# Molecular Modeling and Spectroscopic Studies of Benzothiazole

Authors: V. Sathyanarayanmoorthi; R. Karunathan; V. Kannappan
Journal: Journal of Chemistry
 (2013)

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## Abstract

The Fourier Transform (FT) infrared and FT-Raman spectra of benzothiazole (BT) have been recorded and analyzed. The equilibrium geometry, bonding features, and harmonic vibrational frequencies have been investigated by ab initio and density functional theory (DFT) methods. The assignments of the vibrational spectra have been carried out. The computed optimized geometric bond lengths and bond angles show good agreement with experimental data of the title compound. The calculated HOMO and LUMO energies indicate that charge transfer occurs within the molecule. Stability of the molecule due to conjugative interactions arising from charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The results show that the electron density (ED) in theσ* and π* antibonding orbital and second-order delocalization energies E(2) confirm the occurrence of intramolecular charge transfer (ICT). The calculated results were applied to simulate infrared and Raman spectra BT which show good agreement with recorded spectra.


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## Body

## 1. Introduction

Benzothiazole (BT) molecule contains a thiazole ring fused with benzene ring. Thiazole ring is a five-member ring consists of one nitrogen and one sulfur atom in the ring. Benzothiazole is thus a bicyclic aromatic ring system. A number of BT derivatives have been studied as central muscle relaxants and found to interfere with glutamate neurotransmission in biochemical, electrophysiological, and behavioral experiments [1]. Substituted benzothiazoles have been studied and found to have various chemical reactivity and biological activity. Benzothiazole ring is found to possess pharmacological activities such as antiviral [2], antibacterial [3], anti-microbial [4], and fungicidal activities [5]. They are also useful as antiallergic [6], antidiabeticantitumor [7], antitumor [8], anti-inflammatory [9], anthelmintic [10], and anti-HIV agents. Phenyl substituted benzothiazoles show antitumor activity [11–13] while condensed pyrimido benzothiazoles and benzothiazoloquinazolines show antiviral activity. Substituted 6-nitro- and 6-amino-benzothiazoles show antimicrobial activity.Molecular spectroscopic methods, in particular, experimental IR and Raman spectroscopy, have been successfully employed for structural investigation of complex molecular compounds. These techniques are especially effective when used in combination with direct methods of structural analysis in hydrogen bond investigations. The aim of the present work is theoretical and experimental spectroscopic investigation of BT molecular structure to gain insight into the structure and physical properties of the molecular structure. The FT-IR and FT-Raman spectra were simulated and compared with experimental results. Ab initio and DFT calculations have been performed to support the wave number assignments.


## 2. Methodology

### 2.1. Experimental Details

The compound under investigation, namely, BT, is spectral grade purchased from M/S Aldrich Chemicals, USA, and it is used as such without further purification. The FT-IR spectrum of the compound was recorded in Perkin-Elmer Spectrometer in the range of 4000–100 cm−1 using KBr pellet technique. The spectral resolution is 0.1 cm−1. The FT-Raman spectrum of the compound was recorded in the BRUKER RFS 27 and Standalone FT-Raman Spectrometer in the frequency range 50–4000 cm−1. The Laser source is Nd : YAG laser source operating at 1064 nm line with 200 mW power. The spectra were recorded with scanning speed of 20 cm−1. The frequencies of all sharp bands are accurate to ±1 cm−1.


### 2.2. Computational Details

The molecular geometry optimization and vibrational frequency calculations were carried out on benzothiazole, with GAUSSIAN 09W software package [14] HF functional [15, 16] combined with standard 6-311G and 6-311++G (d, p) basis set (referred to as “large” basis) and the density functional method used is B3LYP, that is, Becke’s three-parameter hybrid functional with the Lee-Yang-Parr correlation functional method with 6-311++G (d, p). The harmonic vibrational frequencies calculated for BT at HF and B3LYP levels using the triple split valence basis set along with the diffuse and polarization functions. It may be pointed out that computed wave number corresponds to the isolated molecular state in the gaseous phase whereas the experimental wave numbers correspond to the solid state spectra. In order to evaluate the energetic behavior of the title compound, we carried out calculations in vacuo and in organic solvent (ethanol). The energies of important molecular orbitals of BT, the highest occupied MOs (HOMO), and the lowest unoccupied MOs (LUMO) were calculated using HF/6-311++G (d, p) method. NBO analysis has been performed on the BT molecule at the HF/6-311++G (d, p) and B3LYP/6-311++G (d, p) level in order to elucidate the intramolecular, rehybridization, and delocalization of electron density within the molecule. The result of interaction is a loss of occupancy from the density of electron in NBO of the idealized Lewis structure into an empty non-Lewis orbital. For each donor (i) and acceptor (j), the stabilization energy E(2) associated with the delocalization i→j is estimated as
(1)E(2)=-nσ〈σ|F|σ〉2εσ*-εσ=-nσFij2ΔE,
where 〈σ|F|σ〉2 or Fij2 is the Fock matrix element i and j NBO orbital’s, εσ* and -εσ are the energies of σ and σ* NBOs, and nσ is the population of the donor σ orbital. Zero point vibrational energy, internal energy and its translational, rotational, and vibrational contributions, entropy, and heat capacity of BT are computed through the calculation of partition functions [17–19].


## 2.1. Experimental Details

The compound under investigation, namely, BT, is spectral grade purchased from M/S Aldrich Chemicals, USA, and it is used as such without further purification. The FT-IR spectrum of the compound was recorded in Perkin-Elmer Spectrometer in the range of 4000–100 cm−1 using KBr pellet technique. The spectral resolution is 0.1 cm−1. The FT-Raman spectrum of the compound was recorded in the BRUKER RFS 27 and Standalone FT-Raman Spectrometer in the frequency range 50–4000 cm−1. The Laser source is Nd : YAG laser source operating at 1064 nm line with 200 mW power. The spectra were recorded with scanning speed of 20 cm−1. The frequencies of all sharp bands are accurate to ±1 cm−1.


## 2.2. Computational Details

The molecular geometry optimization and vibrational frequency calculations were carried out on benzothiazole, with GAUSSIAN 09W software package [14] HF functional [15, 16] combined with standard 6-311G and 6-311++G (d, p) basis set (referred to as “large” basis) and the density functional method used is B3LYP, that is, Becke’s three-parameter hybrid functional with the Lee-Yang-Parr correlation functional method with 6-311++G (d, p). The harmonic vibrational frequencies calculated for BT at HF and B3LYP levels using the triple split valence basis set along with the diffuse and polarization functions. It may be pointed out that computed wave number corresponds to the isolated molecular state in the gaseous phase whereas the experimental wave numbers correspond to the solid state spectra. In order to evaluate the energetic behavior of the title compound, we carried out calculations in vacuo and in organic solvent (ethanol). The energies of important molecular orbitals of BT, the highest occupied MOs (HOMO), and the lowest unoccupied MOs (LUMO) were calculated using HF/6-311++G (d, p) method. NBO analysis has been performed on the BT molecule at the HF/6-311++G (d, p) and B3LYP/6-311++G (d, p) level in order to elucidate the intramolecular, rehybridization, and delocalization of electron density within the molecule. The result of interaction is a loss of occupancy from the density of electron in NBO of the idealized Lewis structure into an empty non-Lewis orbital. For each donor (i) and acceptor (j), the stabilization energy E(2) associated with the delocalization i→j is estimated as
(1)E(2)=-nσ〈σ|F|σ〉2εσ*-εσ=-nσFij2ΔE,
where 〈σ|F|σ〉2 or Fij2 is the Fock matrix element i and j NBO orbital’s, εσ* and -εσ are the energies of σ and σ* NBOs, and nσ is the population of the donor σ orbital. Zero point vibrational energy, internal energy and its translational, rotational, and vibrational contributions, entropy, and heat capacity of BT are computed through the calculation of partition functions [17–19].


## 3. Results and Discussion

### 3.1. Molecular Geometry

The optimized geometry of the molecule under investigation with IUPAC numbering scheme for the atoms is presented in Figure1. The data of structural parameters obtained by ab initio method as compared to density functional theory for benzothiazole are reported in Table 1. The comparative graphs of bond lengths and bond angles of the title molecule are presented in Figure 2. From the computed values, it is found that most of the optimized bond lengths are slightly larger than the experimental values, this may be due to the fact that theoretical calculations belong to isolated molecules in gaseous phase and the experimental results belong to molecules in solid state. Comparing bond angles and lengths obtained by B3LYP method with those obtained by HF, as a whole the values got by the former are higher than those obtained be the later method. It may be pointed out that the values calculated by B3LYP method correlate satisfactorily with the experimental data. From the data shown in Table 1, it is seen that both HF and DFT (B3LYP/6-311++G (d, p)) levels of theory in general estimate the same values of some bond lengths and bond angles. It is well known that HF methods underestimate and DFT method overestimates bond lengths, particularly the C–H bond lengths [20, 21]. This theoretical pattern is also found for benzothiazole molecule.Table 1
Optimized some geometrical parameters of benzothiazole, bond length (Å), and bond angles (°).
Parameters
HF/6-31G
HF/6-311G
HF/6-311++G
B3LYP/6-311G
Bond length
(S1, C2)
1.8159
1.8146
1.7464
1.7651
(S1, C5)
1.8096
1.8043
1.7443
1.7518
(C2, N3)
1.2688
1.2683
1.2638
1.2874
(C2, H10)
1.0665
1.0647
1.0744
1.0827
(N3, C4)
1.4031
1.404
1.3886
1.3877
(C4, C5)
1.3926
1.391
1.3912
1.4139
(C4, C6)
1.3887
1.3882
1.3932
1.4008
(C5, C9)
1.385
1.3844
1.3907
1.3962
(C6, C7)
1.3811
1.3803
1.3761
1.3866
(C6, H11)
1.0713
1.0689
1.0743
1.0832
(C7, C8)
1.3975
1.3976
1.3994
1.405
(C7, H12)
1.0723
1.07
1.075
1.0838
(C8, C9)
1.3843
1.383
1.3774
1.3893
(C8, H13)
1.0726
1.0703
1.0751
1.0839
(C9, H14)
1.0715
1.0694
1.0746
1.0832
Bond angle
(C2, C1, C5)
86.7846
86.8578
88.2122
88.2011
(C1, C2, N3)
115.703
115.6631
116.9227
116.6919
(C1, C2, H10)
119.792
119.7907
119.7167
119.3151
(N3, C2, H10)
124.5047
124.5462
123.3605
123.993
(C2, N3, C4)
112.9102
112.8215
110.755
110.742
(N3, C4, C5)
115.155
115.1091
115.1782
115.2284
(N3, C4, C6)
124.5797
124.5766
124.855
125.1777
(C5, C4, C6)
120.2653
120.3142
119.9668
119.5939
(S1, C5, C4)
109.4469
109.5485
108.9318
109.1366
(S1, C5, C9)
129.1903
129.1251
129.6054
129.4096
(C4, C5, C9)
121.3628
121.3263
121.4628
121.4538
(C4, C6, C7)
118.7264
118.7178
118.7551
118.9556
(C4, C6, H11)
119.3604
119.2699
119.5996
119.307
(C7, C6, H11)
121.9132
122.0123
121.6452
121.7374
(C6, C7, C8)
120.6426
120.6135
120.8677
120.908
(C6, C7, H12)
119.8217
119.8388
119.7498
119.6972
(C8, C7, H12)
119.5357
119.5477
119.3825
119.3948
(C7, C8, C9)
120.9529
120.9354
120.9119
121.0788
(C7, C8, H13)
119.5983
119.6269
119.5658
119.5843
(C9, C8, H13)
119.4487
119.4377
119.5223
119.3369
(C5, C9, C8)
118.0499
118.0927
118.0357
118.0099
(C5, C9, H14)
121.1939
121.1702
121.132
121.2411
(C8, C9, H14)
120.7561
120.7371
120.8323
120.749Figure 1
Optimized structure of benzothiazole.Bond length and bond angle difference between theoretical (HF and DFT) approaches.
(a)
(b)The carbon–carbon bonds in benzene are not of equal length which is justified by the presence of fused thiazole ring. However, the differences between the six C–C distances are small. The longest bond distance in C4–C5 bond is due to the fusion of thiazole moiety at these carbons. Comparing the bond distances of the hetero aromatic ring, it is found that the bond distances in hetero aromatic ring differ significantly from each other due to the difference in electronegativities of the bonded atoms. The S1–C2 bond distance is the longest (1.7651 Å) while the C2–N3 is the shortest (1.2874  Å). The longest S1–C2 distance attributes the pure single bond character. The C5–S1 and C2–S1 bond distances of BT determined by B3LYP/6-311++G (d, p) method are 1.75 Å and 1.7651 Å, respectively, in between the 1.81 Å average distance for a carbon–sulfur bond and the 1.61 Å which indicate that the actual bond order is between one and two which is due to conjugative effect in benzothiazole. Due to ring strain the C2–N3 double bond distance is 1.268 Å, 1.268 Å, 1.263 Å in HF, and 1.2874 Å for B3LYP/6-311++G (d, p) bigger than single bond C2–H10. With the electron donating substituents on the benzene ring, the symmetry of the ring is distorted, yielding ring angles smaller than 120° at the point of substitution and slightly larger than 120° at the ortho- and metapositions [22]. It is observed that in BT molecule the bond angle at the point of substitution C4–C5–C9 is 118.7° in HF and 118.9° in DFT while the bond angles in at ortho to the substituted carbon, C6–C7–C8 position is found to be 120.8677, 120.908 degree at HF and DFT respectively. This may be due to mesomeric effect of the thiazole ring. The meta position angle C7–C8–C9 is greater than 120° and is found to be 120.91°, 121.078°. More distortion in bond parameters is observed in the heteroring than in the benzene ring. The variation in bond angle depends on the electronegativity of the central atom, the presence of lone pair of electrons, and the conjugation of the double bonds. If the electro negativity of the central atom is less, the bond angle decreases. Thus, the bond angle C5–S1–C2 is very less (88.2122°, 88.2011°) than the bond angle C8–N3–C2 (110.755°, 110.742°) which is due to the fact that electronegativity of nitrogen is greater than sulfur.


