# Fukui Function Analysis and Optical, Electronic, and Vibrational Properties of Tetrahydrofuran and Its Derivatives: A Complete Quantum Chemical Study

Authors: Apoorva Dwivedi; Vikas Baboo; Abhishek Bajpai
Journal: Journal of Theoretical Chemistry
 (2015)

---

## Abstract

The spectroscopic, optical, and electronic properties of tetrahydrofuran and its derivatives were investigated by FTIR techniques. We have done a comparative study of tetrahydrofuran and its derivatives with B3LYP with 6-311 G (d, p) as the basis set. Here we have done a relative study of their structures, vibrational assignments, and thermal, electronic, and optical properties of ttetrahydrofuran and its derivatives. We have plotted frontier orbital HOMO-LUMO surfaces and molecular electrostatic potential surfaces to explain the reactive nature of tetrahydrofuran and its derivatives.


---

## Body

## 1. Introduction

Tetrahydrofuran (THF) is an organic compound with the formula (CH2)4O. The compound is classified as heterocyclic compound, specifically a cyclic ether. It is a colorless, water-miscible organic liquid with low viscosity. THF has an odor similar to acetone. Being polar and having a wide liquid range, THF is a versatile solvent. THF is often used in polymer science. For example, it can be used to dissolve polymers prior to determining their molecular mass using gel permeation chromatography. THF is also a starting material for the preparation of tetrahydrothiophene. In the presence of a solid acid catalyst, it reacts with hydrogen sulfide. THF is frequently utilized as a solvent in many pharmaceutical synthetic procedures because of its good solvency for polar and nonpolar compounds. THF is particularly capable of dissolving many ionic species and organometallics which are commonly used in specialty syntheses. In many cases, THF makes higher yields and faster reaction rates possible. In addition, THF’s high volatility and very high purity facilitate solvent removal and recovery without leaving residues in the desired product [1, 2]. Tetrahydrofuran (THF) is a synthesized organic compound that is not found in the natural environment. THF is highly flammable and upon thermal decomposition may form carbon monoxide and carbon dioxide. Under certain conditions, such as prolonged storage in contact with air, THF can decompose into explosive peroxides [3]. THF can also be synthesized by catalytic hydrogenation of furan [4, 5]. THF has been explored as a water-based cosolvent to aid in the deconstruction and delignification of plant lignocellulosic biomass, which are relevant to the production of renewable platform chemicals and sugars. THF is used as a component in mobile phases for reversed-phase liquid chromatography. It has a greater elution strength than methanol or acetonitrile but is less commonly used than these solvents [6].As a part of our ongoing research work [7–9], we report the comparative study of tetrahydrofuran (THF) and its derivatives by DFT study. To the best of our knowledge no comparative quantum chemical calculations of these molecules have been reported so far in the literature.


## 2. Experimental and Computational Methods

### 2.1. Structure and Spectra

The molecular structures of the tetrahydrofuran (THF) and its derivatives are made by molecular modeling. The model molecular structures of tetrahydrofuran (THF) and its derivatives are given in Figure1. We have taken the infrared spectrum of tetrahydrofuran (THF) from literature which was recorded with FTIR Perkin Elmer spectrometer in KBr dispersion in the range of 500 to 4000 cm−1 for the title molecule as shown in Figure 3 [10].Model molecular structures of tetrahydrofuran and its derivatives.
(a)
(b)
(c)
(d)
(e)


### 2.2. Computational Methods

All the calculations were performed by the B3LYP [11, 12] method using the 6-311 G (d, p) basis set of density functional theory [13]. All computations were carried out with the GAUSSIAN 09 package [14]. By combining the results of the GAUSSVIEW’S program [15] with symmetry considerations, vibrational frequency assignments were made with a high degree of accuracy. Vibrational frequencies for these molecules were calculated with these methods and then scaled by 0.9613 [16].


## 2.1. Structure and Spectra

The molecular structures of the tetrahydrofuran (THF) and its derivatives are made by molecular modeling. The model molecular structures of tetrahydrofuran (THF) and its derivatives are given in Figure1. We have taken the infrared spectrum of tetrahydrofuran (THF) from literature which was recorded with FTIR Perkin Elmer spectrometer in KBr dispersion in the range of 500 to 4000 cm−1 for the title molecule as shown in Figure 3 [10].Model molecular structures of tetrahydrofuran and its derivatives.
(a)
(b)
(c)
(d)
(e)


## 2.2. Computational Methods

All the calculations were performed by the B3LYP [11, 12] method using the 6-311 G (d, p) basis set of density functional theory [13]. All computations were carried out with the GAUSSIAN 09 package [14]. By combining the results of the GAUSSVIEW’S program [15] with symmetry considerations, vibrational frequency assignments were made with a high degree of accuracy. Vibrational frequencies for these molecules were calculated with these methods and then scaled by 0.9613 [16].


## 3. Results and Discussion

### 3.1. Geometry Optimization

Alternate dispositions of amino groups have been studied, but finally we get these five optimized structures of THF derivatives. Optimized parameters of tetrahydrofuran (THF) and its derivatives (amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran) calculated by B3LYP method with 6-311 G (d, p) basis set are listed in Table1 in accordance with the atom numbering scheme as shown in Figure 1. Local minimum energies are −232.5134 a.u, −287.8832 a.u, −343.2555 a.u, −398.6109 a.u, and −453.9997 a.u., for tetrahydrofuran (THF), amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran, respectively. Tetrahydrofuran (THF) and all its derivatives have C1 point group symmetry. The amino groups attached to all derivatives do not lie in the plane of ring and alternatively they are in the opposite direction to each other.Table 1
Optimized geometrical parameters of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) method.
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
R
(
1,2
)
1.5432
R
(
1,2
)
1.5418
R
(
1,2
)
1.5292
R
(
1,2
)
1.5423
R
(
1,2
)
1.5325
R
(
1,5
)
1.1011
R
(
1,5
)
1.0999
R
(
1,5
)
1.0924
R
(
1,5
)
1.097
R
(
1,5
)
1.0961
R
(
1,6
)
1.0906
R
(
1,12
)
1.4347
R
(
1,6
)
1.0965
R
(
1,10
)
1.431
R
(
1,9
)
1.4353
R
(
1,13
)
1.4235
R
(
1,13
)
1.4439
R
(
1,11
)
1.4291
R
(
1,11
)
1.4351
R
(
1,19
)
1.437
R
(
2,3
)
1.5535
R
(
2,3
)
1.5295
R
(
2,3
)
1.5337
R
(
2,3
)
1.538
R
(
2,3
)
1.5383
R
(
2,7
)
1.0915
R
(
2,6
)
1.0962
R
(
2,7
)
1.093
R
(
2,6
)
1.1027
R
(
2,8
)
1.1019
R
(
2,11
)
1.0918
R
(
2,10
)
1.0923
R
(
2,10
)
1.0939
R
(
2,14
)
1.46
R
(
2,16
)
1.4594
R
(
3,4
)
1.5422
R
(
3,4
)
1.5356
R
(
3,4
)
1.5521
R
(
3,4
)
1.54
R
(
3,4
)
1.5497
R
(
3,8
)
1.0918
R
(
3,7
)
1.0942
R
(
3,8
)
1.0989
R
(
3,9
)
1.1016
R
(
3,6
)
1.0984
R
(
3,12
)
1.0915
R
(
3,11
)
1.092
R
(
3,15
)
1.4672
R
(
3,17
)
1.4619
R
(
3,13
)
1.462
R
(
4,9
)
1.1012
R
(
4,8
)
1.0935
R
(
4,9
)
1.0945
R
(
4,7
)
1.094
R
(
4,7
)
1.0951
R
(
4,10
)
1.0906
R
(
4,9
)
1.0978
R
(
4,11
)
1.4492
R
(
4,8
)
1.097
R
(
4,9
)
1.4623
R
(
4,13
)
1.4233
R
(
4,12
)
1.4316
R
(
4,12
)
1.4383
R
(
4,10
)
1.4345
R
(
4,10
)
1.4288
A
(
2,1
,
5
)
110.59
R
(
13,14
)
1.0139
R
(
12,13
)
1.0140
R
(
11,12
)
1.0099
R
(
10,11
)
1.0139
A
(
2,1
,
6
)
114.00
R
(
13,15
)
1.0156
R
(
12,14
)
1.0161
R
(
11,13
)
1.013
R
(
10,12
)
1.0164
A
(
2,1
,
13
)
105.68
A
(
2,1
,
5
)
109.82
R
(
15,16
)
1.0146
R
(
14,15
)
1.0148
R
(
13,14
)
1.0168
A
(
5,1
,
6
)
108.53
A
(
2,1
,
12
)
104.71
R
(
15,17
)
1.0158
R
(
14,16
)
1.016
R
(
13,15
)
1.0126
A
(
5,1
,
13
)
110.07
A
(
2,1
,
13
)
118.27
A
(
2,1
,
5
)
113.45
R
(
17,18
)
1.0134
R
(
16,17
)
1.0166
A
(
6,1
,
13
)
107.85
A
(
5,1
,
12
)
108.94
A
(
2,1
,
6
)
110.73
R
(
17,19
)
1.0163
R
(
16,18
)
1.0149
A
(
1,2
,
3
)
103.35
A
(
5,1
,
13
)
106.64
A
(
2,1
,
11
)
104.92
A
(
2,1
,
5
)
108.92
R
(
19,20
)
1.0145
A
(
1,2
,
7
)
110.79
A
(
12,1
,
13
)
108.17
A
(
5,1
,
6
)
108.92
A
(
2,1
,
10
)
103.40
R
(
19,21
)
1.017
A
(
1,2
,
11
)
111.71
A
(
1,2
,
3
)
102.64
A
(
5,1
,
11
)
108.20
A
(
2,1
,
11
)
117.42
A
(
2,1
,
5
)
109.37
A
(
3,2
,
7
)
110.69
A
(
1,2
,
6
)
109.05
A
(
6,1
,
11
)
110.49
A
(
5,1
,
10
)
110.09
A
(
2,1
,
9
)
104.13
A
(
3,2
,
11
)
112.63
A
(
1,2
,
10
)
112.24
A
(
1,2
,
3
)
102.05
A
(
5,1
,
11
)
107.87
A
(
2,1
,
19
)
112.24
A
(
7,2
,
11
)
107.66
A
(
3,2
,
6
)
110.68
A
(
1,2
,
7
)
113.41
A
(
10,1
,
11
)
108.98
A
(
5,1
,
9
)
109.70
A
(
2,3
,
4
)
103.31
A
(
3,2
,
10
)
114.04
A
(
1,2
,
10
)
110.29
A
(
1,2
,
3
)
101.55
A
(
5,1
,
19
)
107.76
A
(
2,3
,
8
)
112.69
A
(
6,2
,
10
)
108.04
A
(
3,2
,
7
)
112.77
A
(
1,2
,
6
)
106.59
A
(
9,1
,
19
)
113.54
A
(
2,3
,
12
)
110.65
A
(
2,3
,
4
)
101.29
A
(
3,2
,
10
)
109.88
A
(
1,2
,
14
)
112.73
A
(
1,2
,
3
)
101.74
A
(
4,3
,
8
)
111.81
A
(
2,3
,
7
)
110.39
A
(
7,2
,
10
)
108.30
A
(
3,2
,
6
)
107.83
A
(
1,2
,
8
)
106.95
A
(
4,3
,
12
)
110.69
A
(
2,3
,
11
)
113.81
A
(
2,3
,
4
)
102.30
A
(
3,2
,
14
)
114.08
A
(
1,2
,
16
)
111.71
A
(
8,3
,
12
)
107.68
A
(
4,3
,
7
)
110.55
A
(
2,3
,
8
)
111.46
A
(
6,2
,
14
)
113.14
A
(
3,2
,
8
)
107.89
A
(
3,4
,
9
)
110.60
A
(
4,3
,
11
)
112.78
A
(
2,3
,
15
)
110.20
A
(
2,3
,
4
)
100.24
A
(
3,2
,
16
)
114.45
A
(
3,4
,
10
)
114.02
A
(
7,3
,
11
)
107.93
A
(
4,3
,
8
)
109.35
A
(
2,3
,
9
)
111.23
A
(
8,2
,
16
)
113.21
A
(
3,4
,
13
)
105.58
A
(
3,4
,
8
)
112.97
A
(
4,3
,
15
)
109.78
A
(
2,3
,
17
)
109.07
A
(
2,3
,
4
)
101.38
A
(
9,4
,
10
)
108.54
A
(
3,4
,
9
)
111.11
A
(
8,3
,
15
)
113.16
A
(
4,3
,
9
)
110.64
A
(
2,3
,
6
)
111.63
A
(
9,4
,
13
)
110.10
A
(
3,4
,
12
)
106.54
A
(
3,4
,
9
)
110.01
A
(
4,3
,
17
)
110.92
A
(
2,3
,
13
)
109.53
A
(
10,4
,
13
)
107.87
A
(
8,4
,
9
)
108.09
A
(
3,4
,
11
)
106.27
A
(
9,3
,
17
)
113.88
A
(
4,3
,
6
)
109.58
A
(
1,13,4
)
105.45
A
(
8,4
,
12
)
108.85
A
(
3,4
,
12
)
112.46
A
(
3,4
,
7
)
110.82
A
(
4,3
,
13
)
110.85
—
—
A
(
9,4
,
12
)
109.18
A
(
9,4
,
11
)
106.73
A
(
3,4
,
8
)
111.61
A
(
6,3
,
13
)
113.23
—
—
A
(
1,12,4
)
110.98
A
(
9,4
,
12
)
107.64
A
(
3,4
,
10
)
107.36
A
(
3,4
,
7
)
110.69
—
—
A
(
1,13,14
)
110.92
A
(
11,4
,
12
)
113.55
A
(
7,4
,
8
)
108.85
A
(
3,4
,
9
)
105.55
—
—
A
(
1,13,15
)
110.93
A
(
1,11,4
)
110.13
A
(
7,4
,
10
)
109.52
A
(
3,4
,
10
)
111.81
—
—
—
—
A
(
4,12,13
)
110.02
A
(
8,4
,
10
)
108.62
A
(
7,4
,
9
)
106.37
—
—
—
—
A
(
4,12,14
)
109.06
A
(
1,10,4
)
109.9819
A
(
7,4
,
10
)
108.40
—
—
—
—
A
(
13,12,14
)
107.59
A
(
1,11,12
)
113.46
A
(
9,4
,
10
)
113.85
—
—
—
—
A
(
3,15,16
)
109.93
A
(
1,11,12
)
113.46
A
(
1,9
,
4
)
110.34
—
—
—
—
A
(
3,15,17
)
109.19
A
(
1,11,13
)
113.56
A
(
4,10,11
)
110.56
—
—
—
—
A
(
16,15,17
)
107.21
A
(
12,11,13
)
111.02
A
(
4,10,12
)
108.57
—
—
—
—
—
—
A
(
2,14,15
)
110.84
A
(
11,10,12
)
108.78
—
—
—
—
—
—
A
(
2,14,16
)
109.77
A
(
3,13,14
)
108.28
—
—
—
—
—
—
A
(
15,14,16
)
106.59
A
(
3,13,15
)
110.98
—
—
—
—
—
—
A
(
3,17,18
)
111.18
A
(
14,13,15
)
109.23
—
—
—
—
—
—
A
(
3,17,19
)
108.87
A
(
2,16,17
)
108.48
—
—
—
—
—
—
A
(
18,17,19
)
108.95
A
(
2,16,18
)
110.81
—
—
—
—
—
—
—
—
A
(
17,16,18
)
106.92
—
—
—
—
—
—
—
—
A
(
1,19,20
)
110.63
—
—
—
—
—
—
—
—
A
(
1,19,21
)
109.69
—
—
—
—
—
—
—
—
A
(
20,19,21
)
107.19For tetrahydrofuran (THF) and its derivatives, C–C bond distances are found to be in the range of 1.542–1.553 Å, 1.529–1.543 Å, 1.529–1.552 Å, 1.540–1.542 Å, and 1.532–1.549 Å while, for C–N (except THF), these values are 1.443 Å, 1.438–1.467 Å, 1.435–1.461 Å, and 1.428–1.462 Å, respectively, for amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran. For C–O, these values are 1.423 Å, 1.434 Å, 1.429 Å, 1.431 Å, and 1.435–1.462 Å, respectively, for THF, amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran. In case of C–H bond distances, they lie in the range of 1.091–1.101, 1.093, 1.092–1.094, 1.097–1.102, and 1.096–1.101, respectively. In the literature, bond lengths for THF-water complex [17] have a little bit lower values of 1.527–1.537 Å (for (C–C)) and a little bit higher values of 1.443–1.446 Å (for (C–O)). This may be due to shifting of charge in interaction of THF with water molecule. Optimized structures of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) method are shown in Figure 1.


