Structural, spectroscopic and nonlinear optical properties of sulfonamide derivatives; experimental and theoretical study

Article abstract of DOI:10.1016/j.molstruc.2019.127393

Nonlinear optical (NLO) materials have broad range applications in the field of optoelectronic devices. Nowadays great interest has been developed for synthesizing the compounds having high NLO response. Herein we are reporting the structural, spectroscopic and NLO properties of two, structurally simple sulfonamide derivatives. Both compounds are synthesized in respectable yields, characterized by using NMR (¹H and ¹³C), FT-IR and UV–vis spectroscopic techniques. X-ray diffraction analysis confirmed the final structures. Density functional theory (DFT) at B3LYP/6-31G(d,p) method are performed for validation of experimental data (X-ray as well as spectroscopic data). Absorption studies of both compounds are performed by using TD-DFT method. Coefficients of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of both compounds reflect the high stability. First hyperpolarizability (β_o), polarizability (α_o) and dipole moment (μ) analyses calculated at LC-BLYP method revealed that both derivatives have reasonable nonlinear optical (NLO) response. The static, dc-Kerr effect and electric field-induced second harmonic generation (ESHG) hyperpolarizability co-efficient are also studied for refractive index (n₂) calculation of both sulfonamides, to further observe their NLO response.

Full text of DOI:10.1016/j.molstruc.2019.127393

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Structural, spectroscopic and nonlinear optical properties of sulfonamide derivatives;
experimental and theoretical study
Muhammad Nadeem Arshad, Hassan M. Faidallah, Abdullah M. Asiri, Naveen Kosar,
Tariq Mahmood
PII:
S0022-2860(19)31502-9
DOI:
https://doi.org/10.1016/j.molstruc.2019.127393
MOLSTR 127393
Reference:
To appear in: Journal of Molecular Structure
Received Date: 22 September 2019
Revised Date: 6 November 2019
Accepted Date: 8 November 2019
Please cite this article as: M.N. Arshad, H.M. Faidallah, A.M. Asiri, N. Kosar, T. Mahmood, Structural,
spectroscopic and nonlinear optical properties of sulfonamide derivatives; experimental and theoretical
study, Journal of Molecular Structure (2019), doi: https://doi.org/10.1016/j.molstruc.2019.127393.
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Structural, Spectroscopic and Nonlinear Optical Properties of Sulfonamide
Derivatives; Experimental and Theoretical Study
a,b
b,c
a,b*
d
Muhammad Nadeem Arshad , Hassan M. Faidallah , Abdullah M. Asiri , Naveen Kosar ,
d
Tariq Mahmood *
a
Chemistry Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203,
Jeddah 21589, Saudi Arabia
b
Centre of Excellence for Advanced Materials Research (CEAMR), King Abdulaziz University,
P. O. Box 80203, Jeddah 21589, Saudi Arabia
c
Department of Chemistry, Faculty of Science, Alexandria University, Alexandria, Egypt
d
Department of Chemistry, COMSATS University Islamabad, Abbottabad Campus,
Abbottabad-22060, Pakistan
*
To whom correspondence can be addressed: E-mail: mahmood@cuiatd.edu.pk (T. M) and
aasiri2@kau.edu.sa (A. M. Asiri)
1

Abstract
Nonlinear optical (NLO) materials have broad range applications in the field of optoelectronic
devices. Nowadays great interest has been developed for synthesizing the compounds having
high NLO response. Herein we are reporting the structural, spectroscopic and NLO properties of
two, structurally simple sulfonamide derivatives. Both compounds are synthesized in respectable
1
13
yields, characterized by using NMR ( H and C), FT-IR and UV-vis spectroscopic techniques.
X-ray diffraction analysis confirmed the final structures. Density functional theory (DFT) at
B3LYP/6-31G(d,p) method are performed for validation of experimental data (X-ray as well as
spectroscopic data). Absorption studies of both compounds are performed by using TD-DFT
method. Coefficients of the highest occupied molecular orbital (HOMO) and the lowest
unoccupied molecular orbital (LUMO) of both compounds reflect the high stability. First
hyperpolarizability (β ), polarizability (α ) and dipole moment (µ) analyses calculated at
o
o
LC-BLYP method revealed that both derivatives have reasonable nonlinear optical (NLO)
response. The static, dc-Kerr effect and electric field-induced second harmonic generation
(
ESHG) hyperpolarizability co-efficient are also studied for refractive index (n ) calculation of
2
both sulfonamides, to further observe their NLO response.
Keywords: Nonlinear optical (NLO); X-ray; Density Functional Theory (DFT); Sulfonamide
2

1
. Introduction
Nonlinear optics (NLO) includes the interactions of different frequencies (including frequency
doubling and tripling) of light with a material [1–3]. NLO materials have profound applications
in optical and electro-optical devices such as optical data storage, optical signal processing,
optical communication, optical data processing devices [4–7], for all-optical data conversion [8],
format switching [9] and wavelength/sign conversion [10]. The study of NLO response
(hyperpolarizabilities) of organic compounds is an interesting topic and has attained the attention
of researchers since last one decade [11,12]. The interest in organic compounds having high
NLO response, have attracted considerable attention because of their ease of synthesis, stability
and usefulness as advance NLO materials. Firstly, the NLO response of organic compounds was
reported by Davydov and colleagues in 1970s [13]. Afterward, large number of organic
compounds have been explored for their linear and nonlinear optical properties, both
experimentally as well as theoretically [14–16].
Since last two to three decades, sulfonamide containing compounds have been used on large
scale in as medicines and various materials applications. Major biological applications are to use
for the treatment of urinary tract infections, antitumor, anticarbonic anhydrase, diuretic,
hypoglycemic, antithyroid, and as protease inhibitor drugs [17–20]. Besides biological activities,
sulfonamide are also used as herbicides and anti-convulsant agents for potential agrochemical
applications [21,22]. Laurent et al. synthesized sulfonamide functionalized protonic conductors
for their potentials applications as coatings, layers or separators membranes in film batteries and
fuel cells under humid conditions [23,24]. Recently, sulfonamides and their derivatives are also
studied both experimentally as well theoretically as NLO materials due to their uneven
3