### 3.2. Vibrational Assignments

The BT molecule consists of 14 atoms and so it has 36 normal vibrational modes. The observed vibrational assignments and analysis of BT are discussed in terms of fundamental bands. The harmonic vibrational frequencies calculated for BT at HF and B3LYP levels along with the observed FT-IR and FT-Raman frequencies for various modes of vibrations have been presented in Table2. The comparative values of IR and Raman intensities are given in Table 3. The recorded FT-IR and FT-Raman spectra of BT are given in in Figures 3(a) and 3(b) respectively. Theoretical FT-IR and FT-Raman spectra are reported in Figures 4 and 5, respectively. It may be pointed out here that computed wave numbers correspond to the isolated molecular state in the gas phase whereas the experimental wave numbers correspond to the solid state spectra. The calculated vibrational frequencies using different methods are compared with experimentally observed values. The calculated vibrational wave numbers are consistent with the experimental results. Few bands predicted theoretically in FT-IR spectra were not observed in the experimental spectrum of BT molecule may be due to their very weak intensity.Table 2
Comparison of the experimental (FT-IR and FT-Raman) and theoretical harmonic wave numbers (cm−1) of  benzothiazole    calculated by HF, B3LYP with 6-311++G(d, p) basis set.
Modes no.
Experimental
6-311G
6-311++G
B3LYP   6-311++G
Assignment
IR
Raman
1.
71.44
185.6993
221.8993
158.2282
C–H—out of plane bending
2.
210.04
244.1506
259.6877
225.0702
C–H—out of plane bending
3.
352.91
372.6441
373.5584
341.0859
Ring stretching
4.
424.17
426.2948
414.1324
350.0611
N–CH Wagging
5.
471.7758
467.2944
429.3019
C–S–C in plane bending
6.
531
505.08
520.8227
507.0766
451.8357
C–C–C—out of plane bending
7.
585
541.0727
532.2922
481.3446
C–C–C—out of plane bending
8.
623.6493
608.7293
560.6751
C–C–C—out of plane bending
9.
667
668.2929
652.4117
600.4245
C–S Stretching
10.
769
706.88
730.3856
717.6507
666.7194
C–C–C Ring breathing
11.
799
801.01
777.8919
759.172
709.0033
C–S Stretching
12.
828
846.4841
825.1871
754.3702
Thiazole Ring Stretching
13.
873
877.3007
872.0681
804.3435
C–C–C—in plane bending
14.
978
974.2327
929.8297
827.145
C–H—out of plane bending
15.
1014
1015.54
1025.745
970.2269
875.2731
C–H—out of plane bending
16.
1058.5012
1030.8954
922.7485
C–S—Stretching
17.
1069
1085.408
1053.4724
985.3864
C–H—in plane bending
18.
1110.2525
1069.5475
993.4765
C–H—in plane bending
19.
1124
1124.88
1124.8897
1096.4601
1015
C–H—in plane bending
20.
1157
1166.0662
1125.1724
1027.9394
C–H—in plane bending
21.
1198
1197.98
1194.0921
1154.4126
1092.4829
C–H—in plane bending
22.
1264
1203.5496
1178.2819
1126.6974
C–H—in plane bending
23.
1292
1291.66
1243.9149
1216.6827
1153.3509
C–C Stretching
24.
1315
1316.01
1338.3513
1309.6226
1244.4551
C–C—Stretching
25.
1423
1394.2405
1364.2723
1268.7322
C–C—Stretching
26.
1454
1424.58
1427.192
1397.859
1275.7476
C–C—Stretching
27.
1490
1468.87
1575.3975
1556.5462
1440.267
C–H in plane bending
28.
1556
1557.01
1585.4282
1562.2713
1444.1304
C–H in plane bending
29.
1592
1654.5209
1642.2366
1519.1381
C=N Stretching
30.
1657
1663.2985
1653.9474
1535.0676
C–C–C Stretching
31.
1692
1716.6492
1703.8545
1628.1791
C=N Stretching
32.
3061
3063.23
3070.1368
3105.7742
3028.6049
C–H Stretching
33.
3150
3082.2096
3116.571
3036.013
C–H Stretching
34.
3085.3847
3118.2409
3037.4297
C–H Stretching
35.
3094.2296
3126.9054
3046.2331
C–H Stretching
36.
3105.5365
3135.3642
3054.1799
C–H StretchingTable 3
Comparative values of IR and Raman intensities between HF/6-311G++(d, p) and  B3LYP/6-311G++(d, p) of benzothiazole.
HF/6-311G (d, p)
HF/6-311++G (d, p)
B3LYP/6-311++G (d, p)
IR intensity
Raman intensity
IR intensity
Raman intensity
IR intensity
Raman intensity
8.55
31.44
7.69
16.97
12.75
32.04
0.87
10.21
1.58
7.93
1.23
7.36
1.11
15.00
1.26
14.27
1.19
13.42
14.98
26.31
17.53
25.42
22.89
22.11
1.14
24.06
0.97
16.81
1.513
19.92
12.88
9.86
11.17
7.72
10.50
5.311
0.17
6.11
2.07
3.90
1.79
4.11
6.63
3.63
5.86
3.62
6.73
2.43
3.04
2.78
4.66
2.08
4.05
2.15
4.84
5.27
5.06
5.14
5.06
2.90
16.16
8.09
14.71
9.23
18.48
11.02
20.38
6.69
26.21
3.72
23.66
1.91
14.24
3.81
15.91
3.61
10.31
3.08
88.08
0.38
78.09
4.38
78.12
0.52
11.60
18.23
24.84
13.09
17.20
4.92
12.48
4.88
10.48
10.79
2.23
1.10
15.42
2.25
16.04
6.34
10.29
9.35
0.58
1.192
5.73
2.50
13.25
17.50
12.94
2.06
7.02
1.59
1.43
1.99
3.15
1.57
4.43
1.34
1.70
2.25
2.39
0.65
0.82
0.11
7.34
18.81
3.40
0.08
8.71
3.65
1.30
7.484
12.76
5.03
16.28
9.62
8.45
1.82
1.98
0.18
1.16
0.13
7.05
0.10
0.07
2.50
1.02
2.27
16.98
4.84
34.14
3.30
40.98
3.72
7.68
0.81
27.04
0.98
14.87
1.57
8.36
1.87
6.66
0.87
29.51
0.63
19.58
0.29
10.29
9.44
13.58
13.94
9.66
13.7
16.35
3.27
8.27
2.84
0.99
1.65
98.69
9.45
112.55
19.48
108.78
11.77
0.30
2.40
0.15
1.97
0.06
2.14
7.94
6.26
4.21
5.60
4.37
10.42
13.26
10.55
9.96
9.44
3.21
6.44
23.65
2.74
14.21
2.44
10.14
3.24
23.43
15.30
12.95
13.86
9.55
16.75Experimental FT-IR and FT-Raman spectrum of benzothiazole.
(a)
(b)Theoretical FT-IR spectrum of benzothiazole.
(a)
(b)
(c)Theoretical FT-Raman spectrum of benzothiazole.
(a)
(b)
(c)


#### 3.2.1. C–H Stretching

Aromatic compounds commonly exhibit multiple weak bands in the region 3100–3000 cm−1 [23–25] due to aromatic C–H stretching vibrations. In the present case, the C–H stretching vibrations are captured at 3061, 3150 cm−1 in (mode no. 32, 33) FT-IR spectrum and corresponding Raman spectrum observed at 3063 cm−1. The aromatic C–H in-plane bending modes of benzene and its derivatives are observed in the region 1300–1000 cm−1. The C–H out-of-plane bending modes [26–29] are usually of medium intensity and absorption in the region 950–600 cm−1. In the case of BT, the bands observed at 1069, 1124, 1157, 1198, and 1264 cm−1 (mode no. 17, 19, 20, 21, and 22) in IR and at 1292 cm−1 in Raman spectra are assigned to the C–H in-plane bending vibrations. The C–H out of plane bending mode of benzene derivatives is observed in the region 1000–600 cm−1. The aromatic C–H out of plane bending vibrations of BT are assigned to the medium to weak bands observed at 1014 and 978 cm−1 (mode no. 14, 15) in the infrared spectrum and 1016 cm−1 in Raman spectrum. The aromatic C–H in-plane and out of plane bending vibrations have substantial overlapping with the ring C–C–C in-plane and out of plane bending modes, respectively.


