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. 2023 Nov 21;127(48):10147–10158. doi: 10.1021/acs.jpca.3c05797

Sigma Hole Potentials as Tools: Quantifying and Partitioning Substituent Effects

Kelling J Donald 1,*, Nam Pham 1, Pranav Ravichandran 1
PMCID: PMC10711721  PMID: 38058158

Abstract

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Empirical substituent constants, such as the Hammett parameters, have found important utility in organic and other areas of chemistry. They are useful both in predicting the impact of substitutions on chemical processes and in rationalizing after-the-fact observations on chemical bonding and reactivity. We assess the impact of substitutions on monoiodinated benzene rings and find that the modifications that substituents induce on the electrostatic potentials at the sigma hole on the terminal I center correlate strongly with established trends of common substituents. As an alternative to the experimental procedures involved in obtaining empirically based substituent constants, the computationally determined constants based on induced electrostatic potentials offer a model for quantifying the influence of mono- and polyatomic, neutral, and ionic substituents on their compounds. A partitioning scheme is proposed that allows us to discretely separate σ and π contributions to generate quantitative measures of substituent effects.

Introduction

Almost 200 years after Faraday’s 1825 isolation and study of what is now called benzene (C6H6)1,2 and just over 150 years after Kekule reported his insightful model of its structure,3−6 the impact of substituents on the properties of that ring remains an area of active research in chemistry. This interest has persisted since substituted benzene rings are ubiquitous in modern chemistry and making a single substitution on the ring (C6H5R′) can radically modify the electron distribution in the ring and alter thus the likelihood that a subsequent substitution (to generate C6H4R′R′′) will occur at one or another of the remaining five C–H positions on the ring.

A given substituent R may operate as an electron donor or an acceptor via the σ skeleton and the π system of the ring and may further influence the electron density distribution in the molecules by field (short-range through-space polarization) interactions. To a first approximation (although the electron density distribution in the σ framework and in the π system are interrelated),7 the overall impacts of a substituent on the σ structure and on the π system, respectively, are summed up under the general categories of “inductive” and “mesomeric”8 effects (with the latter often conflated with ‘resonance’ or treated as a special case of it). The early trans-Atlantic contestation over the resonance and mesomerism concepts9 will not be rehashed here, but both terms remain in use, describing “resonance structures” for examples and “mesomeric effects”.

In addition to developing a qualitative understanding of the impact of substituents on acid ionization and reactivity of benzene derivatives, quantifying those substituent effects has been a major goal as well.10−13 Derick14,15 investigated the ‘Application of Polarity Measured in terms of a Logarithmic Functions of the Ionization Constant’ and the quantitative ‘Correlation of Ionization and Structure’16,17 and traced that effort even farther back to Ostwald.14 But it is Hammett’s culminating contributions, two decades later, to quantifying substituent effects that are the best known today.18,19 Hammett’s review of the field cited efforts by contemporaries to formulate a “definite and simple relation between the reaction rate and the free energy of dissociation [for acids].”20 But he was convinced that some of those efforts were “entirely incompetent,” and he made some key advancements.18

In brief, the general form of Hammett’s relationship linking the equilibrium constant, K, (or, alternatively, the rate constant, k) for the dissociation reaction of a substituted benzoic acid (R–C6H4–COOH) to the identity of the substituent, R, and its position on the ring is19,21

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Here, Ko is the experimentally obtained equilibrium constant (k0 being the corresponding rate constants) for R = H, σ is a substituent constant specific to the identity of the substituent, and ρ is specific to the reaction, including the reaction medium and temperature. And Taft produced in the early 1950s a modified form of this equation to account more reliably for steric effects.22−24

Hammett-type constants have found extensive use in chemistry. They are guides, for instance, in tuning the reactivity of rings, rationalizing the impact of substituents on pKa and reaction mechanisms, understanding weak interactions of rings,25 and even assessing trends in cocrystallization.26 And although the methods employed early on all relied on experimental quantities, some attention, however sporadic, has been given to computational approaches too for quantifying substituent effects.27−30 A 2005 review that is centered broadly on σ- and π-electron delocalization28 includes an account of some computational efforts made up to that point to link derived parameters (e.g., theoretical measures of aromaticity) and substituent constants. Substituent parameters based, for instance, on computed core–electron binding energies for ring carbon atoms29 and point charges30 have also been posited.

We develop here a rigorously defined and general computational descriptor for substituent effects that can be partitioned transparently into σ and π contributions. Our research group31−33 and others34−36 have considered that one viable computational approach for diagnosing the impact of a substitution, including inductive effects, on various properties of compounds is an assessment of the ensuing reorganization of the electron density distribution in the compound.

It is now well-known, for example (despite the expectation that a halogen atom, X, in a molecule, R–Y–X, is electron-rich), that a region of depleted electron density tends to arise on the outer pole of X opposite the Y–X bond, if R–Y is sufficiently electron-withdrawing.37 And that so-called sigma hole38 region is now a standard target of analysis for rationalizing halogen bonding.

