Theoretical Investigation of the Molecular Structure, Vibrational
Journal of Theoretical & Computational Science

Journal of Theoretical & Computational Science
Open Access

ISSN: 2376-130X

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Research Article - (2015) Volume 2, Issue 3

Theoretical Investigation of the Molecular Structure, Vibrational Spectra, NMR, UV, NBO Analysis, Homo and Lumo Analysis of 2-(1-Piperazinyl) Ethanol

Mekala R, Mathammal R* and Sangeetha M
Department of Physics, Sri Sarada College for Women, Salem, Tamil Nadu, India, E-mail:
*Corresponding Author: Mathammal R, Department of Physics, Sri Sarada College for Women, Salem, Tamil Nadu, India, Tel: 0427-2447664 Email:


Quantum chemical calculation of geometries and vibrational wavenumbers of 2-(1-piperazinyl) ethanol in a ground state level are carried out by using density functional theory (DFT/B3LYP) method with 6-31+G(d,p)basis set. The harmonic vibrational frequencies are calculated and scaled values have been compared with experimental FTIR, FT-RAMAN spectra. The stability of the molecule arising from hyper conjugative interaction and the charge delocalization has been analyzed using natural bond orbital (NBO) analysis. A study on the electronic properties such as HOMO and LUMO energies are performed by time-dependent DFT (TD-DFT). NLO property of the title compound is calculated. The 1H and 13C NMR chemical shifts of the molecule are calculated by the gauge independent atomic orbitals method. The mapping of electrostatic potential energy surface (MEP) is performed for the title compound.


Keywords: Vibrational analysis; UV; NBO; NMR; HOMO-LUMO


2-(1-Piperazinyl) ethanol has a general formula C6H14N2O which belongs to the family of piperazine. Molecular weight of 2-(1-piperazinyl) ethanol 130.18 g/mol. Piperazine derivatives are widely used in pharmacological and electro optic applications. The piperazine template forms the molecular backbone; possess versatile binding properties with a frequency occurring binding motif which provides potent and selective ligands for a range of different biological targets in medicinal chemistry. Piperazines are currently the most important building blocks in drug discovery, with a high number of positive hits encountered in biological screens of this heterocyclic and its congeners across a number of different therapeutic areas [1,2]; anticancer [3-5], antifungal [6], antibacterial, antimalarial and antipsychotic agents [7], as well as HIV protease inhibitors [8,9]. Piperazines kill tumor cells directly through the induction of apoptosis. Their anti-tumour modes of action are quite distinct and are significantly more potent. They are active against a variety of different tumor types and orally bioavailable [10] piperazine derivatives can act as stimulants at low doses, while causing hallucinations at higher doses [11] and are designed as designer drugs.

To the best of our knowledge, neither quantum chemical calculations, nor vibrational analysis study of 2-(1-piperazinyl) ethanol has not been reported yet. DFT technique is employed to study the complete vibrational spectra of the title compound and to identify the various normal modes with greater wave number accuracy. Therefore, in the present study, FTIR and FT-RAMAN spectral analysis of 2-(1-piperazinyl) ethanol, have been recorded and verified by using density functional theory (DFT). UV and NMR studies are also carried out by B3LYP /6-31+G(d,p) basis set. The redistribution of electron density (ED) in various bonding, anti-bonding and E2 energies had been calculated by natural bonding orbital (NBO) analysis to give clear evidence of stabilization originating from the hyper conjugation of various intra molecular interactions. The HOMO and LUMO analysis have been used to elucidate information regarding charge transfer within the molecule.

Experimental Details

The sample of the present compound 2-(1-piperazinyl) ethanol was purchased from Merck chemical company, with spectroscopic grade and it is used as such without further purification. The FT-IR spectrum of the compound has been recorded in Perkin-Elmer spectrometer between 4000 and 400 cm-1. The spectral resolution is ± 1 cm-1. The FT-Raman spectrum of the compound is also recorded in the same instrument with FRA 106 Raman module equipped with Nd: YAG laser source operating at 1.064 μm line widths with 200 mW powers. The spectra are recorded with scanning speed of 30 cm-1. The frequencies of all sharp bands are accurate to ± 1 cm-1. 1H and13C nuclear magnetic resonance (NMR)(400 MHz; CDCl3) spectra were recorded on a Bruker HC instrument. Chemical shifts for protons are reported in parts per million scales (δ scale) downfield from tetramethylsilane (TMS).