#### 3.2.2. C–S Stretching

The C–S and S–H bonds are highly polarizable and hence exhibit stronger spectral activity. The C–S stretching vibration is expected in the region 710–685 cm−1 [30]. The C–S stretching vibrations were observed in the region 609–716 cm−1 for 2-mercapto benzothiazole [31]. The calculated values of the vibrations range from 572 cm−1 to 876 cm−1. For 2-mercaptobenzoxazole [32], the calculated values of the vibrations range from 579 cm−1 to 892 cm−1 and the observed C–S stretching vibration is 954 cm−1. In our title molecule, the C–S stretching is observed at 667 and 799 cm−1 (mode no. 9, 11) in FT-IR. The FT-Raman spectrum value at 801 cm−1 as a medium band is assigned to C–S stretching vibration. The calculated frequencies of 668, 652, 600, and 626 cm−1 exactly correlate with experimental observation as well as the literature data. The C–S vibration is a pure mode as evident from Table 2. The in-plane and out-of-plane C–S stretching vibration also exactly correlates with experimental observations.


#### 3.2.3. C=N Vibrations

The C=N stretching vibrations [33–36] are observed in the range 1672–1566 cm−1. Varsanyi [37] has suggested that an IR band at 1626 cm−1 for C=N stretching and Raman frequency is assigned to the C=N stretching vibration of benzothizaole [38]. The respective bands occurring at 1692 and 1592 cm−1 (mode no. 29, 31) in IR spectra is assigned to the C=N stretching vibration for BT molecule. The bands corresponding to the C–C–C and C–S–C in-plane and out of plane bending modes of BT are presented in Table 3. Normal coordinate analysis shows that significant mixing of C–C–C in-plane bending with C–H in-plane bending occurs. Similarly, the skeletal out of plane bending modes are overlapped with C–H out of plane bending modes significantly. The theoretically calculated values of C=N Stretching vibrations are in the region 1717, 1704, and 1629 cm−1.


#### 3.2.4. Ring Vibrations

The carbon–carbon stretching modes of the benzene ring are expected to be in the range from 1650 to 1200 cm−1 and are usually not very sensitive to substitution by small substituents, but heavy halogens diminish the frequency [39, 40]. In the Raman spectrum of BT, the carbon–carbon stretching bands appeared at 1596, 1575, 1478, and 1209 cm−1. The corresponding C–C stretching modes are observed in the infrared spectrum at 1454, 1423, 1315, and 1292.31 cm−1 (mode no. 23, 24, 25, and 26). The theoretically calculated values are calculated at 1604, 1602, 1486, 1454, 1328, and 1304 cm−1 and these values show excellent agreement with experimental data.The infrared band at 873 cm−1 and two Raman bands at 1000 and 700 cm−1 (mode no. 13) are assigned to C–C–C in-plane bending vibrations of BT. The C–C in-plane bending vibrations appeared as the combination vibrations with C–H in-plane bending vibrations. The bands assigned to C–C–C out-of-plane bending vibrations are observed at 585, 531 cm−1 in (mode no. 6,7) FTIR spectrum and 505 cm−1 in Raman spectrum for BT. The ring breathing vibrations are generally very strong in Raman spectrum. This mode is found in the region 1100−1000 cm−1 for a heavy substituted compound and is strongly Raman active. This is confirmed by the very weak intense Raman band at 706 cm−1 which is supported by computed results. The ring stretching mode is captured at 372.6441, 373.5584, and 341.0859 cm−1 (mode no. 3) in HF/6-311++G (d, p) and B3LYP/6-311++G (d, p) for benzothiazole molecule. Comparison of IR intensities and Raman intensities calculated (Table 3) by HF and DFT (B3LYP) at 6-311+G (d, p) level with experimental values exposes the variation of IR intensities and Raman intensities. Most of the cases, the values of IR intensities by HF are found to be higher than B3LYP at 6-311+G (d, p) level whereas in the case of Raman activities the trend is reverse.


### 3.3. NBO Analysis

The natural bond orbital analysis provides an efficient method for studying intra- and intermolecular bonding and interaction among bonds and also provides a convenient basis for investigating charge transfer or conjugative interaction in molecular systems. Some electron donor orbital, acceptor orbital, and the interacting stabilization energy resulting from the second-order microdisturbance theory are reported [41]. NBO analysis has been performed on the title molecule in order to elucidate the intermolecular, rehybridization, and delocalization of electron density within the molecule, which are presented in Tables 4 and 5. A large diversity of energy values was found. The stronger donor character is shown by the p-type lone pair of the nitrogen atoms. The most important interaction (n-σ*) energies, related to the resonance in the molecules, are electron donation from the LP(1)S atoms of the electron donating groups to the antibonding acceptor π*(C–N) of the phenyl ring LP(1) S1→σ* (C2–N3) = 1.50 kJ mol−1. This larger energy shows the hyperconjugation between the electron do nating groups and the phenyl ring. NBO analysis has been performed on the BT at the HF/6-11++G (d, p) and DFT level in order to elucidate the intramolecular, rehybridization, and delocalization of electron density within the molecule. The intramolecular interactions are formed by the orbital overlap between bonding (C–C) and (C–C) antibond orbital which results in intramolecular charge transfer (IC T) causing stabilization of the system. These interactions are observed as increase in electron density (ED) in C–C antibonding orbital that weakens the respective bonds. The strong intramolecular conjugative interaction of the σ electron of (S1–C2) distribute to σ* (S1–C2), C4–C5, C4–C6, and C5–C9 of the ring. On the other hand, the π (C2–N3) in the ring conjugate to the antibonding orbital of π* (C4–C6) leads to strong delocalization of 18.48 kJ/mol. The π (C4–C6) bond is interacting with π* (C2–N3) with the energy 12.45 kcal/mol for BT. The σ (C4–C5) bond is interacting with σ* (C2–H10), σ* (C4–C6), σ* (C5–C9), σ* (C6–H11), σ* (C9–H14) with the energies 0.68, 5.03, 5.14, 2.13, 2.37 kcal/mol for BT. The energy vlaues of MOs of benzene ring σ (C4–C6, C6–C7, C7–C8, C8–C9), π (C9–C5) are respectively 4.16, 4.51, 2.83, 5.69, 3.79 kcal/mol for BT.Table 4
Second-order perturbation theory analysis of Fock matrix in NBO basis for benzothiazole.
Donor (i)
Type
ED/e
Acceptor (j)
Type
ED/e
E(2)
E(j) − E(i)b (a. u.)
F (i, j)c (a. u.)
S1–C2
σ
1.97599
S1–C2
σ
*
0.07093
0.70
0.92
0.023
C4–C5
σ
*
0.03211
0.78
1.46
0.030
C4–C6
σ
*
0.02151
1.04
1.50
0.035
C5–C9
σ
*
0.02268
5.97
1.49
0.084
C5–C9
π
*
0.35040
3.63
0.84
0.054
S1–C5
σ
1.97203
C2–N3
π
*
0.07212
1.82
0.96
0.038
C2–H10
σ
*
0.02234
2.59
1.46
0.055
C5–C9
σ
*
0.02268
0.72
1.54
0.030
C8–C9
σ
*
0.01365
2.97
1.55
0.061
C2–N3
σ
1.99261
C2–H10
σ
*
0.02234
1.26
1.90
0.044
N3–C4
σ
*
0.02497
0.94
1.77
0.037
C4–C6
σ
*
0.02151
3.53
1.99
0.075
C4–C6
π
*
0.34604
0.80
1.34
0.032
C2–N3
π
1.95466
N3–C4
σ
*
0.02497
1.36
1.07
0.034
C4–C6
π
*
0.34604
18.48
0.64
0.106
C2–H10
σ
1.98286
C2–N3
σ
*
0.01757
1.83
1.60
0.048
N3–C4
σ
*
0.02497
8.01
1.33
0.092
N3–C4
σ
1.97560
S1–C2
σ
*
0.07093
1.12
1.15
0.032
C2–H10
σ
*
0.02234
7.02
1.64
0.096
C4–C5
σ
*
0.03211
0.54
1.69
0.027
C4–C6
σ
*
0.02151
1.23
1.73
0.041
C5–C9
σ
*
0.02268
2.69
1.73
0.061
C6–C7
σ
*
0.01185
1.80
1.74
0.050
C4–C5
σ
1.97874
C2–H10
σ
*
0.02234
0.68
1.65
0.030
C4–C6
σ
*
0.02151
5.03
1.74
0.084
C5–C9
σ
*
0.02268
5.14
1.74
0.084
C6–H11
σ
*
0.00915
2.13
1.66
0.053
C9–H14
σ
*
0.01004
2.37
1.66
0.056
C4–C6
σ
1.97510
S1–C5
σ
*
0.01756
4.16
1.22
0.064
C2–N3
σ
*
0.01757
1.50
1.76
0.046
C2–N3
π
*
0.07212
0.53
1.12
0.022
N3–C4
σ
*
0.02497
1.34
1.50
0.040
C4–C5
σ
*
0.03211
5.54
1.68
0.086
C6–C7
σ
*
0.01185
2.72
1.72
0.061
C6–H11
σ
*
0.00915
1.69
1.64
0.047
C7–H12
σ
*
0.00908
2.25
1.64
0.054
C4–C6
π
1.66368
C2–N3
π
*
0.07212
12.45
0.52
0.077
N3–C4
σ
*
0.02497
0.94
0.90
0.028
C5–C9
π
*
0.35040
39.19
0.46
0.120
C7–C8
π
*
0.32093
39.20
0.47
0.122
C5–C9
σ
1.98148
N3–C4
σ
*
0.02497
3.01
1.52
0.060
C4–C5
σ
*
0.03211
5.38
1.70
0.086
C8–C9
σ
*
0.01365
3.05
1.74
0.065
C8–H13
σ
*
0.00886
2.08
1.65
0.052
C9–H14
σ
*
0.01004
1.87
1.65
0.050
C5–C9
π
1.70971
C2–N3
π
*
0.07212
1.23
0.54
0.024
N3–C4
σ
*
0.02497
0.92
0.92
0.028
C4–C6
π
*
0.34604
36.07
0.48
0.120
C7–C8
π
*
0.32093
35.76
0.49
0.120
C6–C7
σ
1.98054
N3–C4
σ
*
0.02497
4.51
1.49
0.07
C4–C6
σ
*
0.02151
3.29
1.71
0.067
C6–H11
σ
*
0.00915
1.53
1.63
0.045
C7–C8
σ
*
0.01359
2.85
1.71
0.062
C7–H12
σ
*
0.00908
1.44
1.63
0.043
C8–H13
σ
*
0.00886
2.56
1.62
0.058
C6–H11
σ
1.98222
N3–C4
σ
*
0.02497
0.55
1.28
0.024
C4–C5
σ
*
0.03211
5.08
1.46
0.077
C4–C6
σ
*
0.02151
1.42
1.50
0.041
C6–C7
σ
*
0.01185
1.33
1.50
0.040
C7–C8
σ
*
0.01359
4.20
1.50
0.071
C7–C8
σ
1.98272
C6–C7
σ
*
0.01185
2.83
1.71
0.062
C6–H11
σ
*
0.00915
2.48
1.63
0.057
C7–H12
σ
*
0.00908
1.55
1.63
0.045
C8–C9
σ
*
0.01365
2.90
1.71
0.063
C8–H13
σ
*
0.00886
1.56
1.62
0.045
C9–H14
σ
*
0.01004
2.59
1.62
0.058
C7–C8
π
1.67584
C4–C6
π
*
0.34604
42.89
0.46
0.126
C5–C9
π
*
0.35040
42.80
0.45
0.125
C7–H12
σ
1.98449
C4–C6
σ
*
0.02151
4.40
1.50
0.073
C6–C7
σ
*
0.01185
1.28
1.50
0.039
C7–C8
σ
*
0.01359
1.29
1.50
0.039
C8–C9
σ
*
0.01365
4.20
1.50
0.071
C8–C9
σ
1.97778
S1–C5
σ
*
0.01756
5.69
1.21
0.074
C5–C9
σ
*
0.02268
3.97
1.70
0.073
C7–C8
σ
*
0.01359
2.83
1.71
0.062
C7–H12
σ
*
0.00908
2.51
1.63
0.057
C8–H13
σ
*
0.00886
1.43
1.63
0.043
C9–H14
σ
*
0.01004
1.53
1.62
0.045
C8–H13
σ
1.98412
C5–C9
σ
*
0.02268
4.70
1.49
0.075
C6–C7
σ
*
0.01185
4.16
1.50
0.071
C7–C8
σ
*
0.01359
1.29
1.50
0.039
C8–C9
σ
*
0.01365
1.26
1.50
0.039
C9–H14
σ
1.98424
C4–C5
σ
*
0.03211
4.44
1.46
0.072
C5–C9
σ
*
0.02268
1.54
1.49
0.043
C7–C8
σ
*
0.01359
4.07
1.50
0.070
C8–C9
σ
*
0.01365
1.33
1.50
0.040
C4–C6
π
*
0.34604
C2–N3
π
*
0.07212
18.62
0.05
0.062
N3–C4
σ
*
0.02497
2.79
0.43
0.072
C5–C9
π
*
0.35040
C2–N3
π
*
0.07212
3.79
0.06
0.030
C7–C8
π
*
0.32093
371.30
0.02
0.122
a
E(2) means energy of hyperconjugative interaction (stabilization energy).
bEnergy difference between donor and acceptor i and j NBO orbitals.
c
F(i, j) is the Fock matrix element between i and j NBO orbitals.Table 5
Second-order perturbation energiesE(2) (donor → acceptor) for benzothiazole.
Donor (i)
Acceptor(j)
E(2) (kJ mol−1)a
E(j) − E(i)b (a. u.)
F (i, j)c (a. u.)
Within unit 1
LP (1) S1
σ
*C2–N3
1.50
1.70
0.045
LP (1) S1
π
*C2–N3
1.38
1.05
0.035
LP (1) S1
σ
*C4–C5
1.77
1.61
0.048
LP (1) S1
σ
*C5–C9
0.52
1.64
0.026
LP (2) S1
π
*C2–N3
8.98
0.59
0.065
LP (2) S1
σ
*C2–H10
1.41
1.09
0.036
LP (2) S1
σ
*C4–C5
1.21
1.14
0.034
LP (2) S1
σ
*C5–C9
1.98
1.18
0.044
LP (1) N3
σ
*C2–N6
2.64
1.17
0.050
LP (1) N3
σ
*C4–C5
9.23
1.38
0.102
LP (1) N3
σ
*C4–H7
3.47
1.25
0.060
LP (1) N3
σ
*S1–C2
27.32
0.77
0.130
LP (1) N3
σ
*C4–C6
0.85
1.35
0.031
LP (1) N3
σ
*C4–C6
1.17
0.70
0.027
a
E(2) means energy of hyper conjugative interaction (stabilization energy).
bEnergy difference between donor and acceptor i and j NBO orbitals.
c
F (i, j) is the Fock matrix element between i and j NBO orbitals.


