A PGSE NMR approach to the characterization of single and multi-site halogen-bonded adducts in solution

Abstract

We demonstrate here that the Pulsed field Gradient Spin Echo (PGSE) NMR diffusion technique can be effectively used as a complementary tool for the characterization of mono- and multi-site intermolecular halogen bonding (XB) in solution. The main advantage of this technique is that it provides the possibility of unambiguously determining the stoichiometry of the supramolecular adduct, information that is particularly important when multi-site molecular systems are studied. As an example, PGSE NMR measurements in chloroform indicate that hexamethylenetetramine (HMTA), a potentially four-site XB acceptor, actually exploits only two sites for the interaction with the XB donor N-bromosuccinimide (NBS), leaving the other two nitrogen sites unoccupied. Charge displacement calculations suggest that this is due also to the anti-cooperativity of the XB interaction between HMTA and NBS.

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Introduction

Halogen bonding (XB),¹ i.e. the non-covalent interaction between a halogen atom (XB donor) and a Lewis base (XB acceptor), mostly reveals its potential in solid state chemistry, being nowadays a powerful tool for the engineering of advanced materials^2–4 and a relevant motif in the structure of biomolecules.⁵ XB has emerged also as an interesting topic for theoretical chemistry, which has tried to determine, not without controversy, the relative weights of charge transfer, electrostatic, dispersion, and polarization effects on XB.⁶ In the past few years, XB has started to find intriguing applications even in solution, mainly in catalysis⁷ and anion recognition.⁸ As a consequence, the characterization of the supramolecular structure of XB adducts in solution and the determination of the formation equilibrium constants have assumed a higher importance, also because the pattern of intermolecular interactions in solution could differ from that found in the solid state.

Recently, it has been suggested⁹ that halogen bonding is not the only interaction that XB donors and acceptors can establish in solution, even when no other obvious interactions are possible, leading to adducts with different geometries but same stoichiometry. We recently demonstrated that ¹⁹F, ¹H HOESY NMR, previously exploited with success to investigate ion pairing¹⁰ and frustrated Lewis pairs,¹¹ can be also exploited to disclose the intermolecular structure of XB adducts.¹² Furthermore, in combination with theoretical studies, it can be used to estimate the relative weights of XB and non-XB interactions.¹²

Concerning the equilibrium constants involved in the XB interactions, many useful titration techniques have been applied^13,14 and the choice of the best one (UV-Vis, IR, NMR…) depends on the nature of the system under investigation. In all cases, the presence of more interactions is a potential complication, because the effect of each interaction on the experimental observable is, in principle, of a different magnitude, and their disentanglement is not easy. An additional layer of complexity arises when multi-site acceptors and donors are taken into account. In this case, the exact nuclearity of the adduct should be known a priori, since the fitting equation depends on the stoichiometry of the adduct (except when the different aggregation steps are clearly consecutive and with very different affinities¹⁴). Information about the latter can be derived from the Job's plot, but the general applicability of this technique is limited¹⁵ and its coupling with other methodologies is always desirable.

Here, we propose the diffusion Pulsed field Gradient Spin Echo (PGSE)^16,17 NMR technique as a tool for the characterization of mono- and multi-site intermolecular halogen bonding systems, with the only requirement that NMR-active nuclei (preferably ¹H, ¹⁹F or ³¹P) are present on at least one, but preferably both, of the components. To the best of our knowledge, such a technique has been applied only in a few recent cases, to support the formation of strong halogen-bonded adducts and to study the counterion influence on the same adduct.^18,19

PGSE NMR allows information about the hydrodynamic volume (V_H) of molecular species in solution to be determined.¹⁷ In the case of an aggregation process, the measured V_H increases, allowing the estimation of the equilibrium constants (K_a) involved in the process.²⁰ Remarkably, in the case of 1 : 1 adducts, the K_a can be evaluated by one single experiment,²¹ making it a useful tool for preliminary measurements.