### 3.2. Assignment of Fundamentals

Tetrahydrofuran has 13 atoms with 33 normal modes of vibration while amino tetrahydrofuran has 15 atoms with 39 normal modes of vibration. 1,2-Diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran have 17, 19, and 21 atoms with 45, 51, and 57 normal modes of vibration, respectively. From our calculated data and experimental FTIR spectra, we observe similarities and differences between the experimental and the calculated frequencies by DFT/B3LYP method. Assignments are done using the animated view of normal mode description. A good agreement is found between the theoretical and experimental data. Here we are discussing only important modes. Vibrational frequencies, calculated for tetrahydrofuran and experimental frequencies (FTIR), have been compared in Table2. We are also discussing the assignments for tetrahydrofuran derivatives which are useful for the experimentalists in absence of its experimental data.Table 2
Vibrational assignments of tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled (in lit.)
IR (int.)
Exp. IR
Exp. Raman
Vibrational assignments
281
271 (267)
8.1672
—
276
Out of plane bend in CH2–O–CH2
644
620 (635)
4.7345
625
—
τ(C–O–C–C)
799
769
5.8498
765
—
Twist CH2
866
834
4.358
825
—
Twist CH2 in whole
901
868 (883)
5.7608
865
—
τ(C–C–C–O)
941
906
22.7829
915
913
Twist CH2 in whole
959
924 (934)
17.9192
930
—
Ring breathing
1046
1007
4.7743
995
—
β(C–C–H) + β(C–O–C)
1097
1056 (1068)
83.1142
1045
1071
Ring deformation
1214
1169
6.4279
1175
1174
β(C–C–H)
1261
1214 (1214)
5.8725
1205
—
Twist CH2
1268
1221
5.1994
1220
1234
Twist CH2
1395
1343
4.7295
1335
1335
β(C–C–H)
1506
1450 (1454)
5.5918
1445
1452
S(CH2)
2958
2848
43.4017
2840
—
ν(C–H)
2964
2854
118.3793
2855
—
ν(C–H)
3052
2939 (2936)
24.963
2930
2938
ν(C–H)
3062
2949
40.015
2950
—
ν(C–H)
3082
2968 (2968)
19.4174
2965
2975
ν(C–H)
3098
2983 (2989)
34.7534
2980
—
ν(C–H)
3110
2995
77.426
2990
—
ν(C–H)


### 3.3. Vibrational Modes Description

#### 3.3.1. C–H Vibrations

We have seen in the literature that the C–H stretching vibrations are usually observed in 2800–3200 cm−1 region. In the study of tetrahydrofuran, the (C–H) functional group is present at 2848, 2854, 2939, 2949, 2968, 2983, and 2995 cm−1 in calculated spectra which is in good agreement with the experimental data as given in Table 2. In vibrational assignments, the C–H stretching vibrations are in the same range for all derivatives of tetrahydrofuran listed in Tables 3, 4, 5, and 6.Table 3
Vibrational assignments of amino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
197
190
48.1062
Rock NH2
378
364
16.1235
Group NH2 bend from joint
778
749
174.8209
Rock NH2
877
845
23.6231
β(C–C–H) + β(C–C–C)
957
922
65.1906
β(C–C–H)
1067
1028
52.4498
Ring deformation
1133
1091
73.4975
β(C–C–C)
1443
1390
25.3256
β(C–C–H)
1647
1586
38.9601
S(NH2)
2971
2861
74.2781
ν(C–H)
2993
2882
62.1676
ν(C–H)
3023
2911
28.6539
ν(C–H)
3058
2945
64.6532
ν(C–H)
3095
2980
55.4994
ν(C–H)
3595
3462
0.4042
ν(N–H)Table 4
Vibrational assignments of 1,2-diamino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
257
247
77.5282
Rock NH2
424
408
30.1483
Twist NH2
753
725
46.0965
τ(C–C–C–C)
859
827
83.126
Rock NH2
905
872
171.3772
Rock NH2
921
887
45.5585
Rock NH2
954
919
112.828
Rock NH2
1029
991
33.4007
Twist CH2
1068
1028
80.3998
Ring deformation
1164
1121
20.3894
β(C–C–H) in whole molecule
1446
1392
14.2825
β(C–C–H)
1645
1584
63.057
S(NH2)
1669
1607
31.4909
S(NH2)
2974
2864
55.4405
ν(C–H)
3010
2899
61.7424
ν(C–H)
3038
2926
34.5478
ν(C–H)
3044
2931
53.5102
ν(C–H)
3074
2960
46.2551
ν(C–H)
3090
2976
46.8808
ν(C–H)
3578
3446
3.4588
ν(N–H)Table 5
Vibrational assignments of 1,2,3-triamino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
187
180
38.0082
Twist NH2
274
264
29.2943
Twist NH2
324
312
23.6603
Twist NH2
376
362
23.1528
Twist NH2
492
474
18.1122
τ(C–C–C–C)
635
612
213.3144
Rock NH2
832
801
68.3448
Rock NH2
859
827
130.0253
Rock NH2
936
901
46.5701
Ring deformation
994
957
65.805
β(C–C–C)
1026
988
47.4846
β(C–C–H)
1076
1036
78.3665
Ring deformation
1132
1090
33.1727
β(C–C–H)
1153
1110
30.0604
β(C–C–H)
1167
1124
48.7819
β(C–C–H)
1442
1389
21.4953
β(C–C–H)
1648
1587
47.0934
S(NH2)
1660
1599
29.1316
S(NH2)
2934
2825
37.6667
ν(C–H)
2950
2841
86.3504
ν(C–H)
3006
2895
115.4219
ν(C–H)
3057
2944
47.6972
ν(C–H)
3579
3447
5.6057
ν(N–H)Table 6
Vibrational assignments of 1,2,3,4-tetra-amino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
260
250
43.2432
Twist NH2
301
290
22.3762
Twist NH2
347
334
25.9587
Rock NH2
366
352
21.3354
Rock NH2
426
410
18.1696
Twist NH2
513
494
54.7952
Torsion in whole molecule
593
571
38.3343
τ(C–C–O–C)
663
638
28.8211
τ(C–C–C–C)
759
731
56.9814
τ(C–C–C–O)
802
772
106.1627
Rock NH2
850
819
60.9417
Rock NH2
865
833
73.3106
Twist NH2 in whole places
881
848
335.8006
Twist NH2
902
869
149.2133
Rock NH2
944
909
85.627
Rock NH2
972
936
31.7804
β(C–C–C) + Twist NH2
1019
981
132.2283
ν(C–O)
1097
1056
16.8407
Twist NH2
1167
1124
27.6511
Bending in whole molecule
1183
1139
25.494
β(C–C–H)
1441
1388
19.585
β(C–C–H)
1635
1575
55.77
S(NH2)
1649
1588
56.9828
S(NH2)
2946
2837
39.5477
ν(C–H)
2984
2874
58.3297
ν(C–H)
3033
2921
82.6875
ν(C–H)
3483
3354
19.1928
ν(N–H)
3585
3452
11.9623
ν(N–H)