### 3.4. Frontier Molecular Orbitals (FMOs)

The highest occupied molecular orbitals (HOMOs) and the lowest-lying unoccupied molecular orbitals (LUMOs) are called frontier molecular orbital’s (FMOs). The FMOs play an important role in the optical and electric properties, as well as in quantum chemistry and UV-vis spectra [37]. The HOMO represents the ability to donate an electron; LUMO as an electron acceptor represents the ability to obtain an electron. The energy gap between HOMO and LUMO determines the kinetic stability, chemical reactivity, and optical polarizability and chemical hardness-softness of a molecule [42, 43].In order to evaluate the energetic behavior of the title compound, we carried out calculations in vacuo and in organic solvent (ethanol). The energies of important molecular orbitals of BT, the highest occupied MOs (HOMO) the lowest unoccupied MOs (LUMO) were calculated using HF/6-311++G (d, p). The energy values of HOMO and LUMO are −0.2449, −0.05227, respectively. The 3D plots of the HOMO, LUMO orbitals computed for BT molecule are illustrated in Figure6. The positive phase is red and the negative one is green. It is evident from the figure that while the HOMO is localized on almost the whole molecule, LUMO is localized on the thiazole ring. Both the HOMOs and the LUMOs are mostly π antibonding type orbitals. The calculated energy value of HOMO is −6.4099 eV and LUMO is −2.038 eV, respectively. The energy separation between the HOMO and the LUMO is −4.4061 eV, respectively. The energy gap of HOMO-LUMO explains the eventual charge transfer interaction within the molecule, which influences the biological activity. The wavelength of maximum absorption, excitation energies E (eV), and oscillator strengths (f) of benzothiazole are calculated and given in Table 6. Figure 7 contains theoretically deduced UV-vis spectrum of BT in ethanol employing the TD-HF/6-311++G (d, p) method.Table 6
Calculated absorption wavelength  (nm), excitation energiesE (eV), and oscillator strengths (f) of  benzothiazole.
TD-HF/6-311++G (d, p)
TD-HF/6-311++G (d, p)
Ethanol
Gas phase
λ (mn)
(
f
)
E (eV)
λ (mn)
(
f
)
E (eV)
308.1
0.0333
4.0241 eV
308.66
0.0265
4.0169 eV
265.01
0.0013
4.6784 eV
267.95
0.001
4.6272 eV
252.77
0.0025
4.9051 eV
254.78
0.0018
4.8663 eVFigure 6
The molecular orbitals and energies for the HOMO and LUMO of the title compound.Figure 7
Theoretical UV-vis spectrum in ethanol for the title molecule calculated with the TD-HF/6-311++G (d, p) method.


### 3.5. Thermodynamic Properties

The values of thermodynamic parameters zero point vibrational energy, thermal energy, specific heat capacity, rotational constants, entropy of BT at 298.15 K in ground state are listed in Table7. The variation in zero point vibrational energies (ZPVEs) seems to be significant. The ZPVE is much lower by the DFT/B3LYP method than by the HF method. The high value of ZPVE of BT is 65.51 kcl/mol obtained at HF/6-311++G (d, p) whereas the smallest values is 61.63 kcal/mol obtained at B3LYP/6-311++G (d, p). Dipole moment reflects the molecular charge distribution and is given as a vector in three dimensions. Therefore, it can be used as descriptor to depict the charge movement across the molecule. Direction of the dipole moment vector in a molecule depends on the centers of positive and negative charges. Dipole moments are strictly determined for neutral molecules. For charged systems, its value depends on the choice of origin and molecular orientation. As a result of HF and DFT (B3LYP) calculations, the highest dipole moment was observed for B3LYP/6-311G++(d,p) whereas the smallest one was observed for HF/6-311++G (d, p) in each molecule.Table 7
The calculated thermodynamical parameter of benzothiazole.
Basis Set
HF/6-31G
HF/6-311G
HF/6-311++G (d, p)
B3LYP/6-311++G (d, p)
Zero point energy(Kcal/Mol)
66.93709
66.140
65.51671
61.63
Rotational constant
2.93435
2.93435
2.93435
2.93435
Rotational temperature
0.14083
0.14083
0.14083
0.14083
Energy(E)
Translational
0.889
0.889
0.889
0.889
Rotational
0.889
0.889
0.889
0.889
Vibrational
68.158
68.168
67.551
64.058
Total
70.689
69.988
69.329
65.836
Specific heat(Cv)
Translational
2.981
2.981
2.981
2.981
Rotational
2.981
2.981
2.981
2.981
Vibrational
17.963
17.973
18.512
15.283
Total
23.627
23.935
20.895
21.245
Entropy(S)
Translational
40.613
40.613
40.613
40.613
Rotational
28.903
28.903
28.903
28.903
Vibrational
10.154
10.167
10.040
12.445
Total
79.436
79.683
79.556
81.961
Dipole moment
2.0974
2.0507
1.6331
1.4713On the basis of vibrational analysis, the statically thermodynamic functions: heat capacity (C), entropy (S), and enthalpy changes (DH) for the title molecule were obtained from the theoretical harmonic frequencies and listed in Table7. From the data in this table, it can be observed that these thermodynamic functions are increasing with temperature ranging from 100 to 600 K due to the fact that the molecular vibrational intensities increase with temperature [44].


### 3.6. Mulliken Atomic Charges

Mulliken atomic charge calculation is an important tool in the application of quantum chemical calculation to molecular system because atomic charges influence dipole moment, molecular polarizability, electronic structure, and other physical properties of molecular systems. The calculated Mulliken charge values are listed in Table8. The atomic charge depends on basis set presumably occur due to polarization. For example, the charge of N (3) atom is −0.43924 for HF/6-31G, −0.377701 for HF/6-311G, 0.038389 for HF/6-311++G (d, p), and 0.055788 for B3LYP/6-311++G (d, p). The charge distribution of sulfur group is increasing trend in HF and B3LYP methods. The charge of H10, H11, H12, H13, and H14 is positive in both HF and DFT diffuse functions. Considering all methods and basis sets used in the atomic charge calculation, the carbon atoms exhibit a substatantial negative charge, which are donor atoms. Hydrogen atom exhibits a positive charge, which is an acceptor atom. The Mulliken charge distribution of BT is increasing trend in B3LYP as compared to HF methods. A comparison of Mullikan’s Atomic charge obtained by the two theoretical (HF and DFT) approaches is illustrated in Figure 8. It may be seen that the two methods give comparable atomic charges.Table 8
Mulliken atomic charges of benzothiazole.
Atoms
HF/6-31G
HF/6-311G
HF/6-311++G (d, p)
B3LYP/6-311++G (d,p)
S1
0.494254
0.283343
-
0.428958
-
0.305656
C2
-
0.223616
-
0.09723
-
0.1285
-
0.174194
N3
-
0.43924
-
0.377701
0.038389
0.055788
C4
0.177233
0.264898
-
0.932014
-
0.938592
C5
-
0.403325
-
0.453121
1.000645
0.984567
C6
-
0.120432
-
0.09318
-
0.43895
-
0.437759
C7
-
0.221659
-
0.167237
-
0.377287
-
0.307896
C8
-
0.184873
-
0.165775
-
0.246147
-
0.081338
C9
-
0.19687
-
0.144593
0.313292
0.218011
H10
0.242781
0.218665
0.275732
0.255925
H11
0.235255
0.192916
0.244504
0.193902
H12
0.209181
0.176608
0.217394
0.172514
H13
0.207899
0.178898
0.216713
0.174776
H14
0.223413
0.18351
0.245187
0.189952Figure 8
Mullikan’s atomic charges between theoretical (HF and DFT) approaches.


