Selina Wireduaah,
Trent M. Parker,
Christina Bagwill,
Charles C. Kirkpatrick* and
Michael Lewis*
Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, MO 63130, USA. E-mail: lewism5@slu.edu
First published on 10th November 2014
This work proposes a new substituent constant, termed Π+, to describe cation–π binding using computational methods at the MP2(full)/6-311++G** level of theory with Symmetry Adapted Perturbation Theory (SAPT) calculations on selected cation–π complexes. The correlations between binding strength (Ebind or ΔH298) and common parameters for describing cation–π binding (∑σm, ∑σp, ∑(σm + σp), or Θzz) are decent (r2 between 0.79 and 0.90). SAPT calculations show that variations in the electrostatic (Eele), exchange (Eexch), induction (Eind), and dispersion (Edisp) component energies to the overall binding are almost entirely due to differences in arene–cation distances (dAr–cat). Eele varies most with dAr–cat; however, Eind seems to be the primary term responsible for the ∑σm, ∑σp, ∑(σm + σp) and Θzz parameters not accurately predicting the cation–π Ebind and ΔH298 values. The Π+ parameter largely reflects electrostatics, but it also includes the impact of exchange, induction, and dispersion on cation–π binding of aromatics, and the resulting correlation between ΔH298 or Ebind and Π+ is excellent (r2 of 0.97 and 0.98, respectively). Importantly, the Π+ parameter is general to cation–π systems other than those reported here, and to studies where the cation–π binding strength is determined using computational levels different from those employed in this study.
Computational work by Cormier and Lewis on the Li+ and Na+ binding of multi-substituted cyclopentadienyl (Cp) anions suggested that cation-substituent interactions were an important factor in Cp–cation binding.15 Furthermore, an excellent correlation between Cp–cation binding energies and the ∑σm of the Cp anions was demonstrated.15 Although the binding of cations to Cp anions is not generally viewed as a cation–π interaction, it does involve a cation interacting with the π-face of an aromatic, and it certainly would not be unreasonable to expect the trends found in Cp–cation complexes to extend to more traditional cation–π complexes. In fact, recent work by Wheeler and Houk shows that cation–π Ebind values of substituted benzenes can be predicted, to a decent degree (r2 = 0.81), by summing the binding energy due to the cation interacting with the parent benzene and the binding energy due to the cation interacting with the substituent.16 Based on this result the authors suggest that differences in cation–π binding of substituted aromatics are due to the interaction of the ion and the substituents on the aromatic, rather than to differences in aromatic π-cloud polarization.16 In a similar vein, Suresh and Sayyed recently discussed the contributions of substituent inductive, resonance, and through-space cation-substituent effects in cation–π interactions of substituted benzenes and, like Houk and Wheeler, they suggest that cation-substituent interactions are an important factor in cation–π interactions of substituted benzenes.17
The computational work presented here, on a large number of substituted benzenes, shows cation–π ΔH298 and Ebind values are predicted, to a decent degree, by either the sum of the aromatic Hammett constant σp (∑σp), the sum of the aromatic Hammett constant σm (∑σm), ∑(σm + σp), which is the σTotal value proposed by Jiang and coworkers,13 or the aromatic Θzz value. The sum of the Hammett constants was used since mono- and multi-substituted benzenes were investigated. The correlation with either ΔH298 or Ebind is best for the ∑(σm + σp) value; however, it is not substantially better than with the other three parameters. Ultimately, the ΔH298 and Ebind correlations are almost identical. Symmetry Adapted Perturbation Theory (SAPT) calculations show that variations in substituted benzene cation–π component energies are directly correlated to variations in the cation–arene distance (dAr–cat). The variations in the dispersion (Edisp), induction (Eind), and exchange (Eexch) component energies of Ebind are only slightly sensitive to dAr–cat; however, the changes in the electrostatic component (Eele) are very sensitive to dAr–cat. As a result of the SAPT calculations, the Na+-mono-substituted benzene ΔH298 values are used to develop a cation–arene binding parameter, which we term Π+, that performs much better than any of the Hammett parameters or the aromatic Θzz values in correlating the cation–π ΔH298 or Ebind values of mono- and multi-substituted benzenes. The generality of the Π+ term is demonstrated by exploring its ability to correlate cation–π binding energies determined in other studies.