Quantum chemical calculations

Calculations of the title compound were carried out with Gaussian 09 software program [12] using the B3LYP/6-31G+(d,p) to predict the molecular structure and vibrational wave numbers. Calculations were carried out with Beck’s three parameter hybrid model using the Lee-Yang-Parr correlation functional (B3LYP) method. The structure optimization was performed to confirm the structure and hence to find the optimized geometry of the examined species, no imaginary wave number modes were obtained by B3LYP/6-31+G(d,p). The wavenumbers values computed contain known systematic errors and therefore, have used the constant scaling factor value of 0.956 for DFT method [13]. The DFT hybrid B3LYP functional method tends to overestimate the wavenumbers of functional modes; therefore scaling factors have to be used for obtaining a considerably better agreement with experimental data [13]. The obtained geometrical parameters (B3LYP) are given in Table 1. The assignment of the calculated wave numbers are aided by the animation option of Gauss view program, which gives a visual presentation of the vibrational modes [14].

Parameters Theoritical bond length (Å)
C1-H2 1.0957
C1-H3 1.0973
C1-C4 1.5362
C1-N13 1.466
C4-H5 1.0971
C4-H6 1.1104
C4-N15 1.4614
C7-H8 1.1104
C7-H9 1.097
C7-C10 1.5361
C7-N15 1.4614
C10-H11 1.0973
C10-H12 1.0957
C10-N13 1.466
N13-H14 1.0184
N15-C16 1.459
C16-H17 1.0967
C16-H18 1.0967
C16-C19 1.5364
C19-H20 1.0994
C19-H21 1.0994
C19-O22 1.4304
O22-H23 0.9651
Bond angle (Å)
H2-C1-H3 107.7412
H2-C1-C4 110.1545
H2-C1-N13 108.7599
H3-C1-C4 108.7978
H3-C1-N13 107.8154
C4-C1-N13 113.397
C1-C4-H5 110.0597
C1-C4-H6 108.6202
C1-C4-N15 109.8313
H5-C4-H6 107.343
H5-C4-N15 108.6565
H6-C4-N15 112.2923
H8-C7-H9 107.3428
H8-C7-C10 108.6196
H8-C7-N15 112.2912
H9-C7-C10 110.0631
H9-C7-N15 108.6577
C10-C7-N15 109.8287
C7-C10-H11 108.7871
C7-C10-H12 110.1583
C7-C10-N13 113.3937
H11-C10-H12 107.742
H11-C10-N13 107.8138
H12-C10-N13 108.7611
C1-N13-C10 111.3619
C1-N13-H14 109.781
C10-N13-H14 109.7811
C4-N15-C7 111.3619
C4-N15-C16 115.437
C7-N15-C16 115.4382
`N15-C16-H17 108.3226
N15-C16-H18 108.3198
N15-C16-C19 116.9573
H17-C16-H18 106.8048
H17-C16-C19 108.0033
H18-C16-C19 107.9999
C16-C19-H20 110.5693
C16-C19-H21 110.5696
C16-C19-O22 106.3501
H20-C19-H21 108.134
H20-C19-O22 110.6175
H21-C19-O22 110.6175
C19-O22-H23 109.3781
H2-C1-C4-H5 64.1556
H2-C1-C4-H6 -53.0962
H2-C1-C4-N15 -176.2596
H3-C1-C4-H5 -53.7368
H3-C1-C4-H6 -170.9887
H3-C1-C4-N15 65.8479
N13-C1-C4-H5 -173.6985
N13-C1-C4-H6 69.0497
N13-C1-C4-N15 -54.1138
H2-C1-N13-C10 173.5921
H2-C1-N13-H14 51.7992
H3-C1-N13-C10 -69.8454
H3-C1-N13-H14 168.3617
C4-C1-N13-C10 50.6738
C4-C1-N13-H14 -71.1191
C1-C4-N15-C7 57.74
C1-C4-N15-C16 -167.5245
H5-C4-N15-C7 178.1783
H5-C4-N15-C16 -47.0862
H6-C4-N15-C7 -63.2369
H6-C4-N15-C16 71.4987
H8-C7-C10-H11 171.0103
H8-C7-C10-H12 53.1152
H8-C7-C10-N13 -69.0327
H9-C7-C10-H11 53.7572
H9-C7-C10-H12 -64.1379
H9-C7-C10-N13 173.7142
N15-C7-C10-H11 -65.8296
N15-C7-C10-H12 176.2753
N15-C7-C10-N13 54.1275
H8-C7-N15-C4 63.2266
H8-C7-N15-C16 -71.5084
H9-C7-N15-C4 -178.1888
H9-C7-N15-C16 47.0763
C10-C7-N15-C4 -57.7471
C10-C7-N15-C16 167.5179
C7-C10-N13-C1 -50.6807
C7-C10-N13-H14 71.1122
H11-C10-N13-C1 69.8345
H11-C10-N13-H14 -168.3727
H12-C10-N13-C1 -173.6024
H12-C10-N13-H14 -51.8096
C4-N15-C16-H17 55.6992
C4-N15-C16-H18 171.196
C4-N15-C16-C19 -66.5558
C7-N15-C16-H17 -171.1758
C7-N15-C16-H18 -55.679
C7-N15-C16-C19 66.5692
N15-C16-C19-H20 -59.8388
N15-C16-C19-H21 59.89
N15-C16-C19-O22 -179.9744
H17-C16-C19- H20 177.7407
H17-C16-C19-H21 -62.5305
H17-C16-C19-O22 57.6051
H18-C16-C19-H20 62.5752
H18-C16-C19-H21 -177.696
H18-C16-C19-O22 -57.5604
C16-C19-O22-H23 -179.9632
H20-C19-O22-H23 59.9325
H21-C19-O22-H23 -59.8585

