B3LYP/6-311++G(d,p) energies using eq 2.

cation−π binding energies and enthalpies of half-sandwich complexes correlating very well with Hammett constants:11b,19 Σσm, Σσp, or Σ(σm + σp) values.19a The r2 values for the correlations of the half-sandwich Ebind,HS values and the σm, σp, or (σm + σp) values are collected in Table 2. The correlations with the (σm + σp) values are best with r2 values of 0.94, although the correlations with the σm values are almost as good with r2 values of 0.91 or 0.92. The correlations between the binding energies and the σp values are markedly worse with r2 2600

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Ebind,add values were positive and nonadditive; the C6H6−Li+− C6H6 complex had a very large Ebind,add value of 10.9 kcal/mol for the gas phase and 8.9 kcal/mol for the solution phase, while the Na+, K+, and NH4+ complexes had much smaller values ranging from 1.6 to 4.0 kcal/mol depending on the ion and whether the complex was in the gas phase or solution phase. The Ebind,add values, as calculated via eq 3, are collected in Table 3, and the results are similar to those of Orabi and

values, and as the aromatics were rotated the binding energies would become more binding with the Figure 2g conformers having the most binding Ebind,S values. The results in Table 1 do not support the hypothesis in the previous paragraph. Rotating the substituted benzenes in the cation−π sandwich complexes from 0° to 180° (Figure 2) results in almost no change in the MP2(full)/6-311++G(d,p)// B3LYP/6-311++G(d,p) and B3LYP/6-311++G(d,p) calculated Ebind,S values; the variability in the F2, Cl2, Br2, CH32, and NH22 complexes is between 0.0 and 0.3 kcal/mol (Table 1). The range for the OH2 complex was slightly greater at 0.7 kcal/mol (MP2(full)/6-311++G(d,p)//B3LYP/6-311++G(d,p)) and 1.3 kcal/mol (B3LYP/6-311++G(d,p)). Still, these variations are quite small considering the absolute Ebind,S values for the OH2 complex conformers is about −41 kcal/mol. If the changes in binding energies upon rotation were greater, the data in Table 1 could be analyzed for which conformers (Figure 2) were most, or least, stable. However, given the relatively small changes in Ebind,S values upon rotation, this seems like a dubious exercise. The only meaningful physical insight appears to be that the substituted aromatics in the cation−π sandwich complexes are far enough apart that dipole−dipole electrostatic interactions do not play a role in dictating the relative position of the arenes. Additivity/Nonadditivity of Binding Energies for Cation−π Sandwich Complexes. Previous studies on the additivity of cation−π sandwich complexes have been contradictory. Jiang et al. reported the cation−π binding in sandwich complexes was additive; that is, the Ebind,S values were approximately twice the respective Ebind,HS values, and the Ebind,add values were essentially 0 kcal/mol.17 Conversely, very recent work by Orabi and Lamoureux18 reported on cation−π sandwich complexes with positive Ebind,add values; the binding energies of the sandwich complexes were less than twice the binding energies of the respective half-sandwich complexes. Orabi and Lamoureux used the term anticooperative to describe positive Ebind,add values,18 but we will simply use nonadditive. A subtle, but noteworthy, difference between the two approaches is how they determined the Ebind,add values. Jiang et al. calculated Ebind,add values as the difference between the arene−cation−arene binding energy and the binding energies of the respective arene−cation complexes.17 Orabi and Lamoureux used the same general approach, but also incorporated the binding energy of the two aromatics interacting with each other in the absence of the cation.18 Ultimately, Orabi and Lamoureux found this arene−arene binding term to be extraordinarily weak, less than 1 kcal/mol at the MP2(fc)/6-311++G(d,p) level of theory, and thus we did not include this arene−arene term in our studies. Of course there were other, more substantial, differences between the two studies; namely, they did not investigate the same complexes, nor did they employ the same computational methods. Jiang et al. employed gas-phase MP2/6-31+G(d,p)//MP2/6-31G(d), B3LYP/6-31+G(d,p)//MP2/6-31G(d) and HF/6-31+G(d,p)//MP2/6-31G(d) calculations to investigate the binding of tetramethylammonium cation (TMA) with combinations of benzene, pyrrole, and indole in cation−π sandwich geometries.17 Orabi and Lamoureux performed gas-phase and solution-phase studies of benzene−cation−benzene systems where the cation was either Li+, Na+, K+, or NH4+. The gasphase studies were carried out at the MP2(fc)/6-311++G(d,p) level of theory, and polarizable models were employed to determine solution-phase binding energies.18 In all cases the