SAPT21,22 binding energy decomposition calculations were performed on selected Na+-substituted benzene complexes in order to determine the contributions from electrostatics, dispersion, induction and exchange to the overall binding energies. The geometries for the SAPT calculations were the MP2(full)/6-311++G** optimized Na+-substituted benzene complex structures. The SAPT monomer wave functions were calculated using the CCSD/6-311++G** theoretical method, using the basis functions for the full dimer. This is the counter-poise approach to determining BSSE-corrected binding energies, and thus the SAPT binding energies reported in this manuscript should be considered BSSE-corrected. All optimization and binding energy calculations were performed using the Gaussian03 suite of programs.23 The SAPT calculations were done via SAPT2008 (ref. 24) using ATMOL1024,25 or Dalton 2.0,26 as the front end for computing integrals.
The MP2(full)/6-311++G** level of theory was chosen because of the good agreement between the calculated Na+–benzene binding energy and the experimental value. There have been three experimentally measured Na+–benzene binding enthalpies: ΔH0 = −28.0 ± 0.1 kcal mol−1,27 ΔH298 = −22.5 ± 1.5 kcal mol−1,28 and ΔH298 = 21.5 ± 1.0 kcal mol−1.29 Recent high-level computational work supports the accuracy of the latter two values;30,31 the calculated Na+–benzene binding energy is ΔE0 = −22.95 kcal mol−1 at the CCSD(T) level with complete basis set approximation30 and ΔE0 = −21.5 kcal mol−1 at the MP2 level with the Sadlej basis set.31 At the MP2(full)/6-311++G** level of theory the Na+ binding energy is ΔH298 = −18.5 kcal mol−1, just outside the experimental range for the smaller two experimental values.
Finally, the aromatic quadrupole moments, Θzz, were also determined at the MP2(full)/6-311++G** level of theory, using a coordinate system centered at the aromatic ring center. The aromatic quadrupole moment is a 3 × 3 tensor and for planar, non-polar aromatics the off-diagonal tensor components are zero and Θzz = Θzz − 0.5(Θxx + Θyy). Of course, not all of the aromatics investigated here are non-polar; the mono-, ortho-di-, and meta-di-substituted aromatics are polar, and the corresponding Θzz off-diagonal tensor components have non-zero values. However, the magnitudes of these off-diagonal tensor components are less than 10% of the value of the diagonal tensor components, and thus the equation for Θzz based on the diagonal terms is an excellent approximation of the aromatic Θzz value for the polar aromatics.
