Predicting the cation–π binding of substituted benzenes: energy decomposition calculations and the development of a cation–π substituent constant

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

Received 14th August 2014 , Accepted 10th November 2014

First published on 10th November 2014


Abstract

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.


1 Introduction

Cation–π interactions1,2 are important in a wide range of chemical and biological fields including enzyme-substrate recognition,3,4 catalyst development,5,6 and nanomaterial design.7 The nature of cation–π interactions was initially described in terms of the aromatic quadrupole moment (Θzz) and the electrostatic potential (ESP).8,9 There is a significant difference in how well they predict cation–π binding energies due to the nature of the two terms. Essentially, the quadrupole moment is part of the multipole expansion series (point charge, dipole, quadrupole, etc.) where the electrostatics of a molecule is described at a single point, while ESPs are defined at each point in space. In most cation–π complexes the interacting species are too close for the multipole expansion series to converge, thus explaining why ESPs perform better at predicting relative cation–π binding. For instance, the aromatic Θzz value shows minimal correlation with the cation–π binding enthalpy (ΔH298) values of ten halo- and cyano-substituted aromatics (r2 = 0.78);10 however, the correlation between the cation–π binding energy (Ebind) and the aromatic ESP values for 11 aromatics was quite strong (r2 = 0.98).9 Similarly, Suresh and Sayyed very recently reported a study with a large number of substituted benzenes and showed the cation–π binding energies correlate to an excellent degree (r2 > 0.97) with the molecular electrostatic potential (MESP).11 Aromatic Θzz and ESP values require calculation, and predicting the strength of cation–π interactions via aromatic substituent constants would be more facile. Dougherty and coworkers appear to be the first researchers to suggest a possible relationship between cation–π binding and Hammett substituent constants,9 though most of their work concentrated on the correlation between the binding energies and the aromatic ESPs.9 More recently, Hunter and coworkers employed their chemical double-mutant cycles towards the investigation of cation–π binding using the N-methyl pyridinium cation, and they found an excellent correlation between the cation–π binding free energy values and the Hammett σp value.12 Additionally, computational work by Jiang and coworkers showed an excellent correlation between the cation–π binding enthalpies of aniline, toluene, phenol, benzene, fluorobenzene, 1,4-difluorobenzene, and 1,3,5-trifluorobenzene and what the authors term the total Hammett parameter, σTotal.13 The investigated cations were Li+, Na+, K+, Be2+, Mg2+, and Ca2+, and the total Hammett parameter was defined as σTotal = (∑σm + ∑σp). This is the only example of using σTotal to understand the non-covalent binding of aromatics, and Jiang and coworkers suggest it means both resonance and induction are important in cation–π binding.13 Sanderson and coworkers provided an example of using Hammett constants to help elucidate the importance of cation–π binding in biological environments in their studies on the binding of 1,2-dimyristoyl-sn-glycero-3-phosphocholine to 5-substituted tryptophan analogs.14

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.

