Introduction

1,3,4-Oxadiazoles are very interesting in medicinal chemistry. Besides, derivatives of 1,3,4-oxadiazoles have been reported to exhibit diverse biological activities. It is frequently used in pharmaceutical industry [1–6]. Various oxadiazole-containing molecular structures were synthesized [7–13]. Furthermore, the 1,3,4-oxadiazole ring which is a new NLO motifs among the heterocyclic compounds were used as a π-bridge on the ground. Its reduced aromaticity may offer better prospects for π-electron delocalization across the D–A links [13]. However, typical electron-transporting materials usually contain a π-electron deficient heterocyclic moiety, such as oxadiazoles, triazoles, triazines, etc., which can effectively improve the electron affinity [14].

Experimental measurements and theoretical calculations on NMR chemical shift become one of the key factors in the molecular structure correlations design. Theoretical determination of NMR chemical shift is quite useful both for understanding the relationship between the molecular structure and electronic properties of molecules. It also provides a guideline to experimentalists for the design and synthesis of organic materials [6].

The aim of the present work is to describe and characterize the relation between the molecular structure and chemical shifts correlations of 2-aryl-1,3,4-oxadiazoles 5a–g. A number of papers have recently appeared in the literature concerning the calculation of NMR chemical shift (c.s.) by quantum-chemistry methods [15–20]. These papers indicate that geometry optimization is a crucial factor in an accurate determination of computed NMR chemical shift. Moreover, it is known that the density functional theory (DFT) (B3LYP) method adequately takes into account electron-correlation contributions, which are especially important in systems containing extensive electron conjugation and/or electron lone pairs. However, as molecular size increases, computing-time also increases. To optimize computing-time the DFT level was used. It was proposed that the single-point calculation of magnetic shielding by DFT methods was combined with a fast and reliable geometry-optimization procedure at the molecular mechanics level [19].

The gage-including atomic orbital (GIAO) [21–24], individual gages for atoms in molecules (IGAIM) [25] and continuous set of gage transformations (CSGT) [25–28] methods are three of the most common approaches for calculating nuclear magnetic shielding tensors. GIAO has been shown to provide results that are often more accurate than those calculated with other approaches, at the same basis set size [29]. In most cases, in order to take into account correlation effects, post-Hartree-Fock calculations of organic molecules have been performed using (i) Møller-Plesset perturbation methods, which are very time consuming and hence applicable only to small molecular systems, and (ii) density functional theory (DFT) methods, which usually provide significant results at a relatively low computational cost [30]. In this regard, DFT methods in which the electron-correlation contributions are not negligible have been preferred in the study of large organic molecules [31], metal complexes [32], organometallic compounds [33]. For these cases GIAO 13C c.s. calculations [29] were used.

2-Aryl-1,3,4-oxadiazoles 5a–g were synthesized and characterized by 1H NMR, 13C NMR, IR, and elemental analysis [6]. And also, theoretical analysis of vibrational spectra and scaling-factor of these molecules were studied in our previous work [34]. To the best of our knowledge, the theoretical calculations of chemical shifts and the effects on chemical shifts of different NMR methods and basis sets for 2-aryl-1,3,4-oxadiazoles 5a–g have not been investigated yet. In this study, GIAO, IGAIM, and CSGT 1H and 13C NMR chemical shifts of the title compounds in the ground state have been calculated by using the Hartree-Fock (HF) and DFT (B3LYP) methods with 6-31G(d), 6-311G(d), 6-31++G(d,p), 6-311++G(d,p), and 6-311++G(df,pd) basis sets. These results were compared with the experimental 1H and 13C NMR chemical shifts (CDCl3). A comparison of the experimental and theoretical spectra can be very useful in making correct assignments and understanding the basic chemical shift-molecular structure relationship. And so, these calculations are valuable for providing insight into molecular structure analysis.

