Aromaticities of Five Membered Heterocycles through Dimethyldihydropyrenes Probe by Magnetic and Geometric Criteria

Aromaticities of five membered heterocycles, containing up to three heteroatoms, are quantified through the dimethyldihydropyrene (DHP) probe. Bond fixation caused by the fusion of heterocycles to the dimethyldihydropyrene nucleus (DHPN)wasmeasured by changes in the H NMR chemical shifts (magnetic) and bond lengths alterations (structural criterion). Chemical shifts of dihydropyrenes were calculated at GIAO HF/6-31G(d)//B3LYP/6-31+G(d). For HNMR chemical shift analysis, two nonaromatic referencemodels are studied. Among the studied heterocycles, pyrazole and triazole are about 80–85% aromatic relative to benzene, through both magnetic and geometric criteria. Thiazole and oxazoles are found least aromatic where quantitative estimates of aromaticities are about 34–42%, relative to benzene. These quantitative estimates of aromaticities of five membered heterocycles are also comparable to those from aromatic stabilization energies. The quantification of aromaticity through energetic, magnetic, and structural criteria can deliver the similar inferences provided that suitable reference systems are chosen.


Introduction
Aromaticity is a fundamental and commonly used concept in chemistry.Aromaticity is universally understood by convention because it is not a directly measurable quantity.Qualitatively, a compound can be easily categorized as aromatic, nonaromatic, or antiaromatic.However, quantifying the extent of aromaticity has become highly controversial.A number of methods have appeared in the literature for the quantification of aromaticity since the concept was first introduced by Kekulé [1].However, no single method could get the universal acceptance.Our perception about the aromaticity of a compound may vary considerably depending on the method chosen for quantitative analysis [2].Any method chosen for quantification of aromaticity generally relies on a single criterion [3], whereas the aromaticity is multidimensional in nature (composed of energetic, magnetic, and structural components).
A third category of methods for the quantification of aromaticity is based on magnetic properties.Magnetic criterion of aromaticity quantification includes magnetic susceptibility exaltation [36][37][38][39][40][41][42][43][44][45][46][47], anisotropy of magnetic susceptibility, NMR (chemical shifts and coupling constant analysis) [42,[48][49][50][51][52][53][54], and nucleus independent chemical shifts (NICS) [55].In the chemical shift analysis, the atom of interest above the aromatic nucleus is either bonded covalently or placed artificially (through noncovalent interactions).The latter includes 3 He and 9 Li nuclei placed above the aromatic nucleus [42,[48][49][50][51][52][53][54], whereas the former involves 1 H chemical shift [56,57] analysis of probe protons, usually in the center of the nucleus under consideration.A probe molecule for 1 H chemical shift analysis must meet the following two requirements: (i) ring current in the probe molecule is only affected by the delocalization of electrons and (ii) through space anisotropic effect should not affect the chemical shifts of the probe protons.15,16-Dimethyldihydropyrene 1 (Figure 1) is an excellent probe molecule in this regard.The internal methyl protons in the dihydropyrene are highly shielded due to diatropic ring current (by 5.2 ppm), compared to the nonconjugated model 2, and [a] or [e] fusion of an arene to the dihydropyrene nucleus results in the reduction of ring current of the dihydropyrene nucleus.This reduction in the ring current is proportional to the aromaticity of the arene fused.A highly aromatic arene will cause much larger reduction in the ring current, and vice versa.For example, fusion of benzene ring to the DHPN (3) causes 58% bond fixation whereas a less aromatic octadehydro [14]annulene (in 4) causes 30% bond fixation [57].Fusion of an arene to DHP not only causes change in the ring current of the DHPN (vide supra) but also affects the geometric parameters.Therefore, the results from magnetic (NMR) criterion can easily be correlated with the geometric parameters (bond fixation).
The dimethyldihydropyrene probe has successfully been applied to the quantification of aromaticities of a number of arenes including polycyclic aromatic hydrocarbons [56] and heteroarenes.Recently, we have successfully applied the chemical shift analysis of DHPN to quantify the aromaticities of six membered nitrogen containing heterocycles (azines) [58].For example, the azine fused DHP 5 is used for the quantification of aromaticity of pyridine.In this work, we extend our recently developed approach to the quantification of aromaticities of five membered heterocycles.Two different nonaromatic reference models are tested for the quantification of aromaticities, and the results are compared with bond fixation values obtained from structural criterion.Moreover, the results are compared to the HOMA and ASE for these heterocycles.

