Introduction

To gain a better understanding of the reaction pathways available to type B mesoionic tetrazoles, we have undertaken an MP2 ab initio study of the energy barriers to ring opening and recyclisation. We have previously studied the relative energies of ten type B mesoionic rings 1 and their valence tautomers 2. The stability of the ring increases with increasing strength of the single bond W-W (S–S > RN-NR > O–O) and with aza substitution (X = N) [1].

figure a

The earliest report of an example of this class of heterocycle was the preparation of dehydrodithizone 3a by Fischer and Bestorn (1882) [2]. A preparation of the exocyclic oxygen analogue 3b was first reported by Bamberger (1898) [3, 4]. Other 1,2-diphenyl analogues are known. The exocyclic imine derivative 3c was described by Bamberger et al. [5] in 1926 but, as with derivatives 3a,b, only later was the mesoionic structure recognised [6]. The carbon analogue 3d was described by Neugebauer and Fischer (1980) but formulated as the tautomer 4d [7]. Based on spectral data (λmax 425) and the relative stability of closely related mesoionic tetrazoles, the open-chain structure 4d is only a transient intermediate in the formation of the mesoionic derivative 3d. Araki et al. in an NMR study have shown that the nitrile analogue 3e (λmax 468) is strongly favoured over the acyclic tautomer 4e [8].

figure b

Much of the chemistry of the mesoionic tetrazole derivatives 3a, c, d can be rationalised in terms of initial ring opening to the corresponding tautomers 4a, c, d. Dehydrothizone 3a is thermally transformed to the benzothiadiazin isomer 7a [9], which is almost certainly formed by recyclisation of a rotamer 5a to the intermediate 6a followed by proton transfer (Scheme 1). In a separate series of studies, Boyd et al. have provided evidence that the tautomer 5a can be trapped by 1,4-cycloaddition across the diazothione fragment [10,11,12].

Scheme 1
scheme 1

The mode of recyclisation of the acyclic valence tautomers 5

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In a re-examination of the work of Bamberger et al. [5], the derivative 3c has been shown to thermally rearrange to the N-oxide 9a, which is rationalised by recyclisation of the transient tautomer 8a (Scheme 2) [13, 14]. A similar mechanism accounts for the triazole 10 accompanying formation of the tetrazole 3d [7]. The mode of deoxygenation of the N-oxide precursor 9b is not clear.

Scheme 2
scheme 2

The alternative mode of recyclisation of the nitroso valence tautomers 8

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Although the tetrazolium-4-olate 3b has been known for over 120 years, surprisingly, its chemistry is limited to salt formation [15, 16]. In contrast to its close analogue 3a, there is no experimental evidence of valence tautomerism (3 ⇌ 4). We now report a study of the energy barriers associated with reaction pathways available to the mesoionic tetrazole derivatives 3a-d.

Results and discussion

Figure 1 shows the generalised energy profile for the ring opening of type B mesoionic rings 3 and recyclisation to the bicyclic products 7. Energy values (Hartrees) and energy differences (kcal mol−1) for the derivatives 3–7 (Y = S, O, N.NO, CH.NO) and transition states T1 and T2 are given in Table 1.

Fig. 1
figure 1

Generalised energy profile for the conversion of the mesoionic tetrazoles 3 to the products 7

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Table 1 Gas phase MP2 calculated energy values (G) and energy differences (ΔG) for the structures shown in Fig. 1
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Gas phase MP2 calculations

The calculated activation energies ΔG3T1 for ring opening via the transition state T1 (Table 1, Entries 1–4) are all in the range 26–31 kcal mol−1. Since there is strong experimental evidence that the derivatives 3a, c, d do undergo thermal valence tautomerism in solution (3 ⇌ 4), it is unlikely that the oxygen analogue 3b will not undergo ring opening under similar conditions. As previously reported [1], the energy differences between the valence tautomers 3a, b, c and 4a, b, c (ΔG34) are in the range 16–18 kcal mol−1. Interestingly, the ΔG34 value for the exocyclic carbon analogue 3d (10.29 kcal mol−1) is much less. We attribute this to the lower electronegativity of carbon providing less stabilisation of the exocyclic negative charge in the mesoionic structure 3d. As might be expected, this also lowers the calculated activation energy ΔG3T1 (26.18 kcal mol−1).

