Association Equilibria of Organo-Phosphoric Acids with Imines from a Combined Dielectric and Nuclear Magnetic Resonance Spectroscopy Approach

Aggregates formed between organo-phosphoric acids and imine bases in aprotic solvents are the reactive intermediates in Brønsted acid organo-catalysis. Due to the strong hydrogen-bonding interaction of the acids in solution, multiple homo- and heteroaggregates are formed with profound effects on catalytic activity. Yet, due to the similar binding motifs—hydrogen-bonds—it is challenging to experimentally quantify the abundance of these aggregates in solution. Here we demonstrate that a combination of nuclear magnetic resonance (NMR) and dielectric relaxation spectroscopy (DRS) allows for accurate speciation of these aggregates in solution. We show that only by using the observables of both experiments heteroaggregates can be discriminated with simultaneously taking homoaggregation into account. Comparison of the association of diphenyl phosphoric acid and quinaldine or phenylquinaline in chloroform, dichloromethane, or tetrahydrofuran suggests that the basicity of the base largely determines the association of one acid and one base molecule to form an ion-pair. We find the ion-pair formation constants to be highest in chloroform, slightly lower in dichloromethane and lowest in tetrahydrofuran, which indicates that the hydrogen-bonding ability of the solvent also alters ion-pairing equilibria. We find evidence for the formation of multimers, consisting of one imine base and multiple diphenyl phosphoric acid molecules for both bases in all three solvents. This subsequent association of an acid to an ion-pair is however little affected by the nature of the base or the solvent. As such our findings provide routes to enhance the overall fraction of these multimers in solution, which have been reported to open new catalytic pathways.


Chemical shifts of the proton H3 S2
Modelling only the NMR chemical shifts S2

Analysis of the dielectric spectra S4
Combined DRS and NMR fit S5

Supporting References S9
S2 Chemical shifts of the proton H3 As described in the main text, we use the chemical shift of the residual solvent protons for referencing the NMR spectra. These shifts of the solvents may however also be affected by the addition of DPP. In Figure S1 we show the chemical shift of H3 of Qu or PhQu as a function of cDPP, which iswithin experimental errorconstant at cDPP ≥ 0.1 mol L -1 . This insensitivity of δH3 to a large excess of DPP suggests that also the protons of the solvent are rather insensitive to the added DPP.

Modelling only the NMR chemical shifts
As described in the main text, we test modelling of the association equilibria based on K1 and K2 (eqs. 2-4 of the main manuscript), or based on K'1 and K'2 (see main text). This is achieved by optimizing the sum of the squared deviations, NMR : where NMR is the number of data points. NMR , are the errors in the experimentally determined chemical shifts, exp . fit corresponds to the fit according to eq 2 of the main manuscript. NMR is optimized using, Qu , IP , , 1 , and 2 (or ′ 1 , and ′ 2 ) as adjustable parameters. Yet, comparing the model taking DPP2 dimerization into account ( 1 and 2 ) to the model neglecting dimerization ( ′ 1 and ′ 2 ) provides no evidence for clearly lower NMR values for one of the two models ( Figure S2).
The insensitivity of the fit quality to the association model can be explained by correlation of the adjustable parameters. As described in the main manuscript, variation of the association constant 1 can bepredominantlycompensated by a variation of the chemical shift of the ion pair, IP , when fitting eq 2 (see main manuscript) to the experimentally determined chemical shifts of Qu's protons. This is illustrated in Figure S3, where we show the variation of IP when fitting eq 4 to the data for Qu in CDCl3 for different values of 1 .

Analysis of the dielectric spectra
In order to quantify the concentration of ion-pairs and multimers in solution, we analyse the dielectric spectra of the imine -DPP mixtures. Therefore, we fit a relaxation model to the experimental spectra. In line with our previous study, we find that a combination of three Debye type equations 1 can describe the experimental spectra (see also Figure 2 of the main manuscript). In this model the relaxation of the multimers (M), ion-pairs (IPs), and the solvent (solv) is each modelled with a separate Debye relaxation. Each relaxation is characterized by its relaxation strength ( ) and relaxation time ( ). Using this model, we assume uncorrelated dipolar relaxation of the different molecules and/or molecular aggregates. All polarizations at frequencies ( ) higher than the experimentally covered frequency range are modelled by the limiting permittivity at infinite frequencies, ∞ . Ohmic losses due to translational polarization are taken into account by the last term of eq S1, with the d.c. conductivity assumed to be real and independent of frequency. 0 is the vacuum permittivity:

Given that all imine bases form either ion-pairs or multimers ( Qu ≈ [IP] + [M])
, which can be justified for an excess of DPP, IP,M is obtained from the analytical concentration of base and from the combined relaxation strength IP,M = IP + M using eq S3. Here, we use the spectra with a five-fold excess of DPP to determine the dipole (see Table S1). These values allow obtaining the equilibrium concentrations [IP] and [M] from the experimental IP and M values (eq S3), respectively, at all three studied concentrations of each measurement series. Combined DRS and NMR fit