That localized electron deficient region shows up as a maximum in the electrostatic potential (ESP) on the molecular surface, Vs, and it tends to expand and become more positive as the “R–Y” fragment becomes more electron-withdrawing.39 In general, for a given “R–Y” fragment, the sigma hole on X becomes larger and Vs much more positive going down group 17 (from F to I), and it becomes increasingly feasible to form halogen bonds (R–Y–X ← base). Indeed, it is now commonly believed that many weak interactions,40−45 organic and otherwise, including certain interactions to central atoms, are fostered by the presence of sigma holes.46−52

We consider the potential utility of the variation in the electrostatic potential maximum, Vs,max, at the sigma hole on iodine centers on substituted iodobenzenes, R–Ph–I, as a proxy for the meta- and para-directing influence of substituents on the ring. Bauzá et al. have examined the relationship between substituent constants and interaction energies of Y–I·N–Y′ complexes formed by the aromatic C6F5I species with certain meta- and para-substituted (pyridine, and cyanobenzene) bases.34 They identified ‘strong linear relationships’ between Hammett’s constants and interaction energies in those complexes and between those energies and the extremum values of the electrostatic potentials on I in the acids and N in the bases. Our results confirm a relationship between the potentials induced on I and the substituent effects for a broad range of substituents. We show the utility of computed potentials as alternatives for the traditional substituent constants, and importantly, a well-defined approach is introduced for partitioning the newly derived potential-based substituent parameters into σ and π contributions to the ring (de)activating tendencies of substituents. This approach allows for measures of (full, σ, and π) substituent effects to be computed as needed and compared for known or novel substituents.

Computational Methods

The compounds considered in this work, including 62 iodobenzene systems and their saturated cyclohexane derivatives, have been optimized to minimum energy geometries on their respective potential energy surfaces and have been confirmed to be minima by vibrational frequency analyses (showing no imaginary frequencies). These computational studies have been carried out using the Gaussian 16 (G16) suite of programs,53 employing the ωB97X-D level of theory54 in combination with correlation-consistent triple-ζ (cc-pVTZ) basis sets55 for all atoms, except iodine, which is the heaviest atom in the compounds considered in this investigation. In the case of iodide, the small-core MDF pseudopotential56 provided by the Stuttgart/Cologne group and the associated triple-ζ basis sets56 were deployed. All calculations to examine the impact of solvent environments on the surface potentials of substituted benzenes were carried out using a self-consistent reaction field (SCRF) method. For all of the cases considered (for ethanol and water), we employed the polarizable continuum model (PCM).57−60 The Chemcraft61 and Gaussview 662 graphical user interfaces have been used for data visualization and are the sources of molecular representations in this work. The electrostatic potential maxima presented herein were generated from formatted G16 checkpoint files using the Multiwfn software.63,64

Results and Discussion

The substitution of a particularly electron-donating or -withdrawing substituent on a halobenzene (X-C6H5) ring can have a significant impact on the nature of the sigma hole on X in that molecule.34 For iodobenzene (where X = I), those effects are expected to be more prominent than they would be for any of the lighter halogen atoms due to the greater polarizability of iodine.31,65 And ipso facto, any interaction of bases with that X atom sigma hole is expected to strengthen as X gets larger, assuming, at least, that contact between the lone pair on the base and X is not frustrated, due to secondary (e.g., steric) effects such as the inconvenient presence of a bulky ortho substituent on an XC6H5–nRn ring66 or an inconvenient structural feature in a cumbersome base that limits the access of X to the lone pair.67 To avoid such scenarios in this work, therefore, and because of the well-established similarities in the electronic effects of ortho- and para-substitutions on the electron distribution in benzene rings, we consider in this contribution only meta- and para-substituted iodobenzenes. The magnitudes of the computed maximum electrostatic potentials (ESPs) in the sigma holes for all meta- and para-substituted iodobenzene systems considered in this work (62 molecules in total) are shown in Table 1.

Table 1. Computed Electrostatic Potential Maxima, Vs,max, at the Sigma Hole on I in kcal·mol–1 Units (on the 0.001 au Isodensity Surface) of the R–C6H4–I Substituted Benzene Ring in the Gas Phasea.

R meta para R meta para R meta para
H 17.67 B(OH)3– –45.29 –40.93 CN 26.15 26.71
F 21.10 20.30 S– –46.18 –43.47 CF3 23.22 23.66
Cl 21.76 21.54 NHBut 14.24 12.89 COOH 21.46 22.19
Br 21.86 21.70 NH2 15.37 14.01 COOCH3 19.46 21.02
I 21.53 21.60 NHCH3 14.66 13.17 NO2 26.29 27.37
CH3 16.68 16.49 NMe2 13.75 12.59 SO3H 25.98 26.52
CH2CH3 16.61 16.42 NHCHO 22.60 21.63 SO2Cl 27.91 29.05
n-Pr 16.24 16.04 OH 18.65 16.73 IF4 26.40 27.35
i-Pr 16.46 16.35 OCH3 16.39 15.92 ICl2 26.97 27.54
t-But 16.11 16.25 CHO 21.70 23.65 N≡N+ 93.68 94.27
Ph 17.64 17.75            
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a

i-Pr: CH(CH3)2; t-But: C(CH3)3; these electrostatic potentials were generated on the 0.001 au surfaces. For R = I, the values are typically identical on both I centers. If they differ in any marginal way, the average values are used. ESP values are often reported in atomic units as well: 1 kcal·mol–1 = 1.5936 × 10–3 au.