Computational details

The molecular structures of the title compounds (5a–g) in the ground state (in vacuo) are optimized HF and B3LYP methods with 6-31G(d), 6-311G(d), 6-31++G(d,p), 6-311++G(d,p), and 6-311++G(df,pd) basis sets. The geometry of tetramethylsilane (TMS) is fully optimized. 1H and 13C NMR chemical shifts for TMS and the title compounds (5a–g) are calculated with GIAO, IGAIM, and CSGT approaches [21–28]. First, these approaches were applied to the B3LYP and HF methods [29, 35] with 6–31G(d), 6-311G(d), 6-31++G(d,p), 6-311++G(d,p), and 6-311++G(df,pd) [36–38] basis sets for dihedral angles at 180.0 (C4–C3–C2–O) and 0.0 (C4–C3–C2–N) degrees. Second, conformational analysis formation was performed by B3LYP/6-31G(d) level; it was carried out by changing the torsional angle (dihedral angle, ϕ, C–C–C–O). For each conformer, the torsional angle was held fixed while all other geometric parameters were optimized. And so, two conformers were obtained at dihedral angles: −135 and −90°. These conformers for the chemical shift calculations of the title compounds (5a–g) were used. Besides, the calculations of 1H and 13C NMR chemical shifts using GIAO and CSGT approaches with the BLYP/6-311++G(df,pd) level for 5a–e were done. The theoretical NMR 1H and 13C chemical shift values were obtained by subtracting isotropic magnetic shielding (IMS) values which are calculated with GIAO, IGAIM, and CSGT from the IMS values of TMS [29, 35, 39]. For instance, the average 13C IMS of TMS are taken into account for the calculation of 13C c.s. of any X carbon atom, and so c.s. can be calculated using the following equation δCSx = σIMSTMS-σIMSx. The 1H and 13C IMS values of TMS were given in Table 1. And these values were used for the calculation of c.s. All the calculations are performed by using Gauss-View molecular visualization program [40] and Gaussian 98 program package [41].

Table 1 The isotropic magnetic shielding constants (in ppm) of TMS for C and H calculated at different GIAO, IGAIM, and CSGT models with basis sets
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Results and discussion

The atomic numbering with the geometric structure of the title compounds (5a–g) are shown in Fig. 1.

Fig. 1
figure 1

The schematic illustration of 2-aryl-1,3,4-oxadiazole derivatives (5a–g). ϕ = C4–C3–C2–O

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The dihedral angles between the five-membered 1,3,4-oxadiazole ring and the aryl ring are 0.0 or 180.0°. Therefore, the molecular structures of 5a–e molecules are planar (Cs-symmetry) and are displayed in Fig. 1. The other molecular structures of 5f,g which are non-planar (adopted C1-symmetry) are demonstrated in Fig. 1. Since these molecular structures of 5f,g include methyl group bounded to the aryl ring. The different meta and para substitutents (–Br, –Cl, and –Methyl) dependent on the aromatic ring are defined by molecular structure and chemical shifts correlations. Also, the orientation of the substitutents with respect to the aryl ring is determined by the torsion angles C–C–C–Br [180.0°] and C–C–C–Cl [180.0°] and C–C–C–CH3 [different from 180.0°] [34]. Besides, two conformers with C1-symmetry of 5a–g which have dihedral angles (ϕ = C4–C3–C2–O) have been obtained to be −135.0 and −90.0° using B3LYP/6-31G(d) level.