Furthermore, since PGSE NMR is based exclusively on the V_H, it takes into account all the possible aggregation processes, irrespectively from the supramolecular structure of the adduct. This offers the possibility to validate the data coming from titration techniques, where the effect of various interactions could be different on the chosen observable, with the general rule that K_a (PGSE) ≥ K_a (titration). In addition, PGSE NMR is very useful when investigating symmetric multi-site XB donors or acceptors, since it gives directly the average size of the adducts and allows the determination of the average number of units that are interacting.

To illustrate the potential of the PGSE approach, we considered here Lewis acids and bases shown in Scheme 1, which already proved to be XB acceptors/donors,²² having different XB strength and number of sites. In particular, 1,4-diazabicyclo[2.2.2]octane (DABCO) and hexamethylenetetramine (HMTA) are commonly used in the fabrication of crystalline materials assembled by XB.²³

Scheme 1 XB donors and acceptors considered in this work. In parenthesis, the respective values for the hydrodynamic volume of the single molecule (V⁰_H) are reported.

In both cases, the number of nitrogen atoms involved in XB interactions depends on the XB donor and the crystallization conditions. 2,4,6-Trimethylpyridine (Me₃Py) is rarely used because the resulting XB adduct is very weak, so weak that other minor interactions, as lone pair/π, cannot be neglected.¹² On the other hand, perfluorinated alkanes and benzenes (as perfluorohexyl-1-iodide, I1, pentafluoroiodobenzene, I2 and 2,4-diiodooctafluorobutane, I3) have always been used in XB studies,²⁴ whereas N-bromosuccinimide (NBS) only recently revealed its potential as XB donor.^22c

Results and discussion

The quantification of the hetero intermolecular aggregation by PGSE NMR asks for the preliminary evaluation of the hydrodynamic volume of the single molecule (V⁰_H) and their tendency to undergo self-aggregation.

For this reason, we initially performed PGSE NMR experiments on solutions of increasing concentration of the single components in toluene-d₈ or chloroform-d, obtaining concentration-independent (within the experimental error of ±10%) values of V⁰_H equal to 220, 168, 128, 137, 135, 132 and 189 ų for I1, I2, I3, NBS, Me₃Py, DABCO and HMTA, respectively (Table 1 and Scheme 1).

Table 1 Diffusion coefficients (D_t, 10⁻¹⁰ m² s⁻¹), hydrodynamic radii (r_H, Å) and hydrodynamic volumes (V_H, ų) of pure Me₃Py, DABCO, I1 and I2 measured in toluene-d₈ and I3, HMTA and NBS in chloroform-d at different concentrations (C, mM)

C	Dt	rH	VH
Me3Py
3.1	16.1	3.18	135
38.0	15.9	3.20	137
175	16.2	3.18	135
385	16.1	3.18	135
DABCO
46.0	16.9	3.17	133
262	17.2	3.14	130
I1
11.0	12.8	3.78	226
123	12.9	3.70	212
181	12.8	3.75	221
I2
17.4	15.3	3.37	160
471	14.5	3.47	175
I3
19.0	14.1	3.11	126
210.0	14.2	3.14	130
HMTA
19.0	12.0	3.54	187
110	12.2	3.58	192
NBS
5.4	14.3	3.20	137
61.0	14.3	3.20	137

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The hydrodynamic volume of any adduct can be calculated by the sum of the V⁰_H values of the constituents (eqn (1)), always under the spherical approximation.¹⁷

V^agg_H(nD, mA) = n × V⁰_H(D) + m × V⁰_H(A) (1)

Me₃Py/I1

As stated in the Introduction, substituted pyridines usually afford quite weak XB interactions. As a confirmation, for an equimolar mixture of Me₃Py and I1, the experimental hydrodynamic volumes of the two components [V_H(Me₃Py) and V_H(I1)] are practically identical to the corresponding values of V⁰_H (Table 2). For this reason, only when a large excess of one of the components is used the measured V_H of the other component is significantly altered (Table 2). In particular, I1 : Me₃Py molar ratios 1 : 3 or 1 : 14 are still not enough to have V_H(I1) markedly different from its V⁰_H, but using a molar ratio around to 1 : 200 leads to an increase of V_H(I1) from 220 to 340 ų [V^agg_H(Me₃Py, I1) = 355 ų]. Being Me₃Py in large excess, V_H(Me₃Py) is clearly close to its V⁰_H, since most of the molecules are not involved in the formation of aggregates. By applying eqn (S1) and (S2) (ESI†) to the experimental data with the lowest I1 : Me₃Py molar ratio (Table 2), a value of K_a = 1.6 ± 0.5 M⁻¹ is obtained.