distribution of electronic density on the entire skeleton [24–26].
Computer-based methods have gained valuable attention not only to validate the experimental
results, but also to understand the structural insight of different types of materials. DFT based
methods are one of the most commonly used methods in computational chemistry those not only
explain experimental investigations, but also serve as valuable tool to explore some
experimentally unexplored areas. In continuation of our previous work of synthesis structural
properties of different scaffolds [27–30], here in we are reporting the synthesis, structural
properties and NLO properties of two structurally simple benzene derived sulfonamide
derivatives 1 and 2 (Scheme 1). Both compounds are synthesized in good yields and structures are
characterized by various spectroscopic as well as single crystal diffraction studies. DFT
investigations are performed in order to validate not only the spectroscopic as well as X-ray
results, but also to investigate the frontier molecular orbital analysis (electronic properties), and
nonlinear optical (NLO) properties.
2
. Experimental
2
.1 Material and methods
All chemicals and solvents (analytical grade) were purchased from Sigma aldrich, Across
organic and used directly without purification. Melting points were measured in open glass
capillaries by using Stuart Scientific (SMP3, version 5.0, UK) melting point apparatus, and
reported as uncorrected. FT-IR spectra were monitored on Thermo Scientific NICOLET iS 50
4

1
13
FT-IR spectrometer (Thermo Scientific) as neat samples. NMR spectra ( H and C-NMR) were
recorded on Bruker-AVANCE-III 600 MHz at 300 K, by using DMSO-d6 as solvent and
tetramethylsilane as an internal standard. Reaction progress was monitored by thin layer
chromatography (TLC) on silica gel-protected aluminum sheets (Type 60 F254, E. Merck).
Density Functional Theory (DFT) studies were simulated by using the Gaussian 09 software
package.
2
.2 Synthesis
Synthesis of both compounds (1 and 2) was performed by adopting the slightly modified
procedure already reported in the literature [31], and synthetic scheme is shown in the Scheme 1.
Scheme 1 Synthetic scheme; Sodiumacetate, Acetylanhydride (1) and Sodiumacetate,
2
-methylpropanoicanhydride (2)
2
.2.1 N-((4-acetamidophenyl)sulfonyl)acetamide (1)
A mixture of sulfanilamide (4-aminobenzenesulfonamide) (1.72g, 10mmol), sodium acetate (10
5

mmol) and the aceticanhydride (20 mmol) was refluxed for 4 hours in a round bottom flask. The
reaction mixture was cooled up to room temperature, and precipitates formed were filtered off,
washed with cold water and recrystallized from ethanol (slow evaporation method) as needles to
-1
obtain (1) in 77 % yield; m. p. 260 ～262 ºC; FT-IR (neat, cm ): 3556, 3438, 3088, 3028, 1702,
1
5
7
1
662, 1584, 1533, 1461, 1401, 1369, 1321, 1240, 1234, 1153, 1089, 998, 834, 713, 614, 612,
1
36; H-NMR (DMSO-d6, ppm): 11.96 (1H, b, NH), 10.37 (1H, b, NH), 7.82 (2H, aromatic),
13
.76 (2H, aromatic), 2.07 (3H, CH ), 1.89 (3H, CH ), C-NMR (DMSO, ppm): 169.1, 168.6,
3
3
43.7, 132.6, 128.8, 118.3, 79.1, 24.1, 23.1; UV-vis, λmax (DMSO) 267 nm, (MeOH) 260 nm.
-1
Crystal data: C H O SN , M = 256.28 g·mol , colorless needles, 0.29 mm × 0.14 mm × 0.08
1
0
12
4
2
r
o
mm, monoclinic, space group P2 /n, a = 8.2492(3), b = 8.1330(3), c = 17.4819(6) Å, α = 90.00 ,
1
o
o
3
-3
ß = 95.308(3) , γ = 90.00 , V = 1167.84(7) Å , Z = 4, D = 1.458 g·cm , F(000) = 536.0, CuKα
c
radiation, λ = 1.54 Å, T = 296.15 K, 2θmax = 10.16 to 153.16°, 7509 reflections collected,
2
376[R(int) = 0.0188], final GOOF = 1.034, R = 0.043, wR = 0.121, R indices based on 1998
2
-1
reflections with I > 2σ(I) (refinement on F ) 165 parameters, µ = 2.548 mm .
2
.2.2 N-(4-sulfamoylphenyl)isobutyramide (2)
A mixture of sulfanilamide (1.72 g, 10 mmol), sodium acetate (10 mmol) and the
-methylpropanoic anhydride (10 mmol) was refluxed for 4 hours in a round bottom flask. Then
2
mixture was cooled up to room temperature, precipitates formed were filtered, washed with cold
water and recrystallized from ethanol as needles under slow evaporation method to obtain 2 in
-1
8
1 % yield; m. p. 248 ～ 249 ºC). FT-IR (neat, cm ): 3460, 3360, 3230, 1670, 1630, 1590,
6

1
1
530, 1500, 1400, 1300, 1250, 1140, 1090, 891, 823, 677, 532; H-NMR (DMSO, ppm): 10.14,
(
1H, b, NH), 7.71-7.75 (4H, m, aromatic), 7.22 (2H, b, NH ), 1.10 (3H, CH ), 1.09 (3H, CH ),
2
3
3
1
3
C-NMR (DMSO, ppm): 175.7, 142.3, 138.0, 126.5, 118.5, 34.9, 19.3, UV-vis, λmax (DMSO)
2
67 nm, (MeOH) 262 nm.
-1
Crystal data: C H N O S, M = 242.29 g·mol , colorless needles, 0.29 mm × 0.25 mm × 0.15
1
0
14
2
3
r
mm, monoclinic, space group P2 /c, a = 8.4150(3), b = 13.7325(4), c = 9.9907(4)Å, ß =
1
o
3
-3
9
1
3.111(3) , V = 1152.81(7)Å , Z = 4, D = 1.396 g·cm , F(000) = 512.0, CuKα radiation, λ =
c
o
.54 Å, T = 296.15 K, 2θmax = 152.9 , 13247 reflections collected, 2426 unique (R = 0.018),
int
Final GOOF = 1.041, R = 0.034, wR = 0.0955, R indices based on 2283 reflections with I > 2σ(I)
2
-1
(
refinement on F ) 156 parameters, µ = 2.476 mm .
2
.3 Crystallography
Single crystals of suitable sizes of each sample were selected under microscope. The crystals
were mounted on Agilent SuperNova (Dual source) Agilent Technologies Diffractometer, having
graphite-monochromatic Cu/Mo Kα radiation source. The data was collected by using
CrysAlisPro software [32] at 296 K. The final structure was solved with the help of SHELXS–
2
9
7, and refined by using full–matrix least–squares methods on F using SHELXL–97 [33],
in-built with X-Seed [34].
Aromatic hydrogens were positioned geometrically and treated as riding atoms with C–H =
0
.93Å and Uiso(H) = 1.2 Ueq(C) carbon atoms. Similarly, the methyl and methine hydrogens
were also positioned geometrically with Cmethyl-H = 0.96Å and Cmethine-H = 0.98Å. The N-H =
7

