Aromatic Character and Relative Stability of Pyrazoloporphyrin Tautomers and Related Protonated Species: Insights into How Pyrazole Changes the Properties of Carbaporphyrinoid Systems

Pyrazoloporphyrins (PzPs), which are porphyrin analogues incorporating a pyrazole subunit, are examples of carbaporphyrin-type structures with a carbon atom within the macrocyclic cavity. DFT calculations were used to assess a series of 17 PzP tautomers, nine monoprotonated species and four related diprotonated PzP dications. The geometries of the structures were optimized using M06-2X/6-311++G(d,p), and the relative stabilities computed with the cc-PVTZ functional. Nucleus independent chemical shifts, both NICS(0) and NICS(1)zz, were calculated, and the anisotropy of the induced current density (AICD) plots were generated for all of the species under investigation. The results for free base PzPs show that fully aromatic PzP tautomers are not significantly more stable than weakly aromatic cross-conjugated species. In addition, strongly aromatic structures with internal CH2′s are much less stable, a feature that is also seen for protonated PzPs. The degree of planarity for the individual macrocycles does not significantly correlate with the stability of these structures. The results allow significant aromatic conjugation pathways to be identified in many cases, and provide insights into the aromatic properties of this poorly studied system. These investigations also complement experimental results for PzPs and emphasize the need for further studies in this area.


Introduction
Investigations into porphyrin-type structures has exploded over the last thirty years [1][2][3]. In 1994, two groups independently discovered N-confused porphyrins (NCPs, 1) ( Figure 1) as by-products in the acid-catalyzed condensation of pyrrole with aromatic aldehydes [4,5], and an efficient synthesis of this system was subsequently reported by Lindsey and Geier [6]. Immediately after the initial disclosure of NCPs, a number of related porphyrinoids were reported, including carbaporphyrins 2 and 3 [7][8][9], azuliporphyrins 4 [10,11], benziporphyrins 5 [12][13][14] and tropiporphyrins 6 [15,16]. Carbaporphyrinoid systems, porphyrinlike molecules with one or more carbon atoms within the macrocyclic core, exhibit diverse and unusual reactivity and may exist as aromatic, nonaromatic or antiaromatic species [1,17,18]. In addition, carbaporphyrin-type systems react with many late transition metal cations to generate stable organometallic derivatives under mild conditions [19][20][21][22]. N-Confused porphyrins have been particularly well studied with regard to their metalation properties [22], but complementary organometallic chemistry has also been described for related systems [19,20]. N-Confused porphyrins have two major tautomeric forms, 1a and 1b, that have dramatically different spectroscopic properties. Tautomer 1a, which is favored in nonpolar solvents including chloroform, is fully aromatic, and the proton NMR spectra for NCPs exhibit a strong diamagnetic ring current that results in the inner CH being shifted upfield to approximately −4 ppm. Tautomer 1b is approximately 5 kcal/mol higher in energy [23][24][25][26][27], but is favored in polar aprotic solvents such as DMF or DMSO [23]. This is due to favorable hydrogen bonding interactions between the solvent and the external NH. As 1b is cross-conjugated, the global aromatic character for the macrocycle is greatly diminished. Carbaporphyrin 2 is structurally similar to NCP tautomer 1b and also exhibits a strongly aromatic character [8]. In order to further investigate these systems, porphyrin analogues 7 with pyrazole subunits were targeted for investigation [28,29]. Structures 2, 1 and 7 provide a series of carbaporphyrinoids with an increasing number of nitrogens in the modified subunit. Therefore, this series can provide new insights into the properties of these systems. In addition, pyrazoloporphyrins (PzPs) might exist in a number of tautomeric