Table 2 Diffusion coefficients (D_t, 10⁻¹⁰ m² s⁻¹) and hydrodynamic volumes (V_H, ų) of Me₃Py/I1 mixtures in toluene-d₈ at different concentrations (C, mM). In all the cases, C(I1) = 24 mM

C(Me3Py)	Dt(Me3Py)	Dt(I1)	VH(Me3Py)	VH(I1)
24.9	16.1	12.9	146	219
64.1	16.1	12.8	144	221
346	16.1	12.4	146	232
4910	15.7	10.3	152	340

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On the other hand, the ¹⁹F NMR titration method gives a value of K_a = 0.85 ± 0.01 M⁻¹ (Fig. S1, ESI†).²⁵ The titration allows to rapidly collect a large number of data, minimizing the experimental error. By the way, the formation constant obtained by diffusion measurements is double with respect to that obtained by the titration method, and this can be explained with the presence of two different 1 : 1 adducts, as already evidenced by HOESY results:¹² the observable of the titration (δ_F of the α fluorine atoms, –CF₂I) is mainly influenced by the XB interaction established between the nitrogen of Me₃Py and the iodine of I1, whereas the observable of the PGSE (V_H) is influenced by all the possible interactions, including electrostatic H⋯F ones.¹² Since the K_a estimated by the PGSE measurement is the sum of all the equilibrium constants active in solution, by coupling the two techniques we can conclude that the formation constant of non-XB adducts is approximately 0.75 M⁻¹.

Remarkably, also combining ¹⁹F, ¹H HOESY results with DFT calculations, the XB adducts resulted to be predominant over the non-XB ones (XB : non-XB = 78 : 22);¹² considering the approximations used in that paper, a reasonably good agreement is obtained.

Interestingly, in the solid state only the XB can be detected,²⁶ demonstrating that the supramolecular behavior of a pair in solution can differ from the structure of the same pair in the crystal.

DABCO/I1

In the case of multi-site XB acceptor, as DABCO is, the possibility of the 1 : 2 adduct must be taken into account. The symmetry of DABCO and the kinetic lability of XB in solution hinder the possibility to use Overhauser-based experiments to determine how many nitrogen atoms are interacting with the Lewis acid. Also in this case, the investigation of non-stoichiometric mixtures is very informative. In fact, studying the pair DABCO/I1 in the presence of an excess of DABCO makes the concentration of the 1 : 2 adduct negligible and the analysis of V_H(I1) trends is related only to the formation of the 1 : 1 adduct (K_a1). On the other side, information about K_a2 can be derived using an excess of I1.

Maintaining C(I1) constant at 20 mM (solvent: toluene-d₈) and increasing C(DABCO) from 3.6 to 108 mM, V_H(I1) increases from 239 to 338 ų, whereas V_H(DABCO) decreases from 221 to 162 ų. As stated before, the effect of aggregation is more visible on the least abundant species, consequently when C(DABCO) < C(I1), V_H(I1) is just slightly larger than V⁰_H(I1) and V_H(DABCO) is markedly larger than V⁰_H(DABCO). On the contrary, when C(DABCO) > C(I1), the situation is the opposite, with V_H(DABCO) similar to V⁰_H(DABCO) and V_H(I1) markedly higher than V⁰_H(I1). Indeed, when the concentration ratio I1 : DABCO is 20 : 108, V⁰_H(I1) approaches V^agg_H(DABCO, I1), which is 352 ų, evidencing an almost complete association of I1 under these conditions.