## 3.1. Molecular Geometry

The optimized geometry of the molecule under investigation with IUPAC numbering scheme for the atoms is presented in Figure1. The data of structural parameters obtained by ab initio method as compared to density functional theory for benzothiazole are reported in Table 1. The comparative graphs of bond lengths and bond angles of the title molecule are presented in Figure 2. From the computed values, it is found that most of the optimized bond lengths are slightly larger than the experimental values, this may be due to the fact that theoretical calculations belong to isolated molecules in gaseous phase and the experimental results belong to molecules in solid state. Comparing bond angles and lengths obtained by B3LYP method with those obtained by HF, as a whole the values got by the former are higher than those obtained be the later method. It may be pointed out that the values calculated by B3LYP method correlate satisfactorily with the experimental data. From the data shown in Table 1, it is seen that both HF and DFT (B3LYP/6-311++G (d, p)) levels of theory in general estimate the same values of some bond lengths and bond angles. It is well known that HF methods underestimate and DFT method overestimates bond lengths, particularly the C–H bond lengths [20, 21]. This theoretical pattern is also found for benzothiazole molecule.Table 1
Optimized some geometrical parameters of benzothiazole, bond length (Å), and bond angles (°).
Parameters
HF/6-31G
HF/6-311G
HF/6-311++G
B3LYP/6-311G
Bond length
(S1, C2)
1.8159
1.8146
1.7464
1.7651
(S1, C5)
1.8096
1.8043
1.7443
1.7518
(C2, N3)
1.2688
1.2683
1.2638
1.2874
(C2, H10)
1.0665
1.0647
1.0744
1.0827
(N3, C4)
1.4031
1.404
1.3886
1.3877
(C4, C5)
1.3926
1.391
1.3912
1.4139
(C4, C6)
1.3887
1.3882
1.3932
1.4008
(C5, C9)
1.385
1.3844
1.3907
1.3962
(C6, C7)
1.3811
1.3803
1.3761
1.3866
(C6, H11)
1.0713
1.0689
1.0743
1.0832
(C7, C8)
1.3975
1.3976
1.3994
1.405
(C7, H12)
1.0723
1.07
1.075
1.0838
(C8, C9)
1.3843
1.383
1.3774
1.3893
(C8, H13)
1.0726
1.0703
1.0751
1.0839
(C9, H14)
1.0715
1.0694
1.0746
1.0832
Bond angle
(C2, C1, C5)
86.7846
86.8578
88.2122
88.2011
(C1, C2, N3)
115.703
115.6631
116.9227
116.6919
(C1, C2, H10)
119.792
119.7907
119.7167
119.3151
(N3, C2, H10)
124.5047
124.5462
123.3605
123.993
(C2, N3, C4)
112.9102
112.8215
110.755
110.742
(N3, C4, C5)
115.155
115.1091
115.1782
115.2284
(N3, C4, C6)
124.5797
124.5766
124.855
125.1777
(C5, C4, C6)
120.2653
120.3142
119.9668
119.5939
(S1, C5, C4)
109.4469
109.5485
108.9318
109.1366
(S1, C5, C9)
129.1903
129.1251
129.6054
129.4096
(C4, C5, C9)
121.3628
121.3263
121.4628
121.4538
(C4, C6, C7)
118.7264
118.7178
118.7551
118.9556
(C4, C6, H11)
119.3604
119.2699
119.5996
119.307
(C7, C6, H11)
121.9132
122.0123
121.6452
121.7374
(C6, C7, C8)
120.6426
120.6135
120.8677
120.908
(C6, C7, H12)
119.8217
119.8388
119.7498
119.6972
(C8, C7, H12)
119.5357
119.5477
119.3825
119.3948
(C7, C8, C9)
120.9529
120.9354
120.9119
121.0788
(C7, C8, H13)
119.5983
119.6269
119.5658
119.5843
(C9, C8, H13)
119.4487
119.4377
119.5223
119.3369
(C5, C9, C8)
118.0499
118.0927
118.0357
118.0099
(C5, C9, H14)
121.1939
121.1702
121.132
121.2411
(C8, C9, H14)
120.7561
120.7371
120.8323
120.749Figure 1
Optimized structure of benzothiazole.Bond length and bond angle difference between theoretical (HF and DFT) approaches.
(a)
(b)The carbon–carbon bonds in benzene are not of equal length which is justified by the presence of fused thiazole ring. However, the differences between the six C–C distances are small. The longest bond distance in C4–C5 bond is due to the fusion of thiazole moiety at these carbons. Comparing the bond distances of the hetero aromatic ring, it is found that the bond distances in hetero aromatic ring differ significantly from each other due to the difference in electronegativities of the bonded atoms. The S1–C2 bond distance is the longest (1.7651 Å) while the C2–N3 is the shortest (1.2874  Å). The longest S1–C2 distance attributes the pure single bond character. The C5–S1 and C2–S1 bond distances of BT determined by B3LYP/6-311++G (d, p) method are 1.75 Å and 1.7651 Å, respectively, in between the 1.81 Å average distance for a carbon–sulfur bond and the 1.61 Å which indicate that the actual bond order is between one and two which is due to conjugative effect in benzothiazole. Due to ring strain the C2–N3 double bond distance is 1.268 Å, 1.268 Å, 1.263 Å in HF, and 1.2874 Å for B3LYP/6-311++G (d, p) bigger than single bond C2–H10. With the electron donating substituents on the benzene ring, the symmetry of the ring is distorted, yielding ring angles smaller than 120° at the point of substitution and slightly larger than 120° at the ortho- and metapositions [22]. It is observed that in BT molecule the bond angle at the point of substitution C4–C5–C9 is 118.7° in HF and 118.9° in DFT while the bond angles in at ortho to the substituted carbon, C6–C7–C8 position is found to be 120.8677, 120.908 degree at HF and DFT respectively. This may be due to mesomeric effect of the thiazole ring. The meta position angle C7–C8–C9 is greater than 120° and is found to be 120.91°, 121.078°. More distortion in bond parameters is observed in the heteroring than in the benzene ring. The variation in bond angle depends on the electronegativity of the central atom, the presence of lone pair of electrons, and the conjugation of the double bonds. If the electro negativity of the central atom is less, the bond angle decreases. Thus, the bond angle C5–S1–C2 is very less (88.2122°, 88.2011°) than the bond angle C8–N3–C2 (110.755°, 110.742°) which is due to the fact that electronegativity of nitrogen is greater than sulfur.


## 3.2. Vibrational Assignments

The BT molecule consists of 14 atoms and so it has 36 normal vibrational modes. The observed vibrational assignments and analysis of BT are discussed in terms of fundamental bands. The harmonic vibrational frequencies calculated for BT at HF and B3LYP levels along with the observed FT-IR and FT-Raman frequencies for various modes of vibrations have been presented in Table2. The comparative values of IR and Raman intensities are given in Table 3. The recorded FT-IR and FT-Raman spectra of BT are given in in Figures 3(a) and 3(b) respectively. Theoretical FT-IR and FT-Raman spectra are reported in Figures 4 and 5, respectively. It may be pointed out here that computed wave numbers correspond to the isolated molecular state in the gas phase whereas the experimental wave numbers correspond to the solid state spectra. The calculated vibrational frequencies using different methods are compared with experimentally observed values. The calculated vibrational wave numbers are consistent with the experimental results. Few bands predicted theoretically in FT-IR spectra were not observed in the experimental spectrum of BT molecule may be due to their very weak intensity.Table 2
Comparison of the experimental (FT-IR and FT-Raman) and theoretical harmonic wave numbers (cm−1) of  benzothiazole    calculated by HF, B3LYP with 6-311++G(d, p) basis set.
Modes no.
Experimental
6-311G
6-311++G
B3LYP   6-311++G
Assignment
IR
Raman
1.
71.44
185.6993
221.8993
158.2282
C–H—out of plane bending
2.
210.04
244.1506
259.6877
225.0702
C–H—out of plane bending
3.
352.91
372.6441
373.5584
341.0859
Ring stretching
4.
424.17
426.2948
414.1324
350.0611
N–CH Wagging
5.
471.7758
467.2944
429.3019
C–S–C in plane bending
6.
531
505.08
520.8227
507.0766
451.8357
C–C–C—out of plane bending
7.
585
541.0727
532.2922
481.3446
C–C–C—out of plane bending
8.
623.6493
608.7293
560.6751
C–C–C—out of plane bending
9.
667
668.2929
652.4117
600.4245
C–S Stretching
10.
769
706.88
730.3856
717.6507
666.7194
C–C–C Ring breathing
11.
799
801.01
777.8919
759.172
709.0033
C–S Stretching
12.
828
846.4841
825.1871
754.3702
Thiazole Ring Stretching
13.
873
877.3007
872.0681
804.3435
C–C–C—in plane bending
14.
978
974.2327
929.8297
827.145
C–H—out of plane bending
15.
1014
1015.54
1025.745
970.2269
875.2731
C–H—out of plane bending
16.
1058.5012
1030.8954
922.7485
C–S—Stretching
17.
1069
1085.408
1053.4724
985.3864
C–H—in plane bending
18.
1110.2525
1069.5475
993.4765
C–H—in plane bending
19.
1124
1124.88
1124.8897
1096.4601
1015
C–H—in plane bending
20.
1157
1166.0662
1125.1724
1027.9394
C–H—in plane bending
21.
1198
1197.98
1194.0921
1154.4126
1092.4829
C–H—in plane bending
22.
1264
1203.5496
1178.2819
1126.6974
C–H—in plane bending
23.
1292
1291.66
1243.9149
1216.6827
1153.3509
C–C Stretching
24.
1315
1316.01
1338.3513
1309.6226
1244.4551
C–C—Stretching
25.
1423
1394.2405
1364.2723
1268.7322
C–C—Stretching
26.
1454
1424.58
1427.192
1397.859
1275.7476
C–C—Stretching
27.
1490
1468.87
1575.3975
1556.5462
1440.267
C–H in plane bending
28.
1556
1557.01
1585.4282
1562.2713
1444.1304
C–H in plane bending
29.
1592
1654.5209
1642.2366
1519.1381
C=N Stretching
30.
1657
1663.2985
1653.9474
1535.0676
C–C–C Stretching
31.
1692
1716.6492
1703.8545
1628.1791
C=N Stretching
32.
3061
3063.23
3070.1368
3105.7742
3028.6049
C–H Stretching
33.
3150
3082.2096
3116.571
3036.013
C–H Stretching
34.
3085.3847
3118.2409
3037.4297
C–H Stretching
35.
3094.2296
3126.9054
3046.2331
C–H Stretching
36.
3105.5365
3135.3642
3054.1799
C–H StretchingTable 3
Comparative values of IR and Raman intensities between HF/6-311G++(d, p) and  B3LYP/6-311G++(d, p) of benzothiazole.
HF/6-311G (d, p)
HF/6-311++G (d, p)
B3LYP/6-311++G (d, p)
IR intensity
Raman intensity
IR intensity
Raman intensity
IR intensity
Raman intensity
8.55
31.44
7.69
16.97
12.75
32.04
0.87
10.21
1.58
7.93
1.23
7.36
1.11
15.00
1.26
14.27
1.19
13.42
14.98
26.31
17.53
25.42
22.89
22.11
1.14
24.06
0.97
16.81
1.513
19.92
12.88
9.86
11.17
7.72
10.50
5.311
0.17
6.11
2.07
3.90
1.79
4.11
6.63
3.63
5.86
3.62
6.73
2.43
3.04
2.78
4.66
2.08
4.05
2.15
4.84
5.27
5.06
5.14
5.06
2.90
16.16
8.09
14.71
9.23
18.48
11.02
20.38
6.69
26.21
3.72
23.66
1.91
14.24
3.81
15.91
3.61
10.31
3.08
88.08
0.38
78.09
4.38
78.12
0.52
11.60
18.23
24.84
13.09
17.20
4.92
12.48
4.88
10.48
10.79
2.23
1.10
15.42
2.25
16.04
6.34
10.29
9.35
0.58
1.192
5.73
2.50
13.25
17.50
12.94
2.06
7.02
1.59
1.43
1.99
3.15
1.57
4.43
1.34
1.70
2.25
2.39
0.65
0.82
0.11
7.34
18.81
3.40
0.08
8.71
3.65
1.30
7.484
12.76
5.03
16.28
9.62
8.45
1.82
1.98
0.18
1.16
0.13
7.05
0.10
0.07
2.50
1.02
2.27
16.98
4.84
34.14
3.30
40.98
3.72
7.68
0.81
27.04
0.98
14.87
1.57
8.36
1.87
6.66
0.87
29.51
0.63
19.58
0.29
10.29
9.44
13.58
13.94
9.66
13.7
16.35
3.27
8.27
2.84
0.99
1.65
98.69
9.45
112.55
19.48
108.78
11.77
0.30
2.40
0.15
1.97
0.06
2.14
7.94
6.26
4.21
5.60
4.37
10.42
13.26
10.55
9.96
9.44
3.21
6.44
23.65
2.74
14.21
2.44
10.14
3.24
23.43
15.30
12.95
13.86
9.55
16.75Experimental FT-IR and FT-Raman spectrum of benzothiazole.
(a)
(b)Theoretical FT-IR spectrum of benzothiazole.
(a)
(b)
(c)Theoretical FT-Raman spectrum of benzothiazole.
(a)
(b)
(c)