forms, including tautomers 7a and 7b, that are analogous to the major species for NCP. Although N-confused porphyrins are commonly synthesized using Rothemund-Lindsey reaction conditions [4][5][6], alternative routes to NCPs have been developed, including '2 + 2' [30] and '3 + 1' strategies [31,32]. The '3 + 1' version of the MacDonald condensation has been a particularly useful method for preparing carbaporphyrinoid systems [33,34] (Scheme 1). The reaction of tripyrrane 8 with indene dialdehyde 9 in the presence of trifluoroacetic acid (TFA) afforded carbaporphyrin 10, while trialdehyde 11 gave modest yields of carbaporphyrin aldehydes 12 [7,35]. Methoxymethylene cyclopentene aldehyde 13 similarly afforded carbachlorin 14, and this can be further oxidized to carbaporphyrin 15 [8]. The same methodology was successfully applied to the preparation of N-confused porphyrins 16 and 17 [31,32]. Unfortunately, attempts to condense pyrazole dialdehyde 18 with 8 failed to give the expected PzP 19 (Scheme 2). However, N-substituted dialdehydes 20 reacted with 8 to give phlorin 21 and careful oxidation with aqueous FeCl 3 afforded PzPs 22 [28,29] The presence of N-phenyl, methyl or ethyl substituents prevents the system from tautomerizing into a fully aromatic porphyrinoid. The proton NMR spectra for PzPs 22 showed that they possess a weak diatropic ring current, and this was attributed to contributions from dipolar resonance contributors such as 22 . The sequential protonation of 22 with TFA initially gave monocation 22H + and then dication 22H 2 2+ . Oxidation of the phlorin intermediate with silver(I) acetate gave oxopyrazolophlorins 23 and 24. Metalation with nickel(II) or palladium(II) acetate afforded the corresponding organometallic derivatives 25 and 26, respectively [28,29]. The proton NMR spectra for 25 and 26 showed the presence of moderate diatropic ring currents. However, all vestiges of an aromatic character were lost upon protonation. The aromatic character of 25 and 26 can be attributed to dipolar resonances 25H + and 26H + that incorporate 18π electron delocalization pathways. However, protonation of the external nitrogens inhibits this interaction because the corresponding canonical forms 25 H + and 26 H + would necessitate the placement of positive charges on adjacent nitrogen atoms. The earliest investigations into pyrazole-containing porphyrinoids were directed at the synthesis of non-aromatic hexaphyrin analogues 27 [36], and texaphyrin analogue 28 has also been reported [37]. More significantly, a fully conjugated hexaphyrin analogue designated Siamese-twin porphyrin 29 has been synthesized [38] (Figure 2). This system proved to be nonaromatic but possesses two binding pockets that are similar to the binding cores of porphyrins. Extensive metalation studies on this system have been reported [39]. Furuta also investigated the synthesis of PzPs [40] (Scheme 3). Tripyrrane 8 was condensed with pyrazole dialdehyde 20d in the presence of trifluoroacetic acid, followed by oxidation with FeCl 3 , but in this case oxopyrazolophlorin 23d was isolated instead of the expected N-benzyl PzP 22d. Cleavage of the benzyl group with AlCl 3 afforded a tautomeric mixture of N-unsubstituted oxopyrazolophlorins 23e and 23e [40]. The favored tautomer 23e self-assembled as a hydrogen bonded dimer (Scheme 3). Tripyrrane analogues can be reacted with dialcohols to give modified porphyrinoids. For instance, tert-butyl N-confused tripyrrane 30 reacted with pyrrole dicarbinol 31 to give tert-butyl NCP 32 and subsequent treatment with aqueous sulfuric acid at 160 • C afforded unsubstituted N-confused porphyrin 1 [41]. However, the acid-catalyzed condensation of pyrazole dialcohol 33 with diphenyltripyrrane 34, followed by oxidation with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ), did not give targeted PzP 35, but instead afforded a mixture of triphenylcorrole 36 and a nonaromatic expanded porphyrinoid 37 that incorporated a 6-carbon chain derived from DDQ [40].