2 Computational methods

Sodium cation-substituted benzene complexes, Na+–C6XnH(6−n), were investigated where the substituted aromatics have X = F, Cl, Br, I, CN, NO2, CH3, OH, NH2, OCH3 and N(CH3)2 substituents with mono-, ortho-di-, meta-di-, para-di-, 1,3,5-tri- and 1,2,4,5,-tetra-substitution patterns. Each Na+-substituted benzene complex is referred to using the shorthand X1, X2o, X2m, X2p, X3 and X4 where X is the substituent, the numbers 1–4 are the number of substituents, and the letters ‘o’, ‘m’ and ‘p’ indicate whether the di-substituted aromatics are ortho-, meta- or para-substituted. The parent Na+–benzene complex is referred to as C6H6. The N(CH3)24 complex binding energy was not calculated because of the steric problems associated with having two large groups ortho to each other. The CN4, NO23 and NO24 complexes were also not calculated, because the resulting complexes with sodium cation are repulsive. The NO22o was not included in the study because the ortho nitro groups are significantly out of plane, due to steric repulsion, and this significantly affects the cation–π binding. All substituted benzenes and sodium cation-substituted benzene complexes were optimized, and frequency calculations were performed, at the MP2(full)/6-311++G** level of theory. The resulting structures were characterized as minima by the absence of imaginary frequencies. Some of the optimized structures had imaginary frequencies, as shown in the ESI, and this is not surprising given the tendency for the MP2 method to give anomalous imaginary frequencies for aromatics, which has been explained as arising from a two-electron basis set incompleteness error (BSIE).18 When these structures were re-optimized at the RHF/6-311++G** level of theory, the resulting frequency calculations did not contain any imaginary frequencies. Two exceptions are the NO21 and NO22p cation–arene complexes. We have previously reported that the NO21 complex is not a minimum, and the only cation–arene minimum for Na+–C6H5NO2 is the cation–dipole complex.19 The same explanation applies to the NO22p complex. For the substituted aromatics containing iodine atoms the MIDI-X basis set was employed for I, while the 6-311++G** basis set was used for all other atoms. The MP2(full)/6-311++G** calculated binding energies were corrected for basis set superposition error (BSSE) using the counter-poise method.20 Cation–π Ebind values were determined by subtracting the calculated energies of each substituted benzene and Na+ from the BSSE-corrected energy of the respective Na+-substituted benzene complex. All reference to MP2(full)/6-311++G** calculated binding energies throughout the remaining text refers to the BSSE corrected values. The ΔH298 values were determined via the equation ΔH298 = Ebind + (Ethermal,complex − (Ethermal,arene + Ethermal,Na+)). Each Ethermal value is obtained via frequency calculation and constitutes the thermal energy correction from vibrational, rotational, and translational energies upon going from 0 K to 298 K for the Na+–C6XnH(6−n) complexes, the arenes, and the Na+ cation.

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.

3 Results and discussion

3.1 Cation–π binding energies (Ebind) and enthalpies (ΔH298) of substituted benzenes

The cation–π Ebind and ΔH298 of substituted benzenes with the general formula shown in Scheme 1 are given in Table 1. From a qualitative perspective, the trend in binding is what would be predicted based on electrostatic arguments. Electron deficient aromatics, such as F4, CN3, NO22m, and NO22p, exhibit very weak cation–π binding, and increasing the number of electron withdrawing substituents on the substituted benzene results in smaller Ebind and ΔH298 binding values. Conversely, electron-rich aromatics, such as the methyl-, hydroxyl-, amino-, methoxy-, and dimethylamino-substituted benzenes have the strongest cation–π binding. For the most part, increasing the number of electron-donating substituents increases the cation–π binding; however, there are a few exceptions worth noting. The OH2o dimer is slightly more binding than would be expected, and this is because the ortho-substitution results in slight rotation of one of the hydroxyl groups, thus allowing the oxygen lone pair to participate in, and enhance, the binding between the aromatic and the cation. The opposite happens with amino-substituted aromatics, and the NH22o and NH24 dimers are less binding than would be expected. This is also due to substituent rotation, however the result is a hydrogen atom repelling the cation, and decreasing the binding energy. The same result is seen for N(CH3)22o.
image file: c4ra08638d-s1.tif
Scheme 1 General structure of Na+-substituted benzene complexes.
Table 1 MP2(full)/6-311++G** calculated Na+-substituted benzene binding energies (Ebind) and enthalpies (ΔH298)a
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.


image file: c4ra08638d-f1.tif
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.