Arene–Na+ complex | Ebind (kcal mol−1) | ΔH298 (kcal mol−1) |
---|---|---|
a All Ebind values have been corrected for basis set superposition error. | ||
C6H6 | −21.41 | −18.53 |
F1 | −17.02 | −14.61 |
F2o | −13.07 | −10.92 |
F2m | −12.87 | −11.45 |
F2p | −12.49 | −11.16 |
F3 | −8.89 | −7.72 |
F4 | −4.87 | −3.27 |
Cl1 | −17.80 | −15.33 |
Cl2o | −15.50 | −12.76 |
Cl2m | −14.78 | −12.45 |
Cl2p | −14.45 | −13.10 |
Cl3 | −11.87 | −10.66 |
Cl4 | −7.96 | −8.80 |
Br1 | −18.00 | −15.61 |
Br2o | −15.89 | −14.40 |
Br2m | −15.41 | −13.25 |
Br2p | −15.01 | −13.64 |
Br3 | −13.19 | −10.89 |
Br4 | −11.77 | −10.71 |
I1 | −18.51 | −16.17 |
I2o | −17.14 | −15.62 |
I2m | −16.43 | −14.30 |
I2p | −16.05 | −14.68 |
I3 | −14.97 | −12.73 |
I4 | −14.45 | −13.46 |
CN1 | −12.19 | −11.23 |
CN2o | −4.37 | −4.93 |
CN2m | −4.28 | −2.41 |
CN2p | −3.95 | −2.92 |
CN3 | 2.47 | 4.36 |
NO21 | −10.56 | −9.84 |
NO22m | −1.29 | −1.89 |
NO22p | −0.65 | −1.32 |
CH31 | −23.21 | −21.33 |
CH32o | −24.45 | −22.95 |
CH32m | −24.68 | −23.21 |
CH32p | −24.79 | −23.10 |
CH33 | −26.33 | −24.66 |
CH34 | −26.87 | −25.84 |
OH1 | −21.22 | −18.56 |
OH2o | −22.11 | −21.02 |
OH2m | −21.26 | −17.98 |
OH2p | −21.69 | −18.00 |
OH3 | −22.73 | −18.83 |
OH4 | −21.89 | −20.87 |
NH21 | −25.37 | −24.20 |
NH22o | −26.93 | −26.08 |
NH22m | −31.06 | −29.76 |
NH22p | −29.97 | −28.16 |
NH23 | −35.17 | −33.52 |
NH24 | −30.28 | −28.95 |
OCH31 | −23.56 | −21.63 |
OCH32o | −25.73 | −22.55 |
OCH32m | −25.59 | −23.18 |
OCH32p | −24.87 | −23.17 |
OCH33 | −27.50 | −24.57 |
OCH34 | −28.04 | −26.47 |
N(CH3)21 | −28.36 | −26.56 |
N(CH3)22o | −28.74 | −27.16 |
N(CH3)22m | −33.53 | −31.81 |
N(CH3)22p | −30.72 | −29.29 |
N(CH3)23 | −39.67 | −37.92 |
The correlation between the cation–π ΔH298 values and the aromatic ∑σp, ∑σm, ∑(σm + σp), or Θzz values are shown in Fig. 1. The correlations are decent, with r2 values ranging from 0.79 to 0.90, and the ∑(σm + σp) value gives the best results. The results for the Ebind values are almost identical, and the correlation graphs are given in the ESI.† The correlations in Fig. 1 comparing cation–π binding energies to Hammett constants or the aromatic quadrupole moment contain significantly more substituted benzenes than have been investigated in prior studies, and in general this results in correlations that are not as strong as was previously reported.9,10,12,15,32 Computational work by Jiang and coworkers showed excellent correlations between cation–π binding enthalpies and ∑(σm + σp) values for seven substituted benzenes, with r2 = 0.98 and 0.99 depending on the cation.32 For the 62 substituted benzenes shown in Table 1, the correlation between the ΔH298 values and the ∑(σm + σp) values has an r2 = 0.90 (Fig. 1a), and while this is the best correlation shown in Fig. 1, it cannot reasonably be described as excellent. There are no computational studies describing the correlation between cation–π binding energies and Hammett σp values; however, Hunter showed an excellent correlation experimentally, via their chemical double-mutant cycles, with three cation–π complexes.12 Obviously, the correlation between cation–π binding enthalpies and ∑σp values in Fig. 1b, with r2 = 0.85, is not excellent. Computational work by Dougherty and coworkers discussed a “rough agreement” between cation–π binding energies and the Hammett σm value for five mono-substituted benzenes,9 and the correlation shown in Fig. 1c, with r2 = 0.83, would be rightly described as rough. Finally, the correlation between cation–π binding enthalpies and the substituted benzene Θzz values has r2 = 0.79 (Fig. 1d), which is about the same as the correlation previously reported by Lewis and Clements.10 It is important to recall that Dougherty showed much better correlations with the aromatic ESPs (r2 = 0.98),9 and Suresh with the aromatic MESP (r2 > 0.97).17 Furthermore, the latter study contained a very large number of substituted benzenes. Still, as stated previously, ESPs and MESPs are calculated values, and it would be preferable to use substituent constants for the prediction of cation–π binding since they don't require calculations before using them. As the work presented here shows, Hammett substituent constants do not suffice to accurately predict cation–π binding strength (ΔH298 or Ebind). Thus, SAPT calculations were performed to determine what forces are important in the cation–π binding of aromatics, and to aid in the development of an improved parameter for correlating cation–π ΔH298 and Ebind values.