0
.76(3) ~ 0.92(2)Å, hydrogen was located by using difference fourier map and refined using
riding model with Uiso (H) = 1.2 Ueq(N).
The CIF files of sulfonamide 1 and 2 have been assigned CCDC numbers 1422690 and 1422691,
respectively, can be obtained free of cost on demand to CCDC 12 Union Road, Cambridge
CB21 EZ, UK. (Fax: (+44) 1223 336-033: data_request@ccdc.cam.ac.uk).
2
.4 Computational methods
All computational studies were performed with the help of Gaussian 09 software [35].
Geometries/graphics were analyzed by using GaussView 5.0 program [36]. The minimum
energy structures of both sulfonamides (1 and 2) were optimized by adopting B3LYP/6-31G (d,
p) method, and frequency analysis is performed at the same method for confirmation of true
optimization. Nuclear magnetic resonance chemical shifts were calculated by using
B3LYP/6-311+G (2d, p) method and tetramethylsilane is used as internal reference standard.
UV-vis absorption studies were simulated with the the help of time delay DFT method at
B3LYP/6-31G (d, p) level of theory. Frontier molecular orbitals (FMOs). LC-BLYP (long-range
corrected BLYP), is used for calculation of dipole moment, polarizability (α ) and first
o
hyperpolarizability (β ) as this method provides excellent balance between computational cost
o
and accuracy. This functional is known to perform well for the investigation of NLO properties
of organic and inorganic compounds [37,38].
3
. Results and discussion
8

Condensation of commercially available 4-aminobenzenesulfanilamide with anhydrides
aceticanhydride for and 2-methylpropanoic anhydride for 2) afforded
(
1
N-((4-acetamidophenyl)sulfonyl) acetamide (1) and N-(4-sulfamoylphenyl)isobutyramide (2) in
good yields. After accomplishing the successful synthesis, both sulfonamides are characterized
1
13
by different spectroscopic techniques ( H and C NMR, FT-IR and UV-vis.), and finally the
structures are confirmed by single crystal X-ray diffraction studies. DFT studies are performed
not only to validate the spectro-analytical results, but also to investigate the detailed structural
properties including NLO and FMOs analyses.
3
.1 Crystal structure descriptions
The ORTEP diagrams of both compounds 1 and 2 are shown in Fig. 1. Both are para-amino
substituted benzene sulfonamide derivatives, where “S” atom adopted distorted tetrahedral
o
o
geometry having O-S -O angle 119.17(1) and 118.73(7) for 1 and 2 respectively. The S -N
1
1
bond length is found with a small difference in both 1 and 2, and it is 1.64 (2) and 1.61 (2)
respectively, and these are in range as per described by Allen et al [39].
The unit cell diagrams of both sulfonamides 1 and 2 are shown in the Fig. 2, and hydrogen bond
parameters are given in Table 1. In compound 1, N-H…O hydrogen bonding interaction
connected the molecules in infinite two-dimensional networks along the plane (010). Individually,
the amido group is involved in N1-H…O4 interactions which formed an infinite chain along (1 0
0
) base vector whereas sulfonamide N2-H…O1 connected the molecule along (0 0 1) base vector
9

in a zig-zag manner. These two interactions connected the molecules to form twentyeight
4
membered ring motifs R (8) [40]. On the other hand C -H …O non-classical hydrogen bonding
4
3
3
2
4
4
formed the inverted dimers and generated ten membered ring motifs R (10)[40] and further these
dimers are connected through another C5-H5…O3 interaction to form infinite chain Fig. 2.
The packing diagram of 2 having isopropyl group over one of nitrogen atom did not show any
non-classical hydrogen bonding interaction. All donor-acceptor atoms are involved in N-H…O
type hydrogen bonding interaction to stabilize the crystal structure. The NH and carbonyl groups
2
(
N -H …O ) are involved in formation of inversion dimers and generated twenty membered ring
2 2N 1
1
1
motifs R (20) [40]. On the other hand the contacts (N -H …O ) and (N -H …O ) formed the
1
1N
2
2
3N
3
infinite long chains along b and c axes respectively (Fig. 2).
1
2
Figure 1: ORTEP diagrams of both sulfonamides 1 and 2
1
0

(1)
(2)
Figure 2: A Unit cell view of 1 and 2 showing intermolecular hydrogen bonding using dashed
lines.
Table 1 Hydrogen-bond Parameters of 1 and 2 (Å, ˚) (Atomic labels are with reference to ORTEP
plot, Fig. 2).
1
D H
A
d(D-H)/Å
0.93
d(H-A)/Å
2.56
d(D-A)/Å
3.166(3)
3.161(3)
2.813(2)
3.014(3)
D-H-A/°
123.2
1
2
3
4
C3 H3 O2
C5 H5 O3
N2 H2N O1
N1 H1N O4
0.93
2.43
135.5
0.76(3) 2.05(3)
172(3)
176(3)
0.82(3) 2.20(3)
1
Symmetry codes ; -X,
2
3
4
1-Y,-Z; 1/2-X,-1/2+Y,1/2-Z; -1/2+X,1/2-Y,1/2+Z; 1+X,+Y,+Z
2
1
N1 H1N O2
N2 H2N O1
N2 H3N O3
0.79(3) 2.21(3)
0.79(3) 2.14(3)
3.0054(17)
2.9192(19)
176(2)
169(2)
165(2)
2
3
0.80(3) 2.18(3)
2.9560(18)
1
2
3
Symmetry codes : 1-X,-1/2+Y, 3/2-Z; -X, 1-Y,1-Z; +X,3/2-Y,1/2+Z
11