The substituents in Table 1 are grouped to reflect both the periodic relationships of the coordinating atoms (the first atom in each chemical formula in Table 1), as well as the generally understood (de)activating tendencies of the substituents. Representations of the computed electrostatic potentials on the surfaces of two pairs of meta- and para-substituted iodobenzene systems spanning the extremes for neutral donors and acceptors in Table 1 (R = N(CH3)2 and NO2) are shown in Figure 1. The potentials are all plotted on the same isodensity surface and on the same ESP color scale, and the two pairs of compounds are contrasted with the unsubstituted iodobenzene case (R = H), which happens to fall close to midway between them.

Figure 1.

Figure 1

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Electrostatic potential (ESP) maps showing the sigma hole on I (on the 0.001 au isodensity surface, all on the same ESP color scale: ±3.019 × 10–2 au) for R = H and inductively distinct substituents (R = N(CH3)2 and NO2) at meta- and para-positions in C6H4RI. Squares are added to help to identify the I site.

In each case in Figure 1, the structures are oriented horizontally (with R on the right of the ring in the meta-substituted species), with the iodine atom pointing out from the plane of the page and the sigma hole facing the reader. ESPs on the same color scale as that used in Figure 1 were generated for two of the ions that we have considered: R = S– and N2+. But, in those more extreme cases (as we show in Table 1 and in the Supporting Information (SI); Figures S1–S2), the magnitudes of the electrostatic potential induced by –C6H4R on I for R = S– and N2+ are very large (about an order of magnitude larger than those depicted in Figure 1). Indeed, |Vs| on the 0.001 au surface is so large in those cases that on the color scale used in Figure 1, the ESP maps are totally and intensely red for S–, where Vs is uniformly negative and completely blue for N2+, where Vs is uniformly positive across the molecular surface (Figures S1–S2). Rescaled ESP maps for those two cases (on the same 0.001 au surface but using a larger, more sensitive range for the color scale) are provided in the SI as well (Figure S3). Although the surface potentials are all negative or positive for S– and N2+, respectively, Vs does in fact vary from one point to another across the isodensity surface, and there is still a maximum (Vs,max) at the I sigma hole in both cases (the least negative Vs on I for R = S– and the most positive Vs on I for R = N2+), and those values are the Vs,max data shown in Table 1 for R = S– and N2+ and similarly for B(OH)3–.

Vs,max is usually at the center of the sigma hole on the isodensity surface. The contrast in the size and strength of the iodine sigma hole (where “strength” is a loose term referring to how positive the Vs,max values are, which is indicated pictorially by the intensity of the blue region in Figure 1, for example) is indicative of the dramatic impact that a substituent (at either the meta or para) position can have on the sigma hole on a halogen atom substituent on a ring. The observation for both S– and N2+—although they lie at the extremes of the potentials in Table 1—implies a definite relationship between the cumulative inductive and other electronic effects of substituents and the nature of the sigma hole on the halogen atom on the ring. More specifically (and in line with evidence provided elsewhere),34,65 substitutions at a given point on the ring may be used to tune or radically alter the potential at the sigma hole on X and, by extension, any halogen bond or other ESP-sensitive interaction in which a sigma hole might be involved.

We will say much more shortly on the sensitivity of Vs,max at the sigma hole on I to the identity of the substituents in the gas phase, and in solution, but, to start with, the graphical representation of the two sets of data in Table 1 proves to be instructive (Figure 2). It provides us with insights, using the sigma hole as a sensor, into the electronic effects arising from changes in the substituent position on the ring.

Figure 2.

Figure 2

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Plot of Vs,max in kcal·mol–1 at I for R at para- vs meta-positions on iodobenzene. All values are listed in Table 1. The (red) R = H data point is identified, partially obscured by R = Ph.

The ESP maxima in the sigma hole at I in Table 1 for the meta- vs the para-positions relative to the position of I show a generally linear trend (see Figure 2). This implies that each substituent will produce about the same enhancement or attenuation of the sigma hole relative to the iodobenzene (R = H) regardless of the (meta vs para) position on the ring. But that is not quite the case. For reference, we include in Figure 2 and in other plots the line y = x. The case where R = H falls of necessity on that line since Vs,max(meta) = Vs,max(para) for R = H. In the idealized case, where mesomeric effects are negligible and the total field and inductive effects of substituents are independent of their positions on the ring, the induced ESP at I for any R at the meta- and para-positions should be identical such that all of the data points in Figure 2 would fall on the reference line y = x. But the distribution of the data (see Figures 2 and S4) is much more nuanced.

Several of the data points in Figure 2 do not fall on the y = x line, but they tend to cluster around it in a distinct pattern. For that reason, no best-fit line is provided, but the imposition of the reference line, y = x, is especially helpful since a close examination of the data evinces a link between the identity of R and the nature of the response of Vs,max at I to substituting for R.

