Sigma Hole Potentials as Tools: Quantifying and Partitioning Substituent Effects

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.


Table of Contents
Table S1: Experiment based Hammett-type substituent constants S8 Table S2:  ( ); , : values for I sigma hole, in kcalmol -1 units, for I in IC6H4R.S8 Table S3: Unscaled ( ; , (R)) values.S9 Table S4: Inductive  ; , () values.S9 Table S5: Mesomeric  ; , () values.S9 Table S6: Unscaled and scaled inductive components for vacuum, and implicit solvent environments -ethanol and water.S10    1 and S2.S3-S4.The scaled values (Table S4) are equal to those unscaled values plus a Vs,max, which is equal to  ( ); , () −  ; , ().This survey allowed us to assess the (in)variability of the potentials at I,  ; , (), as a function of the relative positions of R and I in C6H10RI.Cases with R in the axial position were excluded in order to avoid any possible escalation of steric effects (between bulky R groups and other parts of the ring), and we considered as well that the equatorial C-R bond in C6H10RI, pointing as it does away from the ring, is more consistent with the arrangement of the C-R bond in C6H4RI.
The results (Figure S7) show that the trend is the same in all cases.The actual values differ somewhat but by roughly constant amounts among the various configurations considered.For R = H, of course, the equatorial and axial cases are distinct isomers, but the meta and para forms of each are identical.The reason for the relatively low Vs,max values in the para Req-Iax case is unclear.But, even in that case, the overall trend going from one substituent to another remains essentially the same, which lends support to the assumption that the trend in inductive effects for R on I in the substituted cyclohexane systems is roughly independent of the axial or equatorial position of the I substituent on the ring.So, the general qualitative ordering of the substituents in terms of their inductive tendencies, and the consequences for the sigma hole potential at the terminal I center, is not an accident of the C6H10RI configuration.It reflects, we find, the nature of the particular R substituent.

Figure S1 :
Abbreviated Captions* Page Guide to .xyzFiles S3 Figure S1: ESP maps showing the sigma hole on I in IC6H4R (without shadows on ESP maps), for sample R groups, including charged cases.S4 Figure S2: ESP maps showing the sigma hole on I in IC6H4R (with shadows on ESP maps), for sample R groups, including charged cases.S4 Figure S3: ESP maps on an expanded scale showing the sigma hole on I in IC6H4R (without and with shadows on ESP maps), for sample two charged cases.S5 Figure S4:  ( ); , : Para vs. meta plot of computed electrostatic potential (ESP) maxima at the I sigma hole, in kcalmol -1 units, for I in IC6H4R.S5 Figure S5: Para vs. meta plots of unscaled ( ; , () (a)), and scaled ( ; , () (b)) ESP maxima at the I sigma hole, in kcalmol -1 units, for I on IC6H10R.S6 Figure S6: Para vs. meta plot of  ; , () S6 Supporting Notes 1: On the consistency of computed potentials for different substitution patterns on cyclohexane.S7

Figure S8 :
Figure S8: [Plots for scaling with Vs,max(H) = 0]: Para vs. meta plots for potentials at the sigma hole I on substituted benzene (a) and cyclohexane (b) molecules, with the values of the potentials adjusted so that Vs,max(H) = 0, and the mesomeric component (c).S11 Complete Gaussian 16 Reference S12 *More detailed captions are provided with the individual figures and tables.

Figure S2 :
Figure S2: ESP maps showing the sigma hole on I (on the 0.001 au isodensity surface, all on the same scale: ± 3.019  10 -2 au.) for R = H and four other inductively distinct substituents (R = S -, N(CH3)2, NO2, and N2 + ) at both meta and para positions in C6H4RI.These structures are identical to those shown in Figure S1 but include shadows for depth perception.All structures are oriented with the ring horizontal and with I pointing out of the plane of the page.In the meta substituted species (on the left of this figure), the substituent is on the right of the ring.

Figure S4 :
Figure S4:  ( ); ,: Plot of computed electrostatic potential (ESP) maxima at the sigma hole, in kcalmol -1 units, on I (on the 0.001 au isodensity surface) of the R-C6H4-I substituted benzene ring in the gas phase -including the three charged species.A magnification of the compressed section with uncharged cases is shown.The actual values are in Tables1 and S2.
Figure S5: Plot of the computed (a) unscaled  ; , (R), and (b) scaled  ; ,() electrostatic potential (ESP) maxima at the sigma hole on I in kcalmol -1 units (on the 0.001 au isodensity surface) for the substituted cyclohexane, RC6H10I, ring in the gas phase -including three charged species.The actual values are in TableS3-S4.The scaled values (TableS4) are equal to those

Figure S6 :
Figure S6:  ; , (): (gas phase) ESP contributions associated with  effects after scaled inductive components are removed from  ; , ().See values in Table4in the main text.This graph, which is also discussed in the main text, is included here for completeness.All of the  ; , values are comfortably accommodated in this figure without compression, including the values for the charged cases.Similar plots are obtained for the implicit (ethanol and water) solvent cases.The relevant data for those cases are included in Table4in the main text.
On the Consistency of Computed Potentials for Different SubstitutionPatterns on Cyclohexane: To address the question of whether this outcome is an accident of our selection of the equatorial-equatorial (i.e.Req-Ieq) positions for I and R on the cyclohexane ring, we computed Vs,max values for four different structural arrangements (Req-Ieq and Req-Iax, both with R at the meta and para positions) for R = H, F, Cl, Br, I, NH2, and CN.This subset of R groups was chosen in order to span the range of neutral donor and acceptor species considered (FigureS7).

Figure S7 :
Figure S7: Vs,max values for a diverse set of R substituents and C6H10RI chair isomers.

Figure S8 :
Figure S8: Graphs of computed (gas phase) potentials from I on substituted benzene (a) and cyclohexane (b) molecules adjusted so Vs,max(H) = 0, magnifying the region with the bulk of the data, and the mesomeric component (c).For the latter, no magnification is necessary and the graph, (c), is identical to Figure S6.The corresponding values are shown in the main text.

Table S2 :
Computed  ( ); , electrostatic potential (ESP) maxima at the sigma hole on I, in kcalmol -1 units, on I (on the 0.001 au isodensity surface) for the R-C6H4-I ring in the gas phase (vacuum).
The electrostatic potentials were generated on the 0.001au 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.