3
.2 Geometry optimization
In order to compare and validate the X-ray results, the geometries of sulfonamides 1 and 2 are
optimized at by using B3LYP/6-31G (d, p) method and shown in Fig. 3. The comparison of
some important bond lengths and bond angles with X-ray data is given in Table 2 and Table 3. It
is clear from the data narrated in Tables that there is a slight difference in bond lengths and bond
angles in the optimized and X-ray geometries of both compounds (1 and 2). These slight
differences are due to the variance in molecular states during the experimental and theoretical
studies.
The difference in the selected X-ray and simulated bond lengths/bond angles for compound 1 is
o
found in the range 0-0.042Å/0.09-7.95 . For compound 2, difference in bond lengths/bond
o
angles is in the range of 0.001-0,074 Å/0.02-4.41 . The prominent bond lengths of 1, like S1–
O2, S1–O3, S1–N2, S1–C4, O1–C7, O4–C9, N1–C1, N1–C7 and N2-C9 experimentally found
1
.42, 1.42, 1.64, 1.75, 1.22, 1.21, 1.40, 1.35 and 1.37Å, respectively. Their theoretical
counterparts appeared at 1.46, 1.45, 1.73, 1.78, 1.21, 1.21, 1.40, 1.36 and 1.40Å, respectively.
Similarly, the experimental values of prominent bond lengths in sulfonamide 2, like S1–O2, S1–
O3, S1–N2, S1–C4, O1–C7, N1–C1, N1–C7 and C1–C2 found 1.43, 1.43, 1.61, 1.76, 1.21, 1.40,
1
.35 and 1.39Å, respectively. The theoretical values of same bonds in 2 are 1.46, 1.46, 1.65, 1.79,
1
.22, 1.40, 1.38 and 1.40Å, respectively.
The experimental values of prominent bond angles in 1, like O2–S1–O3, O2–S1–N2, O2–S1–C4,
O3–S1–N2, O3–S1–C4, N2–S1–C4, C7–N1–C1, C9–N2–S1 and C2–C1–N1 are 119.1, 109.5,
o
1
09.4, 103.1, 108.6, 106.0, 129.0, 123.7 and 124.4 , respectively. The theoretical values of same
1
2

o
bond angles are 121.7, 109.1, 108.3, 107.7, 109.1, 98.1, 128.9, 122.2 and 123.1 , respectively
and corroborated nicely with the experimental results. Again in 2 all prominant bond angles
show excellent correlataion both experimentallly as well as theoretically (Table 3, for detailed
values).
1
2
Figure 3: Optimized geometries of both sulfonamides 1 and 2
1
3

Table 2: Some selected X-ray and simulated bond lengths (Å) of 1 and 2 (Atomic labels are with
reference to ORTEP plot, Fig. 2).
(
1)
X-ray
Calc.
(2)
X-ray
Calc.
(B3LYP)
(B3LYP)
S1–O2
S1–O3
S1–N2
S1–C4
O1–C7
O4–C9
1.42 (18)
1.42 (2)
1.64 (2)
1.75 (2)
1.22 (3)
1.21 (3)
1.46
1.45
1.73
1.78
1.21
1.21
S1–O2
S1–O3
S1–N2
S1–C4
O1–C7
N1–C1
1.43 (11)
1.43 (11)
1.61 (15)
1.76 (13)
1.21 (2)
1.46
1.46
1.65
1.79
1.22
1.40
1.40 (18)
N1–C1
N1–C7
N2-C9
1.40 (3)
1.35 (3)
1.37 (3)
1.40
1.36
1.40
N1–C7
C1–C2
1.35 (19)
1.39 (19)
1.38
1.40
Table 3 Some selected X-ray and simulated bond angles (°) of 1 and 2 (Atomic labels are with
reference to Fig. 2).
(
1)
X-ray
Calc.
B3LYP)
(2)
X-ray
Calc.
(B3LYP)
123.1
105.3
107.5
105.4
107.2
107.2
(
O2–S1–O3 119.1 (13)
O2–S1–N2 109.5 (12)
109.4 (10)
O3–S1–N2 103.1 (11)
121.7
109.1
108.3
107.7
109.1
98.1
O2–S1–O3
O2–S1–N2
O2–S1–C4
O3–S1–N2
O3–S1–C4
N2–S1–C4
118.7 (7)
106.8 (7)
107.5 (7)
106.7 (8)
107.9 (7)
108.7 (7)
O2–S1–C4
O3–S1–C4
N2–S1–C4
108.6 (12)
106.0 (10)
C7–N1–C1 129.0 (19)
C9–N2–S1 123.7 (16)
C2–C1–N1 124.4 (18)
128.9
122.2
123.1
C7–N1–C1 128.8 (13) 128.8
C2–C1–N1 117.3 (12) 117.1
C6–C1–N1 123.6 (12) 123.3
3
.3 Vibrational studies
Vibrational spectroscopic analysis is a vital tool for identification of different functional groups
present in the organic compounds. Combined experimental (measured as neat) and simulated
1
4

vibrational spectra of both sulfonamides 1 and 2 are shown in the Fig. 4. A comparison of the
characteristic vibrations is given in Table 4.
-1
For minimization of the oretical errors, the vibrations above 1700 cm are scaled by using
-1
scaling factor of 0.958 and less than 1700 cm are scaled by using scaling factor 0.9627 [41].
The title sulfonamides (1 and 2) mainly have NH, C=O, S=O and aromatic ring functional
groups and excellent correlation is observed among simulated and experimental values.
0
Theoretical IR
200
400
600
800
Practical IR
1
1
1
1
000
200
400
600
4000
3000
2000
1000
0
-
1
Wavenumber cm
0
Theoretical IR
200
400
600
800
Practical IR
1
1
1
1
000
200
400
600
4000
3000
2000
1000
0
-
Wavenumber (cm )
1
Figure 4: Combine experimental and theoretical FT-IR spectra of 1 (above) and 2 (below).
3
.3.1 NH, NH Vibrations
2
As it is clear from crystal structure that compound 1 has only NH and 2 has NH and NH2
functional groups. The NH stretching vibrations usually appears as weak band at 3100-3300
1
5

