Vibrational analysis or IR spectrum or Vibrational assignment or Analysis of vibrational spectra:
C-H vibrations
The C-H stretching vibration present in the hetero aromatic structure lies in the characteristic region 3100-3000cm-1, in which the bands are not affected noticeably by the nature of substituent’s. All the C-H stretching vibrations are weak in intensity. In our case the C-H stretching vibrations were observed at 3083, 3063, 3031 cm-1 in FT-IR spectrum. The calculated wavenumbers at the range 3117–3042 cm-1 (mode no’s: 174–167, 165, 163,162) are assigned to C-H stretching vibrations. All bands have very weak intensities and were obtained in the expected region. As expected, these modes are pure stretching modes as it is evident from TED column in Table 2; they almost contribute around 100%.

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The C-H bending vibrations of benzene rings for the title compound are observed in the range from 1100 to 1613 cm-1, however some vibrations of the title compound observed at values 1576, 1535, 1375, 1277, 1241, 1182, 1097 cm-1 respectively are mixed with CC and SO stretching vibrations. The C-H in-plane bending frequencies appear in the range 1000–1300 cm-1 and are very useful for characterization purpose
Ring vibrations
The ring stretching vibrations are very much important in the spectrum of aromatic compounds and are highly distinctive of the aromatic ring itself. However, empirical assignments of vibrational modes for peaks in the fingerprint region are difficult. The C=C stretching vibrations are generally observed at 1400-1600 cm-1 in benzene derivatives which are assigned to ring vibrations. In general, the bands are of variable intensity and observed at 1625–1590, 1590–1575, 1540–1470, 1460–1430 and 1380–1280 cm-1 from the frequency ranges given by Varsanyi for the five bands in the fingerprint region. In the present compound, the C=C stretching vibrations are observed at 1592, 1561 and 1464cm-1 in FTIR spectrum. The calculated theoretical values were 1584, 1576, 1562, 1553, 1552 and 1535 cm-1 by B3LYP/6-311G (d, p) method shows excellent agreement with the experimental values. The C-C stretching vibration is expected at 1450-1250cm-1. The peaks are observed at 1399 and 1375cm-1 in FTIR are assigned to C-C stretching vibrations. The calculated wave numbers at 1375, 1360, 1286, 1277, 1273, 1252, 1182, 1166, 1150 and 1010cm-1 were assigned C-C stretching vibrations by DFT Method. The C-C-C in-plane and out-of-plane bending vibrations are the modes associated with smaller force constants than the stretching ones, and hence assigned to lower frequencies. The in-plane deformation vibration is at higher frequencies than the out-of plane vibrations. Shimanouchi et al. gave the frequency data for these vibrations for different benzene derivatives as a result of normal coordinate analysis. Although some modes are missing in experimental spectrum, however, the calculated CCC in-plane and out-of-plane bending modes are found to be consistent with the recorded spectral values, as seen in Table 2. The mode no’s 40, 44, 45, 51, 60, 61, 64 and 66 were identified as C-C-C-C torsional deformation τ(CCCC) modes these are shown in Table 2.
Methyl group vibrations
The C-H asymmetric stretching vibrations of CH3 groups are expected in the range 2950-3050 cm-1 and the symmetric stretching vibrations in the range 2900-2950 cm-1 [roeges, colthup]. The calculated values of the asymmetric stretching vibrational modes of the methyl group are 3051, 3011, 3009, 2989, 2975, 2961cm-1 using DFT/B3LYP with 6-311g (d, p) basis set and observed at 2998, 2923 cm-1 in FT-IR spectrum, whereas the values of the symmetric stretching vibrational modes are 2937, 2910 and 2864 cm-1 and at 2880 and 2859cm-1 in FTIR spectrum. The symmetrical and asymmetrical bending vibration involves in-phase and out-of-phase bending of the C-H bonds. The asymmetrical deformations are expected in the range 1400-1485cm-1 [roeges]. The bands observed at 1464, 1448 cm-1 in the FT-IR spectrum are assigned as the methyl asymmetrical deformation and the calculated values are at 1448, 1438, 1437, 1431, 1428, 1426, 1423cm-1 by DFT. The methyl symmetric deformations appears with an intensity varying from medium to strong and expected in the range 1380±25cm-1. These bands have been observed at 1399, 1375cm-1 in the FT-IR spectrum and calculated theoretically at 1383, 1361 cm-1. The CH3 rocking generally appears in the regions 1150±30 and 875±45 cm-1, the wave number is coupled to the CC stretching vibrations, which occurs in the neighborhood of 900 cm-1. The rocking modes of the CH3 group are observed at 759cm-1 in the FTIR spectrum and calculated at 1168, 1138, 1129, 1122, 1022, 1087, 969 cm-1 in DFT. The wavenumbers 115, 107,102, 82, 71 and 62 cm-1 of modes 15, 14, 13, 11, 10 and 9 are due to methyl torsion.