Table 1: Optimized geometrical parameters of 2-(1-piperazinyl) ethanol by B3LYP/6-31G+(d,p).

Results and Discussion

Molecular geometry

The stability of the molecule was studied with the help of conformational analysis. Two conformations gauche and anti with respect to the C16-C19 has been carried out. The global minimum energy was found to be for the most stable conformer -421.76758126 Hartee (anti). The optimized geometrical parameters namely bond lengths, bond angles and dihedral angles are calculated by B3LYP/6- 31+G(d,p) which are listed in Table 1. The molecular structure of 2-(1-piperazinyl) ethanol with the atoms numbering are shown in the Figure 1.


Figure 1: Molecular Structure of 2-(1-piperazinyl) ethanol with atom numbering scheme.

From the table, C-H bonds are having the bond lengths in the range of 1.0957 Å to 1.1104 Å. The presence of the ethanol group attached to the N15 atom has shifted the bond distances of C4-H6 , C7-H8 to higher value (1.1104 Å) The bond lengths of C1-H3 , C7-H9, C10-H9 and C10-H11 are greater than the other C-H bonds lengths, shows that the electronegative atoms N13 is nearly to those bonds. The C–C bond values are ranging from 1.5361 Å to 1.5364 Å. The highly electro negative oxygen atom distorted the angle C16- C19-H20 and C16-C19-H21 to higher angle (110.56°).

The steric hindrance on N atom and column interaction between the H atoms of CH2 and CH3 groups give rise to the lone pair to be oriented in axial position while an ethanol group stays at equatorial position. The N-C bond lengths are found in the range of 1.45 Å to 1.465 Å which is comparing shorter than the experimental N-C bond length. This is due to the conjugation of its electro negativity character of the atom O22 which is present in the ethanol group. The N-H bond length takes the value 1.0184 Å. The other O-H and C-O bond lengths are found at 0.965 Å and 1.4304 Å respectively.

Piperazine can have different conformations which are chair, halfchair, boat, twist boat and envelope forms. Chair conformation was found to be the most stable conformer and Hendrickson proposed that for chair–chair inter conversion the most stable transition state would be one of the possible chair forms [15-17]. The dihedral angle calculated for C1-C4-N15-C16 is found to be -167.5245. Thus, the obtained optimized geometrical parameters from the Table 1 confirm the chair conformation of 2-(1-piperazinyl) ethanol.

Vibrational analysis

The aim of the vibrational analysis is to find the vibrational modes connected with calculated specific molecular structure of the compound. The molecule consists of 23 atoms which undergo 63 normal modes of vibration. The title molecule belongs to C1 point group symmetry. Vibrational band assignments of 2-(1-piperazinyl) ethanol have been made by using Gauss view molecular visualization program [18]. After applying the scale factors, the theoretical calculations reproduce the experimental data which are good agreement with literature value. The observed and scaled theoretical frequencies, IR intensities, Raman activities and normal modes of vibrations are listed in Table 2. The theoretical and experimental FTIR and FT-RAMAN spectrum are shown in the Figure 2.