Choice of the Reference System.
In our recent study on the quantification of aromaticity of azines [58], choice of a suitable reference model is shown to play very crucial role due to anisotropic effect [60], arising from heteroatoms.We had compared different nonaromatic models (shown below in Figure 3) and the best nonaromatic model for reliable estimate of quantification of aromaticity is the one with partial unsaturation of the azine (pyridine).Partially saturated nonaromatic reference model ( 7) is very similar to the azine under study except that it lacks the aromaticity of azine.Compound 8 was used as a nonconjugated reference model for the quantification of aromaticity; however, compound 2 can also be used with negligible effects on the results (Figure 2).
The importance of selecting a suitable reference model was also reported during the quantification of aromaticity of cyclopentadienone 9 [61].The cyclopentadiene fused DHP (10) was more reliable reference model than the cyclopentanone DHP 11.

Parent DHP as a Reference
Model.Over the past three decades, dihydropyrene has emerged as an excellent probe for the quantification of aromaticity [56,61].Generally, change in the ring current of the DHPN by fusion with an arene is described by change in the chemical shift of the internal protons with reference to the parent DHP 1 (DHP 1 is the reference model).For example, change in ring current of the dihydropyrene nucleus (DHPN) on fusion with heterocycle (pyrrole) is follows: O O The equation above is actually a measure of bond fixation in the dimethyldihydropyrene nucleus by fusion with an aromatic moiety.Based on the formula above, aromaticity of arene (pyrrole) relative to benzene can be estimated by This approach has been successful for the quantification of aromaticity of carbocycles such as benzene, naphthalene, anthracene [56], cyclopentadienone [61], and cyclooctatetraene [62] (vide supra).Heterocycles present additional anisotropy effects, as well as potential conjugation effects, therefore, have not been extensively studied for the quantification of aromaticity through DHP probe.For such instances, the parent DHP 1 cannot serve as a better reference model compound; therefore, the reference model and the equations to calculate the aromaticity are modified.
The decrease in the delocalization of pyrrole fused DHP 12 through reference model 14 can be calculated using Aromaticity of pyrrole relative to benzene can be calculated by The chemical shifts of the methyl protons in nonconjugated models (5 and 16) are not very different than the chemical shifts of similar protons in 2 [58], and it is expected that the chemical shifts of the internal protons of 13 will not be significantly different as well.Indeed, the internal methyl protons in 13 appear at  1.14 compared to  1.12 for 2. With these approximations, (4) can be modified to (5).In this study, (2) and ( 5) are used for the quantification of aromaticity of five membered heterocycles.

Computational Methods.
All calculations were performed with Gaussian 09 suite of programs [63].Geometries of the structures were optimized without any symmetry constraints at hybrid B3LYP method using 6-31+G * basis set [64].The B3LYP method consists of three parameter hybrid functional of Becke [65] in conjunction with the correlation functional of Lee et al. [66].The B3LYP method provides a nice balance between cost and accuracy, and it is known to perform very well for the prediction of geometries of a number of dihydropyrenes [67].Each optimized structure was confirmed by frequency analysis at the same level (B3LYP/6-31+G(d)) as a true minimum (no imaginary frequency).
1 H NMR chemical shifts were calculated by Hartree-Fock (HF) gauge independent atomic orbital (GIAO) method at 6-31G * basis set on the B3LYP/6-31+G(d) optimized geometries (GIAO-HF/6-31G(d)//B3LYP/6-31+G * ).GIAO-HF/6-31G * was chosen because the predicted aromaticities of a number of dihydropyrenes through this method correlate very well with the experiment [68].The three hydrogens of the methyl group appeared different due to their fixed positions in magnetically different environment.The reported values are averaged chemical shifts.