Figure 3 represents the data shown in Figure 2 in a way that amplifies certain distinguishing features of the computed potentials. The different marker types in Figure 3 help us to see that the three broad categories of substituents that we identified in Table 1 fall into definite subgroups as we go from the lower end to the upper end of the reference line on the graph.

Figure 3.

Figure 3

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Plot of Vs,max in kcal·mol–1 at I for R at para- vs meta-positions on iodobenzene, exposing different responses of Vs,max as a function of the identity and position of R.

For the weakest Vs,max values (blue diamonds in Figure 3)—where the potentials at the sigma hole on I tend to be noticeably lower (less positive) than Vs,max for R = H—we find that |Vs,max(meta)| > |Vs,max(para)|, that is, para substitution reduces the potential in the sigma hole even more substantially than meta substitution. Put another way, for this group of substituents, para substitution pushes more electron density into the ring, is more activating (toward electrophilic substitution), and diminishes, thus, Vs,max more strongly than meta substitution. There is an intermediate category of substituents (black circles) where |Vs,max(meta)| ≈ |Vs,max(para)|, and going up the reference line from left to right in Figure 3 (as Vs,max increases relative to the R = H case), we find a third subgroup of substituents (red triangles) for which para substitution increases the sigma hole potential more substantially than meta substitution, i.e., |Vs,max(meta)| < |Vs,max(para)|. For that group of substituents, para substitution pulls even more electron density from the ring, is more deactivating, and enhances, thus, Vs,max more strongly than meta substitution.

Moreover, it has been gratifying to find that the substituents in the three categories, respectively, fall roughly into electronically meaningful categories that we might describe as strong overall (i.e., σ + π) donors, intermediates, and strong overall (i.e., σ + π) acceptors. The species classified as strong donors are those in Table 1 from R = NHBut to OCH3 (blue diamonds in Figure 3). Several of them are already known to be good donors and typically have a lone pair of atoms bonded to the ring. Those classified as strong acceptors are the substituents in Table 1 from R = CHO to SO2Cl (red triangles in Figure 3), having, typically, very electronegative substituents (fluorides, such as CF3, and IF4, or double bonds to oxygen) on the central atom of the R group and no lone pair available to donate to the ring. The IF4 fragment, for example, is locally square pyramidal with a lone pair pointing away from the ring, opposite its C–I bond. ICl2 has two lone pairs, but in its T-shaped structure both lone pairs point away as well from the ring.

The systems described as intermediate cases include the halides, where strong σ-acceptor tendencies run counter to π donating tendencies, the phenyl ring ((R = Ph) which is traditionally considered to be weakly σ-withdrawing and weakly π-donating), and the alkyl substituents for which resonance or π contributions are expected to be weak relative to the stronger σ donor tendencies. And, except for the fluoride, these intermediate cases fall on or very close to the line y = x in Figure 3 with mean absolute percentage deviations in the meta and para Vs,max values in Table 1 of 1% or less. The well-known unique properties of the (very electronegative but π-donating) fluorine substituent likely account for their exceptional behavior compared to the other halogen atoms and the alkyl fragments in the intermediate group. A case may be made that F and Ph belong in another group, but we were content to leave them in that middle category for this discussion.

Overall, the double (σ + π) donor systems fall consistently below the line y = x, the double (σ + π) acceptor systems fall above that reference line, and the intermediate systems tend to fall on or close to it (Figure 3). And that outcome provides us with some evidence that the electrostatic potentials induced at the sigma hole on the I center by the R group on the ring are potentially credible computational measures of the electron-withdrawing and -donating tendencies of substituents. Moreover, we find (as we show in Figure 4) that this is indeed the kind of general ordering that the classical (σm and σp) substituent constants accomplish as well. There (in Figure 4) the donors (using identical labels to those used in Figure 3) assemble in the lower left quadrant of the graph, the intermediates in the middle, and the strong donors with their relatively large σm and σp values dominate the upper right. The values plotted in Figure 4 are listed in Table S1.21,68

Figure 4.

Figure 4

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Plot of traditional substituent constants, σm and σp, with distinguishing markers for the general categories of substituent types defined in Table 1.

Since the plot of the para vs meta effects on the I sigma hole succeeds in ordering the systems into categories as strong donors and acceptors (Figure 3; mirroring a pattern seen in the traditional constants (Figure 4)), we were encouraged to consider the extent to which these observations might allow us to rationally partition Vs,max into inductive and mesomeric components.

ESP-Based Ansatz for Partitioning σ and π Contributions

We considered the possibility of partitioning the inductive and mesomeric contributions of the substituents by a scaling method that relies on the transferability of inductive effects from a six-membered-ring system without π-bonds. This approach has some precedence in a much earlier strategy to isolate inductive effects of substituents by assessing experimentally the reactivities of saturated systems—4-substituted bicyclo[2.2.2]octane-1-carboxylic acids—that (unlike substituted benzoic acid from which Hammett’s substituent constants were obtained) have no π-bonds.69

In this case, however, we considered the influence of equatorial substitutions at carbons 3 and 4 relative to the equatorial C–I bond in monoiodocyclohexane (C6H10RI), the saturated product of the meta- and para-substituted benzene systems that we have been discussing so far. The maximum induced electrostatic potentials at the sigma hole on I in each of the optimized benzene and saturated cyclohexane chair systems are listed in Tables S2 and S3 in the SI (and the corresponding minimum energy coordinates are available in the Supporting.xyz files). We will confirm later in this article a general insensitivity of the trends that we have observed so far to the equatorial vs axial position of iodine on the cyclohexane ring in generating transferrable inductive contributions to the overall value of the sigma hole potentials.