To undergo an electrocyclic ring closure to give the intermediates 6, the valence tautomers 4 must equilibrate with a higher energy rotamer 5. The energy differences ΔGD1 are in the range 3.5–7.3 kcal mol−1. A particularly significant difference between the sulphur and oxygen derivatives is the activation energy for electrocyclic ring closure (ΔG5T2). The sulphur tautomer 5a, known to lead to the isolated product 7a, has an activation energy ΔG5T2 of 20.74 kcal mol−1 (Table 1). In contrast, the oxygen analogue 5b has a significantly higher ΔG5T2 value of 31.99 kcal mol−1. Like the transition state, the oxygen intermediate 6b is also correspondingly higher in energy relative to the precursor 5b than the corresponding sulphur intermediate 6a. This is reflected in the reverse activation energies ΔG6T2 (Table 1). These differences in the thermodynamics of the ring closures 5a, b to 6a, b have the consequence that the oxygen intermediate 6b is 43.47 kcal mol−1 (ΔG36) higher in energy than the starting material 3b whereas the sulphur intermediate 6a is only 26.35 kcal mol−1 (ΔG36) higher in energy. Since the energy of prototropic transfer (6 → 7) is almost the same for both species (ΔG67: 6a 27.35 and 6b 26.62 kcal mol−1), it follows that the overall reaction of the sulphur derivative (3a → 7a) is calculated to be weakly exothermic (ΔGR1 −1.00 kcal mol−1) whereas the corresponding reaction for oxygen (3b → 7b) is calculated to be considerably endothermic. Formation of the product 7b is therefore calculated to be highly unfavourable. This difference arises entirely from differences in the energies of the transitions states T2 and the resulting intermediates 6. For cyclisation of the oxygen analogue 5b, the activation energy for formation of the transition state (ΔG5T2) is much higher (≈ 11 kcal mol−1 more than for 5a), and the resulting intermediate 6b, relative to 5b, is also correspondingly higher in energy (≈ 16 kcal mol−1 more than for 6a). This detracts from the overall energy of reaction (ΔGR1).

The cyclisations of the nitrogen and carbon species 5c, d merit comment although these derivatives have an alternative, more favourable, mode of cyclisation (Scheme 2). The cyclisation of the imine 5c is a little less favourable than for the sulphur species 5a. The activation energy is higher (ΔG5T2 25.89 kcal mol−1) but overall, the transformation 3c → 7c is exothermic (ΔGR1 -9.06 kcal mol−1). For the carbon analogue 5d, the activation energy is highest (ΔG5T2 35.15 kcal mol−1), but much of this is regained on formation of 6d, and the tautomerism 6d → 7d is particularly favourable. Overall, the transformation 3d → 7d is calculated to be highly exothermic (ΔGR1 −18.34 kcal mol−1); a contribution to this overall energy gain is the lower stabilisation (≈7 kcal mol−1) of the polar precursor 3d by carbon, as discussed above.

Figure 2 shows the generalised energy profile for the alternative ring-opening/ring-closure reactions of the mesoionic derivatives 3c (Z = N) and 3d (Z = CH). The initial valence tautomerism (3 ⇌ 4) is identical to that in Fig. 1. The rotamers 8 then recyclise, employing the nitroso functions, to give the N-oxide products 9 via transition states T3. In both cases, the calculated activation energies (ΔG8T3) are low (12–13 kcal mol−1), and the overall reactions (ΔGR2) are exothermic (-13.66 and −22.83 kcal mol−1 respectively) (Table 2). As noted previously, the reaction of the carbon analogue 3d is more exothermic, and this is attributable to the lower stabilisation of the mesoionic precursor 3d by the exocyclic carbon atom.

Fig. 2
figure 2

Generalised energy profile for the conversion of the mesoionic tetrazoles 3c, d to the N-oxides 9c, d

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Table 2 MP2 calculated energy values (G) and energy differences (ΔG) for the structures shown in Fig. 2
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Aqueous phase MP2-PCM calculations

The energies and energy differences shown in Tables 1 and 2 relate to the gas phase. It is of interest to investigate the influence of a polar solvent on the energy profiles. Taking water as an example, we have calculated the water-solvated free energies using the PCM (polarised continuum model) method to simulate aqueous solvation. The results for the reaction sequence 3 → 7 are shown in Table 3. A significant conclusion from these results is that solvent has little influence on the second phase of the reaction sequence 4 → 5 → T2 → 6 → 7 (Fig. 1). For the parameters ΔGD, ΔG5T2 and ΔG67, the lowering of energy differences by solvent is small and in the range 0.3–2.0 kcal mol−1. The only exception is ΔG5T2 for Y = CH.CN (Entry 8) for which the energy difference is raised by solvent (−1.92 kcal mol−1). Interestingly, the energy values for the reverse activation energies ΔG6T2 are increased in the range 0.6–1.0 kcal mol−1 with the exception, again, of Y = CH.CN which increases by 4.8 kcal mol−1. Clearly, there is something a little different about the exocyclic CH.CN group, but overall, these small energy changes are of low significance and do not merit further discussion.

