Steven E. Wheeler

Substituent effects in the benzene dimer are due to direct interactions of the substituents with the unsubstituted benzene.

The prevailing views of substituent effects in the sandwich configuration of the benzene dimer are flawed. For example, in the polar/pi model of Cozzi and co-workers (J. Am. Chem. Soc. 1992, 114, 5729), electron-withdrawing substituents enhance binding in the benzene dimer by withdrawing electron density from the pi-cloud of the substituted ring, reducing the repulsive electrostatic interaction with the nonsubstituted benzene. Conversely, electron-donating substituents donate excess electrons into the pi-system and diminish the pi-stacking interaction. We present computed interaction energies for the sandwich configuration of the benzene dimer and 24 substituted dimers, as well as sandwich complexes of substituted benzenes with perfluorobenzene. While the computed interaction energies correlate well with sigmam values for the substituents, interaction energies for related model systems demonstrate that this trend is independent of the substituted ring. Instead, the observed trends are consistent with direct electrostatic and dispersive interactions of the substituents with the unsubstituted ring.

Local Nature of Substituent Effects in Stacking Interactions

Popular explanations of substituent effects in π-stacking interactions hinge upon substituent-induced changes in the aryl π-system. This entrenched view has been used to explain substituent effects in countless stacking interactions over the past 2 decades. However, for a broad range of stacked dimers, it is shown that substituent effects are better described as arising from local, direct interactions of the substituent with the proximal vertex of the other ring. Consequently, substituent effects in stacking interactions are additive, regardless of whether the substituents are on the same or opposite rings. Substituent effects are also insensitive to the introduction of heteroatoms on distant parts of either stacked ring. This local, direct interaction viewpoint provides clear, unambiguous explanations of substituent effects for myriad stacking interactions that are in accord with robust computational data, including DFT-D and new benchmark CCSD(T) results. Many of these computational results cannot be readily explained using traditional π-polarization-based models. Analyses of stacking interactions based solely on the sign of the electrostatic potential above the face of an aromatic ring or the molecular quadrupole moment face a similar fate. The local, direct interaction model provides a simple means of analyzing substituent effects in complex aromatic systems and also offers simple explanations of the crystal packing of fluorinated benzenes and the recently published dependence of the stability of protein-RNA complexes on the regiochemistry of fluorinated base analogues [J. Am. Chem. Soc.2011, 133, 3687-3689].

Bifurcations on Potential Energy Surfaces of Organic Reactions

A single transition state may lead to multiple intermediates or products if there is a post-transition-state reaction pathway bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy minimum. For such systems, the shape of the potential energy surface and dynamic effects, rather than transition-state energetics, control selectivity. This Minireview covers recent investigations of organic reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect experimental observables such as kinetic isotope effects and product distributions.

Toward a More Complete Understanding of Noncovalent Interactions Involving Aromatic Rings

Noncovalent interactions involving aromatic rings, which include π-stacking interactions, anion-π interactions, and XH-π interactions, among others, are ubiquitous in chemical and biochemical systems. Despite dramatic advances in our understanding of these interactions over the past decade, many aspects of these noncovalent interactions have only recently been uncovered, with many questions remaining. We summarize our computational studies aimed at understanding the impact of substituents and heteroatoms on these noncovalent interactions. In particular, we discuss our local, direct interaction model of substituent effects in π-stacking interactions. In this model, substituent effects are dominated by electrostatic interactions of the local dipoles associated with the substituents and the electric field of the other ring. The implications of the local nature of substituent effects on π-stacking interactions in larger systems are discussed, with examples given for complexes with carbon nanotubes and a small graphene model, as well as model stacked discotic systems. We also discuss related issues involving the interpretation of electrostatic potential (ESP) maps. Although ESP maps are widely used in discussions of noncovalent interactions, they are often misinterpreted. Next, we provide an alternative explanation for the origin of anion-π interactions involving substituted benzenes and N-heterocycles, and show that these interactions are well-described by simple models based solely on charge-dipole interactions. Finally, we summarize our recent work on the physical nature of substituent effects in XH-π interactions. Together, these results paint a more complete picture of noncovalent interactions involving aromatic rings and provide a firm conceptual foundation for the rational exploitation of these interactions in a myriad of chemical contexts.