S.No Observed frequencies Calculated frequencies(*) IR intensity Raman PED (%)
  IR Raman Unscaled  IR Scaled IR      
1     70 67 10.91 0.04 τOCHH(63), τHOCC(11)
2     95 91 1.72 0.33 τCCNC(62), τHCNC(18)
3     102 97 0.42 0.32 τOCCN(58), τHOCC(13)
4     228 218 2.43 0.26 τCCNH(33), τHCNC(18)
5     254 243 8.25 0.29 δCCNC(43), τHCNC(14)
6     258 247 114.91 1.68 τHOCC(87), τOCHH(10)
7     312 298. 6.12 2.10 τOCCN(50), τHOCC(30)
8   329 336 321 15.51 0.67 τ HCNC(44), τHHCN(13)
9     371 355 0.22 0.18 τ HHCN(58), τHCNC(28)
10     400 383 11.91 1.48 τHCNC(47), τHCCH(10)
11 460 483 492 471 3.02 2.38 τHCCN(54), τHCCH(23)
12     524 500 0.90 0.59 τCCNH(20), τHCCH(12)
13 585   641 613 35.85 1.45 δCCNC(27), τHCNC(9)
14     773 739 40.85 11.61 τCNHC(44), τHCNC(14)
15     790 755 100.70 4.54 τCNCH(42), τHCNC(20)
16   769 799 764 0.16 0.52 τHCCH(54), τCCNC(17)
17     847 810 0.19 1.18 τ CNCC(17), τHHCN(13)
18   852 896 857 11.81 4.47 τHNCC(13), τHHCN(11)
19 879   911 871 2.78 0.10 βCCN(38), νCC(19) , βCCH(10)
20 936   985 942 44.13 8.78 βCCN(65), νCC(30)
21     1011 967 28.66 7.06 νCC(61), νCN(22), βCH(10)
22     1038 993 2.84 0.34 τHCNC(20), τHHCN(10)
23     1041 995 10.93 1.87 τHCNC(22), τHHCN(13)
24 1011   1061 1014 68.32 10.20 νCO(80), νCN(15)
25 1057 1035 1091 1043 11.94 2.20 νCN(73), βCH(22)
26 1065 1066 1144 1094 12.10 2.55 νCN(70), βCH(13)
27     1144 1094 30.12 0.58 νCN(60), νCC(17), βCH(13)
28 1120   1182 1130 80.05 6.40 νCN(38) , βHCH(18), βCOH(11)
29 1142   1193 1140 9.98 1.36 νCN(41), βHCN(13)
30 1182   1212 1158 6.48 5.30 βHCN(32), νCN(14)
31 1196   1224 1170 21.09 7.23 βCOH(60), βHCH(28), νCN(09)
32 1202 1199 1246 1191 0.68 0.98 νCC(53) , βCCN(18), βHCH(12)
33     1303 1246 5.06 8.74 βCCH(48), νCN(22)
34 1268   1327 1269 7.36 3.83 βCCN(59), νCC(18)
35 1286   1350 1291 1.72 10.9 βHCN(69), βCNC(28)
36     1352 1290 19.58 4.14 βCCN(28), βCNC(10)
37 1297 1299 1356 1296 7.28 0.46 βHCC(58), βHOH(22)
38 1306   1365 1305 4.88 1.88 βHOC(50)
39 1321   1389 1328 1.40 1.40 βHCC(61)
40 1339   1396 1334 8.31 3.58 βHCC(40), νCC(20) , νCN(13)
41 1364   1416 1353 7.07 2.22 νCC(63), βCCN(20)
42     1450 1386 0.81 1.47 βCOH(51), βHCH(13)
43 1407   1477 1412 0.25 20.23 βHCH(79)
44     1480 1415 8.89 3.89 βHNC(47), βHCH(38)
45     1484 1418 8.37 3.79 βHCH RING +ETHANOL(80)
46     1488 1422 4.25 11.60 β HCH RING +ethanol(78)
47     1497 1431 2.72 3.58 βHCH(57), βNHC(21)
48 1445 1447 1503 1437 12.00 2.25 βHCH ring+ethanol(79)
49 1466 1466 1529 1467 3.27 3.71 βHCH ethanol(80)
50 2746   2882 2756 33.66 22.59 νCH(85)
51     2892 2765 145.72 153.17 νCH(83)
52 2879   3002 2870 49.82 112.65 νCH(78)
53     3035 29O2 56.89 88.98 νCH (88)
54     3036 2903 5.04 32.75 νCH(90)
55     3039 2905 36.3817 170.3565 νCH(95)
56     3041 2907 43.7761 48.6382 νCH(92)
57 2917   3059 2924 74.6573 50.1508 νCH(93)
58     3061 2924 32.5528 250.5377 νCH(96)
59 2946 2947 3089 2953 7.3905 122.6584 νCH(98)
60     3089 2953 46.2799 112.7917 νCH(98)
61     3088 2954 66.5198 10.9260 νCH(99)
62 3382   3504 3350 0.6450 73.0198 νNH(100)
63     3837 366 30.0620 164.2640 νOH(100)

(*) –The frequencies calculated for the most stable conformer at the B3LYP/6-31+(d,p)

Table 2: Observed and calculated vibrational frequencies of 2-(1-piperazinyl) ethanol by B3LYP/631+G (d,P).


