Quantifying Through‐Space Substituent Effects

Abstract The description of substituents as electron donating or withdrawing leads to a perceived dominance of through‐bond influences. The situation is compounded by the challenge of separating through‐bond and through‐space contributions. Here, we probe the experimental significance of through‐space substituent effects in molecular interactions and reaction kinetics. Conformational equilibrium constants were transposed onto the Hammett substituent constant scale revealing dominant through‐space substituent effects that cannot be described in classic terms. For example, NO2 groups positioned over a biaryl bond exhibited similar influences as resonant electron donors. Meanwhile, the electro‐enhancing influence of OMe/OH groups could be switched off or inverted by conformational twisting. 267 conformational equilibrium constants measured across eleven solvents were found to be better predictors of reaction kinetics than calculated electrostatic potentials, suggesting utility in other contexts and for benchmarking theoretical solvation models.


S3
Through-space ESPs (ESPthrough-space) were performed using electrostatic potential slices that were calculated for each X substituent fragment and overlaid on the previously minimized geometries of the corresponding full balance ( Figure S1B). The ESPthrough-space was then taken on the slice of the X substituent fragment at the atom-centre position occupied by the carbonyl oxygen in the minimized 'O' conformer of the balance in full balance (Table S1). This ensured that only the influence of the X substituents electrostatic potential propagating through space was taken into account. Excellent correlations were seen for both the experimental balance conformation measured in benzene ( Figure S1C) and ESPipso ( Figure S1D) vs ESPthrough-space as the X-substituent was varied. Table S1. Mean ESPipso values of all phenyl fragments in the 1−X series of balances with the two ESPipso values recorded on each face of the aromatic ring, as well as ESPthrough-space values recorded at the position occupied by the formyl oxygen atom in the O conformer. All structures and surfaces (from which ESPipso values were determined) were minimized and calculated using DFT/B3LYP/6−31G* in Spartan '14. All values in kJ mol −1 .
A B S13

S2. Conformer Assignment by NMR
All molecular torsion balances were fully characterized by NMR in CDCl3 to assign conformer peaks of all balances. Figures S26 to S34 show the NMR spectra ( 1 H, 13 C, HSQC, COSY, HMBC and NOESY) of 1−Me in CDCl3 together with the full assignment of both conformers ( Figure   S26). The 2D and 1D spectra were used to assign the conformers of 1−Me as shown below. In this example, proton resonances have been labelled numerically and carbon resonances alphabetically.
The minor conformer peaks have been denoted with a prime (′). The major conformer in the 19 F spectra were assumed to be the same as that in CDCl3.

S3. Determination of KX and error analysis
All molecular balances were fully characterized and the 'O' and 'H' conformers ( Figure S35)

Equation S1
Where "H conformer" is the 19 F integral of the H conformer and "O conformer" is that of the O conformer.
An error of 3% was applied to the integral of the minor NMR peak (e.g. the integration ratio was  Table S2. Conformer ratios were shown not to vary with concentration within the range used for our NMR study ( Figure S36).

Equation S2
With the conservative error in KX set at 3% in the integral of the minor NMR peak for all compounds, the value of dlog10(KX/KH) was < ±0.04 for series 1−X. The values of −log10(KX/KH) were transposed onto the established Hammett scale through correlation between these values of the 1−X series ( Figure 2B main text). An empirical estimate of the error in p(conf), δp(conf), was taken as the value by which the data point that deviates furthest from S23 the best fit line in Figure 2B in the main text, which was 0.06. Thus, a conservative empirical estimate of the error, δp(conf) < ±0.08 could be assumed.

