1. Introduction

Heterocyclic compounds are ring compounds containing carbon and other element, the component being oxygen, nitrogen and sulphur. Thiadiazoles are heterocyclic compounds containing two nitrogen atoms and one sulfur atom as part of the aromatic five-membered ring. 1,3,4- thiadiazole are important because of their versatile biological actions[1]. There are number of thiadiazoles which contain the nitrogen in different positions such as 1,2,3-thiadiazole [2], 1,2,4-thiadiazole [3], 1,3,4-thiadiazole [4] and 1,2,5-thiadiazole [5] and their benzo derivatives [6] etc. 1,3,4-thiadiazole Derivatives shows a wide range of biological, pharmacological, and antileukemic activities [7-9]. Large number of such compounds have been synthesized and studies for their spectroscopic behavior and biological activity [3-6, 10].

We have selected 2-amino-5-(m-nitrophenyl)-1,3,4 -thiadiazole, abbreviated as AMNT, one of the simplest 1,3,4-thiadiazole derivative for our study. To the best of our knowledge, despite of potential pharmacological applications, this molecule is not undergone any comprehensive stereoelectronic and spectroscopic studies. 2-amino-5-(m-nitrophenyl)-1,3,4- thiadiazole showed monoclinic packing having cell parameter a = 11.832 Å, b = 9.862 Å, c = 8.353 Å, V = 913.63 ų, d_calcd = 1.212 g cm^–3 with space group P21/c [11]. Introduction of a nitro group into the benzene ring is of particular interest both for the elucidation of the influence of electron-withdrawing substituents on the reactivity of donor centers of heterocyclic compounds and for the subsequent synthesis of thiadiazole derivatives based on the reduced nitro group. Replacing the substituent in the phenyl group at position 3 of the 1,3,4-thiadiazole compounds with electron withdrawing groups, like halogens, nitriles, carbonyls etc. leads to affect biological activities [9].

In the present study, in an attempt to understand the structure property relation, the stereoelectronic interactions associated with the structural properties of 2-amino -5-(m-nitrophenyl)-1,3,4-thiadiazole were investigated computationally using density functional theory (DFT) and ab initio methods. Therefore, we report optimized molecular structure confirmed by predictive vibrational spectra (FTIR/Raman) and physicochemical behavior for 2-amino-5-(m-nitrophenyl)-1,3,4-thiadiazole. In order to find conformational stability of the 2-amino-5-(m- nitrophenyl)-1,3,4-thiadiazole molecule, a potential energy scan is performed, and the corresponding relative energies were compared. The equilibrium geometry, harmonic vibrational wavenumbers, electrostatic potential surfaces, absolute Raman scattering activities and infrared absorption intensities have been calculated by DFT [12] with B3LYP functionals using various basis sets and HF/6-311G(d,p) with the help of Gaussian 09W package [13]. The calculated vibrational spectra were analyzed on the basis of the potential energy distribution (PED) of each vibrational mode which allowed us to obtain a quantitative as well as qualitative interpretation of the infrared and Raman spectra. To understand structure property relationship, HOMO-LUMO, electrostatic potential surface and natural bond orbitals have been obtained. Natural bond orbital analysis has been carried out to understand the nature of different interactions responsible for the electron delocalization and the intra-molecular charge transfer between the orbitals. These intra-molecular charge transfer (n–σ*, n–π* and π-π*) can induce biological activities such as antimicrobials, anti-inflammatory, anti-fungal, antibiotic, diuretic, antidepressant, anticancer, anticonvulsants, etc. in the molecule.