In previous work, nuclear magnetic shielding values of TMS were calculated with GIAO and CSGT approach applying B3LYP/6-311+G(2d,p) and HF/6-31G(d) levels [29]. For 13C and 1H chemical shift values, the values of TMS display significant. The convergence of the GIAO and CSGT methods with HF/6-31G(d) and B3LYP/6-311+G(2d,p) levels for absolute shielding constants were demonstrated [29]. The shielding constant of GIAO and CSGT with HF/6-31G(d) and B3LYP/6-311+G(2d,p) levels for C were calculated to be 195.1 and 188.5, and 190.8 and 188.6 ppm, respectively [29]. Besides, nuclear magnetic shielding values of TMS were obtained from GIAO model applying B3LYP method with 6-31G(d), 6-31+G(d), 6-31+G(d,p), 6-31++G(d,p) basis sets and HF method with 6-31G+(d) basis set [42, 43]. These calculations are not sufficient in our study. Since obtained nuclear magnetic shielding values of TMS using the different NMR models and basis sets are different from each other. So, the calculation of new TMS values for C and H are beneficial to compare with experimental chemical shifts. The nuclear magnetic shielding values of TMS are calculated using GIAO, IGAIM, and CSGT approaches applying B3LYP and HF methods with 6-31G(d), 6-311G(d), 6-31++G(d,p), and 6-311++G(d,p) basis sets. These TMS values are depicted in Table 1, and these are used in calculations of chemical shifts. Initially, nuclear magnetic shielding calculations have been based on optimized molecular structures which are dihedral angles at 180.0 (C4–C3–C2–O) and 0.0 (C4–C3–C2–N) degrees by using B3LYP method with 6-31G(d), 6-311G(d), 6-31++G(d), and 6-311++G(d,p). Then, GIAO, IGAIM, and CSGT 13C and 1H c.s. calculations of the title compounds (5a–g) have been carried out using B3LYP and HF method with these basis sets. The 13C and 1H chemical shift values (with respect to TMS) were compared to the experimental 13C and 1H chemical shift values [6]. These results are shown in Tables 2–8. The IGAIM 13C and 1H c.s. calculations of the title compounds (5a–g) are identical to the CSGT ones. Therefore, the results of IGAIM were not given. According to performed calculations for 5a–g, we have found ~176.0 to ~20.0 ppm and ~9.0 to ~1.0 ppm for 13C and 1H the chemical shift values (with respect to TMS). The experimental results were observed to be ~165.0 to ~21.0 ppm and ~8.50 to ~2.0 ppm [6], and so the accuracy ensures reliable interpretation of spectroscopic parameters. As can be seen from Fig. 1, molecular structure of the title compounds (5a–g) includes Br, Cl, and methyl bounded to aromatic rings. The electronegative properties of Br, Cl, etc. atoms are well known, and the resonance at 8.11–7.48 ppm was assigned to the aromatic ring-H atom [6] for 5a. This c.s. calculated at ~9.0 to ~4.8 ppm for all calculations. Besides, in 1,3,4 oxadiazole ring C bounded H chemical shift were observed to be 8.50–8.42 ppm [6]. This chemical shift has been obtained to be 8.51–8.33 ppm for all calculations. The other aromatic-H (5b–g) was observed to be 8.24–7.34 ppm for 5b, 7.98–7.50 ppm for 5c, 8.05–7.44 ppm for 5d, 8.03–7.50 ppm for 5e, 7.90–7.31 ppm for 5f, 7.99–7.18 ppm for 5g [6]. These chemical shifts for 5a–g have been calculated to be ~9.2 to ~4.3 ppm with regard to the different models and basis sets. The data are shown in Tables 2–8. Furthermore, 13C chemical shift values (with respect to TMS) of 1,3,4 oxadiazole ring have been calculated to be ~176.0 ppm (CSGT-HF/6–31++G(d,p)) to ~144.0 ppm (GIAO-B3LYP/6-31G(d)) for 5a, 5f, and 5 g ~175.0 ppm (CSGT-HF/6-31++G(d,p)) to ~144.0 ppm (GIAO-B3LYP/6-31G(d)) for 5b, 5c, 5e ~175.0 ppm (CSGT-HF/6-31++G(d,p)) to ~145.0 ppm (GIAO-B3LYP/6-31G(d)) for 5d, 5e. These shifts were observed to be 164.79 and 152.67 ppm for 5a, 163.53 and 152.87 ppm for 5b, 164.11 and 152.74 ppm for 5c, 163.17 and 152.84 ppm for 5d, 164.01 and 152.73 ppm for 5e, 164.90 and 152.56 ppm for 5f, and 164.89 and 152.37 ppm for 5 g [6]. These shifts are convenient because of the same chemical environment. According to two conformers, the chemical shift of C1 atom increase while the chemical shift of the C2 generally does not changes. These results are tabulated in Tables 9–12. In 13C substituent effects in mono substituted benzenes were studied by Ewing [44]. The chemical shift values of ipso C substituted meta Cl, Br, and methyl group substituents in the benzene ring were observed to be 122.6, 134.9, and 137.8 ppm. In ortho C, these shifts were found to be 131.5, 128.7, and 128.4 ppm. Besides, the chemical shift values of the meta and para C have been calculated to be 130.0, 129.5, 129.2 ppm (meta C) and 126.0, 126.5, and 125.5 ppm (para C) [44]. According to these results, the inductive effect on the ipso and orto C are appeared. Explicitly, effects of these substituents on the title compounds (5a–g) are displayed. The chemical shift values of aromatic-C atom (ipso C) bounded Br and Cl atoms, and methyl group obtained with respect to the different models and basis sets supports to the results of Ewing (in Tables 2–12). Besides, these results demonstrated variation of chemical shift with respect to the electronegativity. That is, the effect of an electronegative group or atom on the chemical shift also depends on its distance from the proton. In aromatic ring, the aromatic C–Cl and –Br are separated from each other by one bond, and their chemical shifts are further downfield than ~130.0 ppm for aromatic C.