Applying eqn (S1) and (S2) (ESI†) to this single data, K_a1 was estimated to be 34 ± 10 M⁻¹, which corresponds to a free energy of association (ΔG_a1) of −2.1 kcal mol⁻¹. The ¹⁹F NMR titration gives K_a1 = 37.2 ± 0.4 M⁻¹ (Fig. S2, ESI†), in agreement within the experimental errors.²⁷ In line with these findings, ¹⁹F, ¹H HOESY NMR data demonstrated that non-XB interactions can be neglected for this particular pair.¹² Obviously, this does not mean that non-XB interactions are absent, but simply that their effects are completely hidden by the much more intense XB interaction, as in the PGSE as in the HOESY NMR experiments.

Successively, maintaining C(DABCO) at 7 mM and increasing C(I1) from 37 to 343 mM, V_H(DABCO) increases from 250 to 517 ų (Table 3). In the last case, the hydrodynamic volume is much higher than V⁰_H(DABCO), even higher than the volume of the 1 : 1 adduct (352 ų) and close to that of the 1 : 2 adduct [V^agg_H(DABCO, 2I1) = 572 ų].

Table 3 Diffusion coefficients (D_t, 10⁻¹⁰ m² s⁻¹) and hydrodynamic volumes (V_H, ų) of DABCO/I1 mixtures in toluene-d₈ at different concentrations (C, mM)

C(DABCO)	C(I1)	Dt(DABCO)	Dt(I1)	VH(DABCO)	VH(I1)
3.6	20.0	12.8	12.3	221	239
17.6	20.0	13.7	11.9	194	250
108	20.0	15.1	10.3	162	328
7.0	37.0	12.0	—	250	—
7.0	85.0	10.5	—	326	—
7.0	216	9.2	—	426	—
7.0	343	8.5	—	517	—

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The data of V_H(DABCO) as a function of C(I1) can be fitted considering two equilibria (Fig. 1 and eqn (S3) and (S4), ESI†),¹⁵ either imposing K_a1 = 34 M⁻¹, as determined previously, to find the best value of K_a2 or optimizing both K_a1 and K_a2. In the former case, K_a2 = 5 ± 1 M⁻¹ (ΔG_a2 = −0.9 kcal mol⁻¹); in the latter case, K_a1 = 17 ± 6 M⁻¹ and K_a2 = 7 ± 2 M⁻¹. The results of the two methodologies are qualitatively similar, even if the second one, having more degrees of freedom, better fits the experimental data (Fig. 1). In any case, K_a2 is lower than K_a1. This is likely due to the low entropy of the adduct formed by three molecules.

Fig. 1 Experimental hydrodynamic volume of DABCO (C = 7 mM) at different concentrations of I1. The two lines represent the best fits obtained keeping K_a1 constant (solid blue line) or not (dashed red line). See text for the details.

More importantly, the PGSE results offer an immediate and intuitive insight into the nuclearity of the adducts, at each concentration ratio (Fig. 1).

DABCO/I2

Three solutions of DABCO (8.8 mM) in toluene-d₈ with increasing concentrations of I2 (44, 177 and 403 mM) have been studied (Table 4). Under these experimental conditions, V_H(DABCO) spans from 194 to 352 ų, reaching a value that is in between V^agg_H(DABCO, I2) and V^agg_H(DABCO, 2I2). The fitting of the data, using V^agg_H(DABCO, I2) = 303 ų and V^agg_H(DABCO, 2I2) = 471 ų, leads to the values of 11.0 ± 0.2 and 2.1 ± 0.1 M⁻¹ for K_a1 and K_a2, respectively (ΔG_a1 = −1.5 kcal mol⁻¹; ΔG_a2 = −0.4 kcal mol⁻¹, Fig. S3, ESI†).