Figure 2: Comparison of experimental and calculated FTIR and FTraman spectrum of 2-(1-piperazinyl) ethanol.

CH2 vibrations: For the assignments of CH2 group frequencies, basically six fundamentals can be associated with each CH2 group namely, CH2 symmetric stretch; CH2 asymmetric stretch; CH2 scissoring and CH2 rocking, which belongs to in-plane vibrations and two out-ofplane vibrations, viz., CH2 wagging and CH2 twisting modes, which are expected to be polarized. The asymmetric CH2 stretching vibrations are generally observed above 3000 cm-1, while the symmetric stretch will appear between 3000 and 2900 cm-1 [19].

The hetero aromatic compounds and its derivatives are structurally very close to benzene. The C-H stretching vibrations of the aromatic and hetero aromatic structures occur in the region 2800-3100 cm-1. This permits the ready identification of the structure. The C-H stretching vibrations are identified at 2954, 2953, 2924, 2907, 2905, 2903, 2902, 2870, 2765, 2756 cm-1. The CH2 bending vibrations are presented at 1461, 1436, 1431, 1422, 1418, 1412 cm-1. The out of-plane vibrations are also identified and the values are presented in the Table 2. The values of CH2 vibrations are good agreement with the experimental data and literature [15].

N-H vibrations: Hetero cyclic compounds containing an N-H group exhibit N-H stretching absorption in the region from 3500-3200 cm-1 [20]. Hence, the N-H stretching vibrations of the title compound identified at 3350 cm-1. The in-plane bending vibrations of HCN, HNC, are observed at 1291, 1415 cm-1. The out-of-plane bending vibrations are also calculated and tabulated in Table 2.

Ring vibrations

With the help of theoretical calculations, C-N, C-C vibrations are identified and assigned in this study. The heterocyclic compound Pyrimidine’s absorb strongly at 1600-1500 cm-1 due to the C=C and C=N ring stretching vibrations. Absorptions are also observed at 1640-1620 cm-1, 1580-1520 cm-1 1000-960 cm-1 and 875-775 cm-1 [21]. Hence, the title compound have the C-N stretching modes are calculated at 1043, 1094, 1094, 1130, 1140 cm-1. The calculated C-C stretching vibrations are predicted at 967,1191,1335 cm-1. Due to the electron with drawing effect of nitrogen in the ring and oxygen in ethanol, the force constant of C-C bond is decreased and so the stretching frequency is lowered. The in-plane vibrations of HCC, CCN, HCN, CNC, HNC are identified in the range 1158-1415 cm-1 and the other values are tabulated in Table 2.

C-O and O-H vibrations: The C-O stretching vibrations in alcohols and phenols produce a strong band near 1260-1000 cm-1 and sensitive to the nature of the substituent’s bonded to carbonyl carbon. For ethyl alcohol, the intense broad band near 3360 cm-1 represents the hydrogen bonded O-H stretching vibration and the weak intensity bands at 1330 and 1270 cm-1 exhibit O-H in plane bending and C-O stretching coupled vibrations. The broad absorption near 650 cm-1 is consistent with O-H out-of-plane bending vibration [22,23].

Hence the title compound, observed the calculated value of C-O stretching at 1014 cm-1. The O-H stretching frequency is predicted at 3368 cm-1 and in plane bending vibrations of COH, HOC, COH predicted at 1170,1305, 1386 cm-1 respectively. The C-O and O-H frequencies are good agreement with available data.

13C NMR and 1H NMR analysis: The isotropic chemical shifts are frequently used as an aid in identification of reactive organic as well as ionic species. It is recognized that accurate predictions of molecular geometries are essential for reliable calculations of magnetic properties. Gauge-independent atomic orbital (GIAO) 1H and 13C chemical shift values (with respect to TMS) were calculated using the DFT (B3LYP) method with 6-31+G(d,p) basis set and compared with experimental 1H and 13C chemical shift values. The results of this calculation are shown in Table 3 together with the experimental values. The result shows that the range of 1H and 13C NMR chemical shift of the typical organic molecule is usually >100 ppm [24,25] the accuracy ensures reliable interpretation of spectroscopic parameters.

