*3.6. Cooperativity*

Hydrogen bonded systems with two hydrogen bond donors to the same acceptor e.g., 1,8-dihydroxyanthraquinones or the monoanion of 1,8,9-trihydroxyanthracene [42] can give rise to cooperativity. A second situation seen in Figure 12 is the trimers of phosphoric, phospinic acids and a third situation seen is the dimers of carboxylic acids (for carboxylic acids encapsulated see Section 4). For the monoanion of 1,8,9-trihydroxyanthracene the primary isotope effects were −0.2 ppm in both DMSO-d6 and in 90%H2O/10% DMSOd6. The degree of deuteration was 50% [42]. The finding of the same effect in those two solvents again showed that the hydrogen bond was strong enough not to be perturbed by the solvent. In the cyclic trimers both cooperative and anti-cooperative effects may be found. In the cooperative case, the X-D bond is weakened and the corresponding XdH bond is strengthened. The opposite is true for the anti-cooperative case [31]. In the cyclic trimers of phosphoric acids, cooperative effects are found [31]. In the case of hetero trimers of phosphinc and phosphoric acids, anti-cooperative effects are found probably due to steric factors [32]. For the trimers of dimethylarsinic acid, cooperativity is found [33].

### **4. Tautomerism**

The use of isotope effects to investigate tautomerism has been treated in several reviews. [3–5] A key point is the observation in non-symmetrical systems of isotope effects on chemical shifts that they consist of both an intrinsic and an equilibrium contribution. A classic case is that of β-diketones, illustrated in Figure 15.

**Figure 15.** Tautomeric equilibrium illustrated by a β-diketone. The mole fraction of the B tautomer is x.

The equilibrium isotope effects can be formulated as seen in Equations (1)–(3).

$$\mathbf{x}^{\mathrm{n}} \Delta \mathbf{X}(\mathbf{D})\_{\mathrm{int}} = (\mathbf{1} - \mathbf{x})^{\mathrm{n}} \Delta \mathbf{X}(\mathbf{D})\_{\mathrm{A}} + \mathbf{x}^{\mathrm{n}} \mathbf{X}(\mathbf{D})\_{\mathrm{B}} \tag{1}$$

$$\text{F}^{\text{in}}\Delta\text{X}(\text{D})\_{\text{eq}} = (\delta\text{X}\_{\text{B}} - \delta\text{X}\_{\text{A}})\,\Delta\text{x} \tag{2}$$

$${}^{\rm n}\Delta\mathcal{X}(\mathcal{D})\_{\rm OBS} = {}^{\rm n}\Delta\mathcal{X}(\mathcal{D})\_{\rm int} + {}^{\rm n}\Delta\mathcal{X}(\mathcal{D})\_{\rm eq} \tag{3}$$

X could be 13C, 1H, 15N, 19F, etc. and x is the mole fraction of B. Δx is the change in the equilibrium upon deuteration.

This way, isotope effects on chemical shifts become a useful tool to establish whether or not tautomerism is present in cases in which this is not obvious. An example is 1,1 ,1"- (2,4,6-trihydroxybenzene-1,3,5-triyl)triethanone (1,3,5-trihydroxy-2,4,6-triacetylbenzene). This was in CDCl3 shown not to be tautomeric based on deuterium isotope effects on 13C chemical shifts and DFT calculation of those [43]. This was further supported by low temperature studies showing that both the isotope effect and the OH chemical shifts were unchanged by lowering the temperature [44]. However, in ethanol this molecule was claimed to be tautomeric based on calculations [45]. This claim was investigated by the measurement of deuterium isotope effects on 13C chemical shifts in a mixture of CDCl3 and CH3OH and CD3OD, the latter in varying amounts. An extrapolation to 100% deuterium gives the isotope effects. A comparison of these with those in CDCl3 are shown in Figure 16. No real differences are found showing that no tautomerism takes place in methanol and by analogy not in ethanol.

**Figure 16.** Deuterium isotope effects in CDCl3 + CD3OD and in brackets in CDCl3. The values are the sums of deuteration at all OH sites. Reprinted with permission from Ref. [44]. Copyright 2014 Elsevier.

Mannich bases are compounds that may or may not be tautomeric depending on the substituents at the aromatic ring. This is demonstrated in derivatives of 2-hydroxy-3,4,5,6 tetrachlorobenzene (Figure 17) as well as other derivatives. Temperature may also play a role [46,47].

Other tautomeric examples based on usnic acid are seen below. Usnic acid has important biological applications. However, it is rather insoluble. An attempt to make it more soluble is to add a pegylated side-chain as shown in Figure 18. Measurements of deuterium isotope effects on 13C chemical shifts showed that the equilibrium of the biologically important C ring is unperturbed [48].

**Figure 17.** Tautomeric equilibrium of the Mannich base based on 2-hydroxy-3,4,5,6-tetrachlorobenzene.

**Figure 18.** Deuterium isotope effects on 13C chemical shifts of a pegylated usnic acid. From Ref. [48].

Another derivative is the Mannich base derived from usnic acid as shown in Figure 19 [49].

Deuterium isotope effects on 13C chemical shifts in piroxicam showed that the addition of water shifted the equilibrium towards the zwitterionic form (Figure 20) [50].