S5. NMR Chemical Shift Data for Central Ring Protons
Chemical shift data (Table S4) of the X substituted ring in the ortho and meta position to the formamide of molecular balances 1−X ( Figure S37). Figure S37. Position of "ortho" and "meta" referred to in Table S4 and in the accompanying discussion regarding 1 H NMR chemical shifts. As discussed in Section S4, a conservative 3% estimate of the error in the integral of the minor conformer NMR peak was applied (e.g. the integration ratio was [∫major conformer = 1] / [∫minor conformer ± 0.03]). The error in Gexp due to integration errors is very small when KX lies close to 1. Thus, where the estimated error determined using the approach above was less than ±0.12 kJ mol -1 , a standard error of ±0.12 kJ mol -1 was used to accommodate potential systematic experimental errors. Indeed, we have previously investigated 3 the errors associated with our conformational ratio measurements from 19 F NMR spectroscopy and found that the largest error at the 95% confidence interval to be ±0.10 kJ mol -1 (twice the standard deviation), with an average 95% confidence interval of ±0.06 kJ mol -1 across the samples. This is within the Gexp value range of −4 kJ mol −1 and +4 kJ mol −1 . Thus, an estimated minimum error of ±0.12 kJ mol -1 is likely to accommodate any systematic experimental variation.       Table S8. Values of Gexp for series 1−X in methanol-d4 and THF-d8 (376.5 MHz, 298 K). All values in kJ mol −1 . All errors were less than ±0.12 kJ mol −1 . Those denoted as "n.s" were not soluble and "n.r" were not resolved.

S7. Linear Regression to Obtain Solvent-Independent Conformational Free Energies (E)
Experimental conformational free energies ΔGsolv were fitted for each balance against ΔGsolv as defined by Equation S4 using the multiple linear regression tool in Origin 2019.

ΔGsolv = ΔE + βsΔα + αsΔβ Equation S4
The βs and αs hydrogen bond constants for each solvent were locked as constants (listed Table S9), while the coefficients E, a and  were iteratively fitted variables to give the best agreement between the experimental ΔGsolv values and modelled ΔGsolv values (across eleven solvents for each balance). The fitting of ΔGsolv against ΔGexp gave a correlation with R 2 = 0.85 ( Figure S40). The output coefficients E, a and  and corresponding fitting errors dE, da and d for each balance are listed in Table S10. The fitted ΔGSolv values are reported in Tables S11-S13, with the errors in ΔGSolv (δΔG) being defined by Equation S5 .
E values were correlated against ESPipso and this plot, with error bars included, is given in Figure   S41.  Figure S41. Plot of dissected solvent-independent E values against ESPipso as given in main text Figure  5, but with error bars included. 1-3

S8. Synthetic Procedures and Standard Characterization Data
All chemicals were obtained from commercial sources and used as received.

S8.1 General procedure for copper-mediated coupling of halophenyls to aryl-amides
A subset of series 1−X were prepared according to the same general copper (I) iodide catalysed cross-coupling conditions. 8

S8.2 General procedure for palladium-mediated cross-coupling of phenylboronic acid derivatives to N-(4-Bromophenyl)-N-(4-fluorophenyl)formamide (1−Br)
A subset of series 1−X were prepared according to the same general palladium-mediated crosscoupling conditions. 9 An oven dried flask was sealed before evacuating and back filling with nitrogen three times before N-(4-bromophenyl)-N-(4-fluorophenyl)formamide, the phenylboronic acid derivative and Pd(PPh3)4 were added. The flask was evacuated and back filled with nitrogen a further three times. Degassed dimethoxyethane (DME) and aq. Na2CO3 (2M) were added via syringe and the reaction mixture was heated at 85 °C for 18 h under a nitrogen atmosphere. The reaction mixture was then cooled to ambient temperature, quenched with sat. aq. NH4Cl and extracted with CHCl3. The combined organic extracts were dried over MgSO4 before concentration in vacuo. The resulting products were further purified by chromatography.
After quenching with sat. aq. NaHCO3, the aqueous phase was extracted with EtOAc Characterization was consistent with existing literature. 11

N-(4-Bromophenyl)-formamide
4-bromoaniline (10.01 g, 50 mmol) was refluxed for 18 h in formic acid (30 mL). Formic acid was removed under reduced pressure before ethyl acetate (110 mL) was added and the reaction mixture washed with sat. aq. NaHCO3, brine, dried (MgSO4) and concentrated in vacuo to yield crude N-(4-bromophenyl)-formamide as a brown solid which was carried to the next step without further purification.
ESPN values were measured on the ESP surface over the pyridine nitrogen atom ( Figure S42, Table   S14). ESP surfaces and slices are given for series 2−X in Figures S43-S59.

