Introduction

To facilitate the following discussion, the numbering of the studied structures is reported in Fig. 1; actually, for protonated molecules, the number of possible structures is larger, but this does not alter this introduction.

Fig. 1
figure 1

Numbering of the studied compounds: n, nature of the substituents from 1 to 5; X, nature of the atom at position 4 (O, S, Se, NH); c/o, closed/open ring; H+, protonated structures

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Mesoionic compounds occupy a singular place among the huge field of heterocyclic chemistry. Their structure and complex system of classification is due to Baker [1, 2], Ollis [3, 4], Potts [5,6,7], and Oziminski [8, 9], among others, although the main contribution is that of Ramsden [10,11,12,13,14,15,16]. Ramsden classification is reported in Fig. 2.

Fig. 2
figure 2

Ramsden classification of heterocyclic mesomeric betaines (HMBs) [8] and the nomenclature of the compounds of the present 5 series (R1 = R2 = Ph, R3 = R5 = Me) belonging to class 5 compounds (pseudo-semi-conjugated HMBs)

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In 1988 [17], we used the SOS (Simulated Organic Synthesis) program due to Barone and Chanon [18,19,20] to find new ways to prepare pyrazoles, different from the classical ones [21,22,23,24,25]. In that paper, we reported a new method and calculated within the MNDO [26] method the minima and TS of the reaction A1 ⇌ TS1 ⇌ B1 (Fig. 3), corresponding to the present numbering of 1(O)c, 1(O)TS, and 1(O)c.

Fig. 3
figure 3

Valence tautomerism in the 1 and 2 series. All values in kJ·mol–1. Data for A2 are from ref. [15] where the corresponding TSs were not calculated

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According to the MNDO calculations, it appeared that 1,3-diminopropan-2-one B1 was much more stable than 1H-pyrazol-2-ium-4-olate (also called 4-hydroxy-1H-pyrazolium inner salt); the barrier TS1 between A1 and the cyclic compound, B1, was very high.

In 2019 Ramsden and Oziminski studied a series of closely related reactions based on MP2 ab initio calculations [15]; in Fig. 3, we have reported one of their examples concerning their A2 compounds [our n = 2(O) compounds of Fig. 1]. Their results concerning the general solvation by water, PCM model [27], and the specific solvation by a water molecule show that the differences in stability can be strongly modified, to the point that A2·H2O (PCM) is more stable than B2·H2O (PCM). The corresponding TSs were not calculated.

A search for 1H-pyrazol-2-ium-4-olates and 2,4-bis(imino)pentan-3-ones in Scifinder [28] afforded compounds 6 to 20 gathered in Fig. 4 and Fig. 5 together with their CAS registered numbers. The simplest compound of Fig. 5 (14, R = H) is only a calculated compound [15].

Fig. 4
figure 4

1H-Pyrazol-2-ium-4-olates. 6 = 2(O)c; 7 = 3(O)c; 10 = 4(O)c; 11 = 5(O)c

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Fig. 5
figure 5

2,4-Bis(arylimino)pentan-3-ones

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Note that compounds 11 (Figs. 4) and 14 (Fig. 5) are valence tautomers. No experimental synthetic method that involve the creation of a N–N bond has any relationship with the procedure of Fig. 3; the reported methods correspond to oxidative synthesis using nitriles and creating simultaneously N–N and C-N bonds [29,30,31]. The synthesis of 1H-pyrazol-2-ium-4-olates uses hydrazines as starting materials [32,33,34].

Concerning the protonated species, only one structure has been reported and always only in patents [35], the perchlorate of 4-hydroxy-1,2-dimethyl-3,5-diphenyl-1H-pyrazol-2-ium 10H+ [R1 = R2 = Me, R3 = R5 = Ph, 4(O)cH+] (Fig. 6); this compound was not prepared by protonation of 10 but by methylation of the corresponding N-methyl pyrazole [34]. These 4-hydroxy-pyrazolium salts were proposed by Begtrup in 1970 as intermediates but were not isolated [36].

Fig. 6
figure 6

4-Hydroxy-1,2-dimethyl-3,5-diphenyl-1H-pyrazol-2-ium 10H+

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Computational methods

The geometry of the molecules has been optimized with the M06-2x [37] functional and the aug-cc-pVDZ basis set [38] in gas phase and with the continuum solvation model PCM [39] using the water parameters, PCM(H2O)-M06-2x. Frequency calculations at the same computational levels were carried out to verify that the structures obtained correspond to energetic minima (no imaginary frequencies) or to transition states (only one imaginary frequency). The IRC of some of the reactions studies has been explored. All these calculations have been carried out using the Gaussian-16 package [40].