#### 3.3.2. N–H Vibrations

There is no NH2 group added to tetrahydrofuran but they are presented in all derivatives of tetrahydrofuran. The N–H stretching vibrations are normally viewed in the region 3300–3600 cm−1. For amino tetrahydrofuran, the N–H stretching vibration is calculated at 3462 cm−1 while it is 3446 cm−1 for 1,2-diamino tetrahydrofuran. A strong scissoring vibration of H–N–H is found at 1586 and 1584 cm−1 for amino tetrahydrofuran and 1,2-diamino tetrahydrofuran, respectively. In case of 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran, the N–H vibration is at 3447 and 3354 cm−1 in calculated spectra. There are also strong scissoring vibrations at 1587 and 1588 cm−1 for 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran. Some strong rocking and twisting vibrations of NH2 are also seen in the assignment of all derivatives of tetrahydrofuran. We see that scissoring modes in THF are lower than all the derivatives of THF. This is due to the addition of amino group (charge transfer) to THF molecule. The interpretation of vibrational spectra of THF is in good agreement with the literature [18] as given in Table 2.


#### 3.3.3. Other Modes of Vibration

In tetrahydrofuran, a ring deformation mode is calculated at 1056 cm−1 which is in good agreement with experimental data, that is, 1055 cm−1, while in all derivatives of tetrahydrofuran (except the last one) ring deformation mode is at 1028, 1028, and 1036 cm−1 having appropriate IR intensity. As expected, torsion modes along with wagging modes appear in the lower frequency range. For tetrahydrofuran, strong torsion mode of C–O–C–C is at 628 cm−1 in calculated spectrum which matches well with the experimental one, that is, 625 cm−1, while strong torsion modes of C–C–C–C are at 725 and 474 cm−1 in calculated spectrum for 1,2-di-ATHF and 1,2,3-tri-ATHF, respectively. A very strong stretching vibration of C–O is found at 981 cm−1 while there is also a strong torsion mode of C–C–C–O at 731 cm−1 in calculated spectra for 1,2,3,4-tetra-ATHF. There are some frequencies in lower region having appreciable IR intensity. Furthermore, the study of low frequency vibrations is of great significance, because it gives information on weak intermolecular interactions, which take place in enzyme reactions [19]. Knowledge of low frequency mode is also essential for the interpretation of the effect of electromagnetic radiation on biological systems [20]. The aim of vibrational analysis is to acquire direct information on lower and higher frequency vibrations of such THF and its derivatives. No experimental FTIR spectrum is available for comparison of derivatives of THF so it will provide a suitable path for experimental researchers.


### 3.4. Electrical, Optical, Dipole Moment and Thermodynamical Properties

Frontier orbital energy gap, that is, the gap between HOMO and LUMO, shows the interaction of that molecule with other species. Frontier orbital energy gap helps to differentiate the chemical reactivity of the molecules. In case of tetrahydrofuran and its derivatives, frontier orbital energy gap is 7.9402, 6.9066, 6.8312, 6.4991, and 6.8870 eV, respectively, and is given in Table7. So it can be concluded that 1,2,3-triamino tetrahydrofuran is the most reactive compound among all. The pictures of HOMO, LUMO, and electrostatic potential (MESP) for tetrahydrofuran and its derivatives are shown in Figure 2.Table 7
Lowest energy, HOMO-LUMO gap (frontier orbital energy gap), and dipole moment of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) method.
Parameters
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
Energy (in au)
−232.5134
−287.8832
−343.2555
−398.6109
−453.9997
Dipole moment (in Debye)
1.585
2.855
1.667
4.022
1.743
HOMO
−0.25509
−0.23322
−0.22235
−0.21917
−0.22375
LUMO
0.03683
0.02070
0.02880
0.01977
0.02945
Frontier orbital energy gap (eV)
7.9402
6.9066
6.8312
6.4991
6.8870Figure 2
Pictures of HOMO-LUMO and molecular electrostatic potential of tetrahydrofuran and its derivatives.Figure 3
Experimental IR spectra of tetrahydrofuran.Dipole moment(
μ
), polarizability α, and total first static hyperpolarizability β [21, 22] can be expressed in terms of x, y, z components and are given by the following equations:
(1)
μ
=
μ
x
2
+
μ
y
2
+
μ
z
2
1
/
2
,
α
=
1
3
α
x
x
+
α
y
y
+
α
z
z
,
β
Total
=
β
x
2
+
β
y
2
+
β
z
2
1
/
2
=
β
x
x
x
+
β
x
y
y
+
β
x
z
z
2
000
+
β
y
y
y
+
β
y
x
x
+
β
y
z
z
2
000
+
β
z
z
z
+
β
z
x
x
+
β
z
y
y
2
1
/
2
.
The β components of Gaussian output are reported in atomic units.Where1
a
.
u
.
=
8.3693
*
10
-
33 e.s.u., the calculated dipole moments for tetrahydrofuran and its derivatives are 1.585, 2.855, 1.667, 4.022, and 1.743 Debye, respectively. So, 1,2,3-triamino tetrahydrofuran is a better solvent among them all. A greater contribution of α
y
y is seen in THF, amino THF, and 1,2,3-triamino THF while α
z
z is seen in 1,2-diamino THF and α
x
x in 1,2,3,4-tetra-amino THF. For THF and 1,2,3-triamino THF, molecules are elongated more towards Y direction and more contracted in the X direction while amino THF molecule is elongated more towards Y direction and more contracted in the X direction. For 1,2-diamino THF, molecule is elongated more towards Z direction and more contracted in the X direction while 1,2,3,4-tetra-amino THF molecule is elongated more towards X direction and more contracted in the Y direction. It is seen that the components β
x
x
z, β
x
x
y, β
y
y
y, β
y
y
y, and β
x
x
x contribute lager part of hyperpolarizability from THF to 1,2,3,4-tetra-amino THF. This shows that X
Z and X
Y planes and Y- and X-axes are more optically active in these directions. The values of hyperpolarizability indicate a possible use of these compounds in electrooptical applications.Internal thermal energy (E), constant volume heat capacity C
v, and entropy S, calculated at B3LYP/6-311 G (d, p) level, are listed in Table 9. We know that conduction band is almost empty at the room temperature, so electronic contribution in total energy is negligible. All the thermodynamic data supplies helpful information for the further study on the THF and its derivatives. They can be used to compute the other thermodynamic energies according to relationships of thermodynamic functions and estimate directions of chemical reactions according to the second law of thermodynamics in the thermochemical field. So thermodynamic properties show that vibrational motion plays an important role.


### 3.5. Reactivity Descriptors

#### 3.5.1. Global Reactivity Descriptors

Global reactivity descriptors are described as(2)
Energy
band
gap
⁡
=
ε
LUMO
-
ε
HOMO
,
Electronegativity
χ
=
-
1
2
ε
LUMO
+
ε
HOMO
,
Chemical
potential
μ
=
-
χ
,
Global
hardness
η
=
1
2
ε
LUMO
-
ε
HOMO
,
Global
softness
S
=
1
2
η
,
Global
electrophilicity
index
ω
=
μ
2
2
η
(see [23–27]). All these parameters for tetrahydrofuran and its derivatives have been listed in Table 6.According to these parameters, the chemical reactivity varies with the structural configuration of molecules. Chemical hardness (softness) value of 1,2,3-amino THF is lesser (greater) among all the three molecules. Thus, 1,2,3-amino THF is found to be most reactive among all, whereas THF configuration is less reactive. THF configuration possesses higher electronegativity while 1,2,3-amino THF possesses lower electrophilicity index among them all as given in Table10. Correlations have been found between electrophilicity of various chemical compounds and reaction rates in biochemical systems.