### 3.2.1. C–H Stretching

Aromatic compounds commonly exhibit multiple weak bands in the region 3100–3000 cm−1 [23–25] due to aromatic C–H stretching vibrations. In the present case, the C–H stretching vibrations are captured at 3061, 3150 cm−1 in (mode no. 32, 33) FT-IR spectrum and corresponding Raman spectrum observed at 3063 cm−1. The aromatic C–H in-plane bending modes of benzene and its derivatives are observed in the region 1300–1000 cm−1. The C–H out-of-plane bending modes [26–29] are usually of medium intensity and absorption in the region 950–600 cm−1. In the case of BT, the bands observed at 1069, 1124, 1157, 1198, and 1264 cm−1 (mode no. 17, 19, 20, 21, and 22) in IR and at 1292 cm−1 in Raman spectra are assigned to the C–H in-plane bending vibrations. The C–H out of plane bending mode of benzene derivatives is observed in the region 1000–600 cm−1. The aromatic C–H out of plane bending vibrations of BT are assigned to the medium to weak bands observed at 1014 and 978 cm−1 (mode no. 14, 15) in the infrared spectrum and 1016 cm−1 in Raman spectrum. The aromatic C–H in-plane and out of plane bending vibrations have substantial overlapping with the ring C–C–C in-plane and out of plane bending modes, respectively.


### 3.2.2. C–S Stretching

The C–S and S–H bonds are highly polarizable and hence exhibit stronger spectral activity. The C–S stretching vibration is expected in the region 710–685 cm−1 [30]. The C–S stretching vibrations were observed in the region 609–716 cm−1 for 2-mercapto benzothiazole [31]. The calculated values of the vibrations range from 572 cm−1 to 876 cm−1. For 2-mercaptobenzoxazole [32], the calculated values of the vibrations range from 579 cm−1 to 892 cm−1 and the observed C–S stretching vibration is 954 cm−1. In our title molecule, the C–S stretching is observed at 667 and 799 cm−1 (mode no. 9, 11) in FT-IR. The FT-Raman spectrum value at 801 cm−1 as a medium band is assigned to C–S stretching vibration. The calculated frequencies of 668, 652, 600, and 626 cm−1 exactly correlate with experimental observation as well as the literature data. The C–S vibration is a pure mode as evident from Table 2. The in-plane and out-of-plane C–S stretching vibration also exactly correlates with experimental observations.


### 3.2.3. C=N Vibrations

The C=N stretching vibrations [33–36] are observed in the range 1672–1566 cm−1. Varsanyi [37] has suggested that an IR band at 1626 cm−1 for C=N stretching and Raman frequency is assigned to the C=N stretching vibration of benzothizaole [38]. The respective bands occurring at 1692 and 1592 cm−1 (mode no. 29, 31) in IR spectra is assigned to the C=N stretching vibration for BT molecule. The bands corresponding to the C–C–C and C–S–C in-plane and out of plane bending modes of BT are presented in Table 3. Normal coordinate analysis shows that significant mixing of C–C–C in-plane bending with C–H in-plane bending occurs. Similarly, the skeletal out of plane bending modes are overlapped with C–H out of plane bending modes significantly. The theoretically calculated values of C=N Stretching vibrations are in the region 1717, 1704, and 1629 cm−1.


### 3.2.4. Ring Vibrations

The carbon–carbon stretching modes of the benzene ring are expected to be in the range from 1650 to 1200 cm−1 and are usually not very sensitive to substitution by small substituents, but heavy halogens diminish the frequency [39, 40]. In the Raman spectrum of BT, the carbon–carbon stretching bands appeared at 1596, 1575, 1478, and 1209 cm−1. The corresponding C–C stretching modes are observed in the infrared spectrum at 1454, 1423, 1315, and 1292.31 cm−1 (mode no. 23, 24, 25, and 26). The theoretically calculated values are calculated at 1604, 1602, 1486, 1454, 1328, and 1304 cm−1 and these values show excellent agreement with experimental data.The infrared band at 873 cm−1 and two Raman bands at 1000 and 700 cm−1 (mode no. 13) are assigned to C–C–C in-plane bending vibrations of BT. The C–C in-plane bending vibrations appeared as the combination vibrations with C–H in-plane bending vibrations. The bands assigned to C–C–C out-of-plane bending vibrations are observed at 585, 531 cm−1 in (mode no. 6,7) FTIR spectrum and 505 cm−1 in Raman spectrum for BT. The ring breathing vibrations are generally very strong in Raman spectrum. This mode is found in the region 1100−1000 cm−1 for a heavy substituted compound and is strongly Raman active. This is confirmed by the very weak intense Raman band at 706 cm−1 which is supported by computed results. The ring stretching mode is captured at 372.6441, 373.5584, and 341.0859 cm−1 (mode no. 3) in HF/6-311++G (d, p) and B3LYP/6-311++G (d, p) for benzothiazole molecule. Comparison of IR intensities and Raman intensities calculated (Table 3) by HF and DFT (B3LYP) at 6-311+G (d, p) level with experimental values exposes the variation of IR intensities and Raman intensities. Most of the cases, the values of IR intensities by HF are found to be higher than B3LYP at 6-311+G (d, p) level whereas in the case of Raman activities the trend is reverse.


## 3.2.1. C–H Stretching

Aromatic compounds commonly exhibit multiple weak bands in the region 3100–3000 cm−1 [23–25] due to aromatic C–H stretching vibrations. In the present case, the C–H stretching vibrations are captured at 3061, 3150 cm−1 in (mode no. 32, 33) FT-IR spectrum and corresponding Raman spectrum observed at 3063 cm−1. The aromatic C–H in-plane bending modes of benzene and its derivatives are observed in the region 1300–1000 cm−1. The C–H out-of-plane bending modes [26–29] are usually of medium intensity and absorption in the region 950–600 cm−1. In the case of BT, the bands observed at 1069, 1124, 1157, 1198, and 1264 cm−1 (mode no. 17, 19, 20, 21, and 22) in IR and at 1292 cm−1 in Raman spectra are assigned to the C–H in-plane bending vibrations. The C–H out of plane bending mode of benzene derivatives is observed in the region 1000–600 cm−1. The aromatic C–H out of plane bending vibrations of BT are assigned to the medium to weak bands observed at 1014 and 978 cm−1 (mode no. 14, 15) in the infrared spectrum and 1016 cm−1 in Raman spectrum. The aromatic C–H in-plane and out of plane bending vibrations have substantial overlapping with the ring C–C–C in-plane and out of plane bending modes, respectively.


## 3.2.2. C–S Stretching

The C–S and S–H bonds are highly polarizable and hence exhibit stronger spectral activity. The C–S stretching vibration is expected in the region 710–685 cm−1 [30]. The C–S stretching vibrations were observed in the region 609–716 cm−1 for 2-mercapto benzothiazole [31]. The calculated values of the vibrations range from 572 cm−1 to 876 cm−1. For 2-mercaptobenzoxazole [32], the calculated values of the vibrations range from 579 cm−1 to 892 cm−1 and the observed C–S stretching vibration is 954 cm−1. In our title molecule, the C–S stretching is observed at 667 and 799 cm−1 (mode no. 9, 11) in FT-IR. The FT-Raman spectrum value at 801 cm−1 as a medium band is assigned to C–S stretching vibration. The calculated frequencies of 668, 652, 600, and 626 cm−1 exactly correlate with experimental observation as well as the literature data. The C–S vibration is a pure mode as evident from Table 2. The in-plane and out-of-plane C–S stretching vibration also exactly correlates with experimental observations.