Table 4 Diffusion coefficients (D_t, 10⁻¹⁰ m² s⁻¹) and hydrodynamic volumes (V_H, ų) of DABCO/I2 mixtures in toluene-d₈ at different concentrations (C, mM)

C(DABCO)	C(I2)	Dt(DABCO)	VH(DABCO)
8.8	44.0	13.6	194
8.8	177	11.2	286
8.8	403	10.1	352

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HMTA/NBS

Crystallographic studies on the pairs HMTA/NIS (NIS = N-iodo-succinimide) and HMTA/NBS revealed many interesting properties of such systems.^22c For example, in the former case all the four basic sites of HMTA interact with a molecule of NIS, while in the latter case only two nitrogen atoms interact with a molecule of NBS. Unfortunately, the solubility of the pair HMTA/NIS is not enough to allow a PGSE NMR study, but the pair HMTA/NBS is soluble enough in chloroform-d, even if very large excesses of one component cannot be explored.

For HMTA/NBS, the calculated hydrodynamic volumes for the 1 : 1, 1 : 2, 1 : 3 and 1 : 4 adducts are 323, 457, 591 and 729 ų, respectively.

Using chloroform-d as solvent and keeping C(NBS) fixed at 3.9 mM, three solutions with C(HMTA) = 12.1, 50 and 179 mM have been analyzed. V_H(NBS) increases as C(HMTA) increases, going from 254 to 317 ų (Table 5), which is very close to V^agg_H(HMTA, NBS). Fitting the data, K_a1 results to be 161 ± 27 M⁻¹ (ESI†).

Table 5 Diffusion coefficients (D_t, 10⁻¹⁰ m² s⁻¹) and hydrodynamic volumes (V_H, ų) of HMTA/NBS mixtures in chloroform-d at different concentrations (C, mM)

C(HMTA)	C(NBS)	Dt(HMTA)	Dt(NBS)	VH(HMTA)	VH(NBS)
a Saturated solution.
12.1	3.9	11.5	10.0	194	254
50.0	3.9	11.9	8.36	166	291
179	3.9	12.0	8.57	166	317
2.1	4.3	10.4	12.8	217	150
2.1	38.5	7.71	12.8	392	144
2.1	56.0	7.62	13.7	408	130
2.1	93.0^a	7.45	13.7	438	131

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In a second set of experiments, to a solution of HMTA (C = 2.1 mM) in chloroform-d, NBS was added to reach C(NBS) = 4.3, 38.5, 56 and 93 mM (Table 5). As before, the hydrodynamic volume of the component in excess decreases as its concentration increases [V_H(NBS) goes from 150 to 131 ų], whereas the hydrodynamic volume of the other component (V_H(HMTA)) increases from 217 to 438 ų. Noteworthy, passing from C(NBS) = 56 to 93 mM, V_H(HMTA) increases of only 30 ų, which is within the experimental error of 10%. Unfortunately, a higher concentration of NBS is not possible because of the solubility limit of the mixture, but the final value of V_H(HMTA) is very close to V^agg_H(HMTA, 2NBS). Such a value is the average of all the volumes of the species present in solution, but considering also that the trend of V_H(HMTA) vs. C(NBS) shows a plateau in the correspondence of V^agg_H(HMTA, 2NBS) (Fig. 2), we can deduce that K_a3 and K_a4 are likely too small to be determined. Consequently, the experimental data can be fitted with the 1 : 2 model, in agreement with the crystal structure of this pair.^22c The absence of a plateau in this range of V_Hs (400–500 ų) would have been an indication for the existence of larger adducts, as 1 : 3 and 1 : 4.

Fig. 2 Experimental hydrodynamic volume of HMTA (C = 2.1 mM) at different concentrations of NBS. The two lines represent the best fits obtained keeping K_a1 constant (solid blue line) or not (dashed red line). See text for the details.

This reveals another great advantage of the diffusion NMR technique: for multi-site systems, the maximum stoichiometry is not a hypothesis, but can be derived from the trend of V_H with the concentration.

Fitting the experimental data with the 1 : 2 model and fixing K_a1 = 161, the best value of K_a2 is 44 ± 12 M⁻¹ (ΔG_a2 = −2.2 kcal mol⁻¹), whereas optimizing both the values the results are 90 ± 20 and 56 ± 8 M⁻¹ for K_a1 and K_a2, respectively (ΔG_a1 = −2.6 kcal mol⁻¹; ΔG_a2 = −2.4 kcal mol⁻¹). Also in this case, both methodologies give similar results and, again, K_a1 is larger than K_a2.