Methylene Vibrations
The stretching vibrations CH2 group is expected in the region 2900-3000 cm-1. The deformation mode of CH2 is expected in regions 1480-1400cm-1(scissoring), 1380-1150cm-1(wagging & twisting) and 800-710 cm-1(rocking). In this study, the bands at 2923 and 2859cm-1 has been assigned to CH2 asymmetric and symmetric vibrations in FT-IR spectrum and computed theoretically at 3044, 2945 cm-1 by DFT. The deformation mode of CH2 are assigned at 1431, 1364, 1340, 699 cm-1 theoretically and bands are observed in the FT-IR spectrum at 1448, 1375, 710 cm-1.
SO2 vibrations
The asymmetric stretching for the SO2, NH2, NO2, CH2 and CH3 etc has magnitude higher than the symmetric stretching.The asymmetric and symmetric stretching modes of SO2 group appear in the region 1360-1310 cm-1 and 1165-1135 cm-1.The stretching vibrations of SO2 for sulfonamide derivatives as reported by Chohan et al. [Z.H. Chohan, M.H. Youssoufi, A. Jarrahpour, and T.B. Hadda, Eur. J. Med. Chem. 45 (2010) 1189–1199] are 1345 and 1110 cm-1 and Hangen et al [A. Hangen, A. Bodoki, L. Opren, G. Alznet, M. Liu-Gonzalez, J. Borras, Polyhedron 29 (2010) 1305–1313] at 1314, 1308, 1274, 1157, 1147, 1133cm-1 respectively. In the present study, the asymmetric and symmetric stretching vibration of SO2 group is observed as very strong peak at 1348cm-1 and 1163 cm-1 in the FTIR spectrum and 1260, 1241, 1083 and 1040cm-1 theoretically assigned to SO2 stretching modes. The SO2 scissoring and wagging vibrations occur in the range 570±60cm-1 and 520±40cm-1. The corresponding bands are observed for the title compound at 544cm-1 and 499cm-1 in the FTIR spectrum.
Carbonyl ester group vibration
The carbonyl compound are added functional group includes the C=O bond, also provide very profound contributions to the spectrum. The C=O stretching vibration exhibits a strong band in the region 1600-1750 cm-1. For the title compound , the stretching vibration of C=O is characterized by very strong peak appearing at 1727 cm-1 in the FTIR spectrum and at 1721cm-1 theoretically which shows a perfect agreement with experimental result.
Methyl ester has the strong absorption bands about the C–O asymmetric stretching modes at 1315–1195 cm−1 and symmetric stretching modes at 1096–900 cm−1. In present case, the strong peak is observed for C-O-C stretching vibrations at 1257 cm-1 and 961 cm-1 in the FTIR spectrum, corresponding to the computed wavenumber 1225cm-1 and 954cm-1, is assigned to the C-O-C stretching vibration. The band at 961 cm−1 in FT-IR spectrum has been assigned to O–CH3 stretching mode.
The band at 857(818) cm−1 in FT-IR spectrum is assigned to C–O–C in-plane deformation mode. The band at 784(760) cm−1 in IR spectrum is out-plane deformation mode. The methyl ester has also two characterized vibration modes in 530–340 cm−1 and 390–250 cm−1 region, corresponding to the CO–O rocking and COC deformation. The DFT calculation gives CO-O rocking and COC deformation at 354 and 242 cm-1.
C-S, S-N, N-C and ON vibrations
C-Cl vibration
The C-Cl bonds are formed in benzene ring in place of hydrogen atoms. The stretching vibration is observed in the strong bands at 760-370cm-1. Since, the title compound has two chlorine atoms, the C-Cl stretching vibrations are observed at 757 cm-1,733 cm-1 in FTIR spectrum. The theoretically calculated values by B3LYP/6-311G(d, p) method at 743 cm-1 , 724 cm-1 and 380 cm-1 is assigned to C-Cl Stretching vibrations is coincides very well with the experimental value. Due to longer bond length() of C-Cl reduction in force constant occurs and C-Cl stretching falls in the lower frequency region.