To compare the computed iodine sigma hole potentials from C6H10RI with the iodine sigma hole potentials obtained for the corresponding planar aromatic ring, the cyclohexane values were scaled according to the following simple ansatz:

(i) The maximum potential (Vs,max) induced at the iodine σ-hole in C6H10RI due to field and inductive effects “I” of the ‘–C6H10R’ fragment (represented by VcyclI;s,max (R)) is scaled by adding a constant ΔV to all of the VcyclI;s,max (R) values. That constant is

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It is defined to be precisely the difference between Vbenz(I+M);s,max (H), which is Vs,max at I in iodobenzene (where R = H) and VcyclI;s,max (H), which is Vs,max at I in iodocyclohexane (where R = H). So, the iodobenzene value and the scaled value are equal for R = H

graphic file with name jp3c05797_m003.jpg 2

Here, the implicit assumption is that for R = H, the substituent effects have no mesomeric contribution. And that same constant from R = H is added to all of the other cyclohexane values (see Tables S3 and S4) such that, in general, for any R, the scaled inductive term is

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And, since VscaledI;s,max excludes π effects for any given R group, we expect that generally

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except for R = H. Recall that, as defined above, the R = H case has no mesomeric component

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But for any arbitrary substituent, R, the corresponding mesomeric component

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is, in general, nonzero. The corresponding values, including those for VscaledI;s,max(R) and VbenzM;s,max (R), are shown in Tables S2–S5 in the SI. For an alternative and insightful route to the same definition for VbenzM;s,max (R), see the approach summarized in the Appendix section.

This scaling procedure provides us with transferable values associated with the specific field-inductive contribution of R to the total electrostatic potential at the sigma hole on I in benzene. It comes, however, with the assumptions that (a) the through bond electronic effect of R in C6H10RI is purely field-inductive and that through-space (field) effects of substituents at the meta- or para-position in the ring fall off rapidly with distance69 and (b) that an additive scaling strategy is valid for linking inductive potentials of the I center in the saturated ring and benzene.

The outcome for the scaled cyclohexane values for the para- vs meta-positions is shown in Figure 5. In that figure, the values all cluster very closely to the reference line, as expected for purely inductive effects. The position on the ring relative to the I center is expected indeed to be far less consequential for inductive effects that can be conveyed more evenly around the ring compared to the mesomeric effects21 such that VI;s,max(meta) ≈ VI;s,max(para). The complete graphs that include the ionic cases are included in the Supporting Information since the values for the charged species would compress the scale used here substantially (see Figures S4–S6 and Tables S2–S5).

Figure 5.

Figure 5

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Scaled iodine σ-hole potential maxima obtained from cyclohexane and associated with field-inductive effects in the benzene ring for the meta and para R substituents.

By subtracting those scaled inductive contributions (Figure 5) from the corresponding total potentials (Figure 3), the partitioning strategy that we just outlined succeeds in isolating the strong π-donor systems (in blue, in Figure 6) from the strong π-acceptor systems (in red) to opposite sides of the reference line, with the intermediate systems falling on or very close to the line, including the R = H case where VbenzM;s,max = 0 by definition as we explained above.

Figure 6.

Figure 6

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Plot of para vs metaVbenzM;s,max (R) values, which are associated with π effects after inductive components are removed from VbenzI+M;s,max (R).

Where R is a π-donor (and for ortho–para directors generally), the electron density in the ring is enhanced, including at I (and especially when R is at the para-position). So VbenzM;s,max (R) is expected to be lowered relative to VbenzM;s,max (H) = 0 for those systems, and therefore negative, as we observe in Figure 6 and Table S5. Since VbenzM;s,max (R) is the difference between the total V(I+M)s,max at I and the putative inductive part, VbenzM;s,max exposes the deterioration of the sigma hole (due to the π donor’s infusion of electron density into the ring) relative to the R = H case.

Conversely, where I is a π-acceptor (and for meta directors generally), the electron density in the ring is diminished, including at I (and especially at the ortho- and para-positions) such that VbenzM;s,max (R) is expected to be increased relative to VbenzM;s,max (H) = 0 and are expected thus to be positive in general, as we observe in Figure 6 and Table S5. Since VbenzM;s,max (R) is the difference between the total V(I+M)s,max at I and the putative inductive part, the VbenzM;s,max (R) values expose, in that case, the enhancement of the sigma hole (due to lower π electron density in the ring) relative to the R = H case.

The selection of the equatorial–equatorial (i.e., Req–Ieq) positions for I and R on the cyclohexane ring leaves unanswered the question of whether this outcome is an accident of our selection. We show in the SI (see the Supporting Notes and Figure S7) that indeed the general qualitative ordering of the substituents in terms of their inductive tendencies (and the impact on the sigma hole potentials) is not an accident of the C6H10RI configuration but is reflective of the nature of each R substituent.