### 3.6. Local Reactivity Descriptors

Fukui function (FF) provides information on the local site reactivity within the molecule and as such it provides a system for understanding of chemical reactions. These values correspond to the qualitative descriptors of reactivity of different atoms in the molecule. A study by Ayers and Parr [27] has shown that FF is larger when attacked by soft reagents and in places where the FF is smaller when attacked by hard reagents. Fukui functions for electrophilic and nucleophilic attacks have been made with the basis of B3LYP/6-311 G (d, p) level of theory. With the help of Mulliken atomic charges of cationic and anionic states, local Fukui functions (
f
k
+
,
f
k
-
), local softness values (
s
k
+
,
s
k
-
), and local electrophilicity indices (
ω
k
+
,
ω
k
-
) have been calculated using the following equation:
(3)
f
k
+
=
q
N
+
1
-
q
N
for
nucleophilic
attack
f
k
-
=
q
N
-
q
N
-
1
for
electrophilic
attack
f
k
0
=
1
2
q
N
+
1
+
q
N
-
1
for
radical
attack
.
Local softness values and electrophilicity indices are calculated using
(4)
s
k
+
=
S
f
k
+
,
s
k
-
=
S
f
k
-
ω
k
+
=
ω
f
k
+
,
ω
k
-
=
ω
f
k
-
,
where + and − signs show nucleophilic and electrophilic attack, respectively.Fukui functions, local softness values, and local electrophilicity indices for selected atomic sites in tetrahydrofuran and its derivatives have been listed in Tables7 and 8. For amino hydrofuran, the maximum value for local nucleophilic reactivity descriptors (
f
k
-
,
s
k
-
,
ω
k
-
) at N13 indicates that this site is more prone to electrophilic attack. But in comparison with N16 of 1,2,3,4-tetra-amino hydrofuran it is found that the N16 of 1,2,3,4-tetra-amino hydrofuran has lower affinity towards electrophile as given in Table 11. This situation changes because of change of position of the nitrogen of 1,2,3,4-tetra-amino hydrofuran, and hence the charge density around N16 decreased.Table 8
Polarizability and hyperpolarizability of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) methods.
Polarizability
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
α
x
x
−29.2994
−35.5422
−41.5883
−43.8040
−55.7761
α
x
y
−0.0137
4.5742
−2.1265
6.8303
0.1740
α
y
y
−34.8626
−40.9807
−41.9550
−50.3155
−50.3145
α
y
z
−0.7807
−0.8029
−0.1374
0.0764
2.3250
α
z
z
−31.4458
−35.4849
−43.4920
−49.1301
−53.4053
α
z
x
0.0077
0.5506
−0.9605
−0.3221
−2.4170
α
31.8692
37.3359
42.3451
47.7498
53.1653
Hyperpolarizability
β
x
x
x
−0.0052
5.6681
−0.2912
−6.3842
−6.7955
β
x
x
y
−4.0970
6.2139
−8.0690
13.6734
−4.4365
β
x
y
y
0.0298
−1.6268
6.3043
−3.2086
−1.8247
β
y
y
y
−0.6535
−0.2718
14.9291
14.4296
−0.2671
β
z
z
z
−1.1489
1.5867
0.4088
2.4337
−0.1471
β
x
x
z
−1.9217
1.5767
−6.1872
−0.5541
−3.9772
β
x
z
z
−0.0222
3.9764
2.7638
6.3393
−2.8358
β
y
z
z
−0.4033
−1.2208
−3.7949
2.7311
−4.7413
β
y
y
z
0.9213
−0.3137
−0.8388
6.3633
1.4539
β
x
y
z
0.0193
−1.1644
−0.5408
−3.0478
−4.4281
β total
5.5840
9.7200
11.4027
32.0675
15.0620Table 9
Calculated thermodynamic properties of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) methods.
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
E  (thermal) (kcalmol−1)
Total
75.553
87.449
99.560
110.546
122.799
Translational
0.889
0.889
0.889
0.889
0.889
Rotational
0.889
0.889
0.889
0.889
0.889
Vibrational
73.776
85.672
97.783
108.769
121.022
C
V (cal K−1mol−1)
Total
14.943
22.356
26.632
32.701
36.652
Translational
2.981
2.981
2.981
2.981
2.981
Rotational
2.981
2.981
2.981
2.981
2.981
Vibrational
8.982
16.394
20.671
26.739
30.690
S (cal K−1mol−1)
Total
67.259
78.055
81.513
88.746
91.737
Translational
38.741
39.305
39.779
40.188
40.548
Rotational
24.911
26.233
27.149
28.115
28.869
Vibrational
3.607
12.517
14.584
20.443
22.320Table 10
Calculatedε
HOMO, ε
LUMO, energy band gap (ε
LUMO
-
ε
HOMO), chemical potential (μ), electronegativity (χ), global hardness (η), global softness (S), and global electrophilicity index (ω) for tetrahydrofuran and its derivatives at B3LYP/6-311 G (d, p) level.
Compounds
ε
H
ε
L
ε
L
-
ε
H
χ
μ
η
S
ω
THF
−0.25509
0.03683
0.29192
0.10913
−0.10913
0.14596
3.425596054
0.0408
1,2 THF
−0.23322
0.02070
0.25391
0.1011
−0.1011
0.13398
3.7319
0.03814
1,2,3-Amino THF
−0.22235
0.02880
0.25114
0.10323
−0.10323
0.12631
3.95867
0.04218
1,2,3,4 THF
−0.21917
0.01977
0.23893
0.09814
−0.09814
0.13043
3.83347
0.03692
Amino THF
−0.22375
0.02945
0.25319
0.10014
−0.10014
0.1349
3.70645
0.03717Table 11
Fukui functions (f
k
+, f
k
-), local softness (s
k
+, s
k
-), and local electrophilicity indices (ω
k
+, ω
k
-) for selected atomic sites of  CPPC, using Mulliken population analysis at B3LYP/6-311 G (d, p) level.
THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.09218
−0.13948
0.308091
0.231663
0.215911
0.793585
0.739625
0.009452
0.008809
C2
0.006981
−0.24299
0.12914
0.249968
0.122159
0.85629
0.418468
0.010199
0.004984
C3
0.00709
−0.24193
0.129566
0.249016
0.122476
0.853029
0.419554
0.01016
0.004997
C4
0.092228
−0.13921
0.307449
0.231433
0.215221
0.792797
0.737261
0.009442
0.008781
O13
−0.198474
−0.23646
0.125765
0.037987
0.324239
0.130128
1.110713
0.00155
0.013229
Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.122663
0.009106
0.241709
0.113557
0.119046
0.420893
0.441238
0.004221
0.004425
C2
−0.008726
−0.24682
0.114327
0.238093
0.123053
0.88248
0.45609
0.00885
0.004574
C3
0.010672
−0.19419
0.113287
0.204865
0.102615
0.759322
0.380337
0.007615
0.003814
C4
0.089502
−0.09679
0.248705
0.186288
0.159203
0.690467
0.590078
0.006924
0.005918
O12
−0.203353
−0.23584
−0.04207
0.032482
0.161283
0.120393
0.597787
0.001207
0.005995
N13
−0.010961
−0.2358
0.323848
0.224837
0.334809
0.833347
1.240953
0.008357
0.012445
1,2-Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.080415
−0.0421
0.22964
0.12251
0.149225
0.457195
0.556893
0.004673
0.005691
C2
0.004480
−0.17372
0.087954
0.178204
0.083474
0.66504
0.311517
0.006797
0.003184
C3
0.035609
−0.10002
0.115193
0.135632
0.079584
0.506165
0.297
0.005173
0.003035
C4
0.119975
0.005564
0.199748
0.114411
0.079773
0.42697
0.297705
0.004364
0.003043
O11
−0.21865
−0.24652
−0.06071
0.02786
0.157941
0.103971
0.58942
0.001063
0.006024
N12
−0.00822
−0.16639
0.232471
0.158162
0.240694
0.590245
0.898246
0.006032
0.00918
N15
−0.01388
−0.27714
0.195416
0.263249
0.209305
0.982419
0.781105
0.01004
0.007983
1,2,3-Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.115624
0.073205
0.190554
0.042419
0.07493
0.167923
0.296623
0.001789
0.003161
C2
0.022828
−0.08061
0.076666
0.103439
0.053838
0.409481
0.213127
0.004363
0.002271
C3
0.025129
−0.0762
0.118366
0.101328
0.093237
0.401124
0.369095
0.004274
0.003933
C4
0.078038
−0.01158
0.206247
0.089616
0.128209
0.35476
0.507537
0.00378
0.005408
O10
−0.20327
−0.22649
−0.09324
0.023211
0.110038
0.091885
0.435604
0.000979
0.004641
N11
−0.00094
−0.20016
0.211528
0.19922
0.212469
0.788646
0.841095
0.008403
0.008962
N14
−0.00158
−0.3101
0.089629
0.308517
0.091209
1.221317
0.361066
0.013013
0.003847
N17
−0.03592
−0.16821
0.20016
0.132288
0.236083
0.523685
0.934575
0.00558
0.009958
1,2,3,4-Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.108686
0.070775
0.163507
0.037911
0.054821
0.145331
0.210155
0.0014
0.002024
C2
0.030688
−0.08776
0.063705
0.118443
0.033017
0.454048
0.12657
0.004373
0.001219
C3
0.028906
−0.0894
0.100662
0.118308
0.071756
0.45353
0.275074
0.004368
0.002649
C4
0.110441
0.02905
0.179846
0.081391
0.069405
0.31201
0.266062
0.003005
0.002562
O9
−0.233907
−0.2548
−0.12637
0.020888
0.107535
0.080074
0.412232
0.000771
0.00397
N10
−0.024483
−0.11068
0.209354
0.086201
0.233837
0.330449
0.896407
0.003183
0.008633
N13
−0.023684
−0.16618
0.165895
0.142499
0.189579
0.546266
0.726745
0.005261
0.006999
N16
0.004591
−0.24299
0.065478
0.24758
0.060887
0.949091
0.233408
0.009141
0.002248
N19
−0.001198
−0.14799
0.177963
0.146794
0.179161
0.56273
0.686808
0.00542
0.006615


