A theoretical study of the parent N H -benzazoles (benzimidazoles, indazoles and benzotriazoles): geometries, energies, acidity and basicity, NMR properties and molecular electrostatic potentials

The three parent N H -benzazoles, benzimidazole, indazole and benzotriazole, have been studied theoretically at the B3LYP/6-311++G(d,p) level. Optimized geometries have been compared with those obtained by X-ray crystallography, energies with studies about tautomerism, acid-base properties with p K a s, and chemical shifts with those reported in the literature. As aromaticity probe, Schleyer's Nuclear Independent Chemical Shifts (NICS) were used and represented in two 3D isosurfaces of the electron density.


Introduction
Although biological properties will not be reported, it is useful to note that the three heterocycles are very different in this respect.Limiting discussion to the NH-derivatives, benzimidazoles are the most natural and relevant in biology (for instance, 5,6-dimethylbenzimidazole, which serves as an axial ligand for cobalt in vitamin B12), 1 indazoles in medicinal chemistry, 2 while benzotriazoles are less important. 3On the other hand, concerning their use as materials, benzimidazole appears to be the most used, 4 but there are also interesting applications for indazoles 5 and benzotriazoles. 6enzazoles bearing no substituents on the N atoms have been the subject of a large number of theoretical papers covering a wide range of levels for benzimidazoles, 7 indazoles 8 and benzotriazoles, 9 the more recent articles using higher levels.None of these publications covers the three heterocycles although some of them include substituted derivatives.In the past, to report literature values (including several from ourselves) and to compare them to those calculated in this study was common usage.Today this is a useless exercise because the methodological approaches are well established.Therefore, we will cite and discuss only the references that deserve our attention.There is also much experimental information about benzazoles that will be reported when comparing calculations and experiments.
The originality of the present work is to include amongst the neutral molecules the nonaromatic tautomers 2 and 8, as well as Arduengo's heterocyclic carbenes 10 3 (benzimidazol-2ylidene) and 9 (indazol-3-ylidene).Cations and anions were studied to allow access to basicity and acidity properties.

Computational details
The geometry of the systems has been optimized at the B3LYP 11,12 /6-311++G(d,p) 13 computational level.Frequencies calculations have been carried out to confirm that the structures obtained correspond to energetic minima.All the calculations have been performed with the Gaussian-09 program. 14he theoretical absolute shieldings (, ppm) and NICS values (ppm) 15 were calculated using the GIAO method 16,17 on the B3LYP/6-311++G(d,p) geometries.To study the spatial distribution of the NICS, their values have been calculated on a 3D cubic grid of 12 Å sides following the procedure described by Stanger. 18The points in the grid are located at 0.2 Å one from other in the three spatial directions.The result is a cube with 226981 NICS values, which, in the next step, have been represented within the electron density isosurfaces of 0.05 and 0.001 au using the WFA program. 19All the calculations have been carried out with the Gaussian 09 facilities.

Results and Discussion
Geometries First we will compare the calculated geometries (Table 1) with those reported in the Cambridge Structural Data base (CSD).The structures and the corresponding Refcodes are reported in Figure 4. 20 We limit the discussion to the five-membered ring (the azole moiety) and only to nonhydrogen atoms (C and N) since the distances involving H atoms are underestimated in X-ray crystallography. 21For compounds 4, 14 and 16, with C2v symmetry, the experimental values have been averaged.Excluding the experimental structure 15 (ULOLUC) for the reasons explained below, the following relationships are found between experimental and calculated values of Table 1: The worst points according to eq. 1 are the 1-2 distances in benzimidazole (1) (-0.022Å) and in indazole (6) (+0.024Å) and those corresponding to eq. 2 are the 2-3-3a angle of benzimidazole (1) (-1.2 º) and the 3a-7a-1 angle of indazole (6) (+1.6 º).
Two of the compounds show polymorphism: benzimidazole (1) and benzotriazole (12). 23,24n the same year (2005), Krawczyk and Gdaniek described the structure of second polymorphs of benzimidazole 25 and benzotriazole. 26The previous structures of these compounds were determined in the 1973-1974 period. 27,28The old benzimidazole polymorph () is stable while the new polymorph () is metastable at room temperature.In both polymorphs, benzimidazole molecules are connected into polymeric chains via N-H•••N hydrogen bonds (HBs).However, the mode of aromatic ring interactions differs significantly in the two crystalline forms.In the  form, the molecules show edge-to-face interactions, whereas in the new  form, a sandwichherringbone arrangement of the aromatic molecules is observed.
The The structure of indazole (6) deserves further comment.The Escande and Lapasset structure shows that the H of the NH group is out-of-plane of the remaining atoms, therefore having diastereogenic center on the N-1 atom (at least, in the crystal where no N inversion occurs). 29his point was verified recently, 8j because it could be the reason why 6 crystallizes in a noncentrosymmetric group (P21); note that 6 shows spontaneous resolution (conglomerate).Concerning the geometries without experimental counterparts, the most interesting are those of the carbenes (Figure 5). is defined as the dihedral H-N•••N-H angle for 3 and H-N-N-H angle for 9.The following structures of type 3′ are found in the CSD (some of them having several independent benzimidazol-2-ylidene molecules, in all, ten different geometries): 20 LOGVUY, POYKOE, RENYEP, RENYIT, RENZEQ, SIRJIN and YUXJUX.The average value of  is 5.3º with one of the structures being planar ( = 0.0º).These geometries clearly belong to singlet carbenes.No data are available for the indazol-3-ylidenes related to 9.