-1
-1
-1
cm . Experimental spectra of both compounds showed NH vibration at 3556 cm , 3438 cm .
The downfield shift is observed due to involvement NH groups in hydrogen bonding, which is
also confirmed from crystal structure packing diagram (Fig. 2). On the other hand, the calculated
-1
NH vibrations of both appeared in the range of 3200-3500 cm [42].
The simulated spectra of compound 2, showed NH symmetric and asymmetric stretching
2
-1
-1
vibration at 3423 cm and 3305 cm and these simulated NH vibrations correlated nicely with
2
-1
the experimental value that appeared at 3360 cm .
3
.3.2 Aromatic vibrations
-1
-1
Aromatic CH appear between 3000-3200 cm (stretching) and 1300-1600 cm (stretching and
bending) [43], respectively. Weak aromatic CH stretching vibrations of both compounds in
-1
-1
simulated spectrum appeared in the range 3071-2984 cm (1), 3070-2980 cm (2) which are in
good agreement with the experimental values. The simulated spectrum of compound 1 showed
-1
-1
-1
-1
symmetric/asymmetric C=Carom. vibrations at 1589 cm , 1575 cm , 1496 cm , 1385 cm , 1290
-1
cm , whereas in 2, these symmetric/asymmetric C=C
stretching vibrations appeared at 1590
arom
-1
-1
-1
-1
-1
cm , 1501 cm , 1478 cm , 1385 cm and 1298 cm . These stretching vibrations are in
-1
-1
excellent correlation with the experimental counterparts, appearing at 1584 cm , 1533 cm ,
-1
-1
-1
-1
1
401 cm , 1331 cm for compound 1 and for compound 2 found at 1630 cm , 1500 cm , 1400
-1
cm . Apart from the aromatic stretching vibrations, several bending, scissoring and rocking
vibrations were shown by both compounds (for details see Table 4) and proved in good
agreement both experimentally as well as theoretically.
1
6

3
.3.3 C=O and S=O vibrations
Compound 1 has two different carbonyls along with S=O functionality, and calculated spectrum
-1
-1
showed two very strong carbonyl stretching vibrations at 1718 cm and 1619 cm , along with
-1
-1
strong S=O vibrations at 1290 cm and 1107 cm . These vibrations (C=O, S=O starching) were
-1
-1
found in full agreement with experimental counter parts depicted at 1702 cm , 1662 cm and
-1
1
240 cm . Similarly, the carbonyl and S=O vibrations of compound 2 showed very nice
agreement between experimental and theoretical values.
Table 4: Comparison of the experimental and simulated FT-IR vibrations of 1 and 2 (cm ).
-1
1
(B3LYP)
2 (B3LYP)
(Intensity)
3423(23.6)
3418(35.6)
3305(24.2)
3070(7.8)
3025(1.2)
3018(0.3)
2980(14.1)
2959(10.0)
2929(53.2)
2925(11.7)
2910(24.8)
2866(17.4)
2860(14.4)
2846(15.5)
1
(Exp.) Assignment
2 (Exp.) Assignment
(
3
3
3
3
3
2
2
2
2
2
2
2
1
1
1
1
1
Intensity)
406(21.3)
365(20.9)
071(8.6)
027(1.3)
021(0.7)
984(12.9)
983(5.0)
975(4.6)
933(11.1)
931(8.2)
870(4.6)
867(3.4)
3556
3438
3088
3028
---
υsNH
υsNH
υsCHarom.
υsCHarom
υsCHarom.
υsCHarom.
υasMe
3460
---
υasNH
υsNH
3360
3230
---
---
---
υsNH
.
υsCHarom.
υsCHarom.
υsCHarom.
υsCHarom.
υasMe
---
---
---
υasMe
---
---
υasMe
---
υasMe
---
υasMe
---
υasMe
---
υsMe
---
υasMe
---
υsMe
---
υ Me, υ CH
s
s
718(277.5) 1702
690(184.1) 1662
589(93.9)
575(75.4)
υsC=O
υsC=O
υsC=Carom.
---
υ Me, υ CH
s
s
---
υMe
1584
1533
1669(165.5) 1670
υsC=O, βNH
υsC=Carom.
υsC=Carom., βNH 1590(79.1)
βNH,
1630
496(449.1) 1461
υsC=C
arom.
1
476(4.2)
---
βNH,υ C=C
βCHarom.
ρMe
1576(92.6)
1528(41.2)
1590
1530
υasC=Carom.
βNH
ρNH2
,
s
arom.,
1
1
445(11.4)
440(10.2)
---
---
ρMe
1501(461.6) 1500
βNH,υ C=C
as arom.
1
7