Atoms Experimental B3LYP/6-31+G(d,p)
C16 58.04 51.00
C19 60.91 47.1
C7 54.54 45.24
C4 54.54 45.24
C10 45.83 39.87
C1 45.83 39.87
H20 3.63 4.007
H21 3.63 4.007
H17 2.52 3.203
H18 2.52 3.203
H3 2.89 3.108
H11 2.89 3.108
H12 2.89 2.87
H2 2.89 2.87
H5 2.48 2.74
H9 2.48 2.74
H8 2.48 2.48
H6 2.48 2.48
H14 - 0.554
H23 - 0.47

Table 3: Experimental and calculated 13C NMR and 1H NMR chemical shift (ppm) 2-(1-piperzinyl) ethanol.

The important aspect is that, hydrogen attached or nearby electron withdrawing atom or group can decrease the shielding and move the resonance of attached proton towards to a higher chemical shift. By contrast electron donating atom or group increases the shielding and moves the resonance towards to a lower chemical shift. In the present investigation, the chemical shift values calculated for hydrogen atom (with respect to TMS) are 4.007 to 0.47 ppm. Due to the electron withdrawing atom of N13 and O22 which decreases the chemical shift value for the hydrogen atom H14 and H23. The calculated 13C chemical shift values are ranging from (with respect to TMS) 51 to 39.87 ppm. Most of the 13C and 1H chemical shift results match with the experimental data.

Frontier molecular orbitals

The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular (LUMO)are named as frontier molecular orbitals (FMO). The FMOs plays an important role in the optical and electrical properties, as well as in quantum chemistry [26]. 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 the molecule [27-31]. In order to evaluate the energetic behavior of the title compound, the HOMO and LUMO energy gap was calculated at the B3LYP/6-31+G(d,p) level, which reveals that the energy gap reflects the chemical activity of the molecule. The energies of four important molecular orbitals of the title compound in gas: the second highest and highest occupied MO’s (HOMO and HOMO-1), the lowest and the second lowest unoccupied MO’s (LUMO and LUMO+1) were calculated. The calculated energy value of HOMO is -5.7044 eV and LUMO is -0.2019 eV in gaseous phase. The value of energy separation between the HOMO and LUMO is 5.5022 eV explains the eventual charge transfer interaction within the molecule, which influences the chemical reactivity of the molecule. The calculated HOMO and LUMO energy values are presented in the Table 4. Consequently, the lowering of the HOMO- LUMO band gap is essentially a consequence of the large stabilization of the LUMO due to strong electron-acceptor ability of the electron group. Other quantum descriptors like electronegativity (χ), chemical hardness (η), electrophilicity (ψ) and softness (ζ) of 2-(1-piperazinyl)ethanol are 5.6035, -5.8053, -0.9652, 0.8612 eV respectively, for the title molecule. The HOMO and LUMO energy diagram is shown in the Figure 3.

 Parameters B3LYP/6-31+G(d,p)
HOMO -5.7044
LUMO -0.2019
HOMO-1  -6.3703
LUMO+1 -0.1801
HOMO-LUMO 5.5022

Table 4: HOMO-LUMO energy calculated by B3LYP/6-31+G (d,p) for 2-(1-piperzinyl)ethanol.


Figure 3: HOMO and LUMO plot of 2-(1-piperazinyl) ethanol.

Analysis of molecular electrostatic potential (MESP), Mulliken atomic charges

The molecular electrostatic potential surface (MESP) is a method of mapping electrostatic potential onto the iso-electron density surface simultaneously displays electrostatic potential (electron+nuclei) distribution, molecular shape, size and dipole moments of the molecule and it provides a visual method to understand the relative polarity. Electrostatic potential maps illustrate the charge distributions of molecules three dimensionally. These maps allow us to visualize variably charged regions of a molecule. Knowledge of the charge distributions can be used to determine how molecules interact with one another. One of the purposes of finding the electrostatic potential is to find the reactive site of a molecule. In the electrostatic potential map, the semi-spherical blue shapes that emerge from the edges of the above electrostatic potential map are hydrogen atoms [31]. The molecular electrostatic potential (MEP) at a point r in the space around a molecule (in atomic units) can be expressed as

equation (1)

Where, ZA is the charge on nucleus A, is the electronic density function for the molecule. The first and second terms represent the contributions to the potential due to nuclei and electrons, respectively. V(r) is the resultant at each point r, which is the net electrostatic effect produced at the point r by both the electrons and nuclei of the molecule. The total electron density and MESP surfaces of the molecules under investigation are constructed by using B3LYP/6- 31+G(d,p) method. The electrostatic potential increases in the order redFigure 4 shows the molecular electrostatic potential surface of (2-(1-piperazinyl) ethanol. Local negative electrostatic potential (red) signal indicates in the O22 and N13 atoms whereas local positive electrostatic potentials (blue) signal indicates in the H23 in ring. Green areas cover parts of the molecule where electrostatic potentials are close to zero (C–C bonds). GAUSSVIEW 5.0.8 visualization program has been utilized to construct the MESP surface.