S10.2 Ionization Energy Surface calculations
Ionization energy surfaces were calculated at the DFT/B3LYP/6−31G* level of theory for the minimized structures using Spartan '14. IEN values were measured on the IE surface over the pyridine nitrogen atom ( Figure S60, Table S14).
IE surfaces are given for series 2−X in Figures S60 to S76.                   Table S15.
The integrals of the signals corresponding to the protons ortho to the pyridine nitrogen atom of both the starting material and the N-methylated product (2,6 and 2,6 protons respectively) were determined at thirty-minute intervals. A representative example of this is given in Figure S77 for pyridine. Figure S77. N-Methylation of 2−H was monitored by 1 H NMR spectra (acetone-d6, 400 MHz, 298 K) over five hours and 30 minutes with the 2,6 and 2,6 signals denoted by one and two red triangles respectively.
Through division of the 2,6 integral with the sum of these integrals, the change in concentration of the starting material, [sm], over the time of the experiment was determined. As an excess of methyl iodide was used, the reaction was under pseudo first order conditions thus allowing the experimental data to be fitted to this rate equation (Equation S6) to obtain the experimental rate constant, kX, through linear regression ( Figure S78).

Equation S6
Where t is time and [sm]0 is the concentration of the starting material at the beginning of the experiment, i.e. when t = 0.  Table S15.

Equation S7
Where kX is the value of each experiment, ̅̅̅ is the average kX value and n is the number of values. Verification that the reaction was indeed under pseudo first order conditions were performed by obtaining rate constants at varying concentrations of compounds whose experimental behavior span the extremes observed ( Figure S79). A Hammett-style analysis using the relationship −log10(kX/kH) was performed on the experimental rate constants, kX, measured in in acetone-d6 at 400 MHz, 298 K (Table S16)

S12.1 General procedure for tetrakis(triphenylphosphine)palladium (0)-mediated coupling of 4-bromopyridine hydrochloride with phenylboronic acids
A subset of series 2−X were prepared according to the same general tetrakis(triphenylphospine)palladium(0)-mediated cross-coupling conditions. 7 An oven dried flask was sealed before evacuating and back filling with nitrogen three times before 4-bromopyridine hydrochloride, the phenylboronic acid derivative and Pd(PPh3)4 were added. The flask was evacuated and back filled with nitrogen a further three times. Degassed dimethoxyethane (DME) and aq.
Na2CO3 (2M) were added via syringe and the reaction mixture was heated at 85 °C for 18 h under a nitrogen atmosphere. For those performed under microwave radiation, the same process was performed but in a microwave vial and not flask. Microwave reactions were heated at normal absorbency at 130 °C for 45 min (with a 2 min pre-stir). The reaction mixture was then cooled to ambient temperature, quenched with sat. aq. NH4Cl and extracted with CHCl3. The combined organic extracts were dried over MgSO4 before concentration in vacuo. The resulting products were further purified by chromatography.

S12.2 Tri(dibenzylideneactone)dipalladium (0)-mediated coupling of 4-bromopyridine hydrochloride with (2-methoxy)phenylboronic acid
Compound 2−g was prepared according to the same general tri(dibenzylideneacetone)dipalladium (0) mediated cross-coupling conditions. 8 An oven dried flask was sealed before evacuating and back filling with nitrogen three times before 4-bromopyridine hydrochloride, the phenylboronic acid derivative, Pd2(dba)3 and PCy3 were added. The flask was evacuated and back filled with nitrogen a further three times. Degassed dioxane and aq. K3PO4 (2M) were added via syringe and the reaction mixture was heated at 100 °C for 48 h under a nitrogen atmosphere. The reaction mixture was filtered through a silica pad, eluting with EtOAc then washed with NaHCO3 and brine.
The combined organic extracts were dried over MgSO4 before concentration in vacuo. The resulting products were further purified by flash column chromatography.