1
1
1
431(11.5)
425(9.0)
385(77.1)
---
---
1401
ρMe
ρMe
υasC=Carom.
βNH
υsCN, βNH,
γMe
1478(35.8)
1473(38.6)
1467(7.5)
1453(4.1)
1451(13.8)
1385(85.1)
1380(8.0)
1356(7.2)
---
---
---
---
υasC=Carom.
ρMe
ρMe
ρMe
ρMe
υasC=Carom.
γMe
γMe
υasS=O
γCH, γMe
υsC=Carom., γCH
βCH
βCHarom.
υsNPh
,
1
1
1
1
1
1
1
1
362(481.5) 1369
357(45.1)
344(46.4)
313(122.4) 1321
290(142.4) ---
278(54.1)
233(87.1)
---
---
1400
---
---
γMe
γMe, βNH
υasC=Carom.
υasS=O
βCHarom.
υsCN
1318(178.9) 1300
1240
---
1305(8.6)
1298(85.4)
1281(3.1)
1278(15.9)
---
---
---
---
1250
---
---
200(107.9) 1234
166(48.6) ---
162(127.2) 1153
107(189.6) ---
1
1
1
υsCN
υsCN, βCHarom. 1234(63.9)
υsCN, βCHarom
υ S=O, υ SC
1200(34.0)
1162(5.4)
1145(25.4)
υsNC=O
βCHarom.
γMe
1102(50.4)
1089
---
998
---
---
---
---
---
---
---
as
s
1
1
1
9
9
9
9
9
9
9
8
8
8
7
7
6
6
6
5
5
5
5
5
5
4
4
4
4
053(73.4)
015(10.7)
013(4.7)
89.3(2.9)
76(31.7)
63.3(1.0)
49.3(45.5)
29.3(1.2)
27.1(1.3)
βCHarom.
---
υ S=O, υ SPh
1105(253.5) 1140
υ S=O, υ SPh
s
s
s
s
τMe
τMe
βPh
τMe
γCHarom.
τMe
γCHarom.
γCHarom.
υsCN
1102(54.9)
1096(9.1)
1057(45.2)
1050(40.7)
1040(2.1)
989(1.7)
960(1.1)
939(0.5)
928(0.4)
914(17.9)
901(3.7)
---
---
1090
---
---
---
---
---
---
891
---
---
823
---
---
---
---
---
677
---
βCHarom.
γMe
υsSPh
βMe
τNH2
βPh
γCHarom.
γMe
γCHarom.
γMe
γMe
---
γCHarom.
βPh.
γCHarom.
γNH2
---
γPh
υsSPh
βPh
γNH2
γNH
γNH2
γPh
01.4(112.8) ---
41.0(16.9)
20.1(5.3)
03.1(13.9)
52.0(117.6) 713
01.3(33.7)
91.4(17.3)
834
---
---
γCHarom.
ρPh, ρNCC
γCHarom.
υsSN
γPh
γPh
βPh
βPh
γNH, τMe
τMe
---
γPh, γNH
γPh
ρSO2
γPh
γNH, βPh
βNH, γPh
846(5.2)
---
---
837(16.9)
817(12.6)
805(6.4)
791(57.3)
715(8.6)
693(4.7)
682(219.1)
621(1.5)
607(454.7)
560(32.6)
542(41.2)
523(34.5)
517(16.8)
465(6.1)
23.2(110.0) 614
16.0(64.4)
94.0(5.6)
73.0(9.2)
61.7(45.8)
33.9(20.1)
19.3(83.0)
04.5(36.6)
73.6(26.9)
47.8(28.1)
17.7(62.2)
02.6(9.5)
612
---
---
---
---
536
---
---
---
---
---
---
---
532
---
---
---
---
---
1
8

3
3
3
3
2
2
2
1
1
79.7(18.1)
52.8(0.1)
36.0(9.3)
08.4(0.3)
92.4(1.5)
34.4(1.4)
00.1(5.4)
76.0(1.1)
42.6(0.8)
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
γPh
---
---
γPh
τMe
τMe
---
453(4.6)
434(8.0)
404(0.1)
389(7.1)
356(1.9)
349(18.7)
339(3.6)
305(1.5)
285(2.7)
273(4.1)
237(1.4)
234(13.6)
201(11.8)
188(2.2)
163(3.2)
104(3.0)
90(2.1)
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
δNH
γCCCarom.
δNH
ρCCC
βC=O
ρCCC
ρCCC
δMe
βNH
τMe
τNH
γSN
βPh
βPh
γPh
---
113.0(1.5)
ρSNC
---
8
7
6
5
3
3
2
1
3.2(1.4)
3.7(1.1)
2.9(3.4)
8.6(1.4)
7.7(8.2)
2.7(0.9)
8.6(1.3)
9.6(3.5)
τMe
τMe
τMe
τMe
τMe
τMe
τMe
βPh
γPh
γPh
γPh
58(2.7)
3
3
2
7(3.9)
4(3.0)
3(1.1)
γPh
1
13
3
.4 Nuclear magnetic resonance (NMR) analysis ( H & C)
1
13
The H and C-NMR chemical shift values play key role for the structure elucidation of organic
1
13
compounds. Experimental H and C NMR chemical shifts of both sulfonamides (1 and 2) were
scanned in d -DMSO. For validation and comparison of the experimental data, the theoretical
6
chemical shift calculations of both compounds (1 and 2) were executed by using the
B3LYP/6-311+G (2d, p) level of theory, adopting GIAO method and referred by using the
internal reference standard i.e. tetramethylsilane. Literature studies reveal that higher basis set
works well for the prediction of nuclear magnetic chemical shift values [27,44]. A detailed
1
comparison of simulated as well as experimental H-NMR values was presented in Table 5.
Both compounds under investigation contain NH and NH protons along with aromatic and alkyl
2
1
9

group protons. NH protons are highly environment and solvent dependent therefore, theoretical
as well as experimental comparison of these protons is very difficult, even in some cases
impossible [45]. As reflected from unit cell diagrams (Fig. 2), the NH protons are being involved
in hydrogen bonding, the experimental and simulated chemical shift values of NH and NH were
2
not matched (for detailed values see Table 5).
The experimental values of aromatic protons in sulfonamide 1 appeared at 7.82～7.76 ppm
range and showed an excellent agreement with the simulated chemical shift values at 9.40～6.83
ppm. Similarly, the computed aromatic C-H protons (with respect to TMS) of 2 appeared in the
range 9.53～6.78 ppm and showed in correlation with the experimental values at 7.75～7.71
ppm. The calculated chemical shifts of methyl protons of compound 1 were found at 2.41～1.66
ppm range, whereas experimental values appeared in the range 2.07～1.08 and proved in good
agreement. Sulfonamide, 2 also has methyl and CH groups and their experimental values
appeared at 2.60 ppm (CH), 1.10～1.09 ppm (CH ) were found in excellent agreement with the
3
computed values depicted at 2.64 ppm (CH) and 2.04-0.87 ppm (CH3).
1
3
Experimental C-NMRs of sulfonamides (1 and 2) were recorded in d6-DMSO, whereas
1
3
theoretical C-NMR chemical shifts were extracted from output files used for calculating
1
13
H-NMR chemical shifts. The experimental C-NMR chemical shift values at 169.1 ppm, 168.6
ppm in 1 were assigned to the quaternary carbons C12 and C20 (carbon labelling is in
accordance with Fig. 3) and showed good agreement with the theoretical values at 173 ppm, 171
ppm, respectively. The chemical shift values in 1 appeared in the range 143.7-118.3 ppm were
assigned to aromatic moiety, and correlated with theoretical values appeared at 135-120 ppm.
Two methyl groups in compound 1 appeared at 24.1 ppm and 23.1 ppm, and showed an
2
0