Probing Substituent Effects in Aryl-Aryl Interactions Using Stereoselective Diels-Alder Cycloadditions

Stereoselective Diels-Alder cycloadditions that probe substituent effects in aryl-aryl sandwich complexes were studied experimentally and theoretically. Computations on model systems demonstrate that the stereoselectivity in these reactions is mediated by differential pi-stacking interactions in competing transition states. This allows relative stacking free energies of substituted and unsubstituted sandwich complexes to be derived from measured product distributions. In contrast to gas-phase computations, dispersion effects do not appear to play a significant role in the substituent effects, in accord with previous experiments. The experimental pi-stacking free energies are shown to correlate well with Hammett sigma(m) constants (r = 0.96). These substituent constants primarily provide a measure of the inductive electron-donating and -withdrawing character of the substituents, not donation into or out of the benzene pi-system. The present experimental results are most readily explained using a recently proposed model of substituent effects in the benzene sandwich dimer in which the pi-system of the substituted benzene is relatively unimportant and substituent effects arise from direct through-space interactions. Specifically, these results are the first experiments to clearly show that OMe enhances these pi-stacking interactions, despite being a pi-electron donor. This is in conflict with popular models in which substituent effects in aryl-aryl interactions are modulated by polarization of the aryl pi-system.

Substituent Effects in Cation/π Interactions and Electrostatic Potentials above the Centers of Substituted Benzenes Are Due Primarily to Through-Space Effects of the Substituents

Substituent effects in cation/pi interactions have been examined using the M05-2X DFT functional and CCSD(T) paired with triple-zeta-quality basis sets. In contrast to popular, intuitive models, trends in substituent effects are explained primarily in terms of direct through-space interactions with the substituents. While there is some scatter in the data, which is attributed to pi polarization, the trend in substituent effects in cation/pi interactions is captured by an additive model in which the substituent is isolated from the aryl ring. Similarly, changes in the electrostatic potential at a point above the center of a substituted benzene arise largely from through-space effects of the substituents; pi polarization is not the dominant underlying cause.

Taking the aromaticity out of aromatic interactions.

The phrase “aromatic interactions” is widely used to describe p stacking, cation–p, and anion–p interactions, among others. These interactions are central to many areas of modern chemistry and molecular biology, and are vital tools in the supramolecular armamentarium. The concept of aromaticity appears almost universally in definitions of these interactions, implying that they are somehow dependent on aromatic p delocalization in the interacting monomers. But does aromaticity actually enhance these interactions, or can stronger noncovalent interactions be achieved, for example, by using planar, nonaromatic polyenes? We show below, through robust ab initio studies of model systems, that the cyclic p-electron delocalization associated with aromaticity often hinders p stacking and anion–p interactions, although it strengthens cation–p interactions. The implication is that more favorable stacking interactions can be achieved in supramolecular complexes by exploiting interactions with nonaromatic polyenes rather than aromatic systems. In 2008, Grimme showed that stacking interactions in the parallel-displaced benzene and naphthalene dimers are comparable in magnitude to the corresponding saturated cyclic systems. However, for larger acenes (i.e., anthracene and tetracene), Grimme reported enhanced stacking interactions in the aromatic dimers that are not mirrored in the saturated systems. This was attributed to long-range correlation effects. The impact of aromaticity on these stacking interactions, however, was not directly addressed. Here, we quantify the effect of aromatic p-electron delocalization on the strength of p stacking, cation–p, and anion–p interactions. We first consider the sandwich dimers of benzene with the unsubstituted rings of 2-methylnaphthalene (1) and 2-methylene-2,3-dihydronaphthalene (2 ; Scheme 1 and Figure 1a). Isomer 2 provides a means of quenching the aromaticity present in 1 while conserving the number of p electrons. Isomers 1 and 2 can thus be used to quantify the electronic effects of aromatic p delocalization on stacking interactions. SCS-MP2/TZVPP interaction energies at equilibrium separations are provided in Figure 1, and are plotted as a function of inter-monomer distance (R) in Figure S1 of the Supporting Information. Across the full range of distances, the stacking interaction of benzene with the nonaromatic isomer 2 is more favorable than with 1. In other words, the nonaromatic isomer engages in stronger stacking interactions with benzene than does the aromatic isomer. This difference is not attributable to differential direct interactions between benzene and the methyl/CH or methylene/ CH2 groups in 1 and 2 (see the Supporting Information), but instead results from the localization of the p system in isomer 2. The homodesmotic dissection of benzene depicted in Scheme 1 provides an alternative means of quantifying the effect of aromatic p delocalization on stacking interactions (Figure 1b and Table 1). Comparing CCSD(T) interaction energies in the benzene sandwich dimer with the interaction between benzene and dissected benzene yields the same conclusion as above: p localization stabilizes sandwich stacking interactions by 0.31 kcal mol 1 at the corresponding Scheme 1. Molecular systems used to quantify the effect of aromatic p delocalization on stacking and other aromatic interactions: 2-methylnaphthalene (1), 2-methylene-2,3-dihydronaphthalene (2), and dissected benzene. In the dissected benzene, the nuclear positions are such that all interatomic distances exactly match those in benzene.