Figure 4: Molecular electrostatic potential of 2-(1-piperazinyl) ethanol.

The Mulliken atomic charge calculation has an impotent role in the application of quantum chemical calculations to molecular system [28,29] because of atomic charges effect dipole moment, molecular polarizability, electronic structure and more a lot of properties of molecular system. The charge distribution over the atoms suggests the formation of donor and acceptor pairs involving the charge transfer in the molecule. The Mulliken population analysis in 2-(1-piperaziniyl) ethanol was calculated using B3LYP level6-31+G (d,p) basis set and are listed in Table 5. All the carbon atoms are having the negative value due to the attachment of the nitrogen and oxygen atoms (N13, N15 and O22). The hydrogen atom H14 and H23 near to N13 and O22 atoms accommodate higher positive charge than the other hydrogen atoms. This is due to presence of electronegative nitrogen and oxygen atoms, the hydrogen atom attract the positive charge from the nitrogen and oxygen atoms.

Atoms Mulliken charges Atomic charges
C1 -0.289 -0.29055
H2 0.132 0.24053
H3 0.152 0.23699
C4 -0.162 -0.27939
H5 0.138 0.24457
H6 0.120 0.19444
C7 -0.162 -0.27939
H8 0.120 0.19444
H9 0.130 0.24457
C10 -0.289 -0.29055
H11 0.152 0.23700
H12 0.132 0.24053
N13 -0.426 -0.71303
H14 0.290 0.38740
N15 -0.124 -0.55738
C16 -0.251 -0.28235
H17 0.147 0.24603
H18 0.148 0.24603
C19 -0.017 -0.13711
H20 0.124 0.20036
H21 0.124 0.20036
O22 -0.528 -0.78573
H23 0.346 0.50218

Table 5: Mulliken atomic charge and natural atomic charges of 2-(1-piperazinyl) ethanol.

NBO analysis

The natural bond orbital (NBO) calculations were performed using NBO 3.1 program [23] as implemented in the Gaussian 09 package at the DFT/B3LYP level in order to understand various second-order interactions between the filled orbital of one subsystem and vacant orbital of another subsystem, which is a measure of the intermolecular delocalization or hyperconjucation. A useful aspect of the NBO method is that it gives information about interactions of the both filled and virtual orbital spaces that could enhance the analysis of intra molecular interactions.

The second order Fock-matrix was carried out to evaluate the donor –acceptor interactions in the NBO basis. The interactions result in a loss of occupancy from the localized NBO of the idealized Lewis structure into an empty non-Lewis orbital. For each donor (i) and acceptor (j) the stabilization energy (E2) associated with the delocalization i→j is determined as qi donor orbital occupancy, Ei, Ej, diagonal elements, Fij, the off diagonal NBO Fock Matrix element.

equation (2)

In NBO analysis large E (2) value shows the intensive interaction between electron donor and electron acceptors and greater the extent of conjugation of the whole system, the possible intensive interactions are given in the Table 3. The second order perturbation theory analysis of Fock matrix in NBO basis shows strong intra-molecular hyper conjugative interactions of σ electrons.

The strong intra-molecular hyper conjugative interaction of C1-C4 and C7-C10 from of N13, C4-H6, C7-H8 and C16-C19 from of N15 and also C19-H20 C19-H21 from of O22 of which increases ED that weakens the respective bonds leading to the stabilization of ~7.81, 9.28 and 5.74 kcal mol-1 respectively.

UV-spectral analysis

All the structures allows strong π→π* or σ→σ* transition in the UVvisible region with high extinction coefficients. TD-DFT/B3LYP/6- 31+G(d,p) calculations have been used to determine the low-lying excited states of 2-(1-piperazinyl) ethanol. The calculated results involving the vertical excitation energies, oscillator strength (f) and wavelength are carried out and it can be seen in Table 6. The calculated absorption maxima values for 2-(1-piperazinylethanol) have been found to be 255.84, 242.88 and 232.16 nm. The oscillator strength for 232.16 is higher in magnitude. These three absorption bands are mainly derived from the contribution of bands due to π→π* transitions. The theoretical spectrum of UV-VIS is shown in Figure 5.

TD DFT/B3LYP/6-31+G(d,p)
Wave length λ (nm) Excitation energy (eV) Oscillator strength (f)
232.16 5.3406 0.0225
242.88 5.1048 0.0094
255.84 4.8461 0.0164

Table 6: Theoretical electronic absorption spectra value of 2-(1-piperazinyl) ethanol.