Five Membered Heteroatomic Rings.
Pyrrole can be fused to DHP in two different ways to deliver dihydropyrenes 12 and 17 (Figure 4).We had shown previously that isomeric fusion of heteroarenes (azines) to the DHPN can deliver somewhat different estimate of aromaticity even though when there is complete delocalization in each fragment.However, if the delocalization in one fragment is blocked by the other fragment, then the estimate of aromaticity is not reliable.Fusion of pyrrole to the DHP fragment in 12 allows equal chance of delocalization of  electron in each fragment; however, the situation is different in 17.Fusion of pyrrole to DHPN in 17 causes almost complete loss of aromaticity of DHPN nucleus (vide infra) because the  electronic cloud is not available for delocalization on DHPN.Therefore, compound 12 is ideal for estimation of aromaticity of pyrrole.
The internal methyl protons in 12 appear at  av −3.31, for both methyl groups, which indicates that the anisotropic effect arising from nitrogen is either negligible or very similar for both methyl groups.The internal methyl protons in 2 are calculated at  1.12.Therefore, the internal protons in 12 are shielded by only 4.43 ppm, compared to 7.40 ppm for the parent DHP 1 ( theor −6.29).The DHPN in pyrrole DHP 12 retains about 59.8% of its aromaticity which means that the pyrrole ring causes 40.2% bond fixation in the DHPN.This bond fixation is relatively small compared to 58.9% bond fixation caused by the benzene ring (see Table 1 for details).The relative aromaticity of pyrrole to benzene, calculated through (2), is 68.2%.It is important to mention that the  experimental chemical shifts are available for the benzo DHP 3; however, to maintain consistency, theoretical values are used for bond fixation calculations in this study.The higher aromaticity of benzene can be rationalized by Clar rule [69].
The internal methyl protons in the isomeric 17 appear at  −0.31 which indicates that the pyrrole ring in this fusion has caused almost complete loss of aromaticity of DHPN (as expected).A similar behavior is also observed in the thiophene fused dihydropyrenes 18 and 19.The internal protons in 19 appear at  0.24 compared to  −4.16 for 18.The bond fixation caused by a thiophene ring in 18 is 28.9% which indicates that the thiophene ring is only 48.9% aromatic relative to benzene.
Among heterocycles bearing three heteroatoms, oxadiazole (26) and triazole (27) are studied.The latter causes more reduction in the ring current (48%) as expressed by downfield signal at  −2.91.The aromaticity of triazaole is 82% relative to benzene, and this is very comparable to pyrazole.The internal methyl protons in oxadiazole are simulated to appear at  −3.59 which indicates 62% aromaticity relative to benzene.
The data in Table 2 reveal that the estimates of aromaticities using the nonaromatic reference models 14, 28-38 (through (5), shown in Table 2) are very similar to those from (2) (Table 1, when parent DHP is used as the reference).For example, the aromaticity of pyrrole relative to benzene is 68% (through (2)) compared to 64% when ( 5) is used for the aromaticity quantification.For thiophene, the difference in aromaticities measured through two different methods is even smaller; 48.9% (2) compared to 49.5% (5).The difference in percent aromaticities relative to benzene is within 5% (for both methods) for most of the heterocycles except that imidazole fused DHP 25, where 56.9% and 49.6% aromaticities are estimated relative to benzene through ( 2) and ( 5), respectively.
Although both methods deliver comparable estimates of aromaticities except imidazole and oxazole which reflects that the anisotropic effect of the heteroatom is very negligible on the chemical shifts of the internal methyl protons of DHPN.Moreover, it is also supported by the fact that both internal methyl protons in dihydropyrenes 12, 17-25 show similar chemical shifts (within 0.02 ppm units).However, to further confirm which of the abovementioned methods is more accurate regarding the estimates of aromaticities, geometric parameters have also been studied.The bond fixation in the DHPN also alters the bond lengths of the DHPN.Degree of change in bond lengths of the DHPN should also reflect the aromaticity of the arene fused.The results of the geometric analysis are given in Table 3 (for numbering scheme, see Figure 7).Analyses of the geometric data reveal that the aromaticity of imidazole relative to benzene is 59% which is very similar to the aromaticity values of 56.9% through (2) (magnetic criteria).Similarly, aromaticity value of oxadiazole through geometric criteria is 62.9% relative to benzene, which is again consistent with the value obtained through (2) (magnetic criteria).In general the results from the geometric criteria are very comparable to the results from (2) (when parent DHP 1 is the reference model).
The results here are contrary to our recent study where we have shown that these saturated reference models containing heteroatoms deliver better estimates of aromaticities.It may be possible that the anisotropic effect may be present in the saturated reference model which leads to unreliable estimates of aromaticities for these heterocycles.
Since both geometric and magnetic (NMR) based methods, in this study, deliver similar inferences about the aromaticities of five membered heterocycles; therefore, we are not only confident about the reliability of the results here but also illustrate that different criteria of aromaticity can deliver the same information if suitable model system is chosen.We also compared the results obtained here  with the literature aromaticity values for these heterocycles through other methods [70] (Table 4).The comparison of the results clearly illustrates that the results here are very comparable to the aromatic stabilization energy values.For example, ASE of pyrrole is higher than thiophene (20.59 versus 18.59) which indicates that the pyrrole ring is more aromatic than the thiophene.This is consistent with our calculations that higher bond fixation is observed caused by pyrrole than thiophene.Moreover, oxazole (Table 4 Entry 3) has even lower ASE which is consistent with our results here that the bond fixation caused by oxazole is lower than both thiophene and pyrrole.Among these heterocycles, the highest ASE is for 1,2,3 triazine (26.66) followed by pyrazole (23.9).It is interesting to note that triazole and pyrazole are the heterocycles which are shown to have the highest bond fixation in DHPN.
We have also compared our results to the HOMA values [71].Trends in estimate of relative aromaticities are very similar in a series of heterocycles.For example, both HOMA and NMR deliver the same trends in aromaticities of azoles: aromaticity of pyrazole > triazole > imidazole.Some differences do exist when two different series of heterocycles are studied (thiophene and pyrrole).With this comparison, we have shown that geometric, magnetic (this work), and energetic (literature) criteria of aromaticity can deliver the same trend in aromaticities of arenes provided that a suitable system is chosen.This further validates the potential of DHPN in quantifying the aromaticity of heteroarenes.