In order to understand better why the 1 : 3 adducts are not easily accessible in solution, DFT calculations have been performed on this system. Optimizing the structure of the 1 : 1, 1 : 2 and 1 : 3 adducts (level of theory M06-2X/def2-TZVP, as suggested by a recent, dedicated benchmark,²⁸ see details in the Computational details), the N⋯Br distances results to be 2.533, 2.585 and 2.628 Å, respectively. The progressive lengthening of the N⋯Br distance already indicates that the interaction is weaker as the number of NBS molecules around the central HMTA increases.

Other information can be obtained with the Charge Displacement (CD) method,²⁹ which already proved to be useful for the characterization of coordinative³⁰ and non-covalent bonds,^11,31 including halogen bonding.³² In particular, CD results demonstrated to be correlated linearly to the formation constants of chalcogen-bonded adducts.³³

In the case of 1 : 1 adducts, the difference of electron density (Δρ) between the adduct and the separate fragments (HMTA and NBS) is shown in Fig. 3a. It clearly shows that the nitrogen of HMTA is in a region of electron depletion, whereas a region of electron accumulation is present between the nitrogen and the bromine. As expected, a charge transfer between the two molecules exists, going from the nitrogen to the bromine. The latter shows a polarization pattern (depletion in the direction of HMTA, accumulation on the other side) and a remarkable region of electron accumulation is on the nitrogen of the NBS. The backbone of the NBS show a small charge accumulation, whereas the nitrogen atoms of the HMTA not involved in the XB show a small charge depletion, indication that the charge flux involve the entire system.

Fig. 3 (a) 3D contour map of the change of electronic density upon formation of the adduct HMTA/NBS (1 : 1). Blue (red) isosurfaces identify regions in which the electron density increases (decreases). Density value at the isosurfaces: ±0.002 au. (b) Charge displacement functions for HMTA/NBS adducts with different stoichiometry. The black dots represent the z coordinate (or the range of coordinates) of the atoms. The light blue vertical band identifies the range of the inter-fragment boundaries.

Integrating Δρ along the axis containing the nitrogen of HMTA and the bromine of NBS (z), the charge transfer (CT) can be quantified as 0.130 e (Fig. 3b).

Applying the same method to the 1 : 2 and 1 : 3 adducts, the corresponding Δρ maps reveal a qualitative similarity with the one calculated for the 1 : 1 adduct (Fig. 4a and S5, ESI†). This is reasonable, since in all the cases the interaction is similar. From the quantitative point of view, the integration of the Δρ functions leads to CT values of 0.110 and 0.095 for the 1 : 2 and 1 : 3 adduct, respectively. The attenuation of the CT as the number of NBS molecules around the central HMTA increases gives a framework to explain the attenuation of the formation constants: the four nitrogen atoms on the HMTA are not mutually independent, and the donation of electronic density from one nitrogen atom to a Lewis acid makes the donation properties of the non-involved nitrogen atoms lower.

Fig. 4 (a) 3D contour map of the change of electronic density upon formation of the adduct HMTA/NBS (1 : 2). Blue (red) isosurfaces identify regions in which the electron density increases (decreases). Density value at the isosurfaces: ±0.00025 au. (b) Charge displacement functions for HMTA/NBS (1 : 2), integrated along the N2⋯Br2 axis. The black dots represent the z coordinate of the atoms. The light blue vertical band identifies the range of the inter-fragment boundaries.

This effect can be quantified applying the CD on a different axis.³⁴ If we consider the adduct between HMTA and two NBS moieties, we obviously have two interactions between two different nitrogen atoms of the HMTA and the two molecules of NBS. They can be labeled N1⋯NBS1 and N2⋯NBS2. Taking as fragments NBS1 and HMTA/NBS2 and integrating Δρ along the axis containing N2 and the bromine of NBS2 (Fig. 4), the effect of the establishment of N1⋯NBS1 on N2⋯NBS2 can be evaluated. In this case, the analysis of the Δρ shows that, upon the formation of N1⋯NBS1, the nitrogen of NBS2 is located in a region of electron density depletion. This indicates a charge transfer from NBS2 to HMTA, leading to a XB weakening. The integration along the axis containing N2 and Br2 confirms the direction of the flux and leads to a weakening of 0.011 e (Fig. 4b).