Table 3 Solvated MP2-PCM calculated energy values (G) and energy differences (ΔG) for the structures shown in Fig. 1
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Solvation has a much greater effect on the first phase of the reaction sequence, i.e. 3 → T1 → 4 (Fig. 1). We have previously reported that for isomers 3 and 4 (Y = O,S) aqueous solvation favours the cyclic mesoionic form by 10–15 kcal mol−1 [1]. For the conjugated exocyclic groups (Y = N.NO, CH.NO), this solvation effect is greater. Table 4 shows the changes in calculated energy differences (ΔΔG) upon solvation together with the calculated gas phase dipole moments (μ). In Table 4, the effect of solvation on the energy difference ΔG34 is shown as ΔΔG34. The magnitude of the solvation effect (ΔΔG34) does correlate with the magnitude of the dipole moment although the particularly low solvent effect on the oxygen analogue (Entry 2) is surprising. A similar variation is seen for the solvent effect (ΔΔG3T1) on the activation energy ΔG3T1. Although of no particular significance, it is interesting to compare ΔΔG34 and ΔΔG36. The variations of these solvent effects are very similar and, since solvation has little effect on the intermediates 6 (Tables 1 and 3), this effect can also be attributed to stabilisation of the dipolar precursors 3.

Table 4 Calculated dipole moments and solvent effects
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The effect of solvation on the overall reaction energy ΔGR1 (Fig. 1) is of some interest. In all cases, the effect of the aqueous environment (ΔΔGR1) (Table 4) adversely affects the reaction energy, but this can all be attributed to stabilisation of the mesoionic precursors 3. Again the smallest solvent effect is on the oxygen analogue (Entry 2), but this is not advantageous since the cyclisation 5 → 6 is particularly unfavourable compared to those of the S, N.NO and CH.NO analogues.

Similar solvation effects are seen for the transformations 8 → 9 (Fig. 2). MP2-PCM energy values for aqueous solvation are shown in Table 5. Comparison with Table 2 shows that aqueous solvation effects are small (< 3 kcal mol−1) for the energies ΔGD2, ΔG8T3 and ΔG9T3. As for the formation of the products 7, there is a significant aqueous solvent effect on the overall energy of reaction ΔGR2, but this can again be almost entirely attributed to solvent stabilisation of the mesoionic precursors 3c,d. The solvent effects (ΔΔGR2) are 15.85 (Z = N) and 16.84 (Z = CH) kcal mol−1, which are consistent with the corresponding values for ΔΔGR1 15.60 and 16.41 kcal mol−1 (Table 4, Entries 3 and 4).

Table 5 MP2-PCM calculated energy values (G) and energy differences (ΔG) for the structures shown in Fig. 2
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Conclusions

This MP2 study sheds some light on the paucity of known reactions of the mesoionic 2,3-disubstituted tetrazolium-5-olates 3b.The calculations indicate that the activation energies (ΔG3T1) for ring opening of the tetrazoles 3a-d differ by only a few kcal mol−1 (Table 1). In view of experimental evidence that the derivatives 3a, c and d are in equilibrium with their valence tautomers 4a, c and d, it is probable that the oxygen analogues 3b can also thermally equilibrate with the open chain form.

It would seem that the tautomer 4b has no accessible reaction pathway other than re-closure to the ring 3b. The calculated activation energy (ΔG5T2) for the electrocyclic ring formation 5 → 6 is much higher for the oxygen derivative 5b (31.99 kcal mol−1) than for the known reaction of the sulphur analogue 5a (20.74 kcal mol−1) (Table 1). It is possible that other thermal pathways may be accessible to the tautomer 5b at high temperature; there is no evidence that this has been investigated. The tautomer 5b may also be trappable by appropriate alkenes and alkynes.

The calculated effects of aqueous solvation on the reaction energetics shown in Figs. 1 and 2 are small with the exception of stabilisation of the mesoionic precursors 3. Only the energy differences directly related to the energy of the precursors 3 are significantly increased by solvation (i.e. ΔΔG34, ΔΔG3T1, ΔΔG36, ΔΔGR1 and ΔΔGR2) (Table 4), and these are consistently attributable to the solvent effect on the precursors 3. This is in accord with their polarity and the calculated dipole moments (Table 4). Clearly, for reactions of these species, the polarity of the solvent should be minimised.

Computational details

Calculations were performed using the Gaussian 16 program [17] at the ab initio Moller–Plesset MP2 level of theory [18]. The correlation consistent aug-cc-pVDZ (ACCD) basis set was used [19, 20]. All geometry optimizations were followed by frequency calculations to establish the nature of the stationary point and to calculate the ZPE and thermal corrections to Gibbs free energy. All obtained transition states have one imaginary frequency which connects the appropriate reactant and product. All minima on the potential energy surface have no imaginary frequencies. All calculations were performed for the gas phase and for the water environment modelled via polarizable continuum model (PCM) [21].