Correction to “Predicting and Understanding Noncovalent Interactions Using Novel Forms of Symmetry-Adapted Perturbation Theory”

Abstract

In a previous Account, (1) we surveyed the use of extended symmetry-adapted perturbation theory (XSAPT), a family of methods for computing accurate intermolecular interaction energies and components thereof. In considering π-stacking interactions, we made comparisons between the XSAPT + many-body dispersion (MBD) method and a model potential introduced in a seminal paper on π–π interactions by Hunter and Sanders (HS). (2) Unfortunately, our implementation of the HS model contained an error in the van der Waals (vdW) term, which is corrected here alongside some additional clarifications. Because there are subtleties in how the vdW parameters were originally reported, (2) as well as ambiguity regarding which point charges constitute the HS model, (2,3) additional details are provided here. The HS model consists of a point-charge electrostatic term (E_elst^Q) and a vdW term (E_vdW), There is some ambiguity regarding the point charges to be used in E_elst^Q. What is clear is that the HS model contains atom-centered point charges for carbon atoms within the π-system (q_C) along with out-of-plane displaced charges (q_π) to represent the π-electrons. In their original 1990 paper, HS first discuss “unpolarized” or “idealized” charges, in which carbon atoms within the π-system are described by charges q_C = +1.0 and q_π = −0.5 (in atomic units). (2) The π charges are displaced from the nuclei by δ = 0.47 Å, both above and below the arene plane, a value that is determined in order to reproduce the experimental quadrupole moment of C₆H₆. (5) Although the HS paper includes a discussion of polarizing this idealized framework, no actual values for hydrogen-atom charges are provided in ref (2). Moreover, Figure 3 of ref (2) depicts only q_C = +1.0 and q_π = −0.5, with no indication that there are charges on the hydrogen atoms. In 1991, Hunter et al. (3) suggested a model in which the charge on carbon is reduced to q_C = +0.95 and a charge q_H = +0.05 is placed on hydrogen, retaining q_π = −0.5. This scheme (in Figure 3 of ref (3)) is attributed to the original HS model even though the value of q_H was not provided in the original. In other work by Hunter and co-workers, only q_C and q_π are discussed, e.g., in Figure 3 of ref (6). These ambiguities are consistent with widespread confusion in the literature regarding what the HS model actually is, as discussed elsewhere. (7) For this Correction, we implemented E_elst^Q according to ref (3) using q_C = +0.95, q_H = +0.05, and q_π = −0.5. For (C₆H₆)₂, the presence or absence of q_H makes only a minor difference. Using the corrected parameters in E_vdW and the updated parameters in E_elst^Q, we recomputed HS potentials for the lateral displacement of parallel and perpendicular arrangements of the benzene dimer. Figure 1 of this Correction should replace Figure 8 in ref (1), illustrating how E_HS and E_elst^Q vary with lateral displacement. Note that the electrostatic component (Figure 1b) remains qualitatively incorrect in comparison to a calculation based on full monomer charge densities, the latter of which can be found in Figure 9 of ref (1). The crux of our argument is unchanged, namely, that electrostatics does not explain parallel-displaced π-stacking. Figure 1. (a) Total HS model potential and (b) its electrostatic component, for lateral displacement of (C₆H₆)₂ in either a coplanar configuration at 3.4 Å separation (consistent with the parallel-displaced minimum-energy geometry) or else a perpendicular edge-to-face arrangement with a 5.0 Å center-to-center distance, consistent with the T-shaped saddle point of (C₆H₆)₂. This figure should replace Figure 8 of ref (1). Figure 2 of this Correction plots E_HS and E_elst^Q for lateral displacement of benzene atop a C₉₆H₂₄ graphene nanoflake; this figure should replace Figure 12a of ref (1). As compared to XSAPT + MBD calculations (in Figure 12c of ref (1)), the corrected version of the HS model potential is qualitatively correct insofar as the zero-displacement structure is a saddle point between symmetry-equivalent minima corresponding to parallel-displaced π-stacking. Nevertheless, the electrostatic component E_elst^Q (Figure 2b of this Correction) is repulsive at all values of the lateral displacement coordinate, which is not consistent with exact electrostatics. (8) Indeed, a central aspect of our “pizza-π” model of π–π interactions, (8) which explains how π-stacking is different from ordinary dispersion, is that electrostatics is attractive for two coplanar arenes separated by typical π-stacking distances of 3.4–3.8 Å. This conclusion is borne out in a wide variety of π–π interactions. (7−11) Figure 2. (a) Total HS model potential and (b) its electrostatic component, for lateral displacement of C₆H₆ atop C₉₆H₂₄ in a cofacial configuration at 3.4 Å separation. This figure should replace Figure 12a of ref (1). A final topic of discussion is the use of δ^± to label the cartoons in Figure 6 of ref (1). This is potentially misleading, as it may suggest that C₆F₆ has a positive charge density on its π faces, which is absurd. Rather, these diagrams are intended to convey the change in quadrupolar electrostatics that occurs when one C₆H₆ monomer is replaced by C₆F₆, since the quadrupole–quadrupole interactions in (C₆H₆)···(C₆F₆) are attractive in the face-to-face orientation. A similar diagram, coloring C₆F₆ opposite to C₆H₆, can be found in Hunter et al. (6) Although these cartoon charge distributions are widely used in discussing π-stacking, (6,12,13) we have elsewhere suggested that they are misleading and that their use ought to be discontinued. (7) We thank Prof. Steven Wheeler (University of Georgia) for bringing these issues to our attention based on his independent implementation of the HS model. This article references 13 other publications. This article has not yet been cited by other publications.