The electronic energies ΔE of the 1 : 1, 1 : 2 and 1 : 3 adducts are −11.6, −20.5 and −28.0 kcal mol⁻¹ (ESI†) with respect to the isolated components (see Table S1, ESI†). If we calculate ΔE/n, where n is the number of NBS involved in the adduct, it results −11.6, −10.2 and −9.3 kcal mol⁻¹, respectively, again indicating that the interactions become weaker for larger aggregates (anti-cooperativity), in agreement with CD results. Therefore, the formation of adducts with higher stoichiometric ratios, as 1 : 3 and 1 : 4, is made difficult not only for obvious entropic reasons (each additional moiety loses its translational degree of freedom, making the ΔG more positive), but also for enthalpic ones (the charge transfer becomes weaker as the number of units increases). Interestingly, in other cases the XB resulted to be cooperative in nature.³⁵

DABCO/I3

A very intriguing combination is when both the acceptor and the donor are multi-site, and, in principle, any n : m adduct can exist. The pair DABCO/I3, for example, is able to form infinite chains in the solid state.³⁶ Also in this case the pair presents a low solubility, limiting the possibility to use non-stoichiometric solutions. Anyway, at least three different situations can be explored: an excess of DABCO, an excess of I3 and a substantial equivalence between the concentrations of the two components. In all the cases the solution is saturated, but both V_H(DABCO) and V_H(I3) are always much lower than 260 ų, which is the value of V^agg_H(DABCO, I3) (Table 6). Consequently, even if the presence of higher adducts cannot be excluded, their concentration should be very low in all cases.

Table 6 Diffusion coefficients (D_t, 10⁻¹⁰ m² s⁻¹) and hydrodynamic volumes (V_H, ų) of DABCO/I3 mixtures in chloroform-d at different concentrations (C, mM)

C(DABCO)	C(I3)	Dt(DABCO)	Dt(I3)	VH(DABCO)	VH(I3)
a Saturated solution.
85.8^a	7.8	13.0	10.8	123	175
29^a	21	12.6	11.8	159	180
16.7^a	58	12.2	13.5	178	146

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Applying eqn (S1) and (S2) (ESI†) to the experiments where one component is in excess [C(DABCO) = 85.8 and C(I3) = 58 mM, Table 6], K_a1 results to be 6 ± 2 and 10 ± 3 M⁻¹, respectively (ΔG_a1 = −1.2 kcal mol⁻¹).

Conclusions

Diffusion NMR demonstrated to afford valuable information on the stoichiometry and the strength of the interactions of halogen-bonded adducts.

In particular, for the pair Me₃Py/I1 the complementarity of the NMR titration and the PGSE method allowed the estimation of the formation constant of the adducts held together by interactions different from the XB (non-XB).

In the case of the ditopic halogen acceptor DABCO, both 1 : 1 and 1 : 2 adducts have been directly detected, either using aliphatic and aromatic perfluorinated XB donors (I1 and I2). The corresponding formation constants have been evaluated and the formation of the 1 : 2 adduct showed an equilibrium constant considerably lower than that of the 1 : 1 adduct. For this system, the formation constant of the 1 : 1 adduct evaluated by NMR titration is in agreement with that measured by PGSE, indication that non-XB adducts are negligible.

The case of HMTA is even more interesting, since it bears four symmetric nitrogen atoms and all of them potentially could establish an interaction with NBS. PGSE NMR data unequivocally demonstrate that only two nitrogen atoms are involved in the interaction with NBS and, again, the formation constant of the 1 : 2 adduct resulted lower than that of the 1 : 1 adduct. DFT and charge displacement investigations demonstrated that each molecule of NBS that binds on a nitrogen atom of the HMTA reduces the electron-donating properties of the other nitrogen atoms (anti-cooperativity).

