A computational study aimed at accurately predicting the strength of the anion−π binding of substituted benzenes is presented. The anion−π binding energies (Ebind) of 37 substituted benzenes and the parent benzene, with chloride or bromide were investigated at the MP2(full)/6-311++G** level of theory. In addition, energy decomposition analysis was performed on 27 selected chloride–arene complexes via symmetry adapted perturbation theory (SAPT), using the SAPT2+ approach. Initial efforts aimed to correlate the anion−π Ebind values with the sum of the Hammett constants σp (Σσp) or σm (Σσm), as done by others. This proved a decent approach for predicting the binding strength of aromatics with electron-withdrawing substituents. For the Cl–-substituted benzene Ebind values, the correlation with the Σσp and Σσm values of aromatics with electron-withdrawing groups had r2 values of 0.89 and 0.87 respectively. For the Br–-substituted benzene Ebind values, the correlation with the Σσp and Σσm values of aromatics with electron-withdrawing groups had r2 values of 0.90 and 0.87. However, adding aromatics with electron-donating substituents to the investigation caused the correlation to deteriorate. For the Cl–-substituted benzene complexes the correlation between Ebind values and the Hammett constants had r2 = 0.81 for Σσp and r2 = 0.84 for Σσm. For the Br–-substituted benzene complexes, the respective r2 values were 0.71 for Σσp and 0.79 for Σσm. The deterioration in correlation upon consideration of substituted benzenes with electron-donating substituents is due to the anion−π binding energies becoming more attractive regardless of what type of substituent is added to the aromatic. A similar trend has been reported for parallel face-to-face substituted benzene–benzene binding. This is certainly counter to what electrostatic arguments would predict for trends in anion−π binding energies, and this discrepancy is further highlighted by the SAPT2+ calculated electrostatic component energies (Eele). The Eele values for the Cl–-substituted benzene anion−π complexes are all more binding than the Eele value for the Cl––benzene complex, with the exception of chloride–1,3,5-trimethylbenzene. Again, this is a similar trend to what has been reported for parallel face-to-face substituted benzene–benzene binding. A discussion on this surprising result is presented. In addition, an improved approach to predicting the relative anion−π binding strength of substituted benzene is developed using the results of the SAPT2+ calculations.

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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.

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.

Hydrogen-bonding, intrastrand base-stacking, and interstrand base-stacking energies were calculated for RNA and DNA dimers at the MP2(full)/6-311G** level of theory. Standard A-form RNA and B-form DNA geometries from average fiber diffraction data were employed for all base monomer and dimer geometries, and all dimer binding energies were obtained via single-point calculations. The effects of water solvation were considered using the PCM model. The resulting dimer binding energies were used to calculate the 10 unique RNA and 10 unique DNA computational nearest-neighbor energies, and the ranking of these computational nearest neighbor energies are in excellent agreement with the ranking of the experimental nearest-neighbor free energies. These results dispel the notion that average fiber diffraction geometries are insufficient for calculating RNA and DNA stacking energies.

Previous work in our group on the cation binding of substituted cyclopentadienyl anions (Cp) showed the curious result that Cp traceless electric quadrupole moments (Θzz) are almost all positive. Probing this issue further here we show that substituted Cp Θzz values are always significantly more positive than the analogous substituted benzenes. Given the nature of aromatic Θzz values, this is the opposite of what would be predicted. Furthermore, we show that the quadrupole moments of Cp anions do not behave as one would expect based on Cp substitutions. Unlike the quadrupole moments of substituted benzenes, which generally become more negative with the addition of electron-donating groups and more positive with the addition of electron-withdrawing groups, Cp quadrupole moments become more positive when any substituent is added, regardless of the electron-donating/withdrawing nature of the substituent. To explain these results we propose a model where the anionic Cp π-electron density repels the substituent electron density toward the molecular periphery and AIM calculations support this view.

The cation binding of dipolar aromatics was investigated employing computational techniques. In most cases, cation binding at the π region of the aromatic (the cation−π interaction), which can be thought of as a cation−quadrupole interaction, is preferred over cation binding at the negative end of the dipole moment. Surprisingly, in some cases, the cation−dipole complex is not even a minimum on the potential energy surface.

Parallel face-to-face arene−arene complexes between benzene and substituted benzenes have been investigated at the MP2(full)/6-311G** and M05-2X/6-311G** levels of theory. A reasonably good correlation was found between the binding energies and the ∑|σm| values of the substituted aromatics. It is proposed that a substituent |σm| value informs on both the aromatic substituent dispersion/polarizability and the effect the substituent has on the aromatic electrostatics. Supporting this hypothesis, a combination of electrostatic (∑σm) and dispersion/polarizability (∑Mr) substituent constant terms gives an excellent, and statistically significant, correlation with the benzene-substituted benzene binding energy. Symmetry adapted perturbation theory energy decomposition calculations show the dominant attractive force is dispersion; however, the sum of all nonelectrostatic forces is essentially a constant, while the electrostatic component varies significantly. This explains the importance of including an electrostatic term when predicting benzene-substituted benzene binding energies.