## 3.1. Geometry Optimization

Alternate dispositions of amino groups have been studied, but finally we get these five optimized structures of THF derivatives. Optimized parameters of tetrahydrofuran (THF) and its derivatives (amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran) calculated by B3LYP method with 6-311 G (d, p) basis set are listed in Table1 in accordance with the atom numbering scheme as shown in Figure 1. Local minimum energies are −232.5134 a.u, −287.8832 a.u, −343.2555 a.u, −398.6109 a.u, and −453.9997 a.u., for tetrahydrofuran (THF), amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran, respectively. Tetrahydrofuran (THF) and all its derivatives have C1 point group symmetry. The amino groups attached to all derivatives do not lie in the plane of ring and alternatively they are in the opposite direction to each other.Table 1
Optimized geometrical parameters of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) method.
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
Parameters
6-311 G (d, p)
R
(
1,2
)
1.5432
R
(
1,2
)
1.5418
R
(
1,2
)
1.5292
R
(
1,2
)
1.5423
R
(
1,2
)
1.5325
R
(
1,5
)
1.1011
R
(
1,5
)
1.0999
R
(
1,5
)
1.0924
R
(
1,5
)
1.097
R
(
1,5
)
1.0961
R
(
1,6
)
1.0906
R
(
1,12
)
1.4347
R
(
1,6
)
1.0965
R
(
1,10
)
1.431
R
(
1,9
)
1.4353
R
(
1,13
)
1.4235
R
(
1,13
)
1.4439
R
(
1,11
)
1.4291
R
(
1,11
)
1.4351
R
(
1,19
)
1.437
R
(
2,3
)
1.5535
R
(
2,3
)
1.5295
R
(
2,3
)
1.5337
R
(
2,3
)
1.538
R
(
2,3
)
1.5383
R
(
2,7
)
1.0915
R
(
2,6
)
1.0962
R
(
2,7
)
1.093
R
(
2,6
)
1.1027
R
(
2,8
)
1.1019
R
(
2,11
)
1.0918
R
(
2,10
)
1.0923
R
(
2,10
)
1.0939
R
(
2,14
)
1.46
R
(
2,16
)
1.4594
R
(
3,4
)
1.5422
R
(
3,4
)
1.5356
R
(
3,4
)
1.5521
R
(
3,4
)
1.54
R
(
3,4
)
1.5497
R
(
3,8
)
1.0918
R
(
3,7
)
1.0942
R
(
3,8
)
1.0989
R
(
3,9
)
1.1016
R
(
3,6
)
1.0984
R
(
3,12
)
1.0915
R
(
3,11
)
1.092
R
(
3,15
)
1.4672
R
(
3,17
)
1.4619
R
(
3,13
)
1.462
R
(
4,9
)
1.1012
R
(
4,8
)
1.0935
R
(
4,9
)
1.0945
R
(
4,7
)
1.094
R
(
4,7
)
1.0951
R
(
4,10
)
1.0906
R
(
4,9
)
1.0978
R
(
4,11
)
1.4492
R
(
4,8
)
1.097
R
(
4,9
)
1.4623
R
(
4,13
)
1.4233
R
(
4,12
)
1.4316
R
(
4,12
)
1.4383
R
(
4,10
)
1.4345
R
(
4,10
)
1.4288
A
(
2,1
,
5
)
110.59
R
(
13,14
)
1.0139
R
(
12,13
)
1.0140
R
(
11,12
)
1.0099
R
(
10,11
)
1.0139
A
(
2,1
,
6
)
114.00
R
(
13,15
)
1.0156
R
(
12,14
)
1.0161
R
(
11,13
)
1.013
R
(
10,12
)
1.0164
A
(
2,1
,
13
)
105.68
A
(
2,1
,
5
)
109.82
R
(
15,16
)
1.0146
R
(
14,15
)
1.0148
R
(
13,14
)
1.0168
A
(
5,1
,
6
)
108.53
A
(
2,1
,
12
)
104.71
R
(
15,17
)
1.0158
R
(
14,16
)
1.016
R
(
13,15
)
1.0126
A
(
5,1
,
13
)
110.07
A
(
2,1
,
13
)
118.27
A
(
2,1
,
5
)
113.45
R
(
17,18
)
1.0134
R
(
16,17
)
1.0166
A
(
6,1
,
13
)
107.85
A
(
5,1
,
12
)
108.94
A
(
2,1
,
6
)
110.73
R
(
17,19
)
1.0163
R
(
16,18
)
1.0149
A
(
1,2
,
3
)
103.35
A
(
5,1
,
13
)
106.64
A
(
2,1
,
11
)
104.92
A
(
2,1
,
5
)
108.92
R
(
19,20
)
1.0145
A
(
1,2
,
7
)
110.79
A
(
12,1
,
13
)
108.17
A
(
5,1
,
6
)
108.92
A
(
2,1
,
10
)
103.40
R
(
19,21
)
1.017
A
(
1,2
,
11
)
111.71
A
(
1,2
,
3
)
102.64
A
(
5,1
,
11
)
108.20
A
(
2,1
,
11
)
117.42
A
(
2,1
,
5
)
109.37
A
(
3,2
,
7
)
110.69
A
(
1,2
,
6
)
109.05
A
(
6,1
,
11
)
110.49
A
(
5,1
,
10
)
110.09
A
(
2,1
,
9
)
104.13
A
(
3,2
,
11
)
112.63
A
(
1,2
,
10
)
112.24
A
(
1,2
,
3
)
102.05
A
(
5,1
,
11
)
107.87
A
(
2,1
,
19
)
112.24
A
(
7,2
,
11
)
107.66
A
(
3,2
,
6
)
110.68
A
(
1,2
,
7
)
113.41
A
(
10,1
,
11
)
108.98
A
(
5,1
,
9
)
109.70
A
(
2,3
,
4
)
103.31
A
(
3,2
,
10
)
114.04
A
(
1,2
,
10
)
110.29
A
(
1,2
,
3
)
101.55
A
(
5,1
,
19
)
107.76
A
(
2,3
,
8
)
112.69
A
(
6,2
,
10
)
108.04
A
(
3,2
,
7
)
112.77
A
(
1,2
,
6
)
106.59
A
(
9,1
,
19
)
113.54
A
(
2,3
,
12
)
110.65
A
(
2,3
,
4
)
101.29
A
(
3,2
,
10
)
109.88
A
(
1,2
,
14
)
112.73
A
(
1,2
,
3
)
101.74
A
(
4,3
,
8
)
111.81
A
(
2,3
,
7
)
110.39
A
(
7,2
,
10
)
108.30
A
(
3,2
,
6
)
107.83
A
(
1,2
,
8
)
106.95
A
(
4,3
,
12
)
110.69
A
(
2,3
,
11
)
113.81
A
(
2,3
,
4
)
102.30
A
(
3,2
,
14
)
114.08
A
(
1,2
,
16
)
111.71
A
(
8,3
,
12
)
107.68
A
(
4,3
,
7
)
110.55
A
(
2,3
,
8
)
111.46
A
(
6,2
,
14
)
113.14
A
(
3,2
,
8
)
107.89
A
(
3,4
,
9
)
110.60
A
(
4,3
,
11
)
112.78
A
(
2,3
,
15
)
110.20
A
(
2,3
,
4
)
100.24
A
(
3,2
,
16
)
114.45
A
(
3,4
,
10
)
114.02
A
(
7,3
,
11
)
107.93
A
(
4,3
,
8
)
109.35
A
(
2,3
,
9
)
111.23
A
(
8,2
,
16
)
113.21
A
(
3,4
,
13
)
105.58
A
(
3,4
,
8
)
112.97
A
(
4,3
,
15
)
109.78
A
(
2,3
,
17
)
109.07
A
(
2,3
,
4
)
101.38
A
(
9,4
,
10
)
108.54
A
(
3,4
,
9
)
111.11
A
(
8,3
,
15
)
113.16
A
(
4,3
,
9
)
110.64
A
(
2,3
,
6
)
111.63
A
(
9,4
,
13
)
110.10
A
(
3,4
,
12
)
106.54
A
(
3,4
,
9
)
110.01
A
(
4,3
,
17
)
110.92
A
(
2,3
,
13
)
109.53
A
(
10,4
,
13
)
107.87
A
(
8,4
,
9
)
108.09
A
(
3,4
,
11
)
106.27
A
(
9,3
,
17
)
113.88
A
(
4,3
,
6
)
109.58
A
(
1,13,4
)
105.45
A
(
8,4
,
12
)
108.85
A
(
3,4
,
12
)
112.46
A
(
3,4
,
7
)
110.82
A
(
4,3
,
13
)
110.85
—
—
A
(
9,4
,
12
)
109.18
A
(
9,4
,
11
)
106.73
A
(
3,4
,
8
)
111.61
A
(
6,3
,
13
)
113.23
—
—
A
(
1,12,4
)
110.98
A
(
9,4
,
12
)
107.64
A
(
3,4
,
10
)
107.36
A
(
3,4
,
7
)
110.69
—
—
A
(
1,13,14
)
110.92
A
(
11,4
,
12
)
113.55
A
(
7,4
,
8
)
108.85
A
(
3,4
,
9
)
105.55
—
—
A
(
1,13,15
)
110.93
A
(
1,11,4
)
110.13
A
(
7,4
,
10
)
109.52
A
(
3,4
,
10
)
111.81
—
—
—
—
A
(
4,12,13
)
110.02
A
(
8,4
,
10
)
108.62
A
(
7,4
,
9
)
106.37
—
—
—
—
A
(
4,12,14
)
109.06
A
(
1,10,4
)
109.9819
A
(
7,4
,
10
)
108.40
—
—
—
—
A
(
13,12,14
)
107.59
A
(
1,11,12
)
113.46
A
(
9,4
,
10
)
113.85
—
—
—
—
A
(
3,15,16
)
109.93
A
(
1,11,12
)
113.46
A
(
1,9
,
4
)
110.34
—
—
—
—
A
(
3,15,17
)
109.19
A
(
1,11,13
)
113.56
A
(
4,10,11
)
110.56
—
—
—
—
A
(
16,15,17
)
107.21
A
(
12,11,13
)
111.02
A
(
4,10,12
)
108.57
—
—
—
—
—
—
A
(
2,14,15
)
110.84
A
(
11,10,12
)
108.78
—
—
—
—
—
—
A
(
2,14,16
)
109.77
A
(
3,13,14
)
108.28
—
—
—
—
—
—
A
(
15,14,16
)
106.59
A
(
3,13,15
)
110.98
—
—
—
—
—
—
A
(
3,17,18
)
111.18
A
(
14,13,15
)
109.23
—
—
—
—
—
—
A
(
3,17,19
)
108.87
A
(
2,16,17
)
108.48
—
—
—
—
—
—
A
(
18,17,19
)
108.95
A
(
2,16,18
)
110.81
—
—
—
—
—
—
—
—
A
(
17,16,18
)
106.92
—
—
—
—
—
—
—
—
A
(
1,19,20
)
110.63
—
—
—
—
—
—
—
—
A
(
1,19,21
)
109.69
—
—
—
—
—
—
—
—
A
(
20,19,21
)
107.19For tetrahydrofuran (THF) and its derivatives, C–C bond distances are found to be in the range of 1.542–1.553 Å, 1.529–1.543 Å, 1.529–1.552 Å, 1.540–1.542 Å, and 1.532–1.549 Å while, for C–N (except THF), these values are 1.443 Å, 1.438–1.467 Å, 1.435–1.461 Å, and 1.428–1.462 Å, respectively, for amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran. For C–O, these values are 1.423 Å, 1.434 Å, 1.429 Å, 1.431 Å, and 1.435–1.462 Å, respectively, for THF, amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran. In case of C–H bond distances, they lie in the range of 1.091–1.101, 1.093, 1.092–1.094, 1.097–1.102, and 1.096–1.101, respectively. In the literature, bond lengths for THF-water complex [17] have a little bit lower values of 1.527–1.537 Å (for (C–C)) and a little bit higher values of 1.443–1.446 Å (for (C–O)). This may be due to shifting of charge in interaction of THF with water molecule. Optimized structures of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) method are shown in Figure 1.