excellent correlation with the computed values appeared at 25 ppm and 24 ppm. Similarly, a
signal at 175.7 ppm in experimental scan of compound 2 was assigned to the quaternary carbon
C12 (theoretical value at 179 ppm). Experimental aromatic methane carbons (CH) in 2 appeared
at 142.3-118.5 ppm range showed good correlation with the simulated values. Compound 2 has
one aliphatic CH and two methyl groups, and their experimental values appeared at 40.0 ppm
(
CH), 43.9 ppm (CH ) and 19.3 ppm (CH ) which are in excellent correlation with theoretical
3 3
values appearing at 40 ppm (CH), 22 ppm (CH ) and 18 ppm (CH ) (for detailed values see
3
3
Table 6).
1
Table 5: Comparison of the experimental and simulated H-NMR chemical shifts of
sulfonamides 1 and 2 (ppm) (atomic labels are in accordance with Fig. 3).
(1)
Exp.
Calc.
(2)
Exp.
Calc.
H (aromatic) 7.76
9.40
8.25
8.16
6.83
6.82
6.47
2.41
H (aromatic) 7.75-7.71 9.53
8
8
H (aromatic) 7.82
H (aromatic) (aromatic) 8.14
9
9
H (aromatic) 7.82
H (aromatic) (protons) 8.07
1
0
10
H (aromatic) 7.76
7
H (NH)
10.14
7.16
6.78
3.74
3.64
11
H (NH)
10.37
11.96
1.89
H (aromatic) ---
11
7
H (NH)
H (NH )
7.22
7.22
1
9
17
2
H (CH )
H (NH )
1
5
3
30
2
H (CH )
1.89
2.07
2.07
2.09
1.93
1.81
H (CH)
2.60
1.09
1.10
2.64
2.04
1.36
1
4
3
14
H (CH )
H (CH )
2
7
3
25
3
H (CH )
H (CH )
28 3
2
6
3
H (CH )
1.87
2.07
1.78
1.66
H (CH )
1.10
1.09
1.29
1.11
1
6
3
29
3
H (CH )
H (CH )
24 3
2
8
3
H (CH )
1.10
1.09
0.99
0.87
2
7
3
H (CH )
2
3
3
2
1

13
Table 6: Comparison of the experimental and simulated C-NMR chemical shifts of
sulfonamides 1 and 2 (ppm) (atomic labels are in accordance with optimized geometries shown
in Fig. 3).
(
1)
Exp.
Calc.
(2)
Exp.
Calc.
(B3LYP)
179
150
149
139
132
124
120
40
(
B3LYP)
173
171
150
144
135
135
123
120
25
C12
C20
C2
C5
C6
C4
C3
C1
C13
C25
169.1
168.6
---
C12
C5
C2
C4
C6
C3
C1
C13
C22
C26
175.7
---
---
142.3
138.0
126.5
118.5
40.0
34.9
19.3
---
143.7
132.6
128.8
118.3
24.1
23.1
22
18
24
3
.5 Frontier molecular orbital (FMOs) analysis and UV-vis absorption studies
The FMOs (frontier molecular orbitals) analysis plays an active role in explaining molecular
reactivity, electronic properties and electronic transitions of molecules [46]. Chemical stability
of molecules can be explained on the basis of band gap between frontier orbitals (HOMO and
LUMO). A large HOMO–LUMO band gap reflects high kinetic stability, low chemical reactivity
and vice versa [47–49].
FMOs analysis of both sulfonamides 1 and 2 was executed by using B3LYP/6-31G(d,p) method
of DFT. The calculation reveals, that compound 1 contains 67 occupied molecular orbitals
whereas 2 has 64 occupied orbitals. Isodensities of both sulfonamides 1 and 2, along with
2
2

corresponding energies and band gap are given in Fig. 5. The energy of HOMO orbital reflects
the ionization energy (I. E.) and energy of LUMO reflects the electron affinity (E. A.) [50].
Considering the chemical hardness of compounds, large HOMO–LUMO gap means a hard
molecule/least reactive and vice versa. The FMOs band gap of sulfonamide 1 is equal to 5.38 eV
whereas for 2 is 5.33 eV. The band gap reflects, that stability of both compounds is relatively
high.
Experimental UV–vis absorption spectra of both sulfonamides 1 and 2, were recorded in
methanol and DMSO as solvents within the 200–600nm range, and theoretical absorption
studies were executed with the help of TD-DFT/B3LYP/6-31G (d, p) method in gas phase and
for solvent effect polarizable continuum model (PCM) was applied. Experimental and
theoretical absorption spectra of both derivatives are shown in the Fig. 6. Characteristic
experimental and simulated maximum absorption wavelengths (λmax) along with absorption
intensity and oscillating strength are given in Table 7. Data given in table 7, reflects that
excellent correlation exists between experiment and theory. Experimental UV-vis absorption
maxima of sulfonamide 1 in methanol and DMSO appeared at 260 nm and 267 nm, correlated
nicely with simulated values appearing at 251 nm in gas phase, 254 nm in methanol and 255 nm
in DMSO. Similarly, 2 depicted experimental λmax. at 262 nm and 267 nm in methanol and
DMSO respectively, whereas simulated value appeared at 248 nm, 253 nm and 254 nm in gas
phase, methanol and DMSO, respectively. The HOMO-LUMO surfaces (Fig. 5) of both 1 and 2
show, that isodensities are localized over the entire molecules except methyl groups and
electronic transitions are mainly due to π → π* transition [27]. The maximum absorption
wavelength in both sulfonamides is red shifted in DMSO, therefore it is concluded that excited
2
3