2. Computational Details

Computational aspects for geometry optimization and electronic structure of the stable conformers of the molecule have been done by density functional theory [12] by using the Gaussian 09W program package[13] employing different basis sets and Becke’s three parameter (local, nonlocal, Hartree–Fock) hybrid exchange functionals with Lee–Yang–Parr correlation functionals (B3LYP) [14-16]. Infrared absorption intensities and Raman intensities have been calculated in the harmonic approximation with the help of same functional and basis sets as used for the optimized geometries, from the derivatives of the dipole moment and polarizability of each normal mode, respectively. The normal-mode analysis was used to calculate PED for each of the internal coordinates using no symmetry [17-18]. In order to prepare PED a complete set of 57 internal coordinates was defined using Pulay’s recommendations [19, 20]. The vibrational assignments of the normal modes were proposed on the basis of the PED calculated using the program GAR2PED [21]. Calculated DFT vibrational wavenumbers are known to be higher than the experimental wavenumbers as the anharmonicity effects are neglected. Therefore, wavenumbers obtained by DFT were scaled down by the wavenumber linear scaling procedure (WLS) ν_obs = (1.0087–0.0000163ν_calc.) ν_calc. cm^-1 [22]. The WLS method using this relationship predicts vibrational wavenumbers with high accuracy and is applicable to a large number of compounds, except for those where the effect of dispersion forces is significant. All the calculated vibrational wavenumbers reported in this study are the scaled values. In order to investigate intra-molecular charge transfer interactions, rehybridization and delocalization of electron density within the molecule, the natural bonding orbitals (NBO) analysis has been performed. The main natural orbital interactions were analyzed on the basis of NBO calculations done at DFT/B3LYP level using Gaussian 09W package. In the NBO analysis [23, 24], the electronic wave functions are interpreted in terms of a set of occupied Lewis-type (bond or lone pair) and a set of unoccupied non-Lewis (antibond or Rydberg) localized NBO orbitals. Delocalization of electron density (ED) between these orbitals corresponds to a stabilizing donor–acceptor interaction. The second-order perturbation theory has been employed to evaluate the stabilization energies of all possible interactions between donor and acceptor orbitals in the NBO basis. The delocalization effects can be estimated from off-diagonal elements of the Fock matrix in the NBO basis.

3. Results and Discussion

3.1. Geometry Optimization

The theoretical structure of title molecule have been calculated by DFT using B3LYP functional having extended basis sets 6-311++G(d,p), 6-311+G(d,p), 6-311G(d,p) and HF/6-311G(d,p) with the help of Gaussian 09W package and geometry obtained from B3LYP/6-311++G(d,p) is shown in Fig.1.

Figure 1. Optimized structure of AMNT at the B3LYP/6-311++G(d;p) level of theory

Geometry of C₈H₆N₄O₂S (AMNT) was optimized without any constraint to the potential energy surface using given X-ray diffraction data as initial point [11]. All the optimized bond lengths and bond angles of the calculated C₈H₆N₄O₂S molecule are tabulated in Table-1 along with the reported molecular parameters [11]. The title compound contains phenyl, amino, nitro and thiadiazole moieties. The five-membered thiadiazole ring is essentially planar. The dihedral angles between the phenyl and the thiadiazole ring is calculated at -0.135°, but experimental data shows a twist of 39.73°. This may be attributed to intermolecular interaction in the crystal packing. Only two bond distances in the thiadiazole ring show a double bond character C6=N5, C2=N4 with bond lengths 1.297 Å, 1.305 Å respectively and bonds S3-C6, S3–C2 with bond lengths 1.775 Å, 1.757 Å show the values of a single bond character. The S–C bond distances are found in good agreement with the accepted value for an S–C(sp2) single bond of bond length 1.76 Å [25]. In general, the calculated structural parameters match well with experimental data with few exceptions. The difference found in calculated values (in gas phase) from the experimental values may be due to the solid state intermolecular interactions related to crystal packing effects. It is worth noting that the C9–N13 bond distance value of 1.481 Å falls into the C=N double bond distance region and is shorter than the C=N double bond distance found in a related thiadiazole ring structure [26]. The bond C2-N1 shows the partial double bond character with bond length 1.367 Å.

Table 1. Optimized geometrical parameters of AMNT by DFT in comparison with XRD data

3.2. Potential Energy Scan Studies

In order to investigate all possible conformations of 2-amino-5-(m-nitrophenyl)-1,3,4-thiadiazole, a detailed potential energy scan was performed for the dihedral angle ϕ(C12–C7–C6–S3) at B3LYP/6-311++g(d,p) level of theory with constraint nosymmetry. The scan studies was obtained by minimizing the potential energy in all geometrical parameters by varying the torsion angles at a step of 5° in the range of 0–360° rotation around the bond. The variations of the potential energy change from its equilibrium with the torsional perturbation are presented in Fig. 2. The PES scan revealed that the 2-amino-5- (m-nitrophenyl)-1,3,4 -thiadiazole molecule may have less stable conformer at torsion angle (C12–C7–C6–S3) equal to -5.23709° having energy -1076.029 Hartree (-2825114.354 kJ/mol). The most stable equilibrium state belongs to (C12–C7–C6–S3) =179.862° and potential energy equal to -1076.309 Hartree (-2825851.595 kJ/mol).