## 3.2. Assignment of Fundamentals

Tetrahydrofuran has 13 atoms with 33 normal modes of vibration while amino tetrahydrofuran has 15 atoms with 39 normal modes of vibration. 1,2-Diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran have 17, 19, and 21 atoms with 45, 51, and 57 normal modes of vibration, respectively. From our calculated data and experimental FTIR spectra, we observe similarities and differences between the experimental and the calculated frequencies by DFT/B3LYP method. Assignments are done using the animated view of normal mode description. A good agreement is found between the theoretical and experimental data. Here we are discussing only important modes. Vibrational frequencies, calculated for tetrahydrofuran and experimental frequencies (FTIR), have been compared in Table2. We are also discussing the assignments for tetrahydrofuran derivatives which are useful for the experimentalists in absence of its experimental data.Table 2
Vibrational assignments of tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled (in lit.)
IR (int.)
Exp. IR
Exp. Raman
Vibrational assignments
281
271 (267)
8.1672
—
276
Out of plane bend in CH2–O–CH2
644
620 (635)
4.7345
625
—
τ(C–O–C–C)
799
769
5.8498
765
—
Twist CH2
866
834
4.358
825
—
Twist CH2 in whole
901
868 (883)
5.7608
865
—
τ(C–C–C–O)
941
906
22.7829
915
913
Twist CH2 in whole
959
924 (934)
17.9192
930
—
Ring breathing
1046
1007
4.7743
995
—
β(C–C–H) + β(C–O–C)
1097
1056 (1068)
83.1142
1045
1071
Ring deformation
1214
1169
6.4279
1175
1174
β(C–C–H)
1261
1214 (1214)
5.8725
1205
—
Twist CH2
1268
1221
5.1994
1220
1234
Twist CH2
1395
1343
4.7295
1335
1335
β(C–C–H)
1506
1450 (1454)
5.5918
1445
1452
S(CH2)
2958
2848
43.4017
2840
—
ν(C–H)
2964
2854
118.3793
2855
—
ν(C–H)
3052
2939 (2936)
24.963
2930
2938
ν(C–H)
3062
2949
40.015
2950
—
ν(C–H)
3082
2968 (2968)
19.4174
2965
2975
ν(C–H)
3098
2983 (2989)
34.7534
2980
—
ν(C–H)
3110
2995
77.426
2990
—
ν(C–H)


## 3.3. Vibrational Modes Description

### 3.3.1. C–H Vibrations

We have seen in the literature that the C–H stretching vibrations are usually observed in 2800–3200 cm−1 region. In the study of tetrahydrofuran, the (C–H) functional group is present at 2848, 2854, 2939, 2949, 2968, 2983, and 2995 cm−1 in calculated spectra which is in good agreement with the experimental data as given in Table 2. In vibrational assignments, the C–H stretching vibrations are in the same range for all derivatives of tetrahydrofuran listed in Tables 3, 4, 5, and 6.Table 3
Vibrational assignments of amino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
197
190
48.1062
Rock NH2
378
364
16.1235
Group NH2 bend from joint
778
749
174.8209
Rock NH2
877
845
23.6231
β(C–C–H) + β(C–C–C)
957
922
65.1906
β(C–C–H)
1067
1028
52.4498
Ring deformation
1133
1091
73.4975
β(C–C–C)
1443
1390
25.3256
β(C–C–H)
1647
1586
38.9601
S(NH2)
2971
2861
74.2781
ν(C–H)
2993
2882
62.1676
ν(C–H)
3023
2911
28.6539
ν(C–H)
3058
2945
64.6532
ν(C–H)
3095
2980
55.4994
ν(C–H)
3595
3462
0.4042
ν(N–H)Table 4
Vibrational assignments of 1,2-diamino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
257
247
77.5282
Rock NH2
424
408
30.1483
Twist NH2
753
725
46.0965
τ(C–C–C–C)
859
827
83.126
Rock NH2
905
872
171.3772
Rock NH2
921
887
45.5585
Rock NH2
954
919
112.828
Rock NH2
1029
991
33.4007
Twist CH2
1068
1028
80.3998
Ring deformation
1164
1121
20.3894
β(C–C–H) in whole molecule
1446
1392
14.2825
β(C–C–H)
1645
1584
63.057
S(NH2)
1669
1607
31.4909
S(NH2)
2974
2864
55.4405
ν(C–H)
3010
2899
61.7424
ν(C–H)
3038
2926
34.5478
ν(C–H)
3044
2931
53.5102
ν(C–H)
3074
2960
46.2551
ν(C–H)
3090
2976
46.8808
ν(C–H)
3578
3446
3.4588
ν(N–H)Table 5
Vibrational assignments of 1,2,3-triamino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
187
180
38.0082
Twist NH2
274
264
29.2943
Twist NH2
324
312
23.6603
Twist NH2
376
362
23.1528
Twist NH2
492
474
18.1122
τ(C–C–C–C)
635
612
213.3144
Rock NH2
832
801
68.3448
Rock NH2
859
827
130.0253
Rock NH2
936
901
46.5701
Ring deformation
994
957
65.805
β(C–C–C)
1026
988
47.4846
β(C–C–H)
1076
1036
78.3665
Ring deformation
1132
1090
33.1727
β(C–C–H)
1153
1110
30.0604
β(C–C–H)
1167
1124
48.7819
β(C–C–H)
1442
1389
21.4953
β(C–C–H)
1648
1587
47.0934
S(NH2)
1660
1599
29.1316
S(NH2)
2934
2825
37.6667
ν(C–H)
2950
2841
86.3504
ν(C–H)
3006
2895
115.4219
ν(C–H)
3057
2944
47.6972
ν(C–H)
3579
3447
5.6057
ν(N–H)Table 6
Vibrational assignments of 1,2,3,4-tetra-amino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
260
250
43.2432
Twist NH2
301
290
22.3762
Twist NH2
347
334
25.9587
Rock NH2
366
352
21.3354
Rock NH2
426
410
18.1696
Twist NH2
513
494
54.7952
Torsion in whole molecule
593
571
38.3343
τ(C–C–O–C)
663
638
28.8211
τ(C–C–C–C)
759
731
56.9814
τ(C–C–C–O)
802
772
106.1627
Rock NH2
850
819
60.9417
Rock NH2
865
833
73.3106
Twist NH2 in whole places
881
848
335.8006
Twist NH2
902
869
149.2133
Rock NH2
944
909
85.627
Rock NH2
972
936
31.7804
β(C–C–C) + Twist NH2
1019
981
132.2283
ν(C–O)
1097
1056
16.8407
Twist NH2
1167
1124
27.6511
Bending in whole molecule
1183
1139
25.494
β(C–C–H)
1441
1388
19.585
β(C–C–H)
1635
1575
55.77
S(NH2)
1649
1588
56.9828
S(NH2)
2946
2837
39.5477
ν(C–H)
2984
2874
58.3297
ν(C–H)
3033
2921
82.6875
ν(C–H)
3483
3354
19.1928
ν(N–H)
3585
3452
11.9623
ν(N–H)


### 3.3.2. N–H Vibrations

There is no NH2 group added to tetrahydrofuran but they are presented in all derivatives of tetrahydrofuran. The N–H stretching vibrations are normally viewed in the region 3300–3600 cm−1. For amino tetrahydrofuran, the N–H stretching vibration is calculated at 3462 cm−1 while it is 3446 cm−1 for 1,2-diamino tetrahydrofuran. A strong scissoring vibration of H–N–H is found at 1586 and 1584 cm−1 for amino tetrahydrofuran and 1,2-diamino tetrahydrofuran, respectively. In case of 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran, the N–H vibration is at 3447 and 3354 cm−1 in calculated spectra. There are also strong scissoring vibrations at 1587 and 1588 cm−1 for 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran. Some strong rocking and twisting vibrations of NH2 are also seen in the assignment of all derivatives of tetrahydrofuran. We see that scissoring modes in THF are lower than all the derivatives of THF. This is due to the addition of amino group (charge transfer) to THF molecule. The interpretation of vibrational spectra of THF is in good agreement with the literature [18] as given in Table 2.


### 3.3.3. Other Modes of Vibration

In tetrahydrofuran, a ring deformation mode is calculated at 1056 cm−1 which is in good agreement with experimental data, that is, 1055 cm−1, while in all derivatives of tetrahydrofuran (except the last one) ring deformation mode is at 1028, 1028, and 1036 cm−1 having appropriate IR intensity. As expected, torsion modes along with wagging modes appear in the lower frequency range. For tetrahydrofuran, strong torsion mode of C–O–C–C is at 628 cm−1 in calculated spectrum which matches well with the experimental one, that is, 625 cm−1, while strong torsion modes of C–C–C–C are at 725 and 474 cm−1 in calculated spectrum for 1,2-di-ATHF and 1,2,3-tri-ATHF, respectively. A very strong stretching vibration of C–O is found at 981 cm−1 while there is also a strong torsion mode of C–C–C–O at 731 cm−1 in calculated spectra for 1,2,3,4-tetra-ATHF. There are some frequencies in lower region having appreciable IR intensity. Furthermore, the study of low frequency vibrations is of great significance, because it gives information on weak intermolecular interactions, which take place in enzyme reactions [19]. Knowledge of low frequency mode is also essential for the interpretation of the effect of electromagnetic radiation on biological systems [20]. The aim of vibrational analysis is to acquire direct information on lower and higher frequency vibrations of such THF and its derivatives. No experimental FTIR spectrum is available for comparison of derivatives of THF so it will provide a suitable path for experimental researchers.


## 3.3.1. C–H Vibrations

We have seen in the literature that the C–H stretching vibrations are usually observed in 2800–3200 cm−1 region. In the study of tetrahydrofuran, the (C–H) functional group is present at 2848, 2854, 2939, 2949, 2968, 2983, and 2995 cm−1 in calculated spectra which is in good agreement with the experimental data as given in Table 2. In vibrational assignments, the C–H stretching vibrations are in the same range for all derivatives of tetrahydrofuran listed in Tables 3, 4, 5, and 6.Table 3
Vibrational assignments of amino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
197
190
48.1062
Rock NH2
378
364
16.1235
Group NH2 bend from joint
778
749
174.8209
Rock NH2
877
845
23.6231
β(C–C–H) + β(C–C–C)
957
922
65.1906
β(C–C–H)
1067
1028
52.4498
Ring deformation
1133
1091
73.4975
β(C–C–C)
1443
1390
25.3256
β(C–C–H)
1647
1586
38.9601
S(NH2)
2971
2861
74.2781
ν(C–H)
2993
2882
62.1676
ν(C–H)
3023
2911
28.6539
ν(C–H)
3058
2945
64.6532
ν(C–H)
3095
2980
55.4994
ν(C–H)
3595
3462
0.4042
ν(N–H)Table 4
Vibrational assignments of 1,2-diamino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
257
247
77.5282
Rock NH2
424
408
30.1483
Twist NH2
753
725
46.0965
τ(C–C–C–C)
859
827
83.126
Rock NH2
905
872
171.3772
Rock NH2
921
887
45.5585
Rock NH2
954
919
112.828
Rock NH2
1029
991
33.4007
Twist CH2
1068
1028
80.3998
Ring deformation
1164
1121
20.3894
β(C–C–H) in whole molecule
1446
1392
14.2825
β(C–C–H)
1645
1584
63.057
S(NH2)
1669
1607
31.4909
S(NH2)
2974
2864
55.4405
ν(C–H)
3010
2899
61.7424
ν(C–H)
3038
2926
34.5478
ν(C–H)
3044
2931
53.5102
ν(C–H)
3074
2960
46.2551
ν(C–H)
3090
2976
46.8808
ν(C–H)
3578
3446
3.4588
ν(N–H)Table 5
Vibrational assignments of 1,2,3-triamino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
187
180
38.0082
Twist NH2
274
264
29.2943
Twist NH2
324
312
23.6603
Twist NH2
376
362
23.1528
Twist NH2
492
474
18.1122
τ(C–C–C–C)
635
612
213.3144
Rock NH2
832
801
68.3448
Rock NH2
859
827
130.0253
Rock NH2
936
901
46.5701
Ring deformation
994
957
65.805
β(C–C–C)
1026
988
47.4846
β(C–C–H)
1076
1036
78.3665
Ring deformation
1132
1090
33.1727
β(C–C–H)
1153
1110
30.0604
β(C–C–H)
1167
1124
48.7819
β(C–C–H)
1442
1389
21.4953
β(C–C–H)
1648
1587
47.0934
S(NH2)
1660
1599
29.1316
S(NH2)
2934
2825
37.6667
ν(C–H)
2950
2841
86.3504
ν(C–H)
3006
2895
115.4219
ν(C–H)
3057
2944
47.6972
ν(C–H)
3579
3447
5.6057
ν(N–H)Table 6
Vibrational assignments of 1,2,3,4-tetra-amino tetrahydrofuran (modes having high IR intensity only) with B3LYP/6-311 G (d, p).
B3LYP (calculated) unscaled
B3LYP (calculated) scaled
IR (int.)
Vibrational assignments
260
250
43.2432
Twist NH2
301
290
22.3762
Twist NH2
347
334
25.9587
Rock NH2
366
352
21.3354
Rock NH2
426
410
18.1696
Twist NH2
513
494
54.7952
Torsion in whole molecule
593
571
38.3343
τ(C–C–O–C)
663
638
28.8211
τ(C–C–C–C)
759
731
56.9814
τ(C–C–C–O)
802
772
106.1627
Rock NH2
850
819
60.9417
Rock NH2
865
833
73.3106
Twist NH2 in whole places
881
848
335.8006
Twist NH2
902
869
149.2133
Rock NH2
944
909
85.627
Rock NH2
972
936
31.7804
β(C–C–C) + Twist NH2
1019
981
132.2283
ν(C–O)
1097
1056
16.8407
Twist NH2
1167
1124
27.6511
Bending in whole molecule
1183
1139
25.494
β(C–C–H)
1441
1388
19.585
β(C–C–H)
1635
1575
55.77
S(NH2)
1649
1588
56.9828
S(NH2)
2946
2837
39.5477
ν(C–H)
2984
2874
58.3297
ν(C–H)
3033
2921
82.6875
ν(C–H)
3483
3354
19.1928
ν(N–H)
3585
3452
11.9623
ν(N–H)