Additional calculations at domain-based local pair natural orbital coupled cluster with single-, double-, and perturbative triple excitation level [41], DLPNO-CCSD(T)/aug-cc-pVDZ, have been performed with the Orca5 program [42]. This methodology provides similar results to those obtained with the standard CCSD(T) method [43].

The electron density of the molecules has been analyzed with the quantum theory of atoms in molecules (QTAIM) [44] using the AIMAll program [45]. The presence of (3,-1) critical points associated to interatomic interactions allows to classify such contact in covalent and non-covalent.

The analysis of the IRC profile has been carried out with the Eyringpy program [46].

Results and discussion

Neutral molecules, comparison between n(X)c and n(X)o

Energetic comparisons between closed (pyrazolium-olates and related compounds) and open structures [2,4-bis(arylimino)pentan-3-ones and related compounds] are reported in Fig. 7 and Table 1, and the geometries are listed in the Supplementary data.

Fig. 7
figure 7

The ring/chain isomerism of neutral compounds. c-o means cyclic-open

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Table 1 Energies (in kJ·mol–1) of the valence tautomerization between n(X)c and n(X)o. Relative energies to the open structures n(X)o
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Several of the 20 values of Table 1 columns are linearly related, and the simple linear regression equations, y = a + bx, obtained from these values are reported in Table 2.

Table 2 Statistical analyses of Table 1 data
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The square correlation coefficients are not very good, and that is also apparent in the relatively large errors of the coefficients. The first three equations are a consequence of the Hammond postulate, which states that the transition state resembles the structure of the nearest stable species, in this case the cyclic compounds. Equation 4 corresponds to the fact that CCSD(T) calculations increase considerably the differences in stability between open and cyclic structures compared with M06-2x ones. General water solvation stabilizes the mesoionic compounds compared to the neutral open forms due to their high dipole moments (see Supplementary data), Eqs. 5. Equations 6 and 7 have slopes near 1.00; thus, the intercepts can be directly compared; the values are relatively small, + 15.3 for the CCSD(T)/M06-2x pair, positive like in Eq. 4 but lower, and –11.4 for the PCM(H2O)/M06-2x comparison, again similar and lower to that of Eq. 5.

The solvent effect produces an elongation of the N–N distance in the TS between 0.03 and 0.12 Å (see Supplementary data, Table S2).

A clear relationship is found between the energetic values of the TS structures in gas phase and their N–N distances as can be observed in Fig. 8. The shorter the N–N distance in the TS, the larger is the barrier. Linear correlations between these two parameters show R2 values larger than 0.98 for each family of compounds (1–5) and a R2 value of 0.92 considering all the points together. A linear correlation is only the simplest model, for instance, a second order polynomial affords an R2 = 0.936. A similar relationship is obtained when the values in PCM(H2O) are considered (see Supplementary data, Fig. S1):

Fig. 8
figure 8

Energy of the TS structures (kJ·mol–1) in gas phase vs. their N–N distances (Å)

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The analysis of the electron density of the structures within the QTAIM methodology [44] shows the presence of a bcp between the nitrogens involved in the reaction in the closed and TS structures but not in the open ones. The ρBCP in the closed structures range between 0.387 and 0.331 au with negative values of ∇2ρBCP and HBCP that are large. In contrast, the ρBCP for the TS structures range between 0.175 and 0.071 au with positive values of ∇2ρBCP and negative values of HBCP as indication of partial covalent character of this contact in the TS [47].

The IRCs (Intrinsic Reaction Coordinate) of some selected transformations have been calculated. Using these values, the reaction force profile along the reaction has been derived. One example is given in Fig. 9. The reaction force divides the IRC in three regions: (i) from the reactant to the minimum (ξ1) which is associated to structural reordering, (ii) from ξ1 to the maximum ξ2 where the electronic variation dominates, and (iii) between ξ2 and the products that corresponds to a structural relaxation. It should be noted that the TS (ξTS) is located between ξ1 and ξ2 allowing to divide the reaction in four regions. Table 3 shows the energetic values between the critical points in the IRC and reaction force along the reaction coordinate for some of the reactions. The structural reorderings (W1 and W4) are larger in the processes of reaching the TS from the products and the reactants than the electronic reorganization (W2 and W3). Good linear correlations (R2 > 0.96) of each term with the corresponding TS have been obtained when the two families (1 and 3) are considered separately.