Table 2 Theoretical and experimental 13C and 1H isotropic chemical shifts (with respect to TMS, all values in ppm) for 2-Phenyl-1,3,4-oxadiazole (5a)
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Table 3 Theoretical and experimental 13C and 1H isotropic chemical shifts (with respect to TMS, all values in ppm) for 2-(3-Bromophenyl)-1,3,4-oxadiazole (5b)
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Table 4 Theoretical and experimental 13C and 1H isotropic chemical shifts (with respect to TMS, all values in ppm) for 2-(4-Bromophenyl)-1,3,4-oxadiazole (5c)
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Table 5 Theoretical and experimental 13C and 1H isotropic chemical shifts (with respect to TMS, all values in ppm) for 2-(3-Chlorophenyl)-1,3,4-oxadiazole (5d)
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Table 6 Theoretical and experimental 13C and 1H isotropic chemical shifts (with respect to TMS, all values in ppm) for 2-(4-Chlorophenyl)-1,3,4-oxadiazole (5e)
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Table 7 Theoretical and experimental 13C and 1H isotropic chemical shifts (with respect to TMS, all values in ppm) for 2-m-Tolyl-1,3,4-oxadiazole (5f)
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Table 8 Theoretical and experimental 13C and 1H isotropic chemical shifts (with respect to TMS, all values in ppm) for 2-p-Tolyl-1,3,4-oxadiazole (5g)
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Table 9 Theoretical and experimental 13C and 1H isotropic chemical shifts in different dihedral angles (with respect to TMS, all values in ppm) for 2-Phenyl-1,3,4-oxadiazole (5a)
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Table 10 Theoretical and experimental 13C and 1H isotropic chemical shifts in different dihedral angles (with respect to TMS, all values in ppm) 2-(3-Bromophenyl)-1,3,4-oxadiazole (5b) and 2-(4-Bromophenyl)-1,3,4-oxadiazole (5c)
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Table 11 Theoretical and experimental 13C and 1H isotropic chemical shifts in different dihedral angles (with respect to TMS, all values in ppm) for for 2-(3-Chlorophenyl)-1,3,4-oxadiazole (5d) and 2-(4-Chlorophenyl)-1,3,4-oxadiazole (5e)
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Table 12 Theoretical and experimental 13C and 1H isotropic chemical shifts in different dihedral angles (with respect to TMS, all values in ppm) for for 2-m-Tolyl-1,3,4-oxadiazole (5f) and 2-p-Tolyl-1,3,4-oxadiazole (5g)
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The chemical shifts for ortho-protons and carbons changes related to the two conformers. While the chemical shifts of ortho-protons decrease with the different dihedral angles (−135.0 and −90.0°), the chemical shifts of ortho-carbons increase with the different dihedral angles (−135.0 and −90.0°). This situation can be clearly seen in Tables 2 and 3. In addition to this, the dihedral angle with −90.0° more increase for ortho-protons than the −135.0°. Similarly, the dihedral angle with −90.0° more decrease for ortho-carbons than the −135.0°. As a result, the magnitudes of the chemical shifts of 5a–g are dependent on dihedral angles in different conformers. The electron-correlation effects are well known to influence 13C chemical shifts deeply in cases. In relation to this, the choice of basis sets is also a critical point in any computational study on spectroscopic properties. Therefore, the 13C and 1H chemical shift values of 5a–g were calculated using HF, B3LYP, and BLYP methods with 6-311++G(df,pd) basis set. These results are given in Tables 2–8. Calculated with GIAO model, 13C chemical shift values of 5a–g are bigger than the other calculations. But, 1H chemical shift values of 5a–g are lower than the others. The results of CSGT model with HF/6-311++(df,pd) level for 13C and 1H chemical shifts are similar to the HF/6-311++(d,p) level. The results of CSGT model obtained with BLYP and B3LYP/6-311++(df,pd) levels for 13C and 1H chemical shifts are roughly similar to the HF/6-311++(d,p) levels. In this sense, due to the deficient of electron correlation, we expected that the results obtained at HF method with larger basis sets (6-311++G(3df,3pd), etc.) are bigger than DFT methods with the same basis sets.