3.2 SAPT energy decomposition calculations

Symmetry Adapted Perturbation Theory (SAPT) calculations were performed on the following 12 selected substituted benzenes: OH4, NH22o, N(CH3)21, OH2o, OCH32o, CH32p, C6H6, F3, Cl1, CN1, CN2m, and NO22m. The substituted benzenes were chosen to cover a broad range of Hammett constant values. For instance, the ∑σp range of the 12 substituted benzenes chosen for SAPT calculations is −1.48 to 1.56, and only NH24, N(CH3)23, NH23, N(CH3)22o, N(CH3)22m, and N(CH3)22p are outside this range on the electron-donating end of the spectrum, while just CN3 is outside the range on the electron-withdrawing end of the spectrum. The chosen aromatics cover a similarly broad range of the ∑(σm + σp), ∑σm, and Θzz values. The component energies Eele, Eexch, Eind, and Edisp, and the ESAPT energies for the 12 selected Na+-substituted benzene dimers are given in Table 2. Note that the ESAPT energy is the sum of the Eele, Eexch, Eind, and Edisp energies, and is thus equivalent to the Ebind energies in Table 1. Of course, the Ebind energies were determined using the MP2(full)/6-311++G** optimized Na+-substituted benzene geometries, with BSSE correction, while the ESAPT energies were determined at the CCSD/6-311++G** level of theory using the MP2(full)/6-311++G** optimized geometries, and thus the Ebind and ESAPT numbers differ slightly in absolute value; the mean absolute difference between the Ebind and ESAPT values is 1.51 kcal mol−1. More importantly, the relative values are almost identical, with the only difference among the complexes in Table 2 being that OH2o has a slightly more binding Ebind value than OH4, while OH4 has a slightly more binding ESAPT value. Therefore, we have great confidence that the trends in the component energy data for the 12 selected Na+-substituted benzene complexes (Table 2) are representative of the entire set of complexes in Table 1.
Table 2 SAPT calculated component energies (Eele, Eexch, Eind, Edisp), in kcal mol−1, for selected Na+-substituted benzene complexesa
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.


image file: c4ra08638d-f2.tif
Fig. 2 The SAPT calculated contributions from electrostatics (Eele), exchange (Eexch), induction (Eind), and dispersion (Edisp) to the overall Na+ binding energy of OH4, NH22o, N(CH3)21, OH2o, OCH32o, CH32p, C6H6, F3, Cl1, CN1, CN2m, and NO22m. The aromatics are arranged, from left to right, in: (a) increasing ∑(σm + σp) value; (b) increasing ∑σp value; (c) increasing ∑σm value; and (d) increasing Θzz value.
Table 3 Correlation coefficients, r2, for the correlation between SAPT calculated component energies (Eele, Eexch, Eind, Edisp) and ∑(σm + σp), ∑σp, ∑σm, Θzz, or ∑Π+ values
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


3.3 The correlation between SAPT component energies and cation-substituted benzene distances (dAr–cat)

Inspection of the Na+-substituted benzene ion–arene centroid distance (dAr–cat), via the lens of the relative component energies, reveals some interesting trends. Fig. 3 shows that the Eele, Edisp, and Eexch component energies all correlate very well with dAr–cat with r2 values of 0.96, 0.96, and 0.97, respectively. In contrast, the correlation between Eind and dAr–cat is comparatively poor with an r2 value of 0.76. This analysis further supports the view that the induction term is primarily responsible for the Na+-substituted benzene ΔH298 and Ebind values not correlating very well with the aromatic ∑(σm + σp), ∑σp, or ∑σm parameters, or with the Θzz values.
image file: c4ra08638d-f3.tif
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.

3.4 The cation–π substituent constant Π+

The fact that Eind values correlate so poorly with the ∑(σm + σp), ∑σp, ∑σm, and Θzz values (Table 3), and the fact that Eind does not correlate very well with dAr–cat (Fig. 3), suggests the reason the ∑(σm + σp), ∑σp, and ∑σm, parameters, and the and Θzz values, do not perform better in predicting cation–π ΔH298 and Ebind values is because of the energy due to induction. Two approaches were considered for developing an enhanced method to predict cation–π ΔH298 and Ebind values: a two-parameter equation, such as the one we employed for substituted benzene–benzene dimers,34 or the development of a new parameter to specifically account for how a cation interacts with substituted aromatics. Taking the latter approach, a cation–π substituent constant, termed Π+, was developed using Na+-mono-substituted benzene ΔH298 values, as shown in eqn (1). Dividing by the Na+–C6H6 ΔH298 value and applying the −log function yields an H atom Π+ value of 0.000.
 
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.