Figure 2. Potential energy scan of AMNT about dihedral angle (C12–C7–C6–S3) at B3LYP/6-311++g(d,p) level of theory

3.3. Natural Bond Orbital Analysis

NBO analysis is an efficient method for study of the intramolecular and intermolecular bonding and interactions among bonds. This analysis also provides the study of filled NBOs (donors) and empty NBOs (acceptors) and their interactions with the stabilization energy E⁽²⁾ resulting from the second-order perturbation theory. The larger the E⁽²⁾ value, the more intensive is the interaction between electron donors and acceptors, i.e. the more electron donating tendency from electron donors to acceptors and the greater the extent of conjugation of the whole system. This interaction results a loss of occupancy from the concentration of electron NBO of the idealized Lewis (bond or lone pair) structure into an empty (anti-bond or Rydberg) non-Lewis orbital. For each donor (i) and acceptor (j), the stabilization energy E⁽²⁾ associated with the delocalization i – j is estimated as [23, 27, 17]:

(1)

Where is the Fock matrix element which corresponds to i and j NBO orbitals. is the population of the donor orbital, and are the energies of and NBOs. NBO calculations were performed using the NBO 5.9 program as implemented in the Gaussian 09 package at the DFT/B3LYP/6-311++G(d,p) level of the theory. The second-order perturbation theory analysis of Fock matrix in NBO basis of AMNT molecule display strong intra-molecular conjugative and hyperconjugative interactions and demystify the rehybridization and delocalization of electron density within the molecule. Some important interactions between Lewis and non-Lewis orbitals along with their interacting stabilization energies are shown in Table-2.

Table 2. Second-order perturbation theory analysis of Fock matrix in NBO basis

The Fock matrix analysis shows strong intra-molecular hyperconjugative interactions of π electrons between π bond orbitals and anti bonding orbitals. These interactions are established by the orbital overlapping between π(C–C or C-N) and π*(C–C or C-N) bond orbitals resulting ICT (Intramolecular charge transfer) causing stabilization of the system.

The electron density (ED) at the six conjugated π bonds (1.6–1.7e) and π* antibonds (0.1–0.4 e) of the phenyl ring clearly shows strong delocalization leading to stabilization of energy in the range of 12–23 kcal/mol. These results are consistent with as reported by C. James et al. [18]. The important interaction (n–π) energies associated with the resonance in the molecule are electron donation from the LP(1) of atom N1, LP(2) of atom S3 (electron donating groups) to the anti-bonding acceptors π*(C2-N4) and π*(C2-N4) ,π*(N5-C6) of thiadiazole ring which correspond to the stabilization energies 38.22 and 27.80, 24.16 kcal/mol respectively. Similar interaction is observed from LP(3) of atom O14 to the anti-bonding acceptor π*(N13-O15) of nitro group having stabilization energy equal to 12.90 kcal/mol. These π*(C2-N4) and π*(N5-C6) antibonding orbitals of the thiadiazole ring further show hyperconjugation with π*(N5-C6) and π*(C7-C8) of phenyl ring respectively. This shows the intramolecular charge transfer from thiadiazole ring to phenyl ring with enormous amount of stabilization energies 173.73 and 101.66 kcal/mol respectively. A strong intramolecular interaction of π electrons occurs from π(C7-C8) and π(C11-C12) bonds to the π*(C9–C10) antibond corresponding to the stabilization energies 20.36 and 23.43 kcal/mol respectively. This enhanced π*(C9–C10) NBO further hyperconjugates with π*(C11–C12) correspond the high stabilization energy 223.26 kcal/mol.