Finally, PGSE NMR data demonstrated also that the interaction between DABCO and I3 is too weak in chloroform-d to produce aggregates larger than the 1 : 1 adduct, despite both the XB acceptor and donor possess two binding sites and despite the existence in the solid state of infinite chains.

In conclusion, PGSE NMR can be surely considered a powerful technique, which gives information that could be a complement for the titration methods routinely used up to now. For this reason, an integrated multi-technique approach, which include titrations, diffusion and Overhauser NMR techniques (but also DFT calculations, when needed) is highly desirable, for a complete characterization of XB systems in solution.

Experimental section

All solvents and chemicals were purchased from Sigma-Aldrich and Cortecnet at the highest purity available and used as received. 1D and 2D NMR spectra were measured at 298 K on a Bruker DRX Avance 400 spectrometer equipped with a BBFO probe, on a Bruker Avance III HD 400 spectrometer equipped with a smartprobe. Referencing is relative to residual of undeuterated solvents (¹H) and CCl₃F (¹⁹F).

PGSE NMR measurements

¹H and ¹⁹F PGSE NMR measurements were performed by using the double-stimulated echo sequence with longitudinal eddy current delay³⁷ at 298 K without spinning. The dependence of the resonance intensity (I) on a constant waiting time and on a varied gradient strength G is described by the following equation:where I is the intensity of the observed spin echo, I₀ the intensity of the spin echo in the absence of gradient, D_t the self-diffusion coefficient, Δ the delay between the midpoints of the gradients, δ the length of the gradient pulse, and γ the magnetogyric ratio. The shape of the gradients was rectangular, their length δ was 4–5 ms, and their strength G was varied during the experiments. All spectra were acquired for 32k points and a spectral width of 5000 (¹H) and 18 000 (¹⁹F) and processed with a line broadening of 1.0. The semi-logarithmic plots of ln (I/I₀) versus G² were fitted by using a standard linear regression algorithm, and a correlation factor better than 0.99 was always obtained. Different values of Δ, G, and number of transients were used for different samples.

The self-diffusion coefficient D_t, which is directly proportional to the slope m of the regression line obtained by plotting ln (I/I₀) versus G², was estimated by evaluating the proportionality constant for a sample of HDO (5%) in D₂O [known diffusion coefficients in the range 274–318 K (ref. 38)] under the exact same conditions as the sample of interest. The solvent or TMS was taken as internal standard.

Computational details

All the optimizations and thermodynamic calculations were performed using the Gaussian 09 program,³⁹ using density functional theory employing hybrid meta-generalized gradient approximation functional M06-2X⁴⁰ and the triple-ζ def2-TZVP basis set. The solvent and its polarity has been modeled through the PCM procedure (chloroform).⁴¹ All the optimized adducts show only positive vibrations, except HMTA–3NBS, which showed three small uneliminable negative frequencies that could not be avoided during optimization. The negative vibrational modes were checked to make sure that they did not correspond to any motion along the halogen bond axes (bond formation or breaking). Rather, they refer to the rotation/vibration of the NBSs around the halogen bond axis.

All the charge displacement²⁹ calculations were carried out using density functional theory employing the same level of calculation used for optimizations. Such an approach relies on the integration along a given direction z (eqn (3)) of the difference of electronic density [Δρ(x, y, z)] between the adduct and its non-interacting fragments, frozen in the same positions they occupy in the adduct.

The value of Δq(z′) defines the amount of the electronic charge that, upon formation of the adduct, has moved across a plane perpendicular to the axis through the coordinate z′. At the boundary between the fragments (the point on the z axis at which equal-valued isodensity surfaces of the isolated fragments are tangent) the value of Δq is represented by CT.

The electronic density matrices have been manipulated through the suite of tools “Cubes”.⁴²

Acknowledgements

Instituto de Física da Universidade Federal da Bahia is acknowledged for computational resources. C. Z. thanks the University of Perugia (Fondo Ricerca di Base 2014 D. D. n. 170, 23/12/2014) for financial support.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra17455h

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