Modeling the Impact of Solvent Environments

To model the influence of solvents on the strength of the sigma hole, we considered separately the two polar solvents (ethanol and water dielectric environments as defined by the implicit solvent PCM model in Gaussian 16) used in the solutions employed experimentally by Hammett.18,19,21 The analyses just reported for the gas-phase case were repeated, and those studies (see Figure 7 and Table 2) showed remarkable alignment with the data obtained from the gas-phase calculations (Figure 3), except that the actual magnitudes of the total Vs,max values are altered somewhat in those high dielectric environments, and we say more about that presently. An explicit solvent model affords vital insights where solvent–solute interactions are critical.70,71 We utilized an implicit solvent model, however, since, in addition to somewhat lower computational costs, the latter model allows us to assess the impact of substituents on the potentials in different dielectric environments (for the substituted benzenes and cyclohexanes (R–Y–I)), prior to any solute–solvent complex formation (e.g., R–Y–I·OEtH or R–Y–I·OH2 halogen bonds for water or ethanol, respectively). Such I·O type interactions are known to arise in solution70 and would necessarily inhibit our ability to locate and assess the isolated Vs,max(I) (prior to any complex formation) in which we are interested here.

Figure 7.

Figure 7

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Plot of para vs meta Vbenz(I+M);s,max values at I for (a) ethanol and (b) water. The values in the two graphs are very similar due to a rapid convergence of Vs,max with the relative permittivity, ε.

Table 2. Total Vs,max at the I σ-Hole in C6H4RI, Vbenz(I+M);s,max, for Both the meta- and para-Positions in Different Solvent Environments.

graphic file with name jp3c05797_0009.jpg

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For iodobenzene, the computed potential maxima in the sigma hole at I, in kcal·mol–1 units, are Vs,max (R = H, vacuum) = 17.6, Vs,max (R = H, ethanol) = 16.7, and Vs,max (water) = 16.7. So, the solvent Vs,max values (listed in full in Table 2) agree for R = H up to three significant figures, which is in line with an earlier observation of an exponential convergence of ESP values as relative permittivity increases.72 That general qualitative agreement between results from the gas phase and from (implicit) solvent environments (Figures 3 and 7) extends to the isolated field-inductive terms as well. As we see in Figure 8, the computed scaled inductive potentials coalesce in general around the reference line y = x in all cases indicating little (para vs meta) position dependence of the trends in the inductive donating or withdrawing power of the substituents.

Figure 8.

Figure 8

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Scaled inductive potentials, VscaledI;s,max, at I for (a) ethanol and (b) water solvent environments. Identical trends are obtained for the unscaled VcyclI;s,max before adding ΔVbenz-cycl.

As we will show later in the article, results that are qualitatively very similar to those obtained from the gas phase (Figure 5) are obtained for the mesomeric components for the potentials in ethanol and water using the implicit solvent model described in the Computational Methods Section.

Efficacy of Potentials for Quantifying Substituent Effects

A significant observation from the analysis so far is that the trends in the overall electron-withdrawing tendencies of the R groups considered, as expressed in the strengths of the sigma holes induced on I by ‘–C6H4R’, persist going from vacuum conditions to the (implict) solvent environments. In Table 2, the R groups are listed in order based on the value of the total maximum potential at the σ-hole on I in C6H4RI, that is, Vbenz(I+M);s,max. The values are shown for both the meta- and para-positions on benzene since the total effect of a given substituent can vary drastically with the position on the ring. Shading is used here to indicate the previously defined categories (Table 1) to which each R group was assigned.

The sensitivity of the induced electrostatic potentials to the position of R on the ring is evident in Table 2, for example, by shifts in the relative positions of the –NHCHO and −COOH groups in the meta vs the para columns for the three different conditions considered. Of note, the ordering appears to be less dependent on changes in ε (going across the three meta or the three para columns in Table 2) than they are on where R is on the ring. Notice, however, that the actual values of the potential maxima shrink by a few kcal·mol–1 (typically by much less than 10%) on going from the gas phase to ethanol and water in the implicit solvent models, except for the moderate to strong neutral acceptors (category 3 cases) at the bottom of the table. In those cases, the opposite response to the solvent environments is observed with the potentials increasing slightly.

Curiously, Vs,max shrinks as well in the solvent environments (Table 2) for both the positively and negatively charged species in the list. For those charged systems, the |Vs,max| values are quite large relative to the neutral cases (see Table 2), and the percentage change in Vs,max relative to the gas phase, |ΔVs,max|, is somewhat larger as well (up to 35%). Since we only consider three instances of charged (anionic or cationic) R groups here, however, we refrain in this context from making any generalization on the response of such substituents to the chemical environment.

Since the meta and para values for the scaled field-inductive (VscaledI;s,max (R)) potentials are rather close in value (cf. Figures 5 and 8), only the averages, [VscaledI;s,max (Rmeta) + VscaledI;s,max (Rpara)]/2, are presented in Table 3, but the full list of the individual meta and para values from which these averages are obtained are included in Table S6.