The hyperconjugative interaction of σ(N1–H17) and conjugative interaction of σ(S3–C6) distribute over σ*(C2–S3) and (N1–C2) leads to the stabilization energies 6.51 and 5.53 kcal/mol respectively. The hyperconjugative interaction (n–σ*) between the electron-donating nitrogen atoms n1(N4) and n1(N5) of the thiadiazole ring and antibonding orbitals σ*(C2–S3), (N5-C6) and σ*(C2-N4), (S3–C6) leads to the stabilization energies 15.21,5.53 and 5.35,16.31 kcal/mol respectively. The charge transfer from lone pairs of n2(O14) and n2(O15) to antibonding orbitals σ*(C9–N13), (N13-O15) and σ*(C9–N13), (N13-O14) correspond to the stabilization energies 12.37, 18.95 and 12.47, 19.03 kcal/mol due to small energy difference between donor and acceptor respectively. These intramolecular charge transfer (n–σ*, n–π* and π-π*) may induced biological activities such as antimicrobials, anti-inflammatory, anti-fungal, antibiotic, diuretic, antidepressant, anticancer, anticonvulsants, etc. in the title molecule.

3.4. Molecular Electrostatic Potential

Various weak interactions in 2-amino-5- (m-nitrophenyl)- 1,3,4-thiadiazole molecule, such as C–H… and weak hydrogen-bonding interactions have very important significance in determining stability of the molecule. The presence of amino and nitro group leads to the electronic coupling between ring electrons and nitrogen lone pair electrons which provides stabilization to the molecular structure and enhance its antilukemic properties. Hence it is important to study the electrostatic potential distribution in the molecule. The molecular electrostatic potential (MEP) is a property that the electrons and nuclei of a molecule create at each point r in the surrounding space [28]. Electrostatic potential provides very useful information to explain hydrogen bonding, reactivity and structure–activity relationship of molecules and correlates with dipole moment, electronegativity, partial charges and site of chemical reactivity of the molecule. It gives a visualization to understand the relative polarity of a molecule. The regions with negative MEP, correspond to the areas of high electron density representing a strong attraction between the proton and the points, on the molecular surface have the brightest red color. The positive valued regions, areas of lowest electron density, have deep blue to indigo color indicating the regions of maximum repulsion. The electron density isosurface onto which the electrostatic potential surface has been mapped is shown in Fig. 3 for 2-amino-5- (m-nitrophenyl)-1,3,4-thiadiazole. The different values of the electrostatic potential at the surface are represented by different colors; yellow represents regions of most negative electrostatic potential, blue represents regions of most positive electrostatic potential over the amino group and green represents regions of zero potential. From Fig. 3, it is visible that the region of the most negative electrostatic potential is spread over the O14, O15 atom of NO₂ group and N4, N5 of the thiadiazole ring. This indicates the delocalization of π electrons over the nitro group and thiadiazole ring. This also reveals extended conjugation of the phenyl rings with the nitro group.

Figure 3. Molecular electrostatic potential mapped on the isodensity surface for AMNT calculated at the B3LYP/6-311++G(d;p) level of theory

3.5. HOMO-LUMO Analysis

The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are the main orbitals that plays an important role in chemical stability [29]. The HOMO exhibits the ability to donate an electron and LUMO as an electron acceptor serves the ability to obtain an electron. The HOMO and LUMO energy calculated by B3LYP/6-311++G (d,p) level of theory show the energy gap which reflects the chemical activity of the molecule.

HOMO energy (B3LYP) = −782.609 kJ/mol

LUMO energy (B3LYP) = −548.520 kJ/mol

HOMO − LUMO energy gap (B3LYP) = 234.089 kJ/mol

The HOMO is positioned over the thiadiazole ring and amino group, the HOMO→LUMO transition implies an electron density transfer to Phenyl ring and nitro group from thiadiazole ring and amino group. This ICT between thiadiazole ring and Phenyl ring is responsible for existing biological activities. The atomic orbital compositions of the frontier molecular orbital are shown in Fig. 4.