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Fig. 1 Correlation between cation–π binding enthalpies (ΔH298) and either (a) ∑(σm + σp), (b) ∑σp, (c) ∑σm, or (d) Θzz, for the substituted benzenes in Table 1. |
Na+–arene complex | Eele | Eexch | Eind | Edisp | ESAPT |
---|---|---|---|---|---|
a SAPT calculations performed at CCSD/6-311++G** level of theory with basis set superposition error correction. Geometries are from the optimized MP2(full)/6-311++G** structures. | |||||
OH4 | −15.31 | 8.47 | −16.52 | −0.70 | −24.06 |
NH22o | −21.52 | 10.59 | −17.53 | −0.78 | −29.24 |
N(CH3)21 | −21.54 | 10.48 | −18.10 | −0.79 | −29.95 |
OH2o | −15.98 | 8.98 | −15.98 | −0.71 | −23.68 |
OCH32o | −19.18 | 10.22 | −17.95 | −0.77 | −27.68 |
CH32p | −18.29 | 10.29 | −17.49 | −0.79 | −26.28 |
C6H6 | −15.39 | 8.93 | −15.29 | −0.70 | −22.45 |
F3 | −1.64 | 5.59 | −13.62 | −0.55 | −10.22 |
Cl1 | −10.62 | 8.19 | −15.79 | −0.69 | −18.91 |
CN1 | −4.15 | 6.86 | −15.30 | −0.64 | −13.23 |
CN2m | 5.34 | 4.91 | −14.93 | −0.56 | −5.24 |
NO22m | 7.46 | 4.55 | −14.31 | −0.54 | −2.84 |
The major contributors to the overall cation–π binding energies (Ebind or ESAPT) are the Eele and Eind values (Table 2); however, there is much greater variability in the Eele values compared to the Eind values. As a result, sometimes the Eele values are the greatest contributor to the overall cation–π binding strength, and sometimes the Eind values contribute most. For the electron-rich aromatics the Eele component energy either contributes slightly more, or about the same, to the overall binding energy as Eind. In contrast, for the electron-poor aromatics the Eind component energy generally contributes much more to the overall binding strength than the Eele value. In fact, for CN2m and NO22m the cation–π complexes are binding solely due to induction; the Eele component is repulsive for these two complexes.