Substituent Effects on Non‐Covalent Interactions with Aromatic Rings: Insights from Computational Chemistry

Non-covalent interactions with aromatic rings pervade modern chemical research. The strength and orientation of these interactions can be tuned and controlled through substituent effects. Computational studies of model complexes have provided a detailed understanding of the origin and nature of these substituent effects, and pinpointed flaws in entrenched models of these interactions in the literature. Here, we provide a brief review of efforts over the last decade to unravel the origin of substituent effects in π-stacking, XH/π, and ion/π interactions through detailed computational studies. We highlight recent progress that has been made, while also uncovering areas where future studies are warranted.

Are Anion/π Interactions Actually a Case of Simple Charge–Dipole Interactions?

Substituent effects in Cl(-)...C(6)H(6-n)X(n) complexes, models for anion/pi interactions, have been examined using density functional theory and robust ab initio methods paired with large basis sets. Predicted interaction energies for 83 model Cl(-)...C(6)H(6-n)X(n) complexes span almost 40 kcal mol(-1) and show an excellent correlation (r = 0.99) with computed electrostatic potentials. In contrast to prevailing models of anion/pi interactions, which rely on substituent-induced changes in the aryl pi-system, it is shown that substituent effects in these systems are due mostly to direct interactions between the anion and the substituents. Specifically, interaction energies for Cl(-)...C(6)H(6-n)X(n) complexes are recovered using a model system in which the substituents are isolated from the aromatic ring and pi-resonance effects are impossible. Additionally, accurate potential energy curves for Cl(-) interacting with prototypical anion-binding arenes can be qualitatively reproduced by adding a classical charge-dipole interaction to the Cl(-)...C(6)H(6) interaction potential. In substituted benzenes, binding of anions arises primarily from interactions of the anion with the local dipoles induced by the substituents, not changes in the interaction with the aromatic ring itself. When designing anion-binding motifs, phenyl rings should be viewed as a scaffold upon which appropriate substituents can be placed, because there are no attractive interactions between anions and the aryl pi-system of substituted benzenes.

Accurate Reaction Enthalpies and Sources of Error in DFT Thermochemistry for Aldol, Mannich, and α-Aminoxylation Reactions

Enthalpies for bond-forming reactions that are subject to organocatalysis have been predicted using the high-accuracy CBS-QB3 model chemistry and six DFT functionals. Reaction enthalpies were decomposed into contributions from changes in bonding and other intramolecular effects via the hierarchy of homodesmotic reactions. The order of the reaction exothermicities (aldol < Mannich approximately alpha-aminoxylation) arises primarily from changes in formal bond types mediated by contributions from secondary intramolecular interactions. In each of these reaction types, methyl substitution at the beta- and gamma-positions stabilizes the products relative to the unsubstituted case. The performance of six DFT functionals (B3LYP, B3PW91, B1B95, MPW1PW91, PBE1PBE, and M06-2X), MP2, and SCS-MP2 has been assessed for the prediction of these reaction enthalpies. Even though the PBE1PBE and M06-2X functionals perform well for the aldol and Mannich reactions, errors roughly double when these functionals are applied to the alpha-aminoxylation reactions. B3PW91 and B1B95, which offer modest accuracy for the aldol and Mannich reactions, yield reliable predictions for the two alpha-aminoxylation reactions. The excellent performance of the M06-2X and PBE1PBE functionals for aldol and Mannich reactions stems from the cancellation of sizable errors arising from inadequate descriptions of the underlying bond transformations and intramolecular interactions. SCS-MP2/cc-pVTZ performs most consistently across these three classes of reactions, although the reaction exothermicities are systematically underestimated by 1-3 kcal mol(-1). Conventional MP2, when paired with the cc-pVTZ basis set, performs somewhat better than SCS-MP2 for some of these reactions, particularly the alpha-aminoxylations. Finally, the merits of benchmarking DFT functionals for the set of simple chemically meaningful transformations underlying all bond-forming reactions are discussed.