## 3.2.3. C=N Vibrations

The C=N stretching vibrations [33–36] are observed in the range 1672–1566 cm−1. Varsanyi [37] has suggested that an IR band at 1626 cm−1 for C=N stretching and Raman frequency is assigned to the C=N stretching vibration of benzothizaole [38]. The respective bands occurring at 1692 and 1592 cm−1 (mode no. 29, 31) in IR spectra is assigned to the C=N stretching vibration for BT molecule. The bands corresponding to the C–C–C and C–S–C in-plane and out of plane bending modes of BT are presented in Table 3. Normal coordinate analysis shows that significant mixing of C–C–C in-plane bending with C–H in-plane bending occurs. Similarly, the skeletal out of plane bending modes are overlapped with C–H out of plane bending modes significantly. The theoretically calculated values of C=N Stretching vibrations are in the region 1717, 1704, and 1629 cm−1.


## 3.2.4. Ring Vibrations

The carbon–carbon stretching modes of the benzene ring are expected to be in the range from 1650 to 1200 cm−1 and are usually not very sensitive to substitution by small substituents, but heavy halogens diminish the frequency [39, 40]. In the Raman spectrum of BT, the carbon–carbon stretching bands appeared at 1596, 1575, 1478, and 1209 cm−1. The corresponding C–C stretching modes are observed in the infrared spectrum at 1454, 1423, 1315, and 1292.31 cm−1 (mode no. 23, 24, 25, and 26). The theoretically calculated values are calculated at 1604, 1602, 1486, 1454, 1328, and 1304 cm−1 and these values show excellent agreement with experimental data.The infrared band at 873 cm−1 and two Raman bands at 1000 and 700 cm−1 (mode no. 13) are assigned to C–C–C in-plane bending vibrations of BT. The C–C in-plane bending vibrations appeared as the combination vibrations with C–H in-plane bending vibrations. The bands assigned to C–C–C out-of-plane bending vibrations are observed at 585, 531 cm−1 in (mode no. 6,7) FTIR spectrum and 505 cm−1 in Raman spectrum for BT. The ring breathing vibrations are generally very strong in Raman spectrum. This mode is found in the region 1100−1000 cm−1 for a heavy substituted compound and is strongly Raman active. This is confirmed by the very weak intense Raman band at 706 cm−1 which is supported by computed results. The ring stretching mode is captured at 372.6441, 373.5584, and 341.0859 cm−1 (mode no. 3) in HF/6-311++G (d, p) and B3LYP/6-311++G (d, p) for benzothiazole molecule. Comparison of IR intensities and Raman intensities calculated (Table 3) by HF and DFT (B3LYP) at 6-311+G (d, p) level with experimental values exposes the variation of IR intensities and Raman intensities. Most of the cases, the values of IR intensities by HF are found to be higher than B3LYP at 6-311+G (d, p) level whereas in the case of Raman activities the trend is reverse.


## 3.3. NBO Analysis

The natural bond orbital analysis provides an efficient method for studying intra- and intermolecular bonding and interaction among bonds and also provides a convenient basis for investigating charge transfer or conjugative interaction in molecular systems. Some electron donor orbital, acceptor orbital, and the interacting stabilization energy resulting from the second-order microdisturbance theory are reported [41]. NBO analysis has been performed on the title molecule in order to elucidate the intermolecular, rehybridization, and delocalization of electron density within the molecule, which are presented in Tables 4 and 5. A large diversity of energy values was found. The stronger donor character is shown by the p-type lone pair of the nitrogen atoms. The most important interaction (n-σ*) energies, related to the resonance in the molecules, are electron donation from the LP(1)S atoms of the electron donating groups to the antibonding acceptor π*(C–N) of the phenyl ring LP(1) S1→σ* (C2–N3) = 1.50 kJ mol−1. This larger energy shows the hyperconjugation between the electron do nating groups and the phenyl ring. NBO analysis has been performed on the BT at the HF/6-11++G (d, p) and DFT level in order to elucidate the intramolecular, rehybridization, and delocalization of electron density within the molecule. The intramolecular interactions are formed by the orbital overlap between bonding (C–C) and (C–C) antibond orbital which results in intramolecular charge transfer (IC T) causing stabilization of the system. These interactions are observed as increase in electron density (ED) in C–C antibonding orbital that weakens the respective bonds. The strong intramolecular conjugative interaction of the σ electron of (S1–C2) distribute to σ* (S1–C2), C4–C5, C4–C6, and C5–C9 of the ring. On the other hand, the π (C2–N3) in the ring conjugate to the antibonding orbital of π* (C4–C6) leads to strong delocalization of 18.48 kJ/mol. The π (C4–C6) bond is interacting with π* (C2–N3) with the energy 12.45 kcal/mol for BT. The σ (C4–C5) bond is interacting with σ* (C2–H10), σ* (C4–C6), σ* (C5–C9), σ* (C6–H11), σ* (C9–H14) with the energies 0.68, 5.03, 5.14, 2.13, 2.37 kcal/mol for BT. The energy vlaues of MOs of benzene ring σ (C4–C6, C6–C7, C7–C8, C8–C9), π (C9–C5) are respectively 4.16, 4.51, 2.83, 5.69, 3.79 kcal/mol for BT.Table 4
Second-order perturbation theory analysis of Fock matrix in NBO basis for benzothiazole.
Donor (i)
Type
ED/e
Acceptor (j)
Type
ED/e
E(2)
E(j) − E(i)b (a. u.)
F (i, j)c (a. u.)
S1–C2
σ
1.97599
S1–C2
σ
*
0.07093
0.70
0.92
0.023
C4–C5
σ
*
0.03211
0.78
1.46
0.030
C4–C6
σ
*
0.02151
1.04
1.50
0.035
C5–C9
σ
*
0.02268
5.97
1.49
0.084
C5–C9
π
*
0.35040
3.63
0.84
0.054
S1–C5
σ
1.97203
C2–N3
π
*
0.07212
1.82
0.96
0.038
C2–H10
σ
*
0.02234
2.59
1.46
0.055
C5–C9
σ
*
0.02268
0.72
1.54
0.030
C8–C9
σ
*
0.01365
2.97
1.55
0.061
C2–N3
σ
1.99261
C2–H10
σ
*
0.02234
1.26
1.90
0.044
N3–C4
σ
*
0.02497
0.94
1.77
0.037
C4–C6
σ
*
0.02151
3.53
1.99
0.075
C4–C6
π
*
0.34604
0.80
1.34
0.032
C2–N3
π
1.95466
N3–C4
σ
*
0.02497
1.36
1.07
0.034
C4–C6
π
*
0.34604
18.48
0.64
0.106
C2–H10
σ
1.98286
C2–N3
σ
*
0.01757
1.83
1.60
0.048
N3–C4
σ
*
0.02497
8.01
1.33
0.092
N3–C4
σ
1.97560
S1–C2
σ
*
0.07093
1.12
1.15
0.032
C2–H10
σ
*
0.02234
7.02
1.64
0.096
C4–C5
σ
*
0.03211
0.54
1.69
0.027
C4–C6
σ
*
0.02151
1.23
1.73
0.041
C5–C9
σ
*
0.02268
2.69
1.73
0.061
C6–C7
σ
*
0.01185
1.80
1.74
0.050
C4–C5
σ
1.97874
C2–H10
σ
*
0.02234
0.68
1.65
0.030
C4–C6
σ
*
0.02151
5.03
1.74
0.084
C5–C9
σ
*
0.02268
5.14
1.74
0.084
C6–H11
σ
*
0.00915
2.13
1.66
0.053
C9–H14
σ
*
0.01004
2.37
1.66
0.056
C4–C6
σ
1.97510
S1–C5
σ
*
0.01756
4.16
1.22
0.064
C2–N3
σ
*
0.01757
1.50
1.76
0.046
C2–N3
π
*
0.07212
0.53
1.12
0.022
N3–C4
σ
*
0.02497
1.34
1.50
0.040
C4–C5
σ
*
0.03211
5.54
1.68
0.086
C6–C7
σ
*
0.01185
2.72
1.72
0.061
C6–H11
σ
*
0.00915
1.69
1.64
0.047
C7–H12
σ
*
0.00908
2.25
1.64
0.054
C4–C6
π
1.66368
C2–N3
π
*
0.07212
12.45
0.52
0.077
N3–C4
σ
*
0.02497
0.94
0.90
0.028
C5–C9
π
*
0.35040
39.19
0.46
0.120
C7–C8
π
*
0.32093
39.20
0.47
0.122
C5–C9
σ
1.98148
N3–C4
σ
*
0.02497
3.01
1.52
0.060
C4–C5
σ
*
0.03211
5.38
1.70
0.086
C8–C9
σ
*
0.01365
3.05
1.74
0.065
C8–H13
σ
*
0.00886
2.08
1.65
0.052
C9–H14
σ
*
0.01004
1.87
1.65
0.050
C5–C9
π
1.70971
C2–N3
π
*
0.07212
1.23
0.54
0.024
N3–C4
σ
*
0.02497
0.92
0.92
0.028
C4–C6
π
*
0.34604
36.07
0.48
0.120
C7–C8
π
*
0.32093
35.76
0.49
0.120
C6–C7
σ
1.98054
N3–C4
σ
*
0.02497
4.51
1.49
0.07
C4–C6
σ
*
0.02151
3.29
1.71
0.067
C6–H11
σ
*
0.00915
1.53
1.63
0.045
C7–C8
σ
*
0.01359
2.85
1.71
0.062
C7–H12
σ
*
0.00908
1.44
1.63
0.043
C8–H13
σ
*
0.00886
2.56
1.62
0.058
C6–H11
σ
1.98222
N3–C4
σ
*
0.02497
0.55
1.28
0.024
C4–C5
σ
*
0.03211
5.08
1.46
0.077
C4–C6
σ
*
0.02151
1.42
1.50
0.041
C6–C7
σ
*
0.01185
1.33
1.50
0.040
C7–C8
σ
*
0.01359
4.20
1.50
0.071
C7–C8
σ
1.98272
C6–C7
σ
*
0.01185
2.83
1.71
0.062
C6–H11
σ
*
0.00915
2.48
1.63
0.057
C7–H12
σ
*
0.00908
1.55
1.63
0.045
C8–C9
σ
*
0.01365
2.90
1.71
0.063
C8–H13
σ
*
0.00886
1.56
1.62
0.045
C9–H14
σ
*
0.01004
2.59
1.62
0.058
C7–C8
π
1.67584
C4–C6
π
*
0.34604
42.89
0.46
0.126
C5–C9
π
*
0.35040
42.80
0.45
0.125
C7–H12
σ
1.98449
C4–C6
σ
*
0.02151
4.40
1.50
0.073
C6–C7
σ
*
0.01185
1.28
1.50
0.039
C7–C8
σ
*
0.01359
1.29
1.50
0.039
C8–C9
σ
*
0.01365
4.20
1.50
0.071
C8–C9
σ
1.97778
S1–C5
σ
*
0.01756
5.69
1.21
0.074
C5–C9
σ
*
0.02268
3.97
1.70
0.073
C7–C8
σ
*
0.01359
2.83
1.71
0.062
C7–H12
σ
*
0.00908
2.51
1.63
0.057
C8–H13
σ
*
0.00886
1.43
1.63
0.043
C9–H14
σ
*
0.01004
1.53
1.62
0.045
C8–H13
σ
1.98412
C5–C9
σ
*
0.02268
4.70
1.49
0.075
C6–C7
σ
*
0.01185
4.16
1.50
0.071
C7–C8
σ
*
0.01359
1.29
1.50
0.039
C8–C9
σ
*
0.01365
1.26
1.50
0.039
C9–H14
σ
1.98424
C4–C5
σ
*
0.03211
4.44
1.46
0.072
C5–C9
σ
*
0.02268
1.54
1.49
0.043
C7–C8
σ
*
0.01359
4.07
1.50
0.070
C8–C9
σ
*
0.01365
1.33
1.50
0.040
C4–C6
π
*
0.34604
C2–N3
π
*
0.07212
18.62
0.05
0.062
N3–C4
σ
*
0.02497
2.79
0.43
0.072
C5–C9
π
*
0.35040
C2–N3
π
*
0.07212
3.79
0.06
0.030
C7–C8
π
*
0.32093
371.30
0.02
0.122
a
E(2) means energy of hyperconjugative interaction (stabilization energy).
bEnergy difference between donor and acceptor i and j NBO orbitals.
c
F(i, j) is the Fock matrix element between i and j NBO orbitals.Table 5
Second-order perturbation energiesE(2) (donor → acceptor) for benzothiazole.
Donor (i)
Acceptor(j)
E(2) (kJ mol−1)a
E(j) − E(i)b (a. u.)
F (i, j)c (a. u.)
Within unit 1
LP (1) S1
σ
*C2–N3
1.50
1.70
0.045
LP (1) S1
π
*C2–N3
1.38
1.05
0.035
LP (1) S1
σ
*C4–C5
1.77
1.61
0.048
LP (1) S1
σ
*C5–C9
0.52
1.64
0.026
LP (2) S1
π
*C2–N3
8.98
0.59
0.065
LP (2) S1
σ
*C2–H10
1.41
1.09
0.036
LP (2) S1
σ
*C4–C5
1.21
1.14
0.034
LP (2) S1
σ
*C5–C9
1.98
1.18
0.044
LP (1) N3
σ
*C2–N6
2.64
1.17
0.050
LP (1) N3
σ
*C4–C5
9.23
1.38
0.102
LP (1) N3
σ
*C4–H7
3.47
1.25
0.060
LP (1) N3
σ
*S1–C2
27.32
0.77
0.130
LP (1) N3
σ
*C4–C6
0.85
1.35
0.031
LP (1) N3
σ
*C4–C6
1.17
0.70
0.027
a
E(2) means energy of hyper conjugative interaction (stabilization energy).
bEnergy difference between donor and acceptor i and j NBO orbitals.
c
F (i, j) is the Fock matrix element between i and j NBO orbitals.