Table 3. B3LYP/6-311++G(d,p) and MP2(full)/6-311+ +G(d,p)//B3LYP/6-311++G(d,p) Calculated Ebind,add Values (kcal/mol) for the Cation−π Sandwich Complexes complex

Ebind,add MP2

Ebind,add B3LYP

Bz2 BzF1 BzCl1 BzBr1 BzCH31 BzOH1 BzNH21

2.6 2.0 2.1 2.1 2.8 2.7 3.1

5.5 4.7 5.0 5.1 6.0 5.7 6.5

complex

Ebind,add MP2

Ebind,add B3LYP

F2 Cl2 Br2 CH32 OH1 NH22

1.4 1.6 1.5 2.9 2.2 3.9

4.0 4.5 4.6 6.4 7.1 7.6

Lamoureux18 and contrary to those of Jiang et al.;17 the cation−π sandwich complexes investigated here have nonadditive binding energies. The MP2(full)/6-311++G(d,p)// B3LYP/6-311++G(d,p) calculated Ebind,add values are almost identical to the values reported by Orabi and Lamoureux, and this is not surprising given that the levels of theory are very similar; structural optimizations were performed at different theoretical levels, but the energies were determined at almost the same theoretical level and with the exact same basis set. The one direct comparison between the work presented here and the work of Orabi and Lamoureux is the C6H6−Na+−C6H6 cation−π sandwich complex; Orabi and Lamoureux report a gas-phase Ebind,add value of 3.9 kcal/mol and a solution-phase value of 2.8 kcal/mol,18 while a value of 2.6 kcal/mol is reported here. The rest of the MP2(full)/6-311++G(d,p)// B3LYP/6-311++G(d,p) calculated Ebind,add values are in the range of 1.4−3.9 kcal/mol. The B3LYP/6-311++G(d,p) calculated Ebind,add values are significantly more positive, though not quite as positive as the C6H6−Li+−C6H6 Ebind,add values reported by Orabi and Lamoureux.18 The B3LYP/6-311+ +G(d,p) calculated Ebind,add values have a range of 4.0−7.6 kcal/ mol. It is worth noting in comparing the results of the present work, the work of Orabi and Lamoureux,18 and the work of Jiang et al.17 that the difference between the three sets of results is ultimately not that large. The C6H6−TMA−C6H6 cation−π sandwich complex Ebind,add values calculated by Jiang et al. using the electron-correlated methods MP2/6-31+G(d,p)//MP2/631G(d) and B3LYP/6-31+G(d,p)//MP2/6-31G(d) are 0.2 and 0.8 kcal/mol, respectively.17 This is only marginally smaller than the comparable C6H6−NH4+−C6H6 Ebind,add values reported by Orabi and Lamoureux (2.8 kcal/mol for gas phase at the MP2(fc)/6-311++G(d,p) level of theory, and 3.0 kcal/mol for solution phase using polarizable models).18 The Ebind,add ranges for the four cation−π sandwich complexes reported by Jiang et al. are −0.7 to 0.5 kcal/mol at the MP2/631+G(d,p)//MP2/6-31G(d) level of theory and 0.6 to 1.4 kcal/mol at the B3LYP/6-31+G(d,p)//MP2/6-31G(d) level of theory.17 Again, this is only marginally smaller than the 1.6−4.0 kcal/mol range reported for the C6H6−Na+−C6H6, C6H6−K+− 2601