Plotting the data for each component energy in Table 2 against the respective ∑(σm + σp), ∑σp, ∑σm, or Θzz values (Fig. 2a–d), where the data is always arranged from most negative to most positive ∑(σm + σp), ∑σp, ∑σm, or Θzz value, reveals why these parameters do not perform as well as might be expected in predicting cation–π binding energies of substituted benzenes. Although the Eele component varies much more so than the other component energies, the Eexch, Eind, and Edisp values also vary depending on the aromatic substitution pattern (Fig. 2). As would be expected, the variations in the Eele, Eexch, Eind, and Edisp component energies do not all correlate well with the ∑(σm + σp), ∑σp, and ∑σm Hammett parameters, and the aromatic Θzz values. Table 3 shows the correlation coefficients, r2, for the correlation between the component energies and either the ∑(σm + σp), ∑σp, ∑σm, or Θzz values, and in each case, except for ∑σm, the best correlation is found for Eele. For the ∑σm value the correlation with Eele is still good, but a slightly better correlation is found with Eexch. In fact, for the ∑(σm + σp), ∑σm, and Θzz values the correlations with Eele, Eexch, and Edisp are always decent to very good, with r2 values ranging from 0.85 to 0.95. The correlations with Eind are quite poor, and thus it appears the failure of the ∑(σm + σp), ∑σm, and Θzz values to properly predict the effects of induction ultimately leads to their less than desirable performance in predicting cation–π ΔH298 or Ebind values (Fig. 1 and ESI†). The ∑σp value does not perform well in predicting any of the component energies (Table 3); the correlation with Eele is best with r2 = 0.80, which makes it surprising that ∑σp values perform decently in predicting ΔH298 or Ebind (Fig. 1 and ESI†). Still, from a relative standpoint the correlation between ∑σp and Eind is the worst among the component energies, and it appears safe to say that like the ∑(σm + σp), ∑σm, and Θzz values, the ∑σp value also does a poor job predicting the effects of induction on cation–π binding. Thus, the less than ideal correlations between the aromatic ∑(σm + σp), ∑σp, ∑σm, or Θzz values and the cation–π ΔH298 or Ebind values (Fig. 1 and ESI†) can largely be attributed to the Eind component energies.
Parameter | r2 with Eele | r2 with Eexch | r2 with Eind | r2 with Edisp |
---|---|---|---|---|
∑(σm + σp) | 0.94 | 0.86 | 0.62 | 0.86 |
∑σp | 0.80 | 0.69 | 0.50 | 0.62 |
∑σm | 0.90 | 0.92 | 0.65 | 0.89 |
Θzz | 0.95 | 0.92 | 0.60 | 0.85 |
∑Π+ | 0.99 | 0.97 | 0.75 | 0.94 |
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Fig. 3 Correlation between Na+-substituted benzene distances (dAr–cat) and Eele (blue diamonds), Eind (red squares), Edisp (purple circles), and Eexch (green triangles). |
The relationship between the attractive forces governing ion-neutral interactions and the distance between the ion and the neutral molecule are well understood,33 and the slopes of the lines in Fig. 3 are what would be expected. For instance, for classic ion-neutral complexes at long distances, the Eele term should vary as dAr–cat−3, Eind should vary as dAr–cat−4, and Edisp should vary as dAr–cat−6. Thus, electrostatics should be most sensitive to changes in dAr–cat, followed by induction, and then dispersion. An increase in the sensitivity of the component energy towards changes in dAr–cat should manifest itself in greater slopes in Fig. 3, and this is exactly what is observed. Plotting Eele against dAr–cat yields a line with a slope of approximately 130, for Eind the slope is about 17, and for Edisp the slope is barely above 1. Note, the relationship between exchange energies and ion-neutral molecule intermolecular distances has not been widely studied.
Π+ = −log[(ΔH298(Na+–C6H5X))/(ΔH298(Na+–C6H6))] | (1) |
The Π+ values for the substituents used in this study are collected in Table 4, and Fig. 4 shows how well the substituent constant performs at predicting the cation–π ΔH298 and Ebind values from Table 1. Thus, the aromatics included in the correlations in Fig. 1 and 4 are the exact same. Of course, ∑Π+ values were employed since mono- and multi-substituted aromatics were investigated. It is worth noting that the Π+ parameter, as determined via eqn (1), accounts for how the cation binding of an aromatic increases, or decreases, upon substituting an H atom for a substituent. The −log function results in electron withdrawing substituents having positive values and electron donating substituents having negative values, in a similar fashion to Hammett constants. The correlations between the Eele, Eind, Edisp, and Eexch values in Table 2 and the ∑Π+ parameter are 0.99, 0.75, 0.94, and 0.97, respectively (Table 3). Each correlation is better than the corresponding component energy correlations for the ∑(σm + σp), ∑σp, ∑σm, and Θzz values (Table 3) and, importantly, for Eind the correlation is significantly improved, although it is still not great. This explains why the ∑Π+ values do a much better job at predicting cation–π ΔH298 and Ebind values than ∑(σm + σp), ∑σp, ∑σm, or Θzz: Π+ does a much better a job of taking into account the effects of induction on cation–π binding, and it also does a better job of taking into account the effects of electrostatics, exchange, and dispersion.