Table 3. Average VscaledI;s,max (R) Values for C6H4RI in Different Dielectric Environments.

graphic file with name jp3c05797_0010.jpg

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The averaged scaled field-inductive potentials (Table 3) show an ordering different from that observed for the total values in Table 2. The general separation of the (σ + π) donors and strong acceptors that is highlighted for the overall potentials in Table 2 is also observed for the purely inductive part (Table 3), but in the latter case, the alkyl substituents yield the lowest VI;s,max potentials and are thus at the top of the table, that is, the alkyl groups, which are great σ-donors (species with substantial inductive donor effects), are the most successful R groups at inductively weakening the sigma hole on I relative to the unsubstituted C6H11I case. And, evidently, the alkyl groups lead to those low inductively induced VI;s,max values on I in C6H10RI by donating so much electron density to the ring that (inductively, through the σ-framework) VI;s,max is substantially attenuated relative to R = H (Table 3). The systems that are good (σ + π) donors, including the amines, appear after S– and the alkyl groups, an indication that, without the π component, those R groups are really weakened as donors, becoming even weaker than the alkyl groups (hence their downward shift in Table 3 relative to that in Table 2). The halides, which are good inductive σ-acceptors (stripped in Table 3 of their counteracting π donor effects), appear even farther down in the columns in Table 3 among other strong inductive σ acceptors.

And what of the mesomeric contributions to the total potential under different dielectric environments? The component of the total sigma hole potential that is associated with mesomeric effects, VbenzM;s,max, has been obtained as before (see Figure 6) using data that we generated under the specified solvent conditions by subtracting (see eq 6) the scaled inductive contributions from the total V(I+M)s,max potentials (Table 4). For the sake of completeness, the gas-phase values (see Figure 6) are included in Table 4.

Table 4. Resonance-Linked VbenzM;s,max (R) Values for C6H4RI in Different Dielectric Environments.

graphic file with name jp3c05797_0011.jpg

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Those outcomes are remarkably consistent with what we know about and expect classically from the π donors and acceptors that are considered here, signaling the substantial promise of terminal halogen sigma holes as tools in assessing the potential impact of novel substituent fragments on the π system of a ring and thus on the bonding in and reactivity of compounds.

For para substitution (see data on the right in Figure 4), the computed VbenzM;s,max values separate the (σ + π) donors and (σ + π) acceptors completely, with the intermediate cases sandwiched between them. That outcome is fully in line with the grouping of substituents adopted in Table 1 based on traditional assignments of the substituents as strong, weak, and intermediate (de)activating groups. And these results, consistent as they are with the experimentally rooted chemical intuition, suggest that the ESP analysis employed here may be readily applied to elucidate the influence of even less common or novel chemical substituents on aromatic rings.

The ordering is somewhat different for the meta-position, echoing a distinction between the influence of substituents in the meta-position versus the para-position that we saw in the unpartitioned total Vs,max values (Table 2) and which is a feature in the experimentally based Hammett substituent constants, σm and σp (Table S1).

Overall, a general increase is observed in the absolute value of the mesomeric component, |VbenzM;s,max|, for neutral R groups going from the gas phase to polar solvents. So, the ansatz employed here suggests that π (accepting and donating) effects are enhanced in high dielectric environments, i.e., π donors are expected to become more successful at diminishing the strength of the sigma hole on I, and π acceptors will be more successful at accomplishing the reverse. Mesomeric effects influence the sigma hole indirectly, increasing (or decreasing) the electron density in the electron belt that surrounds the sigma hole on I, partially masking (or further exposing) the sigma hole as a consequence. Those π effects can be substantial, and they are recovered well by the partitioning scheme presented herein.

Electrostatic Potentials as Alternative Measures of Substituent Effects

The computational derivation of substituent parameters that we have outlined in this work provides a new measure of the impact of substitutions on the electron distribution in compounds. The rigorously defined overall parameters are accessible at a low computational cost for substituents and may be employed in the interpretation of physicochemical properties of compounds and reaction processes analogous to experimental substituent constants. Beyond current computational approaches that propose descriptors for overall substituent effects or sigma constants only, for instance,27−30 a scheme is introduced here for partitioning the overall potential-based substituent parameters into distinct σ and π contributions. The provision of a partitioning framework is important since it provides a specific and rational basis for the systematic quantitative assessment and selection (from among known and potentially interesting novel options) substituents that are particularly suited for desired σ vs π electron-withdrawing and -donating tendencies.

Summary and Outlook

A computational strategy is provided that allows us to examine the relationship between inductive and mesomeric influences of chemical substituents (on benzene) through an analysis of the induced potential at the sigma hole on a terminal atom on the ring. The investigation allows us to consider further as well the utility of induced electrostatic potentials as diagnostic tools in chemistry, even as we debate the role of electrostatics in accounting for weak interactions such as halogen bonding.73 We examine the influence of several mono- and polyatomic substituents, R, on the induced σ-holes on terminal I centers in substituted iodobenzene. The analysis allows us to probe and better understand the connection between inductive and mesomeric tendencies of substituents and the perturbation of the electron density in molecules and a few charged species.

A general correspondence is demonstrated between the computed potentials at sigma holes on I in substituted iodobenzene and classical empirical substituent constants. A readily implemented theoretical ansatz based on computed electrostatic potentials is proposed that partitions the potentials into reasonably well-defined categories as (σ and π) donors and acceptors.