Due to the many difficulties encountered in the synthesis of pyrazoloporphyrins, this system is not well studied. N-Unsubstituted PzPs are presently unknown, and it has not been possible to contrast their tautomeric properties with closely related NCPs. In order to gain a better understanding of the pyrazoloporphyrin system, a computational study was conducted. The goals were threefold. Firstly, the conformations and relative stabilities of 17 potential PzP tautomers were considered. Secondly, the aromatic characteristics of these tautomers were assessed using nucleus independent chemical shift (NICS) calculations and the anisotropy of induced current density (AICD) plots. Thirdly, these methods were used to predict the relative stabilities and aromatic characteristics of protonated PzPs.

Aromatic and Nonaromatic Tautomers of Pyrazoloporphyrins
Computational methods can provide valuable insights into the structures and aromatic properties of porphyrinoid systems [42][43][44][45][46][47][48][49][50]. In our earlier work, we have assessed the relative stabilities and aromatic properties of a wide range of tautomeric structures and protonated species for carbaporphyrins [51], benzo-and naphthocarbaporphyrins [52,53], heterocarbaporphyrins [54], carbachlorins [8,55], dicarbaporphyrins [56][57][58], benziporphyrins [59], pyreniporphyrins [60], neo-confused porphyrins [52,61], azuliporphyrins [62], 21-oxyazuliporphyrins [63], tropiporphyrins [62], oxyquinoliziniporphyrins [64] and carbatriphyrins [65]. In this study, a series of 17 free base PzP tautomers (Tables 1 and 2) were examined. The structures were optimized using M06-2X with the triple-ζ basis set 6-311++G(d,p). Seven tautomers are fully conjugated (Table 1), or contain a cross-conjugated element, while the 10 remaining tautomers have methylene bridges ( Table 2) that interrupt macrocyclic conjugation. The relative stability and π-delocalization pathways in these tautomers were investigated. The peripheral atoms for PzP are numbered 1-20, and the inner atoms are designated 21-24, as shown for structure 7a in Figure 1. Two hydrogens are relocated in each of the tautomeric structures, and the numerical positions of these hydrogens are designated in the structure notation. For instance, the most stable tautomer of pyrazoloporphyrin is PzP-22,24-H, where the "mobile" hydrogens are located at positions 22 and 24.   (Table 1). This differs from NCPs, where the equivalent aromatic tautomer is approximately 5 kcal/mol lower in energy than the cross-conjugated version. It is noteworthy that the relative energies and Gibbs free energies are very similar for all of the calculated tautomers, demonstrating that entropic factors are not significant. As is the case for aromatic carbaporphyrins and NCPs, PzP has three internal hydrogens, and the crowded cavity leads to the pyrazole ring being pivoted out of the macrocyclic plane (Table 3) (Table 1). This is due to less effective hydrogen bonding interactions within the core [66][67][68][69], as well as less than optimal placement of the hydrogens leading to unfavorable steric interactions. Two additional fully conjugated forms with internal methylene units, PzP-21,22-H and PzP-21,23-H, are possible, but these are 18.32 and 11.27 kcal/mole higher in energy, respectively, than PzP-22,24-H. The former is less stable due to the core arrangement being less well suited for hydrogen bonding interactions as well as placing the internal hydrogens at adjacent positions. Nevertheless, both tautomers are virtually planar and possess 18π electron conjugation pathways [70]. This result demonstrates that global aromaticity and overall planarity are not in themselves sufficient to determine the stability of these structures. It is noteworthy that only one example of a carbaporphyrinoid system with an internal CH 2 is