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C6H6, and C6H6−NH4+−C6H6 Ebind,add values in the Orabi and Lamoureux study18 and the 1.4−3.9 kcal/mol range reported here for the MP2(full)/6-311++G(d,p)//B3LYP/6-311++G(d,p) calculated Ebind,add values. The larger discrepancies appear for the C6H6−Li+−C6H6 complex in the Orabi and Lamoureux study18 and for the B3LYP/6-311++G(d,p) calculated Ebind,add values reported here. In fact, in the current study Ebind,add values above 6 kcal/mol are observed only for cation−π sandwich complexes containing aromatics with electron-donating substituents and only when the B3LYP/6-311++G(d,p) level of theory is employed. Thus, triple-ζ basis sets, as employed here and in the work by Orabi and Lamoureux,18 appear to give Ebind,add values approximately 2−3 kcal/mol more positive than double-ζ basis sets, as employed by Jiang et al.17 Furthermore, more positive Ebind,add values are obtained when less polarizable ions are employed, as demonstrated by the C6H6−Li+−C6H6 results reported by Orabi and Lamoureux,18 and when more electron-rich aromatics are incorporated into the cation−π sandwich complexes, as shown here. Finally, B3LYP calculated Ebind,add values are more positive than MP2 calculated values when the basis set is held constant, as demonstrated by Jiang et al.17 and in the work presented here. The trend described above between the electron-donating/ withdrawing nature of the substituents and the degree of nonadditivity is illustrated in Figure 3. Cation−π sandwich

Table 4. Correlation Coefficients (r2) for the Correlations of Cation−π Sandwich Complex Ebind,add Values with Σσm, Σσp, or Σ(σm + σp) Values Σσm Ebind,add MP2 Ebind,add B3LYP

2

r = 0.92 r2 = 0.70

Σσp

Σ(σm + σp)

r = 0.71 r2 = 0.87

r2 = 0.88 r2 = 0.85

2

cation−π sandwich complexes are nonadditive; complexes with aromatics that have electron-donating substituents, as defined by Hammett parameters, have more positive Ebind,add values than cation−π sandwich complexes with electron-withdrawing substituents. Figure 3 and Table 4 show that the Ebind,add values are not constant for all aromatic substitution patterns. Thus, while Ebind,S is not simply twice the respective Ebind,HS values (Ebind,S ≠ 2•Ebind,HS), it is not possible to develop a single correction term to calculate Ebind,S from the corresponding Ebind,HS values (i.e., it is not possible to develop equations such as Ebind,S = 2•Ebind,HS + C or Ebind,S = C(2•Ebind,HS) where C is a single correction term derived from Ebind,add). This is because such a correction term C would be required for each aromatic substituent. As Figure 3 and Table 4 indicate, while the Ebind,S values of cation−π sandwich complexes are greater when the aromatics contain electron-donating substituents than when they contain electron-withdrawing groups, the additive effect in comparing the sandwich complex binding (Ebind,S) to that of the respective half-sandwich complexes (Ebind,HS) is muted for sandwich complexes with electron-rich aromatics when compared to complexes with electron-poor aromatics. The correlation coefficients in Table 4 show that the extent to which the Ebind,add values are muted correlates well with the Hammett (Σσm, Σσp, or Σ(σm + σp)) definition of electron donation/ withdrawal. If the Hammett parameters Σσm, Σσp, or Σ(σm + σp) suggest the aromatic substituents are strongly electrondonating, the Ebind,S values will be significantly less than the sum of the respective Ebind,HS values due to the large Ebind,add values. Conversely, if the Σσm, Σσp, or Σ(σm + σp) terms suggest the substituents are electron-withdrawing, the Ebind,S values will be close to the sum of the respective Ebind,HS values due to the small Ebind,add values. Thus, the Hammett correlations provide a qualitative gauge for how much the Ebind,S values deviate from the sum of the respective Ebind,HS values.

Figure 3. Correlation between cation−π sandwich complex binding energies (Ebind,S) and additivity energies (Ebind,add): blue diamonds, Ebind,S vs Ebind,add values at the MP2(full)/6-311++G(d,p)//B3LYP/6311++G(d,p) level of theory; red squares, Ebind,S vs Ebind,add values at the B3LYP/6-311++G(d,p) level of theory.