Fig. 9
figure 9

IRC (black) and reaction force (blue) of 1(O)c. The locations of the critical points in the IRC (R, P, and ξTS) and reaction force (ξ1 and ξ2) are indicated

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Table 3 Energy decomposition (kJ·mol–1) using the reaction coordinate and the reaction force critical points. W1–W4 are the energy difference (kJ·mol–1) between the corresponding stationary points
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Protonated molecules, comparison between n(X)cH+ and n(X)oH+/n(X)o'H+

The situation for cations is much more complex than in neutral molecules because instead of two minima, now they are five. In Fig. 10 are represented the five minima of protonated structures and in Table 4 the corresponding energy results.

Fig. 10
figure 10

The ring opening sequence in protonated 1H-pyrazol-2-ium-4-olates and related compounds. c-o means cyclic-open

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Table 4 Energies (in kJ·mol–1) of the valence tautomerization between n(O)cH+ and n(O)oH+ (open a and open d); the TS-co correspond to the ring opening of the closed structure to yield the open compound of type a. Relative energies to the cyclic n(O)cH+ structures
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In Table 4 are reported the same results as in Sect. 2.1 for protonated species, but only for X = O, the remaining X groups are reported in the Supplementary data. Here the most stable is the cyclic compound and no longer the open compound like in neutral molecules. Note that open compounds a and c are related by a proton transfer, while structure d present a new N–H···N HB.

There are five minima and four TS. TS-co corresponds to the N–N bond breaking, TS-ab to the rotation about a CC single bond, TS-bc to a intramolecular proton transfer between X and N, and TS-cd to a second rotation about a CC single bond. In the case of X = O, these barriers (from left to right, Fig. 11a) correspond to 246.0, 12.9, 7.7, and 27.3 kJ·mol–1. The direct migration of a proton between a and d being too far away cannot take place without the assistance of water or solvent molecules or counterions.

Fig. 11
figure 11

The energy profile of 2(O)H+ in the gas-phase. a 2(O)H+. b 2(S)H+. c 2(Se)H+. d 2(NH)H+

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There are two groups of structures, before proton transfer, a and b, and after proton transfer, c and d. Taking into account that some b structures have not been localized because they evolve spontaneously to type c structures, b is always more stable than a (mean = 39.6 kJ·mol–1, extreme values 6.5 kJ·mol–1, 4(Se)H+ and 55.5 kJ·mol–1, 5(O)H+; even for 4(NH)H+, the differences is much lower, 13.0 kJ·mol–1, respectively than the mean (see Table S5)).

The different character of 4 series is probably due to a hydrogen bond between the acidic OH and the adjacent N atom (Fig. 12); the three other X+–H groups are less acidic, NIST gas basicity values in kJ·mol–1 H2O (660.0), H2S (673.8), H2Se (676.4), and H3N (819.0) [48].

Fig. 12
figure 12

Comparison of the types a and c of structures 3(O)oH+ and 4(O)oH+

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After proton transfer, d is always more stable than c due to the very favorable structure for a strong hydrogen bond, pseudo-six membered ring. The mean value is smaller than in the preceding case (10.4 kJ·mol–1).

Statistical analyses of Table 4 data similar to those of Table 2 are much more complicated due to the existence of four open cations. Only the correlation relating the TSs calculated by two methods was acceptable (Table 5).

Table 5 Statistical analyses of Table S5 data. The corresponding data for neutrals from Table 2 has been added for comparison
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When the four profiles of Fig. 11, illustrated for the a series, are compared, it appear that those of X = O (Fig. 11a), X = S (Fig. 11b), and X = Se (Fig. 11c) are similar but that of X = NH (Fig. 11d) is different. A closer look indicated that the amino profile has two parts both similar to the other profiles but different between them (Fig. 13).

Fig. 13
figure 13

Comparison of the 2(NH)oH+ and 2(O)oH+ series

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The three values of the left side (blue) and the two values of the right side (red) are correlated with the black values of the 2(O)oH+ series: 2(NH)oH+ = (1.07 ± 0.07) 2(O)oH+ – (68 ± 13), n = 5, R2 = 0.9995; the value –68 kJ·mol–1 corresponds to the difference between both sides, the red minus the blue, and it is related to the much larger basicity of NH compared with that of O (see previously NIST data [48]).