presently known [57]. Tautomers with interrupted conjugation due to the presence of a methylene bridge (Table 2)   The aromatic character of the individual tautomers were probed using nucleus independent chemical shift (NICS) calculations and the anisotropy of induced current density (AICD) plots. NICS calculations [71] were carried out using the GIAO method. NICS calculations assess the chemical shifts that might be observed in proton NMR studies but does not require a nucleus to be present at the site of interest. Large negative values correspond to highly shielded regions that result from aromatic ring currents, while positive values correspond to deshielded regions. The latter could result from paratropic ring currents (antiaromaticity), but will also emerge when a ring is placed just outside of a major aromatic conjugation pathway. Two types of NICS calculations, NICS(0) and NICS(1) zz , were conducted. Standard NICS calculations take into account the effects due to σ and π electrons and do not always reliably assess aromatic properties, but NICS zz primarily measures the effects due to the π system [72][73][74][75]. NICS zz calculations were performed 1 Å above the ring. The two techniques were mostly consistent, but the numerical values obtained for NICS(1) zz are much larger than those obtained using NICS(0). In the discussion, the NICS (1) Table 1). The NICS(0)/NICS(1) zz values for the individual pyrazole and pyrrole rings in these structures were also determined. These rings were designated a, b, c and d, where ring a corresponds to the pyrazole unit (Tables 1 and 2). For PzP-22,24-H, rings b and d gave NICS(1) zz strongly negative values (ca. −30 ppm) but ring c gave a smaller negative value of −11.73 ppm and ring a was only −2.12 ppm. These results suggest that an 18π electron circuit that passes through the inside of rings a and c and the outside of rings b and d is favored (Figure 3). This type of conjugation pathway is also favored for NCP 1a and carbaporphyrins 2 and 3 ( Figure 1). For tautomer PzP-2,23-H, ring a gives a strongly negative value of ca. −20 ppm, indicating that the pyrazole unit is strongly aromatic but primarily isolated from the rest of the macrocycle. This is also seen for tautomers PzP-2  In addition to the NICS calculations, all the investigated structures were probed using anisotropy of induced current density (AICD) [76] (see Supporting Information). AICD plots show the induced flow of electrons due to an applied magnetic field and allow the visualization of aromatic ring currents. The plot for PzP-22,24-H confirms the presence of the proposed 18π electron circuit (Figure 4), but a degree of bifurcation is also present. The main aromatic pathways pass through the inside of the pyrazole ring, but the routes are less well delineated in ring c. This observation is also consistent with the NICS calculations. Unfavored aromatic tautomer PzP-21,23-H also shows the presence of an 18π electron pathway, but alternative routes through the pyrrolic subunits are clearly evident. Bond length calculations provide further insights ( Figure 5). For PzP-22,24-H, the closed circuit representing the proposed aromatic pathway shows little bond length alternation apart from the carbon-carbon bonds within the individual pyrrole units. C6-C7, C7-C8, C16-C17 and C18-C19, all of which fall within the aromatic pathway, gave values of 1.432-1.433 Å, but the equivalent bonds in ring c, C11-C12 and C13-C14, gave slightly longer values of 1.462 Å. C12-C13 for ring c gave a relatively short bond length of 1.345 Å compared to the equivalent bonds C7-C8 and C17-C18 in rings b and d, which came out as 1.368 Å. These trends are consistent with the proposed conjugation pathway. For PzP-2,23-H, a substantial bond length alternation is evident, as would be expected for a nonaromatic porphyrinoid.