## 3.3.2. N–H Vibrations

There is no NH2 group added to tetrahydrofuran but they are presented in all derivatives of tetrahydrofuran. The N–H stretching vibrations are normally viewed in the region 3300–3600 cm−1. For amino tetrahydrofuran, the N–H stretching vibration is calculated at 3462 cm−1 while it is 3446 cm−1 for 1,2-diamino tetrahydrofuran. A strong scissoring vibration of H–N–H is found at 1586 and 1584 cm−1 for amino tetrahydrofuran and 1,2-diamino tetrahydrofuran, respectively. In case of 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran, the N–H vibration is at 3447 and 3354 cm−1 in calculated spectra. There are also strong scissoring vibrations at 1587 and 1588 cm−1 for 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran. Some strong rocking and twisting vibrations of NH2 are also seen in the assignment of all derivatives of tetrahydrofuran. We see that scissoring modes in THF are lower than all the derivatives of THF. This is due to the addition of amino group (charge transfer) to THF molecule. The interpretation of vibrational spectra of THF is in good agreement with the literature [18] as given in Table 2.


## 3.3.3. Other Modes of Vibration

In tetrahydrofuran, a ring deformation mode is calculated at 1056 cm−1 which is in good agreement with experimental data, that is, 1055 cm−1, while in all derivatives of tetrahydrofuran (except the last one) ring deformation mode is at 1028, 1028, and 1036 cm−1 having appropriate IR intensity. As expected, torsion modes along with wagging modes appear in the lower frequency range. For tetrahydrofuran, strong torsion mode of C–O–C–C is at 628 cm−1 in calculated spectrum which matches well with the experimental one, that is, 625 cm−1, while strong torsion modes of C–C–C–C are at 725 and 474 cm−1 in calculated spectrum for 1,2-di-ATHF and 1,2,3-tri-ATHF, respectively. A very strong stretching vibration of C–O is found at 981 cm−1 while there is also a strong torsion mode of C–C–C–O at 731 cm−1 in calculated spectra for 1,2,3,4-tetra-ATHF. There are some frequencies in lower region having appreciable IR intensity. Furthermore, the study of low frequency vibrations is of great significance, because it gives information on weak intermolecular interactions, which take place in enzyme reactions [19]. Knowledge of low frequency mode is also essential for the interpretation of the effect of electromagnetic radiation on biological systems [20]. The aim of vibrational analysis is to acquire direct information on lower and higher frequency vibrations of such THF and its derivatives. No experimental FTIR spectrum is available for comparison of derivatives of THF so it will provide a suitable path for experimental researchers.


## 3.4. Electrical, Optical, Dipole Moment and Thermodynamical Properties

Frontier orbital energy gap, that is, the gap between HOMO and LUMO, shows the interaction of that molecule with other species. Frontier orbital energy gap helps to differentiate the chemical reactivity of the molecules. In case of tetrahydrofuran and its derivatives, frontier orbital energy gap is 7.9402, 6.9066, 6.8312, 6.4991, and 6.8870 eV, respectively, and is given in Table7. So it can be concluded that 1,2,3-triamino tetrahydrofuran is the most reactive compound among all. The pictures of HOMO, LUMO, and electrostatic potential (MESP) for tetrahydrofuran and its derivatives are shown in Figure 2.Table 7
Lowest energy, HOMO-LUMO gap (frontier orbital energy gap), and dipole moment of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) method.
Parameters
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
Energy (in au)
−232.5134
−287.8832
−343.2555
−398.6109
−453.9997
Dipole moment (in Debye)
1.585
2.855
1.667
4.022
1.743
HOMO
−0.25509
−0.23322
−0.22235
−0.21917
−0.22375
LUMO
0.03683
0.02070
0.02880
0.01977
0.02945
Frontier orbital energy gap (eV)
7.9402
6.9066
6.8312
6.4991
6.8870Figure 2
Pictures of HOMO-LUMO and molecular electrostatic potential of tetrahydrofuran and its derivatives.Figure 3
Experimental IR spectra of tetrahydrofuran.Dipole moment(
μ
), polarizability α, and total first static hyperpolarizability β [21, 22] can be expressed in terms of x, y, z components and are given by the following equations:
(1)
μ
=
μ
x
2
+
μ
y
2
+
μ
z
2
1
/
2
,
α
=
1
3
α
x
x
+
α
y
y
+
α
z
z
,
β
Total
=
β
x
2
+
β
y
2
+
β
z
2
1
/
2
=
β
x
x
x
+
β
x
y
y
+
β
x
z
z
2
000
+
β
y
y
y
+
β
y
x
x
+
β
y
z
z
2
000
+
β
z
z
z
+
β
z
x
x
+
β
z
y
y
2
1
/
2
.
The β components of Gaussian output are reported in atomic units.Where1
a
.
u
.
=
8.3693
*
10
-
33 e.s.u., the calculated dipole moments for tetrahydrofuran and its derivatives are 1.585, 2.855, 1.667, 4.022, and 1.743 Debye, respectively. So, 1,2,3-triamino tetrahydrofuran is a better solvent among them all. A greater contribution of α
y
y is seen in THF, amino THF, and 1,2,3-triamino THF while α
z
z is seen in 1,2-diamino THF and α
x
x in 1,2,3,4-tetra-amino THF. For THF and 1,2,3-triamino THF, molecules are elongated more towards Y direction and more contracted in the X direction while amino THF molecule is elongated more towards Y direction and more contracted in the X direction. For 1,2-diamino THF, molecule is elongated more towards Z direction and more contracted in the X direction while 1,2,3,4-tetra-amino THF molecule is elongated more towards X direction and more contracted in the Y direction. It is seen that the components β
x
x
z, β
x
x
y, β
y
y
y, β
y
y
y, and β
x
x
x contribute lager part of hyperpolarizability from THF to 1,2,3,4-tetra-amino THF. This shows that X
Z and X
Y planes and Y- and X-axes are more optically active in these directions. The values of hyperpolarizability indicate a possible use of these compounds in electrooptical applications.Internal thermal energy (E), constant volume heat capacity C
v, and entropy S, calculated at B3LYP/6-311 G (d, p) level, are listed in Table 9. We know that conduction band is almost empty at the room temperature, so electronic contribution in total energy is negligible. All the thermodynamic data supplies helpful information for the further study on the THF and its derivatives. They can be used to compute the other thermodynamic energies according to relationships of thermodynamic functions and estimate directions of chemical reactions according to the second law of thermodynamics in the thermochemical field. So thermodynamic properties show that vibrational motion plays an important role.


## 3.5. Reactivity Descriptors

### 3.5.1. Global Reactivity Descriptors

Global reactivity descriptors are described as(2)
Energy
band
gap
⁡
=
ε
LUMO
-
ε
HOMO
,
Electronegativity
χ
=
-
1
2
ε
LUMO
+
ε
HOMO
,
Chemical
potential
μ
=
-
χ
,
Global
hardness
η
=
1
2
ε
LUMO
-
ε
HOMO
,
Global
softness
S
=
1
2
η
,
Global
electrophilicity
index
ω
=
μ
2
2
η
(see [23–27]). All these parameters for tetrahydrofuran and its derivatives have been listed in Table 6.According to these parameters, the chemical reactivity varies with the structural configuration of molecules. Chemical hardness (softness) value of 1,2,3-amino THF is lesser (greater) among all the three molecules. Thus, 1,2,3-amino THF is found to be most reactive among all, whereas THF configuration is less reactive. THF configuration possesses higher electronegativity while 1,2,3-amino THF possesses lower electrophilicity index among them all as given in Table10. Correlations have been found between electrophilicity of various chemical compounds and reaction rates in biochemical systems.


## 3.5.1. Global Reactivity Descriptors

Global reactivity descriptors are described as(2)
Energy
band
gap
⁡
=
ε
LUMO
-
ε
HOMO
,
Electronegativity
χ
=
-
1
2
ε
LUMO
+
ε
HOMO
,
Chemical
potential
μ
=
-
χ
,
Global
hardness
η
=
1
2
ε
LUMO
-
ε
HOMO
,
Global
softness
S
=
1
2
η
,
Global
electrophilicity
index
ω
=
μ
2
2
η
(see [23–27]). All these parameters for tetrahydrofuran and its derivatives have been listed in Table 6.According to these parameters, the chemical reactivity varies with the structural configuration of molecules. Chemical hardness (softness) value of 1,2,3-amino THF is lesser (greater) among all the three molecules. Thus, 1,2,3-amino THF is found to be most reactive among all, whereas THF configuration is less reactive. THF configuration possesses higher electronegativity while 1,2,3-amino THF possesses lower electrophilicity index among them all as given in Table10. Correlations have been found between electrophilicity of various chemical compounds and reaction rates in biochemical systems.