To estimate protonation effects, i.e., the basicity of the compounds of Table 1, the latter and Table 4 and Supplementary data should be compared; some relationships could be found. For instance for the M06-2x calculations between n(X)oH+ type c = (188.6 ± 3.5) – (0.63 ± 0.04) n(X)c – (101.6 ± 6.3) b series, = 20, R2 = 0.98 (Eq. 10). Equation 10 shows the energetic difference between the a (0) and the b (1) series, the b series being in average 102 kJ·mol–1 more stable than the a series.

The TS ring opening shows barriers bigger than in the neutral systems and N–N distance systematically larger (0.35 Å in average) in the protonated ones. As in the cases, of the neutral systems, linear correlations are obtained between the barriers and the interatomic N–N distances for each family of compounds with R2 > 0.97.

The analysis of the electron density between both nitrogen atoms in the TS(c-o) shows a BCP like in the case of the neutral molecules. The representation of ρBCP and ∇2ρBCP vs. the interatomic N–N distance for all the closed and TS(c-o) complexes (neutral and protonated) is shown in Fig. 14. The ρBCP values follow an almost perfect exponential relationship with the distance in agreement with previous reports for covalent and non-covalent interactions [49,50,51,52]. The figure corresponding to ∇2ρBCP (Fig. 14 right) shows the changing nature of the bond. Negative values are obtained for covalent N–N bonds in the closed systems, while the positive values are obtained for the TSs, but at the shortest distances, they tend towards negative values.

Fig. 14
figure 14

ρBCP and ∇2ρBCP vs. the interatomic N–N distances. The fitted curves (blue) show R2 values larger than 0.999

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The IRC analysis of the ring opening through the TS-co for molecules 1 and 3 (Table 6) show that in the latter ones, 3(O)H+ and 3(S)H+, the structural reordering (W1 and W4) is larger in absolute value than the corresponding electronic reorganization (W2 and W3) in analogy to what was observed for the neutral systems. In contrast, 1(O)H+ and 1(S)H+ shows a larger electronic reorganization W2 than the geometrical reordering W1.

Table 6 IRC analysis of the ring opening through the TS-co for molecules 1 and 3
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Comparison with geometries calculated and experimental X-ray data

Unfortunately there are no experimental geometries of 1H-pyrazol-2-ium-4-olates and related compounds (CSD) [53]. However, of the structures reported in Table 5 that of compound 21 has been determined (COPLAV) [54] and COPLAV01 [55]), this compound is related to 5(O)o, but the presence of two i-propyl at positions 2 and 6 of the phenyl rings should modify the conformation (Fig. 15).

Fig. 15
figure 15

Comparison of the geometries of COPLAV and 5(O)o

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The calculated structure has a symmetry axis (C2) that is lost in the experimental structures that are different; the main difference between experimental and calculated geometries concerns one of the OCCN angles that are rotated to values (105.3 and 76.6°) much lower than the other N-phenyl group (169.6 and 176.2°) and to our calculated angles (178.0°).

Conclusions

Our conclusions agree with those of Ramsden and Oziminski [15] taking into account that protonation produces the same effect that hydrogen bonds with a water molecule but stronger.

Selecting for the conclusion, the two experimentally studied X atoms or groups, X = O and X = NH (X = S and X = Se were not included in Fig. 16), it is possible to summarize the calculated energy of the stationary states, minima, and transitions states, in Fig. 16. The values for the “open” protonated compounds correspond to “open-d”.

Fig. 16
figure 16

Energy means values (for the five n values, from 1 to 5) in kJ·mol–1 units

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While in the neutral molecules the open structure is the most stable, in the cations, it is the opposite, the pyrazoliums are the most stable; although nobody has reported an example of ring/chain isomerization in these series, it should be possible by protonation/deprotonation, i.e., by simply changing the pH. The values reported in Fig. 16 indicate that solvation by water decreases the difference in stability between valence isomers so the experiments should be carried in the gas phase (by mass spectrometry, the open structure should be transformed in the cyclic structure of the cation) or in aprotic non-dipolar solvents, like benzene or other aromatic solvents.

The isomerization barriers lie in the range 162.1–237.6 (M06-2x), 167.2–218.1 [CCSD(T)], and 157.3–245.5 kJ·mol–1 (PCM water). These are high barriers that correspond to slow processes, in the order of 10–3 to 10–2 s–1 [56]. Even so, a 1H-pyrazol-2-ium-4-olate like 11 = 5(O)c in an aprotic solvent (e.g., 1,4-dichlorobenzene-d4) and heating the solution at 400 K for 2 weeks, or shorter in a microwave oven, should open it (the reaction can be followed by NMR).