Table 4 Cation–π Substituent Constants Π+a
Substituent Π+
a Cation–π substituent constants, Π+, calculated using eqn (1).
H 0.000
F 0.103
Cl 0.082
Br 0.074
I 0.059
CN 0.218
NO2 0.275
CH3 −0.061
OH −0.001
OCH3 −0.067
NH2 −0.116
N(CH3)2 −0.156



image file: c4ra08638d-f4.tif
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.

4 Conclusions

Cation–π interactions of substituted benzenes have been shown to correlate, to a decent degree, with the aromatic ∑(σm + σp), ∑σp, ∑σm, or Θzz values (Fig. 1). Previous studies had shown better correlations with some of these parameters; however, the current study contains significantly more points. SAPT calculations show the electrostatic (Eele) and induction (Eind) terms are generally the largest contributors to cation–π binding, and that electrostatics is most sensitive to changes in cation–arene distances (dAr–cat). SAPT calculations also suggest that Eind is the primary reason for the poorer than expected correlation between cation–π binding (ΔH298 or Ebind) and the ∑(σm + σp), ∑σp, ∑σm, or Θzz values; these values correlate to a decent degree with the SAPT calculated Eele, Eexch, and Edisp values, but the correlation with Eind is quite poor (Table 3). Further support that induction is the primary factor contributing to the poor correlation between cation–π ΔH298 or Ebind values and the ∑(σm + σp), ∑σp, ∑σm, or Θzz values was found in the correlation between the SAPT calculated component energies and Na+-substituted benzene ion–arene centroid distances, dAr–cat (Fig. 3). Due to the inability of the ∑(σm + σp), ∑σp, ∑σm, or Θzz values to accurately predict cation–π ΔH298 values a cation–π substituent constant, Π+, was developed from Na+-mono-substituted benzene binding enthalpies using eqn (1). The Π+ parameters developed here (Fig. 4) physically represent the effect on the strength of cation-substituted benzene binding when an aromatic H atom is replaced by a substituent. The ∑Π+ values correlate very well with the cation–π ΔH298 values, and they correlate better with the SAPT calculated component energies than the Hammett parameters or the Θzz values (Table 3); the most significant difference between the correlations with the ∑(σm + σp), ∑σp, ∑σm, or Θzz values and the correlation with the ∑Π+ parameter is for Eind. While the SAPT calculations show that electrostatics are the dominant force in cation–π binding, they also show that the ∑(σm + σp), ∑σp, ∑σm, or Θzz values will never accurately predict cation–π ΔH298 values due to the induction energy. The Π+ parameter presented here is superior to (σm + σp), σp, σm, or Θzz for the accurate prediction of cation–π binding, and it is worth noting that the reason may simply be because these parameters, especially the Hammett parameters, were not developed for such purposes. Hammett constants were derived from the relative rates of ionization of substituted benzoic acids, which have little in common with the non-covalent cation–π binding of aromatics. Parameters specifically derived to describe cation–π binding, as was done here with Π+, would reasonably be expected to perform better than Hammett constants at predicting the relative strength of cation–π binding, and that is certainly the result of this work. Importantly, the Π+ parameter is general, as was demonstrated by using it to correlate the cation–π binding energies of substituted aromatics reported in work performed by other research groups. The correlations between the Π+ parameters and the cation–π binding energies of cation–arene complexes where the cation was not Na+, which was used here to derive the Π+ values, were excellent. This includes complexes where the cations were Li+, K+, NH4+, Mg+, and Cu+.

Acknowledgements

This work was supported by the American Chemical Society Petroleum Research Fund (47159-GB4), the National Center for Supercomputing Allocations (CHE050039N) via time on the SGI Altix supercomputer and the Dell Intel 64 Linux Cluster, and the Saint Louis University Beaumont Faculty Development Fund. Calculations were partially performed on the Saint Louis University supercomputing facility, which has been supported by the Air Force Office of Scientific Research DURIP (FA9550-10-1-0320) and by Silicon Mechanics. Recent renovations to the research laboratories in Saint Louis University's Department of Chemistry were accomplished through a National Science Foundation grant (CHE-0963363).

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Footnote

Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra08638d

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