The assumptions built into this model and its successes and limitations are discussed. The results emphasize the relevance of the π density in ring systems on σ-holes on terminal atoms. Donating electron density into the π system, for example, at both the meta- and the para-positions, leads to an evident expansion of the belt of electron density around the I nucleus perpendicular to the C–I bond in iodobenzene and an incipient contraction and weakening of the σ-hole. The σ-hole is π-dependent.

Acknowledgments

Our work was supported by the National Science Foundation NSF-RUI Award (CHE-2055119) and NSF-MRI Grants CHE-0958696 (University of Richmond) and CHE-1662030 (the MERCURY consortium). N.P. and P.R. thank the NSF for summer research support. K.J.D. acknowledges the support of the Henry Dreyfus Teacher-Scholar Awards Program. The support of the University of Richmond is also gratefully acknowledged.

Appendix: An Alternative Approach to Obtaining VbenzM;s,max

Having computed Vbenz(I+M);s,max (R) and VcyclI;s,max (R), both sets of values may be scaled by subtraction to ensure that when R = H, Vbenz(I+M);s,max (H) = 0, and VcyclI;s,max (H) = 0. That is,

graphic file with name jp3c05797_m008.jpg A1
graphic file with name jp3c05797_m009.jpg A2

where the superscript ‘(H) = 0’ signifies that in both scaled data sets, Vs,max(H) = 0. And, for any R,

graphic file with name jp3c05797_m010.jpg A3

which will return exactly the VbenzM;s,max values given in the main text. An advantage to this approach is that it yields smaller numerical values for potential use as parameters for total, inductive, and mesomeric electronic effects (Table A1).

Table A1. Scaled (Gas Phase) ESP-Based meta and para Substituent Parameters, Vbenz;(H) = 0(I+M);s,max (Total), and Their Inductive Vcycl;(H) = 0I;s,max and Mesomeric VbenzM;s,max Parts (See Figure S8).

  meta
 para
  total I M total I M
H 0 0 0 0 0 0
F 3.43 4.20 –0.78 2.63 4.22 –1.59
Cl 4.09 5.00 –0.91 3.87 4.95 –1.07
Br 4.19 5.15 –0.96 4.03 5.05 –1.02
I 3.86 4.90 –1.04 3.93 4.84 –0.91
CH3 –0.99 –0.039 –0.95 –1.18 0.083 –1.27
CH2CH3 –1.06 –0.21 –0.85 –1.25 –0.081 –1.17
n-Pr –1.43 –0.28 –1.15 –1.63 –0.10 –1.53
i-Pr –1.21 –0.34 –0.87 –1.32 –0.11 –1.21
t-But –1.56 –0.37 –1.19 –1.42 –0.19 –1.23
Ph –0.029 0.70 –0.73 0.076 0.98 –0.90
B(OH)3– –62.96 –61.71 –1.26 –58.60 –56.35 –2.25
S– –63.85 –58.50 –5.35 –61.14 –53.21 –7.93
NHBut –3.43 –0.026 –3.40 –4.78 0.31 –5.09
NH2 –2.30 1.11 –3.41 –3.66 0.43 –4.09
NHCH3 –3.01 0.15 –3.16 –4.50 0.49 –4.98
NMe2 –3.92 0.11 –4.03 –5.08 0.46 –5.54
NHCHO 4.93 6.04 –1.11 3.97 6.08 –2.11
OH 0.98 1.26 –0.28 –0.94 1.91 –2.85
OCH3 –1.28 1.03 –2.32 –1.75 1.57 –3.31
CHO 4.03 2.43 1.59 5.98 3.75 2.23
CN 8.48 7.57 0.91 9.04 7.29 1.74
CF3 5.55 4.99 0.57 5.99 4.89 1.11
COOH 3.79 3.40 0.38 4.52 2.84 1.68
COOCH3 1.79 2.60 –0.81 3.35 2.07 1.29
NO2 8.62 8.15 0.47 9.70 7.88 1.82
SO3H 8.31 8.12 0.20 8.85 7.07 1.77
SO2Cl 10.24 9.28 0.96 11.39 9.20 2.19
IF4 8.73 8.65 0.078 9.68 8.59 1.09
ICl2 9.30 9.59 –0.29 9.87 9.23 0.64
NN+ 76.02 70.64 5.37 76.60 65.62 10.98
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Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.3c05797.

  • Additional notes; electrostatic potential maps for sample substituted iodobenzenes; plots of computed maximum potentials at the iodine sigma hole for para- and meta-substituted benzene and cyclohexane rings; computed maximum electrostatic potentials, and their partitioned inductive and mesomeric components (PDF)

  • xyz Files (ZIP)

Author Contributions

K.J.D. led the project, generated and analyzed data, revised drafts, and finalized the manuscript. N.P. generated and analyzed data and wrote a draft report. P.R. generated and analyzed data.

The authors declare no competing financial interest.

Supplementary Material

jp3c05797_si_001.pdf (1.8MB, pdf)
jp3c05797_si_002.zip (111KB, zip)

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