Figure 4. The molecular orbitals of AMNT at B3LYP/6-311++ G(d;p) level

On the basis of HOMO-LUMO energies global reactivity descriptors, such as the energies of frontier molecular orbitals (ε_HOMO, ε_LUMO), energy band gap (ε_HOMO − ε_LUMO), electronegativity (χ), chemical potential (µ), global hardness (η), global softness (S) and global electrophilicity index (ω), which describe the electrophilic behaviour [30-34], have been calculated for AMNT using Eqs. (2)–(6):

(2)

(3)

(4)

(5)

(6)

Electrophilic charge transfer (ECT) [30] is defined as the difference between the ΔN_max values of interacting molecules. For two molecules I and II approaching each other (i) if ECT > 0, charge flows from II to I and (ii) if ECT < 0, charge flows from I to II. ECT is calculated using Eq. (7):

(7)

where (ΔN_max)_I = − µ _I/ η_I and (ΔN_max)_II = − µ_II/η_II.

3.6. Vibrational Spectral Analysis

The vibrational spectra of 2-amino-5-(m-nitrophenyl) -1,3,4-thiadiazole molecule have been calculated by DFT with B3LYP functional having extended basis set 6-311G(d,p), 6-311+G(d,p), 6-311++G(d,p) and by HF with basis set 6-311++G(d,p) using Gaussian 09W package. Due to exclusion of anharmonicity, the calculated wave numbers are higher and therefore, scaled down by the wave number linear scaling procedure (WLS) [ν_obs/ν_cal = (1.0087 – 0.0000163 *ν_cal) cm^-1] given by Yoshida et al. [22]. This molecule has 21 atoms, which gives 57 (3n-6) normal modes. AMNT has phenyl and thiadiazole rings with different functional groups namely nitro and amino respectively. Vibrational mode assignments have been made on the basis of relative intensities, line shape and potential energy distribution obtained from normal coordinate analysis. All the 57 fundamental vibrations of the free molecule are both IR and Raman active. The calculated vibrational wave-numbers and their PED for each normal mode are presented in Table 3. The calculated (scaled) infrared absorbance and Raman spectra are shown in Fig. 5 and Fig. 6, respectively.

Table 3. Potential Energy Distribution and vibrational wavenumbers of AMNT

Figure 5. Calculated infrared spectra of AMNT at various level of theory

Figure 6. Calculated Raman spectra of AMNT at various level of theory

In order to make better understanding, the vibrational assignments have been studied separately for all groups and rings. We have discussed here only the dominant contributions to the total potential energy of normal modes of vibration out of several internal coordinates that may be present in the PED as shown in Table-3.

AMNT consist a thiadiazole ring (ring-1) having amino group attached at position 2. Ring-1 has two CS stretching vibrations which are calculated at 653 and 665 cm^-1. These modes have prominent contribution (10-60%) from CS stretch along with other vibrations of the ring-1and amino group. Two C-N antisymmetric and symmetric stretching vibrations are calculated at frequencies 1497 and 1507 cm^-1 and are reported at 1517 and 1619 cm^-1 [11] and for AMNO [35] it is reported at 1630 cm^-1. One prominent N-N stretching(49%) vibration is calculated at 1154 cm^-1, this mode is reported to be observed at 995 cm^-1 [11]. These vibrations also have the contribution from other modes of ring-2 and amino group. The in-plane bending of ring-1 calculated at 440 cm^-1 and out-of-plane bending of ring-1 occurs at 607 cm^-1 having contribution from ring-2 deformation and other vibrations of amino group in the frequency range 85-740 cm^-1.