To make comparison with experimental results, we present linear correlation coefficients (R2) for linear regression analysis of theoretical and experimental 13C isotropic chemical shifts. These values are given in Table 13. The linear correlation coefficients of BLYP/6-311++G(df,pd) level of theory with GIAO and CSGT methods have been found to be 0.89903 and 0.90224 for 5a, 0.68276 and 0.63057 for 5b, 0.62452 and 0.56665 for 5c, 0.90604 and 0.84959 for 5d, and 0.93029 and 0.89324 for 5e. These results are approximately the same number of B3LYP/6-311++G(df,pd) method. As one can easily see from linear correlation coefficients in Table 13, the experimental shifts are in better agreement with the CSGT-HF/6-31++G(d,p) for 5a, GIAO-HF/6-311++G(df,pd) for 5b, 5d, and 5f, CSGT-HF/6-31G(d) for 5c, CSGT-B3LYP/6-31G(d) for 5e, and GIAO-B3LYP/6-31G(d) for 5g. As can be seen from Tables 2–12, there is a good agreement between the experimental and theoretical 1H chemical shift results for the title compounds (5a–g).

Table 13 Linear correlation coefficients (R2) of linear regression analysis of theoretical and experimental 13C isotropic chemical shifts for 2-aryl-1,3,4-oxadiazole derivatives (5a–g)
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Conclusions

In this study, to test the different theoretical approaches GIAO and CSGT at both HF and DFT level of theory with different basis sets reported. The computed at dihedral angles in different conformers and experimental chemical shifts of the title compounds (5a–g) have been compared. With respect to the different conformers, the changes of chemical shifts of ortho-protons and carbons for 5a–g are explicitly displayed. The comparison of the GIAO and CSGT methods shows that the latter are more sensitive to the quality of the basis set employed. In other words, convergence of calculated chemical shifts is faster with the CSGT method. In particular, calculations by HF method with 6-31G(d), 6-31++G(d,p), and 6-311++G(df,pd) basis sets provide quite good results for 5a–d and 5f. While the linear correlation coefficients of GIAO and CSGT models for the molecules (5b–d) which aromatic ring is bounded at meta or para positions of different electronegative atoms (Cl and Br) are different, the molecules (5a, 5e–g) are roughly similar. Although the B3LYP level of theory includes the effects of electron correlation, the B3LYP is not quite as accurate as HF for 13C chemical shifts. In these state, geometric parameters and chemical shifts for diverse molecular structure analysis change with respect to the different theoretical approaches. However, the NMR spectrum is used in chemical analysis to determine the structures of complicated organic molecules.

The 13C chemical shifts calculations of the title compounds (5a–g) are directly related to linear correlation coefficients (R2) of GIAO and CSGT calculations. Linear correlation coefficients (R2) of the larger molecules 5f and 5g have been obtained as better than the others (5a–e). Further variation in meta and para positions of the aromatic-substituent groups and the π-conjugation network containing the oxadiazole ring in the core structure is necessary for reaching a concrete inference.