Figure 5: Theoretically calculated UV-vis spectrum of 2-(1-piperazinyl) ethanol.

Polarizability and first order hyperpolarizability

In order to investigate the relationships among molecular structures and nonlinear optical properties (NLO), the polarizibilities and first order hyperpolarizibilities of the 2-(1-piperazinylethanol) compound was calculated using DFT/B3LYP method with 6-31+G (d,p) basis set, based on the finite field approach

The polarizability and hyper polarizability tensors (αxx, αxy, αyy, αxz, αyz, αzz and βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz, βyzz, βzzz) can be obtained by a frequency job output file of Gaussian. The mean polarizability (αtot), anisotropy of polarizability (Δα) and the average value of the first order hyperpolarizibilities (βtot) can be calculated using the equations.

αtot =α xx+αyyzz/3 (3)



In Table 7, the calculated parameters described above and electronic dipole moment μi(i=x,y,z) and the total dipole moment μ for the title compound are listed. The total dipole moment can be calculated using the following equation.

equation (6)

It is well known that the higher values of dipole moment, molecular polarizibility and first order hyper polarizability are important for more active NLO properties. The first order hyper polarizability (βtot) and the component of hyper polarizability βx, βy, βz of 2-(1-piperazinylethanol) along with the related properties (μ, αtot, Δα) are reported in Table 7. The calculated value of dipole moment was found to be 1.3549 Debye. The highest value of dipole moment is observed at 0.5692 Debye for component μx and the lowest value of the dipole moment is observed at -0.7781 Debye for component μz. The calculated polarizibility and anisotropy of polarizability 2-(1-piperazinylethanol) are 13.6492 × 10-24 e.s.u and 26.056 × 10-24 e.s.u., respectively. The magnitude of the molecular hyperpolarizibility (β) is one of the key factors in a NLO system. The B3LYP/6-31+G(d,p) calculated first order hyper polarizability (βtot) value of 2-(1-piperazinylethanol) is equal to 1.499 × 10-30 e.s.u, which is 11.5 times that of urea (0.13 × 10-30 e.s.u) [32]. This result clearly indicates that the title compound is a strong candidate to develop a nonlinear optical material.

Parameters Values
µx 0.5692
µy -0.3034
µz -0.7781
µtot 1.3549
αxx 101.2163
αxy -1.4535
αyy 88.8266
αxz 8.2137
αyz -2.6602
αzz 86.2593
αtot 13.49×10-24e.s.u
Δα 3240.33
βxxx 42.1762
βxxy -9.8546
βxyy 4.8639
βyyy -31.615
βxxz -12.9023
βxyz -8.7636
βyyz -41.5162
βxzz 4.4543
βyzz -4.1116
βzzz -105.0195
βtot 259.79×10-30 e.s.u

Table 7: Electric dipole moment μ (debye), mean polarizibilityαtot (× 1024 e.s.u), anisotropy polarizibility βtot(× 1030 e.s.u) for 2-(1-piperazinyl) ethanol.


The geometrical parameters of the optimized structure were studied in detail and the influence of the substituted groups is explained. The vibrational frequency analysis by B3LYP method agrees satisfactorily with experimental results. On the basis of calculated potential energy distribution result, assignments of the fundamental vibrational frequencies have been made unambiguously. The HOMOLUMO energy gap and other related molecular properties were discussed and reported. The value of energy gap indicates that it is a good chemical reactive molecule. NBO study reveals that the lone pair orbital participates in electron donation to stabilize the compound. The MEP study shows that the electrophilic attack takes place at the N13 and O22 position of the title compound. The Mulliken atomic charges and natural atomic charges obtained are tabulated that gives the proper understanding of the atomic theory. Thus the present investigation provides complete vibrational assignments, structural information properties of the compound, 1H and 13C NMR chemical shifts values satisfactorily coincide with experimental results. The UV data indicated that the electronic transition in the compound has π-π* transitions. The values of dipole moment (μtot), linear polarizability (αtot) and first-order hyperpolarizability (βtot) of the molecule were calculated. It has been found that the value of first-order hyperpolarizability is 11.5 times greater than that of urea, which shows that the molecule is a good NLO material.


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Citation: Mekala R, Mathammal R, Sangeetha M (2015) Theoretical Investigation of the Molecular Structure, Vibrational Spectra, NMR, UV, NBO Analysis, Homo and Lumo Analysis of 2-(1-Piperazinyl)Ethanol J Theor Comput Sci 2:127.

Copyright: © 2015 Mathammal R, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.