**Figure 20.** Zwitter ionic form of piroxicam.

Tautomerism may also occur in the solid state. An example is found in pyridoyl benzoyl β-diketones (Figure 21) [51]. In the liquid state, the two-bond deuterium isotope effects at C-1 and C-3 are slightly different reflecting that the equilibrium constant is slightly different from 1. In the solid state, the picture is very different (Figure 21). For **2** and **3** the effects are a clear sign of an equilibrium. However, for **1** a change in the crystal structure as a consequence of deuteration is suggested [51].

**Figure 21.** Deuterium isotope effects on 13C chemical shifts in the liquid and solid state. Only one tautomer is shown (see Figure 15). Numbers in brackets are from the solid state. Deuteration may also take place at C-2. Those isotope effects are small and do not tell us about the equilibrium and are left out for clarity. See Ref. [51].

Changes in the crystal structure and the hydrogen bond structure is also discussed by Shi et al [52]. Ip et al. found in the triclinic phase a <sup>1</sup>ΔN(D) of −2.7\* ppm at 297 K. They concluded that deuteration of the XH proton of the complex between pentachlorophenol and 4-methylpyridine led a monoclinic structure with a weaker hydrogen bond than in the triclinic form [53].

Protonated proton sponges show both strong hydrogen bonds and tautomerism. The effect of the counter ion has been studied. In Figure 22, the counter ion is a proton-like sponge [54]. The effects in the proton sponge are similar to previous examples.

**Figure 22.** Deuterium isotope effects on 13C chemical shifts of a proton sponge. Reprinted with permission from Ref. [54]. Copyright 2013 Wiley.

One of the questions in symmetric tautomeric systems with strong intramolecular hydrogen bonds is the position of the chelate proton. Two scenarios have been suggested: the chelate proton is jumping from one acceptor to the other or the proton is positioned at the center of the hydrogen bond. The difference being in a double-well potential or a single-well potential. For an early review see [55]. Based on calculations, Bogle and Singleton [56] proposed based that a coupling between a desymmetrizing mode and an anharmonic isotope-dependent mode could lead to isotope effects of the size found in, e.g., the phthalate monoanion (Figure 23A). In response to that, Perrin et al. studied 18O-labelled difluoromaleimide [57] (Figure 23B). 19F is a very chemical shift sensitive nucleus. It is thus very appropriate for the detection of small variations. The compound showed different chemical shifts for the two fluorines. This difference was related to a perturbation of the acidity of the carboxylic acid of the carboxylic acid due to the 18O substitution and not a simple isotope effect, as the dianion did not show chemical shift differences.

**Figure 23.** 18O-labelled dicarboxylic acids. (**A**). phthalate monoanion; (**B**). difluoromaleimide; (**C**). cyclohexenedicarboxylic acid.

More recently, Perrin and Burke [58] found a temperature dependence of the C=O chemical shift of the 18O-labelled carboxylic acid of 18O-labelled cyclohexenedicarboxylic acid (Figure 23C). Based on this finding, they suggested an equilibrium.

In response to the paper by Bogle and Singleton, Perrin et al. [59] have studied 18Olabelled 1,2-cyclohexendicarboxylate monoanion (Figure 23C) as well as the difluoromaleate anion (Figure 23B). In both cases they found a larger isotope effect at a lower temperature, which is against a desymmetrization, as this should become smaller at a lower temperature.

Limbach et al. [60] studied deuterated maleate and phthalate anions (Figure 23A) as well as a series of homoconjugated anions of carboxylic acid (deuteration at the OH proton). The primary isotope effects are plotted vs. the two-bond deuterium isotope effects on 13C chemical shifts as seen in Figure 24. One can of course wonder why a distinction between a single-well and a double-well potential is so important, but this becomes clear when making plots such as the one in Figure 24. For maleate and phthalate, a single-well potential is assumed. Analysis of the data also allowed the construction of a rather complex correlation between <sup>2</sup>ΔC(OD), q1 and three fitting parameters.

**Figure 24.** Plot of two-bond deuterium isotope effects on 13C chemical shifts of a series of primarily homoconjugated anions of carboxylic acids vs. q1. Data points for **11** and **12** are heteroconjugated dimers. q1 = 0.5(rOH − rHO). Reprinted with permission from Ref. [60]. Copyright 2012 American Chemical Society.

Succinic acid, *meso* and *rac*-succinic acid and methyl succinic acid with tetraalkylammonium ions as counter ions measured in CDF3/CDF2Cl at 300 to 120K showed double-well potential-based on isotope effects [61]. A plot of primary isotope effects vs. OH chemical shifts showed a large spread [62].

Carboxylic acid dimers have been studied trapped in a capsule. In case of partial deuteration, the encapsulation leads to slow exchange. The deuterium isotope effects on the OH chemical shift varies from 0.14 to 0.29\* ppm for encapsulated acid vs. ~0.1\* ppm for non-encapsulated acids. This can be related to the pressure of the encapsulation leading to a shorter O ... O distance and a stronger hydrogen bond. Isotope effects correlate with OH chemical shifts [63].

In Figure 25, a plot of primary deuterium isotope effects vs. OH chemical shifts for a series of primarily salicylates is shown [42]. This plot is very similar to plots in Refs. [3,62]. The change in the sign of the primary isotope effect was explained by Gunnarson et al. [40] finding a positive effect for weak double-well potentials and an increasing value as the anharmonicity increases. For those cases in which a single-well potential is the case, a negative value is found. As seen in Figure 25, the primary isotope effect for each compound

is within 0.1 ppm in the different solvents showing that a solvent including water plays no special role for these hydrogen bonds.