Energies
We report in Table 2 the energies corresponding to compounds 1 to 16.These energies will be discussed in relation to tautomerism and to acid-base properties.][33] Experimental results concern only the NH-tautomers and they confirm that 6 > 7, 12 ≈ 13.The case of the indazole 6/7 pair is well known of old.34a The case of the benzotriazole 1H/2H (12/13) pair, although discussed in Minkin's review, 34 has been revisited many times, with the conclusion that both tautomers have similar stabilities and that the actual situation depends on the environment. 9he benzotriazolium cations 14/15 are a less studied case.Catalán et al. favored the 1,3-diH tautomer 14 based on thermodynamic considerations.9a Others authors have drawn the cation with the 1,3-diH structure 14 or with the 1,2-diH structure 15, but without any proof. 35,36In the solid state (see "Geometries" section) only cations 14 have been reported.
The tautomerism of indazoles and benzotriazoles is related to their aromaticity and to lone pair/lone pair repulsion on adjacent N atoms (for instance in 12).8b,9a,b, 37,38 Acid-base equilibria From two sources we have found data relevant to this part of our paper.In the National Institute of Standards and Technology (NIST) database the following values are reported: 39 proton affinity, PA, (benzimidazole) = -953.8;PA (indazole) = -900.8;acidity Hº (indazole) = 1457; Hº (benzotriazole) = 1415 kJ mol -1 .In our review 40 Equations 3 and 4 are excellent; however, equation 5 is far from acceptable.The values of the pKas determined in water that correspond to deprotonation (from neutral to anion) are probably contaminated by solvent and counterion effects.The fact that the pK a s of azoles and benzazoles can be calculated theoretically with accuracy is well established.9k,41

Chemical shifts
All the calculated absolute shieldings as well as all the known chemical shifts are reported in Table 3. Due to fast prototropic exchange between the N atoms, some values of compounds 1, 12 and 15 in solution have been averaged.The data of Table 3 when analyzed afford the following equations: Equations 9, 11, and 13 were calculated to afford a value for the carbon C-2 of benzimidazole, that systematically deviated by about 7 ppm.It appears that the B3LYP/6-311++G(d,p) cannot reproduce satisfactorily this atom, may be because it is situated between an N(H) pyrrole-like and an N pyridine-like nitrogen atom.An attempt to improve the results using GIAO/MP2/6-111++G(d,p) calculations failed.Using equations 7 and 13 the following values are predicted for the carbenes 3 (benzimidazol-2-ylidene) and 9 (indazol-3-ylidene) in their singlet and triplet states (Figure 6).The chemical shifts are very different, including some carbons of the benzene ring, particularly in the case of 9.][52]