## 3.4. Frontier Molecular Orbitals (FMOs)

The highest occupied molecular orbitals (HOMOs) and the lowest-lying unoccupied molecular orbitals (LUMOs) are called frontier molecular orbital’s (FMOs). The FMOs play an important role in the optical and electric properties, as well as in quantum chemistry and UV-vis spectra [37]. The HOMO represents the ability to donate an electron; LUMO as an electron acceptor represents the ability to obtain an electron. The energy gap between HOMO and LUMO determines the kinetic stability, chemical reactivity, and optical polarizability and chemical hardness-softness of a molecule [42, 43].In order to evaluate the energetic behavior of the title compound, we carried out calculations in vacuo and in organic solvent (ethanol). The energies of important molecular orbitals of BT, the highest occupied MOs (HOMO) the lowest unoccupied MOs (LUMO) were calculated using HF/6-311++G (d, p). The energy values of HOMO and LUMO are −0.2449, −0.05227, respectively. The 3D plots of the HOMO, LUMO orbitals computed for BT molecule are illustrated in Figure6. The positive phase is red and the negative one is green. It is evident from the figure that while the HOMO is localized on almost the whole molecule, LUMO is localized on the thiazole ring. Both the HOMOs and the LUMOs are mostly π antibonding type orbitals. The calculated energy value of HOMO is −6.4099 eV and LUMO is −2.038 eV, respectively. The energy separation between the HOMO and the LUMO is −4.4061 eV, respectively. The energy gap of HOMO-LUMO explains the eventual charge transfer interaction within the molecule, which influences the biological activity. The wavelength of maximum absorption, excitation energies E (eV), and oscillator strengths (f) of benzothiazole are calculated and given in Table 6. Figure 7 contains theoretically deduced UV-vis spectrum of BT in ethanol employing the TD-HF/6-311++G (d, p) method.Table 6
Calculated absorption wavelength  (nm), excitation energiesE (eV), and oscillator strengths (f) of  benzothiazole.
TD-HF/6-311++G (d, p)
TD-HF/6-311++G (d, p)
Ethanol
Gas phase
λ (mn)
(
f
)
E (eV)
λ (mn)
(
f
)
E (eV)
308.1
0.0333
4.0241 eV
308.66
0.0265
4.0169 eV
265.01
0.0013
4.6784 eV
267.95
0.001
4.6272 eV
252.77
0.0025
4.9051 eV
254.78
0.0018
4.8663 eVFigure 6
The molecular orbitals and energies for the HOMO and LUMO of the title compound.Figure 7
Theoretical UV-vis spectrum in ethanol for the title molecule calculated with the TD-HF/6-311++G (d, p) method.


## 3.5. Thermodynamic Properties

The values of thermodynamic parameters zero point vibrational energy, thermal energy, specific heat capacity, rotational constants, entropy of BT at 298.15 K in ground state are listed in Table7. The variation in zero point vibrational energies (ZPVEs) seems to be significant. The ZPVE is much lower by the DFT/B3LYP method than by the HF method. The high value of ZPVE of BT is 65.51 kcl/mol obtained at HF/6-311++G (d, p) whereas the smallest values is 61.63 kcal/mol obtained at B3LYP/6-311++G (d, p). Dipole moment reflects the molecular charge distribution and is given as a vector in three dimensions. Therefore, it can be used as descriptor to depict the charge movement across the molecule. Direction of the dipole moment vector in a molecule depends on the centers of positive and negative charges. Dipole moments are strictly determined for neutral molecules. For charged systems, its value depends on the choice of origin and molecular orientation. As a result of HF and DFT (B3LYP) calculations, the highest dipole moment was observed for B3LYP/6-311G++(d,p) whereas the smallest one was observed for HF/6-311++G (d, p) in each molecule.Table 7
The calculated thermodynamical parameter of benzothiazole.
Basis Set
HF/6-31G
HF/6-311G
HF/6-311++G (d, p)
B3LYP/6-311++G (d, p)
Zero point energy(Kcal/Mol)
66.93709
66.140
65.51671
61.63
Rotational constant
2.93435
2.93435
2.93435
2.93435
Rotational temperature
0.14083
0.14083
0.14083
0.14083
Energy(E)
Translational
0.889
0.889
0.889
0.889
Rotational
0.889
0.889
0.889
0.889
Vibrational
68.158
68.168
67.551
64.058
Total
70.689
69.988
69.329
65.836
Specific heat(Cv)
Translational
2.981
2.981
2.981
2.981
Rotational
2.981
2.981
2.981
2.981
Vibrational
17.963
17.973
18.512
15.283
Total
23.627
23.935
20.895
21.245
Entropy(S)
Translational
40.613
40.613
40.613
40.613
Rotational
28.903
28.903
28.903
28.903
Vibrational
10.154
10.167
10.040
12.445
Total
79.436
79.683
79.556
81.961
Dipole moment
2.0974
2.0507
1.6331
1.4713On the basis of vibrational analysis, the statically thermodynamic functions: heat capacity (C), entropy (S), and enthalpy changes (DH) for the title molecule were obtained from the theoretical harmonic frequencies and listed in Table7. From the data in this table, it can be observed that these thermodynamic functions are increasing with temperature ranging from 100 to 600 K due to the fact that the molecular vibrational intensities increase with temperature [44].


## 3.6. Mulliken Atomic Charges

Mulliken atomic charge calculation is an important tool in the application of quantum chemical calculation to molecular system because atomic charges influence dipole moment, molecular polarizability, electronic structure, and other physical properties of molecular systems. The calculated Mulliken charge values are listed in Table8. The atomic charge depends on basis set presumably occur due to polarization. For example, the charge of N (3) atom is −0.43924 for HF/6-31G, −0.377701 for HF/6-311G, 0.038389 for HF/6-311++G (d, p), and 0.055788 for B3LYP/6-311++G (d, p). The charge distribution of sulfur group is increasing trend in HF and B3LYP methods. The charge of H10, H11, H12, H13, and H14 is positive in both HF and DFT diffuse functions. Considering all methods and basis sets used in the atomic charge calculation, the carbon atoms exhibit a substatantial negative charge, which are donor atoms. Hydrogen atom exhibits a positive charge, which is an acceptor atom. The Mulliken charge distribution of BT is increasing trend in B3LYP as compared to HF methods. A comparison of Mullikan’s Atomic charge obtained by the two theoretical (HF and DFT) approaches is illustrated in Figure 8. It may be seen that the two methods give comparable atomic charges.Table 8
Mulliken atomic charges of benzothiazole.
Atoms
HF/6-31G
HF/6-311G
HF/6-311++G (d, p)
B3LYP/6-311++G (d,p)
S1
0.494254
0.283343
-
0.428958
-
0.305656
C2
-
0.223616
-
0.09723
-
0.1285
-
0.174194
N3
-
0.43924
-
0.377701
0.038389
0.055788
C4
0.177233
0.264898
-
0.932014
-
0.938592
C5
-
0.403325
-
0.453121
1.000645
0.984567
C6
-
0.120432
-
0.09318
-
0.43895
-
0.437759
C7
-
0.221659
-
0.167237
-
0.377287
-
0.307896
C8
-
0.184873
-
0.165775
-
0.246147
-
0.081338
C9
-
0.19687
-
0.144593
0.313292
0.218011
H10
0.242781
0.218665
0.275732
0.255925
H11
0.235255
0.192916
0.244504
0.193902
H12
0.209181
0.176608
0.217394
0.172514
H13
0.207899
0.178898
0.216713
0.174776
H14
0.223413
0.18351
0.245187
0.189952Figure 8
Mullikan’s atomic charges between theoretical (HF and DFT) approaches.


## 4. Conclusion

In the present work, we have performed the experimental and theoretical vibrational analysis of a pharmaceutically important heterocyclic aromatic molecule, benzothiazole for the first time. The optimized molecular geometry, vibrational frequencies, infrared activities, and Raman scattering activities of the molecule in the ground state have been calculated by using ab initio HF and DFT (B3LYP) methods with 6–311++G (d, p) basis set. The vibrational frequencies were calculated and scaled values are compared with the recorded FT-IR and FT-Raman spectra of the compound. The observed and the calculated frequencies are found to be in good agreement. Furthermore, the thermodynamic and total dipole moment properties of the compound have been calculated in order to get insight into molecular structure of the compound. These computations are carried out with the main aim that the results will be of assistance in the quest of the experimental and theoretical evidence for the title molecule in biological activity and coordination chemistry.



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