Mono-and Diprotonated Pyrazoloporphyrins
A series of 9 monoprotonated pyrazoloporphyrin tautomers were considered (Table 4). For this series, only structures that were fully conjugated were investigated. The most stable tautomer, PzP-2,22,24-H + , was protonated onto an external nitrogen. The lowest energy tautomer that had been internally protonated, PzP-22,23,24-H + , was calculated to be nearly 17 kcal/mol higher in energy. The two remaining externally protonated tautomers, PzP-2,22,23-H + and PzP-2,23,24-H + , are only approximately 4 kcal/mol higher in energy, and the differences can be attributed to a combination of steric and poorer hydrogen bonding interactions. Five of the monocations have internal methylene units. The most stable of these, PzP-2,21,23-H + , is still over 17 kcal/mol higher in energy than PzP-2,22,24-H + . This species is externally protonated, but the most stable version with an inner CH 2 that is internally protonated, PzP-21,22,24-H + , is nearly 21 kcal/mol higher in energy. The three most favored tautomers, PzP-2,22,24-H + , PzP-2 (Figure 7). In contrast, the AICD plot for PzP-22,23,24-H + (Figure 6b) indicates that a 19-atom pathway is favored (Figure 8), and this corresponds to the presence of an 18π electron cationic [19]annulene component. This analysis is supported by the NICS(1) zz data, as these show large negative values for rings b, c and d, but not for the pyrazole ring. PzP-2,21,22-H + , which is externally protonated but with an internal methylene unit, gave an AICD plot (Figure 6c) that was consistent with the presence of an 18-atom 18π electron pathway, while the AICD plot for PzP-21,22,24-H + (Figure 6d), which also has an internal methylene unit but is protonated internally, favors a 19-atom 18π electron circuit ( Figure 8). Again, these conjectures are supported by the NICS(1) zz calculations (Table 5).   2+ show extensive bond length alternation (Figure 7), as would be expected for a weakly aromatic species.

Computational Methods
All DFT calculations used the Gaussian 16 revision C.01 [77]. Geometry optimizations were performed using M06-2X/6-311++G(d,p) [78][79][80]. Using the same functional and basis set, the corresponding vibrational frequencies were computed to confirm the absence of imaginary frequencies and derive zero-point energy and vibrational entropy corrections from unscaled frequencies. Single point energy calculations were performed on the optimized minima using M06-2X/cc-PVTZ [81]. NICS values were calculated using the GIAO method, and AICD plots were obtained from CGST calculations. NICS(0) was calculated at the mean position of the four heavy atoms at the center of the macrocycle. NICS(a), NICS(b), NICS(c), and NICS(d) were calculated at the mean position of the five atoms that make up each component ring in the macrocycle. Additionally, NICS(1) zz , NICS(1a) zz , NICS(1b) zz , NICS(1c) zz , and NICS(1d) zz were obtained by applying the same calculations 1 Å above each of the corresponding points extracting the zz contribution of the magnetic tensor. The resulting energies, cartesian coordinates, and AICD plots can be found in the Supplementary Materials.

Conclusions
Pyrazoloporphyrins (PzPs) represent a logical extension of the structural concepts associated with N-confusion, but to date research on this system has been limited, and N-unsubstituted pyrazoloporphyrins are not presently known. DFT calculations have been used to assess the properties of N-unsubstituted PzPs, and the results provide new and unexpected insights. The aromatic properties were probed using anisotropy of induced current density (AICD) plots and nucleus independent chemical shift (NICS) calculations. The two most stable tautomers of PzP differ in energy by <0.4 kcal/mol, even though one form is strongly aromatic, while the other version is cross-conjugated and only weakly aromatic. Tautomers with internal CH 2 units are also very aromatic species, but have much higher calculated energies. Monoprotonation can give rise to a number of monocationic species, nine of which were considered. The favored tautomers are externally protonated with very weak diatropic characteristics. Internal protonation gives a cation that is strongly aromatic, but it is nearly 17 kcal/mol higher in energy than the most favorable externally protonated form. Cations with internal methylenes are also very aromatic species but are relatively unstable. Diprotonated PzP dications were also considered. The most stable dication is weakly aromatic, and fully aromatic cations with inner CH 2 s are >15 kcal/mol higher in energy. The results are in accord with the reported properties for 2-substituted PzPs, and highlight the profoundly altered properties of this system compared to NCPs and carbaporphyrins.
Author Contributions: All computational studies were performed by D.I.A.; based upon concepts developed by T.D.L. The manuscript was written by T.D.L., and this author was also responsible for project administration and funding acquisition. All authors have read and agreed to the published version of the manuscript.