Aromaticity
We discuss the aromaticity of the compounds of the present work using Schleyer's NICS.We have calculated their values at 0, 1 and 2 Å (Table 4), but we will use the NICS(1) values as a good compromise between NICS(0), too close to the sigma frame, and NICS(2), less sensitive.For non-planar compounds, carbenes 3t (triplet), 9s (singlet) and 9t (triplet), we have calculated the NICS above and below the ring plane.However, as the perturbation arises from H atoms, the values are very similar and in Figure 7 we have averaged their values.We also report the sum of the NICS of the 6-and the 5-membered rings (, ppm).The values reported in Table 5 deserve several comments: i) If we consider  as a descriptor of the aromaticity of the benzazoles,  increases in absolute value (the compound becomes more aromatic) in the order benzimidazole < indazole < benzotriazole and in the order cation < neutral < anion.Thus, the less aromatic is the cation benzimidazolium (4) and the most aromatic is the benzotriazolate anion (16).Martin et al. reported that, according to NICS approach, indazole is more aromatic than benzimidazole. 53ovak et al. reported that the NICS of the 6-membered ring is lower for 13 than for 12. 54 ii) The singlet carbenes, 3s and 9s, are aromatic compounds with  values about -20 ppm similar to the cations, 4 and 10.Using other aromaticity criteria, imidazol-2-ylidenes appear slightly less aromatic than imidazolium cations. 55For Arduengo's N-heterocyclic carbene 17 a NICS(1) value of -9.4 ppm (Scheme 7) has been recently reported. 56ii) The 6-membered ring is always aromatic but varies from -5.85 (9t) to -11.8 (4).Tautomerism affects the NICS of this ring, being greater in the more aromatic tautomer (benzenoid: 6, 12) than in the less aromatic tautomer (quinonoid: 7, 13).In singlet carbenes, NICS values of the 6-membered ring are similar to those of the corresponding cations.In triplet carbenes, the 6-membered ring suffers a great decrease in aromaticity, more in indazoles than in benzimidazoles probably related to the distance between the carbene and the benzene ring.iv) Excluding triplet carbenes, the values of the NICS(1) of the 5-membered ring range from -9.1 (4) to -15.2 ppm ( 16), as reflected in the  values.v) Triplet carbenes, 3t and 9t have non-aromatic 5-membered rings.This is a new and interesting result.It is known that between singlet and triplet states there is an inversion of aromaticity and antiaromaticity. 57Here, we move from an aromatic singlet to a non-aromatic triplet.
We decided to use a technique we have recently developed to represent the NICS values on one van der Waals isosurface. 58Figure 7 illustrates the NICS values on the electron density isosurface of 0.001 au (vdW).Blues areas correspond to regions with NICS values less than -5 ppm, while red ones belong to positive NICS values.For instance, similar distributions can be found in the 6-membered ring when comparing 1H-benzimidazole (1) and 1H-indazole (6), but some differences appear in the 5-membered ring.Thus, comparing 6 and 7, the effect of the position of the NH proton, either on N-2 or on N-1, is observed.When the proton changes from N-2 to N-1, there is an enlargement of the negative area on the 5-membered ring concomitantly with a contraction of the area over the 6-membered ring.These effects are reflected in the minimum values on the vdW surface, which suffer an inversion from 6 (-6.2, -5.7 ppm, 6-and 5-membered rings, respectively) to 7 (-5.6,-6.4 ppm, 6-and 5-membered rings, respectively) (Table 6).The same features can be observed for the compounds 12 and 13.Cations 4 and 10, present very similar NICS arrangement to those observed in the neutral parent molecules (1 and 6) with a main difference, the negative area on the 5-membered ring is considerably smaller that in the neutral ones.The protonation of 12 to afford 14 is accompanied by a slight decrease (in absolute value) of the minimum NICS value on the 5-membered ring (from -6.5 to -6.0 ppm), while that of the 6-membered ring remains almost constant.The same occurs in going from 13 to 15 that present slight differences, appreciable in both rings.In the comparison between 14 (1,3-diH) and 15 (1,2-diH), the effect of the position of the proton is again apparent, following the same pattern observed in the comparison between 6 and 7 (or between 12 and 13).The comparison of the negative zones over the rings in the anions 5, 11 and 16 shows the increasing negative NICS values on both rings in going from benzimidazolate to indazolate and to benzotriazolate, being this increase larger for the 5-membered ring than for the 6-membered ring.
The case of the singlet carbenes can be observed comparing the 3s and 9s compounds.The position of the carbene corresponds to the yellow region around the C atoms (C-2 and C-3), showing more negative values around it than in the vicinal C atoms.Finally, one interesting observation results from the comparison between singlet and triplet states.When the surfaces of 3s and 3t are examined, the increase of the NICS values is evident.The minimum located on the 6-membered ring becomes less deep (from -6.2 to -4.5 ppm, Table 6) and that over the 5membered one completely disappears.Instead of the minima, a large positive NICS value area is present over the 5-membered ring.Similar, but enhanced features, are observed in the 9s vs. 9t comparison, where the variation of the 6-membered ring minimum is more pronounced (from -6.2 to -3.4 ppm).These are in agreement with the non-aromatic nature of the triplet carbenes discussed previously.

Conclusions
Because here, for the first time, the most significant neutral (including Arduengo's carbenes), cationic and anionic structures of the three benzazoles have been compared, some interesting conclusions can be reached: -Some errors in the literature concerning the position of NH-protons in one X-ray structure (ULOLUC) have been found.
-The calculated relative energies of the different tautomers agree with experimental results.
-The acid base properties of the three benzazoles are in excellent agreement with gas-phase measurements; for aqueous pKas the calculations agree very well with the basicity but only poorly with the acidity.
-The correlations found between experimental chemical shifts and calculated absolute shieldings could be used to estimate the chemical shifts of the compounds where no data are available.For instance, the estimated values for the C-2 atoms in 3s (223.3 ppm) and in 3t (112.2 ppm) when compared with the experimental value of carbene 3″ (223.0 ppm) are further proofs that 3″ is a singlet carbene.
-The aromaticity of all the compounds were discussed based on Schleyer's NICS values.The most important conclusion is that the triplet carbenes are not aromatic while the singlets are aromatic.
-The representation of NICS values over the van der Waals surface is a useful approach to visualize the aromaticity of these systems.

Figure 5 .
Figure 5. Structures of the carbenes.Those of 3′ were determined by X-ray crystallography and  = 5.3º correspond to the average.

a
Values correspond to up (down) positions over the ring.

Table 3a .
aCalculated absolute shieldings (, ppm) and experimental chemical shifts (, ppm) aHere we list only the compounds for which experimental data are available.

Table 4 .
NICS values on both rings of benzazoles determined in the center of the ring at 0, 1 and 2 Å above the ring plane

Table 6 .
Minimum NICS values on the van der Waals surfaces