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Fig. 4 Correlation between the cation–π substituent constant Π+ and the cation–π ΔH298 (a) or Ebind (b) values. |
The generality of the Π+ parameter was examined by using it to correlate the cation–π binding energies of substituted benzenes where the cation is not Na+, and where different theoretical methods were employed to calculate the binding strength. A study by Sayyed and Suresh investigated the Li+, Na+, K+, and NH4+ binding of benzene, mono-, para-di-, 1,3,5-tri- and hexa-substituted benzenes where the substituents were N(CH3)2, NH2, CH3, OH, F, Cl, CN, and NO2.11 The cation–π binding energies were calculated at the B3LYP/6-311+G(d,p) level of theory, and correlating the Ebind value with the ∑Π+ parameters determined here yields r2 values of 0.95 for the Li+–arene complexes and 0.94 for the Na+-, K+-, and NH4+–arene complexes. The Sayyed and Suresh study involved 30 substituted benzenes, and unlike the study we present here they included three hexa-substituted aromatics: hexaamino-, hexamethyl-, and hexafluoro-benzene.11 The hexaamino- and hexamethyl-benzene cation–arene complexes would have the same steric issues discussed above for N(CH3)24 and NO22o, and this likely explains why they are the primary cause for the correlations not being closer to unity. Omitting the hexaamino- and hexamethyl-benzene cation–arene complexes, the correlations between the Sayyed and Suresh Li+-, Na+-, K+-, and NH4+-substituted benzene binding energies and the ∑Π+ values have r2 values of 1.00, 0.99, 0.98, and 0.98 respectively. In addition to including hexa-substituted aromatics, many of the multi-substituted aromatics in the Sayyed and Suresh study had different substituents. For instance, one of the 1,3,5-substituted aromatics investigated by Sayyed and Suresh was 3-cyano-5-fluoroaniline.11 This is different from the work reported here where all substituted benzenes contain the same substituent. Another study by Sayyed and Suresh reported the Mg+ and Cu+ binding of benzene and mono-substituted aromatics where the substituents were N(CH3)2, NH2, CH3, OH, F, Cl, CN, and NO2,35 and the correlations of the B3LYP/6-311+G(d,p) calculated cation–π binding energies and the Π+ parameters determined here have r2 values of 0.99 for the Mg+–arene complexes and 0.97 for the Cu+–arene complexes. Thus, the Π+ parameters developed here are general, as they correlate cation–π binding energies calculated with cations other than Na+, which was used to derive the parameters, and they correlate cation–π binding energies calculated using a theoretical level and basis set not used to derive the parameters.
The Π+ parameters perform as well at predicting the relative cation–π binding strength of substituted benzenes as the aromatic MESP values. The study by Suresh and Sayyed, with a large number of substituted benzenes, had correlations between cation–π binding energies and the aromatic MESP values with r2 > 0.97.11 The correlations between the Π+ values and the cation–π ΔH298 and Ebind values reported here (Fig. 4), also with large numbers of substituted benzenes, have r2 = 0.97 and r2 = 0.98, respectively. This might lead to speculation about a relationship between the Π+ parameters and aromatic MESP values. While such a relationship may exist, what can safely be said without the requisite thorough investigation is that both the Π+ parameters and the MESP values directly represent the effects of a substituent on an aromatic π-electron density. Hammett constants, however, directly represent the effect of an aromatic substituent on the ionization of meta- and para-substituted benzoic acids, and the aromatic quadrupole moment is a measure of anisotropy. Thus, it is not surprising that the Π+ parameters and the MESP values perform so much better than Hammett constants and the quadrupole moment at predicting relative cation–π binding strengths.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra08638d |
This journal is © The Royal Society of Chemistry 2014 |