Conclusions
Aromaticities of five membered heterocycles containing up to three heteroatoms are quantified through the dimethyldihydropyrene (DHP) probe.Bond fixation caused by fusion of heterocycle to the dimethyldihydropyrene nucleus (DHPN) was measured by changes in the 1 H NMR chemical shifts (magnetic) and bond lengths alterations (structural criterion).Chemical shift data for dihydropyrenes were calculated at GIAO HF/6-31G(d)//B3LYP/6-31+G(d).For 1 H NMR chemical shift analysis, two nonaromatic reference models are studied.The parent DHP serves a better reference model for the quantification of aromaticities.The aromaticities of these heterocycles are descried relative to benzene.Among the studied heterocycles, pyrazole and triazole are the most aromatic which are about 80-85% aromatic relative to benzene, through both magnetic and geometric criteria.On the other hand, thiazole and oxazoles are found least aromatic where quantitative estimates of aromaticities are about 34-42% relative to benzene.The quantitative estimates of aromaticities through magnetic (2) and geometric parameters correlate nicely (within 5%).The maximum deviation between the two parameters is observed for pyrazole where 86.1% aromaticity is calculated through NMR, and 81.6% is calculated through geometric parameters.These quantitative estimates of aromaticities of five membered heterocycles are also comparable to those from aromatic stabilization energies.The quantification of aromaticity through energetic, magnetic, and structural criteria can deliver the same information provided that suitable systems are chosen.

Table 3 :
Bond fixation in DHPN and % aromaticity of heteroarenes calculated through geometric parameters.