## 3.6. Local Reactivity Descriptors

Fukui function (FF) provides information on the local site reactivity within the molecule and as such it provides a system for understanding of chemical reactions. These values correspond to the qualitative descriptors of reactivity of different atoms in the molecule. A study by Ayers and Parr [27] has shown that FF is larger when attacked by soft reagents and in places where the FF is smaller when attacked by hard reagents. Fukui functions for electrophilic and nucleophilic attacks have been made with the basis of B3LYP/6-311 G (d, p) level of theory. With the help of Mulliken atomic charges of cationic and anionic states, local Fukui functions (
f
k
+
,
f
k
-
), local softness values (
s
k
+
,
s
k
-
), and local electrophilicity indices (
ω
k
+
,
ω
k
-
) have been calculated using the following equation:
(3)
f
k
+
=
q
N
+
1
-
q
N
for
nucleophilic
attack
f
k
-
=
q
N
-
q
N
-
1
for
electrophilic
attack
f
k
0
=
1
2
q
N
+
1
+
q
N
-
1
for
radical
attack
.
Local softness values and electrophilicity indices are calculated using
(4)
s
k
+
=
S
f
k
+
,
s
k
-
=
S
f
k
-
ω
k
+
=
ω
f
k
+
,
ω
k
-
=
ω
f
k
-
,
where + and − signs show nucleophilic and electrophilic attack, respectively.Fukui functions, local softness values, and local electrophilicity indices for selected atomic sites in tetrahydrofuran and its derivatives have been listed in Tables7 and 8. For amino hydrofuran, the maximum value for local nucleophilic reactivity descriptors (
f
k
-
,
s
k
-
,
ω
k
-
) at N13 indicates that this site is more prone to electrophilic attack. But in comparison with N16 of 1,2,3,4-tetra-amino hydrofuran it is found that the N16 of 1,2,3,4-tetra-amino hydrofuran has lower affinity towards electrophile as given in Table 11. This situation changes because of change of position of the nitrogen of 1,2,3,4-tetra-amino hydrofuran, and hence the charge density around N16 decreased.Table 8
Polarizability and hyperpolarizability of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) methods.
Polarizability
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
α
x
x
−29.2994
−35.5422
−41.5883
−43.8040
−55.7761
α
x
y
−0.0137
4.5742
−2.1265
6.8303
0.1740
α
y
y
−34.8626
−40.9807
−41.9550
−50.3155
−50.3145
α
y
z
−0.7807
−0.8029
−0.1374
0.0764
2.3250
α
z
z
−31.4458
−35.4849
−43.4920
−49.1301
−53.4053
α
z
x
0.0077
0.5506
−0.9605
−0.3221
−2.4170
α
31.8692
37.3359
42.3451
47.7498
53.1653
Hyperpolarizability
β
x
x
x
−0.0052
5.6681
−0.2912
−6.3842
−6.7955
β
x
x
y
−4.0970
6.2139
−8.0690
13.6734
−4.4365
β
x
y
y
0.0298
−1.6268
6.3043
−3.2086
−1.8247
β
y
y
y
−0.6535
−0.2718
14.9291
14.4296
−0.2671
β
z
z
z
−1.1489
1.5867
0.4088
2.4337
−0.1471
β
x
x
z
−1.9217
1.5767
−6.1872
−0.5541
−3.9772
β
x
z
z
−0.0222
3.9764
2.7638
6.3393
−2.8358
β
y
z
z
−0.4033
−1.2208
−3.7949
2.7311
−4.7413
β
y
y
z
0.9213
−0.3137
−0.8388
6.3633
1.4539
β
x
y
z
0.0193
−1.1644
−0.5408
−3.0478
−4.4281
β total
5.5840
9.7200
11.4027
32.0675
15.0620Table 9
Calculated thermodynamic properties of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) methods.
THF
Amino THF
1,2-Diamino THF
1,2,3-Triamino THF
1,2,3,4-Tetra-amino THF
E  (thermal) (kcalmol−1)
Total
75.553
87.449
99.560
110.546
122.799
Translational
0.889
0.889
0.889
0.889
0.889
Rotational
0.889
0.889
0.889
0.889
0.889
Vibrational
73.776
85.672
97.783
108.769
121.022
C
V (cal K−1mol−1)
Total
14.943
22.356
26.632
32.701
36.652
Translational
2.981
2.981
2.981
2.981
2.981
Rotational
2.981
2.981
2.981
2.981
2.981
Vibrational
8.982
16.394
20.671
26.739
30.690
S (cal K−1mol−1)
Total
67.259
78.055
81.513
88.746
91.737
Translational
38.741
39.305
39.779
40.188
40.548
Rotational
24.911
26.233
27.149
28.115
28.869
Vibrational
3.607
12.517
14.584
20.443
22.320Table 10
Calculatedε
HOMO, ε
LUMO, energy band gap (ε
LUMO
-
ε
HOMO), chemical potential (μ), electronegativity (χ), global hardness (η), global softness (S), and global electrophilicity index (ω) for tetrahydrofuran and its derivatives at B3LYP/6-311 G (d, p) level.
Compounds
ε
H
ε
L
ε
L
-
ε
H
χ
μ
η
S
ω
THF
−0.25509
0.03683
0.29192
0.10913
−0.10913
0.14596
3.425596054
0.0408
1,2 THF
−0.23322
0.02070
0.25391
0.1011
−0.1011
0.13398
3.7319
0.03814
1,2,3-Amino THF
−0.22235
0.02880
0.25114
0.10323
−0.10323
0.12631
3.95867
0.04218
1,2,3,4 THF
−0.21917
0.01977
0.23893
0.09814
−0.09814
0.13043
3.83347
0.03692
Amino THF
−0.22375
0.02945
0.25319
0.10014
−0.10014
0.1349
3.70645
0.03717Table 11
Fukui functions (f
k
+, f
k
-), local softness (s
k
+, s
k
-), and local electrophilicity indices (ω
k
+, ω
k
-) for selected atomic sites of  CPPC, using Mulliken population analysis at B3LYP/6-311 G (d, p) level.
THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.09218
−0.13948
0.308091
0.231663
0.215911
0.793585
0.739625
0.009452
0.008809
C2
0.006981
−0.24299
0.12914
0.249968
0.122159
0.85629
0.418468
0.010199
0.004984
C3
0.00709
−0.24193
0.129566
0.249016
0.122476
0.853029
0.419554
0.01016
0.004997
C4
0.092228
−0.13921
0.307449
0.231433
0.215221
0.792797
0.737261
0.009442
0.008781
O13
−0.198474
−0.23646
0.125765
0.037987
0.324239
0.130128
1.110713
0.00155
0.013229
Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.122663
0.009106
0.241709
0.113557
0.119046
0.420893
0.441238
0.004221
0.004425
C2
−0.008726
−0.24682
0.114327
0.238093
0.123053
0.88248
0.45609
0.00885
0.004574
C3
0.010672
−0.19419
0.113287
0.204865
0.102615
0.759322
0.380337
0.007615
0.003814
C4
0.089502
−0.09679
0.248705
0.186288
0.159203
0.690467
0.590078
0.006924
0.005918
O12
−0.203353
−0.23584
−0.04207
0.032482
0.161283
0.120393
0.597787
0.001207
0.005995
N13
−0.010961
−0.2358
0.323848
0.224837
0.334809
0.833347
1.240953
0.008357
0.012445
1,2-Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.080415
−0.0421
0.22964
0.12251
0.149225
0.457195
0.556893
0.004673
0.005691
C2
0.004480
−0.17372
0.087954
0.178204
0.083474
0.66504
0.311517
0.006797
0.003184
C3
0.035609
−0.10002
0.115193
0.135632
0.079584
0.506165
0.297
0.005173
0.003035
C4
0.119975
0.005564
0.199748
0.114411
0.079773
0.42697
0.297705
0.004364
0.003043
O11
−0.21865
−0.24652
−0.06071
0.02786
0.157941
0.103971
0.58942
0.001063
0.006024
N12
−0.00822
−0.16639
0.232471
0.158162
0.240694
0.590245
0.898246
0.006032
0.00918
N15
−0.01388
−0.27714
0.195416
0.263249
0.209305
0.982419
0.781105
0.01004
0.007983
1,2,3-Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.115624
0.073205
0.190554
0.042419
0.07493
0.167923
0.296623
0.001789
0.003161
C2
0.022828
−0.08061
0.076666
0.103439
0.053838
0.409481
0.213127
0.004363
0.002271
C3
0.025129
−0.0762
0.118366
0.101328
0.093237
0.401124
0.369095
0.004274
0.003933
C4
0.078038
−0.01158
0.206247
0.089616
0.128209
0.35476
0.507537
0.00378
0.005408
O10
−0.20327
−0.22649
−0.09324
0.023211
0.110038
0.091885
0.435604
0.000979
0.004641
N11
−0.00094
−0.20016
0.211528
0.19922
0.212469
0.788646
0.841095
0.008403
0.008962
N14
−0.00158
−0.3101
0.089629
0.308517
0.091209
1.221317
0.361066
0.013013
0.003847
N17
−0.03592
−0.16821
0.20016
0.132288
0.236083
0.523685
0.934575
0.00558
0.009958
1,2,3,4-Amino THF
M
M−
M+
f
k
+
f
k
-
s
k
+
s
k
-
ω
k
+
ω
k
-
C1
0.108686
0.070775
0.163507
0.037911
0.054821
0.145331
0.210155
0.0014
0.002024
C2
0.030688
−0.08776
0.063705
0.118443
0.033017
0.454048
0.12657
0.004373
0.001219
C3
0.028906
−0.0894
0.100662
0.118308
0.071756
0.45353
0.275074
0.004368
0.002649
C4
0.110441
0.02905
0.179846
0.081391
0.069405
0.31201
0.266062
0.003005
0.002562
O9
−0.233907
−0.2548
−0.12637
0.020888
0.107535
0.080074
0.412232
0.000771
0.00397
N10
−0.024483
−0.11068
0.209354
0.086201
0.233837
0.330449
0.896407
0.003183
0.008633
N13
−0.023684
−0.16618
0.165895
0.142499
0.189579
0.546266
0.726745
0.005261
0.006999
N16
0.004591
−0.24299
0.065478
0.24758
0.060887
0.949091
0.233408
0.009141
0.002248
N19
−0.001198
−0.14799
0.177963
0.146794
0.179161
0.56273
0.686808
0.00542
0.006615


## 4. Conclusions

All calculated wave numbers are real in nature for all the molecules and thus all the compounds are stable. We have done density functional calculations on tetrahydrofuran and its derivatives. The calculated parameters (bond lengths and band angles) and wave numbers show a good agreement with the corresponding experimental data showing the strength of density functional calculations. Normal modes are discussed in detail with the help of Gauss view program. The chemical reactivity of molecules shows the supremacy of 1,2,3-triamino tetrahydrofuran over the remaining molecules. A possible use of these compounds in electrooptical applications is discussed with the help of hyperpolarizability. In addition, to assess the utility of global reactivity descriptors, the relationships between the reactivity and electrophilicity have been discussed. THF configuration possesses higher electronegativity while 1,2,3-amino THF possesses lower electrophilicity index among them all. Correlations have been found between electrophilicity of various chemical compounds and reaction rates in biochemical systems.



---

*Source: 345234-2015-01-05.xml*