4. CONCLUSIONS A quantum mechanical computational study of the binding in cation−π sandwich complexes involving substituted benzenes and Na+ shows the sandwich complex binding energies (Ebind,S) correlate reasonably well with the aromatic Σσm or Σ(σm + σp) values. The correlation coefficients (r2) are above 0.9 and are slightly better for the Σ(σm + σp) values than for Σσm. The correlations between the Σσm or Σ(σm + σp) and the Ebind,S values are approximately the same as they are for the halfsandwich complex Ebind,HS values. The Σσp values correlate to a lesser degree with either the sandwich complex or halfsandwich complex Ebind values. The distance between the two aromatics in the cation−π sandwich complexes appears to be too great for the relative conformation of the substituents to be an issue. The variability in the Ebind,S values calculated at the MP2(full)/6-311+ +G(d,p)//B3LYP/6-311++G(d,p) or B3LYP/6-311++G(d,p) levels of theory among the seven possible conformations shown in Figure 2 is very small. This result renders moot any

complexes containing aromatics with electron-donating groups have larger binding energies, and they also have larger Ebind,add values. In fact, the correlation between the Ebind,S values and the Ebind,add values is very good: r2 = 0.95 for Ebind,S and Ebind,add values calculated at the MP2(full)/6-311++G(d,p)//B3LYP/6311++G(d,p) level of theory; r2 = 0.87 for Ebind,S and Ebind,add values calculated at the B3LYP/6-311++G(d,p) level of theory (Figure 3). Further support for this general trend is found in the correlations between the Σσm, Σσp, or Σ(σm + σp) and the Ebind,add values. The correlation coefficients are collected in Table 4, and while there is significant variability in the r2 values, from 0.70 to 0.92 depending on the correlation, four of the six r2 values are above 0.8 and the average of the r2 values in Table 4 is r2 = 0.82. Thus, there is clearly a relationship between the nature of the aromatic substituents and the extent to which 2602

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discussion on the effects of the aromatic dipole moments interacting with each other within the cation−π sandwich complex to dictate conformation. Finally, the binding energies of the cation−π sandwich complexes investigated here are nonadditive; that is, the binding energies of the sandwich complexes were less than twice the binding energies of the corresponding half-sandwich complexes. This is in agreement with previous work by Orabi and Lamoureux,18 but counter to results reported by Jiang et al.17 Combining the work presented here with these two previous studies, it appears that triple-ζ basis sets are required to observe the nonadditive nature of cation−π sandwich complexes, and more positive Ebind,add values are obtained when (i) the B3LYP method is employed, rather than the MP2 method; (ii) less polarizable ions such as Li+ are employed, rather than Na+, K+, or ammonium cations; (iii) more electronrich aromatics are incorporated into the cation−π sandwich complexes. Importantly, the present work does not allow for any comment on the nature of the cation, point (ii), as only Na+ was investigated. Furthermore, the only aromatic molecules studied were benzenes. Thus, it is possible that the additivity observed by Jiang et al. is partially due to the fact that the cation Me4N+ was investigated and/or because the aromatics indole and pyrrole were studied. Point (iii) is explored for the first time in the current work and offers an approach to understanding and predicting the binding energy of cation−π sandwich complexes. Although more electron-rich aromatics result in greater cation−π sandwich complex binding energies, the effect is muted compared to half-sandwich complexes, and the diminished effect of increasing the electron-donating ability of the substituent qualitatively correlates with the Hammett constants Σσm, Σσp, or Σ(σm + σp). Thus, simply extrapolating the effects of adding electrondonating substituents to cation−π half-sandwich complexes does not adequately inform on the effects of adding electrondonating substituents to cation−π sandwich complexes. Instead, there is an increase in nonadditivity (Ebind,add) when electron-donating substituents are added to the aromatics in cation−π sandwich complexes involving substituted benzenes.

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ASSOCIATED CONTENT

S Supporting Information *

Computational data for all structures and full citations for truncated references. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 314-977-2853. Fax: 314-977-2521. E-mail: LewisM5@ slu.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was partially supported by the American Chemical Society Petroleum Research Fund (47159-GB4) and the Saint Louis University Beaumont Faculty Development Fund. Computer time was supported by the National Center for Supercomputing Applications (CHE050039N) through an allocation on the SGI Altix system, by the Air Force Office of Scientific Research DURIP (FA9550-10-1-0320), and by Silicon Mechanics. 2603

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