Calculated phenyl ring vibrations are in good agreement with the experimental data [11]. The selection rule for meta-substituted phenyl ring allows four C–H stretching vibrations. Although the DFT predict all these four bands, but these are observed as inseparable in IR. Usually Raman has one strong band in this zone [36]. The ring CH stretching vibrations appear to be very weak, which is due to steric interaction that induces effective conjugation and charge carrier localization resulting in twisted phenyl ring [37]. The carbon hydrogen stretching vibrations give rise to bands in the region 3100–3000 cm⁻¹ in all the aromatic compounds [38]. The C–H stretching vibrations of phenyl ring are calculated at 3084, 3070 and 3048 cm^-1 in AMNT but in CDMABA[39], these bands are found at 3045, 3061 cm^-1 in IR spectra and at 3057, 3069 cm^-1 in Raman spectra respectively while in AMNO[35] these modes are observed at 3080 cm^-1 . Minor shift may arise due to the influence of nitro group attached to the phenyl ring in title compound. There are six vibrational modes of C-C stretching with a contribution of ring bending, which are more substituent dependent, calculated corresponding to the peaks at 1003, 1097, 1335, 1426, 1587 and 1625 cm^-1 with other mode of vibrations [39]but in AMNO[35] these are reported at 1569 and 1480 cm^-1, shown in PED table-3. These modes of phenyl ring are also having contributions in the vibrations of substituent nitro group and thiadiazole ring. The in-plane CH bending vibrational modes of the phenyl ring, are found as a series of bands at 1178, 1299, 1316, 1426 and1478 cm^-1 in the range 1003-1626 cm^-1. PED assignment shows that these vibrations have coupling with C-C stretching of the ring and the other vibrational modes of substituents. The CH out-of-plane bending modes of the phenyl ring vibrations corresponding to medium, strong and weak bands are calculated at 813, 913, 953 and 1007 cm^-1, having contribution in other modes are shown in Table 3 and are assigned to ring in-plane deformation modes. The puckering modes of phenyl ring (ring-2) with a contribution of out-of-plane bending of the substituents are calculated at 674 cm^-1. Other fundamental modes of phenyl ring that show similar characteristics like torsional modes and their assignments have also been calculated and shown in table 3 with their corresponding potential energy distributions.

Nitro group compounds show a very strong asymmetric stretch at 1540–1614 cm^-1 and a strong symmetric stretch at 1320–1390 cm^-1 [40]. For this title compound a very strong band corresponding to asymmetric stretch at 1557 cm^-1 and a strong band at 1351 cm^-1 corresponding to symmetric stretch are calculated by DFT and reported at 1550 and 1350 cm^-1 for AMNO[35]. According to Peticolas and co-workers it has been found that the NO₂ symmetric stretching vibration occurs at 1364 cm^-1 in a series of chemically related p-nitro substituted derivatives [41]. NO₂ group scissoring modes are assigned at frequencies 739 and 879 cm^-1. Rocking modes of NO₂ are found at 541 cm^-1 and out of plane bending of NO₂ group calculated at 729 cm^-1.

The N–H group attached to the hetero aromatic molecule shows stretching mode in the usual range 3500–3220 cm⁻¹ of appearance for NH₂, CH₃ and C–H stretching vibrations. These absorptions depend upon the degree of hydrogen bonding and the physical state of the sample or the polarity of the solvent [42]. The N–H stretching vibrational bands are sharper and weaker than O–H stretching vibrations by virtue of which they can be easily identified [43]. The N–H stretching fundamental of piperidine was observed in the vapor phase at 3364cm⁻¹ [44] and in the liquid phase at 3340cm⁻¹ for the N–H stretching of the piperidine [34, 45]. For our compound the stretching vibrations of the amino group associated with thiadiazole ring are experimentally observed in the range 3050–3225 cm^-1 [11], which are calculated at 3393 and 3494 cm^-1 conforms the NH stretching vibrations. The out-of-plane bending of amino group are calculated at 489 and 528 cm^-1 mixed with other modes of vibrations of ring-1, which are shown in Potential energy distribution table.

4. Conclusions

Geometry of AMNT molecule was optimized using DFT at various levels of theory and also HF employing 6-311++G(d,p) basis set. The calculated values are also compared with experimental data. In general the structural parameters matches well with the experimental one, with few exceptions caused due to constraints imposed by isolated molecule model. Potential energy scan suggested one less stable conformer in which two rings are almost twisted by 180°. A detailed normal coordinate analysis of all the normal modes along with PED very clearly indicates the composition of each normal mode in terms of internal coordinates. Predictive IR and Raman spectra are very useful in the absence of experimental data. HOMO-LUMO, EPS and NBO may serve as a useful quantity to explain hydrogen bonding, reactivity and structure–activity relationship of molecules.

ACKNOWLEDGEMENTS

Financial assistance to Mahesh Pal Singh Yadav from Jaypee University of Engg. & Technology, Guna is gratefully acknowledged.