state is more stable in DMSO as compared to methanol.
Figure 5: HOMO and LUMO surfaces 1 and 2 along energy gap.
2
.0
.8
.6
1.4
.2
1.0
1
2
2
1
1
0
0
.5
.0
.5
.0
.5
.0
1
Methanol
DMSO
1
Methanol
DMSO
0
0
0
0
0
.8
.6
.4
.2
.0
200
300
400
500
600
2
00
300
400
500
600
Wavelength (nm)
Wavelength (nm)
3
2
2
1
1
0000
5000
0000
5000
0000
5000
0
3
2
2
1
1
0000
5000
0000
5000
0000
Methanol
DMSO
Methanol
DMSO
5
000
0
200
300
400
500
600
200
300
400
500
600
Wavelength (nm)
Wavelength (nm)
2
4

Figure 6: Experimental (above) and simulated (below) UV-vis. spectra of both 1 and 2 in
methanol and DMSO.
Table 7: Experimental and theoretical UV-vis λmax (nm) of sulfonamides 1 and 2 in methanol
and DMSO.
Theoretical (TD-SCF/B3LYP/6-31G(d,p)
Experimental
Compound Solvent
λmax (abs.) Solvent
λmax (f)
E(eV) Assignment
-
--
---
Gas
251(0.27) 4.93
π → π*
π → π*
π → π*
Methanol 260(2.28) Methanol 254(0.48) 4.87
1
2
DMSO
--
267(1.22) DMSO
--- Gas
255(0.60) 4.86
248(0.54) 5.0
-
π → π*
π → π*
π → π*
Methanol 262(1.53) Methanol 253(0.66) 4.89
DMSO 267(1.22) DMSO 254(0.64) 4.88
3
.6 Non-linear optical (NLO) properties
Organic molecules possessing non-linear optical response (NLO) attract scientific community
due to their wide spread applications in electronics and optoelectronics devices of
telecommunications, information storage, optical switching, signal processing, medical imaging
and terahertz(THz) wave generation [52–54]. Different strategies are acquired for enhancing
NLO properties of materials i.e. π stacking, diffuse excess electron and electron push full
mechanism. In electron push-full mechanism. Organic molecules having electron donor and
acceptor groups, have very high first hyperpolarizability value due to intramolecular charge
transfer, and show tremendous NLO response. In current study, carbamide and sulfonamide
functional groups are attached to benzene ring (1 and 2). Where carbamide and sulfonamide act
as electron donating group and electron withdrawing group, respectively. The polarizability and
first hyperpolarizability values are calculated with the help of following mathematical
2
5

expression.
Polarizability (α ) is mathematically represented by the following equation:
o
α = 1/3(α + α + α )…………………………..(1)
o
xx
yy
zz
Whereas, first hyperpolarizability (β ) is mathematically represented as;
o
2
2
2 1/2
βo = [(βxxx + β + β ) + (β + β + β ) + (β + β +β ) ] …………………(2)
xyy
xzz
yyy
yzz
yxx
zzz
zxx
zyy
βo is the first hyperpolarizability is also known as nonlinear optical response coefficient.
The dipole moment, polarizibilty and hyperpolarizability values of both sulfonamides are given
in the Table 8. Both sulfonamides 1 and 2 have higher dipole moments i.e. 9.77 and 8.44 Debye,
respectively. The polarizability values of both 1 and 2 are 143 au and 140 au, respectively.
Greater the dipole moment results in higher the hyperpolarizability value and vice versa. The
2
1
hyperpolarizability of sulfonamides 1 and 2 is 3.34×10 and 8.7×10 au, respectively. The three
parameters indicate the NLO behavior of both sulfonamides and can be used as potential optical
materials for optics and optoelectronics. Overall, comparative analysis of dipole moment,
polarizability and hyperpolarizability of 1 is more pronounced and it can be selectively used as
potent molecule in NLO materials for future study.
Table 8: The dipole moment (Debye), polarizability (au) and hyperpolarizability (au) values of
sulfonamides 1 and 2.
Dipole moment Polarizability
(ꢀ (α
Hyperpolarizability
(β
Compound
o
)
o
)
)
o
2
1
1
2
9.77
8.44
143
140
3.34×10
8.70×10
3
.7 Non-linear refractive index (n ) analysis
2
The other parameters which are responsible for enhancing non-linear response of NLO materials,
2
6

include Kerr effect, electric field-induced second harmonic generation (ESHG) and refractive
index [8,55]. Sum-over-state (SOS) method is used to calculate the quadratic non-linear
refractive index (n ) of both 1 and 2 compounds [56]. The SOS method includes electric
2
field-induced second harmonic generation γ(-2ω; ω, ω, 0) and dc-Kerr effect γ(ω; ω, ω, 0). The
frequency parameters calculated at wavelength of 532 nm and 1064 nm, are well known for
commonly used laser technology [57]. The gamma values at ω = 0 nm are 31861.7 au and
3
0971.5 au for 1 and 2, respectively. The electric field-induced second harmonic generation
(ESHG) values for both are in the range 43055.2 au to 562631au at selected frequency values
(532 nm and 1064 nm). The large positive EFSHG value (562631 au) is obtained at ω = 532 nm
for compound 1. Both compounds also showed more pronounced dc-Kerr effect. The dc-Kerr
coefficients range from 34320.6 au to 50712.4 au (at 532 nm and 1064 nm), where large positive
coefficient (50712.4 au) is observed for 1 compound at 532 nm. These values are further used to
DFWM
calculate degenerated four waves mixing gamma values (γ
(ω) = (-ω; ω, -ω, ω) using the
following equation (3), proposed by Tarazker et al. [58].
DFWM
γ
(-ω; ω, -ω, ω) = (1/3) γ(-2ω; ω, ω,0) + (1/3) γ(-ω; ω, 0,0) + (1/3) γ(0; 0,
0
,0)……………(3)
The terms γ(0; 0, 0,0), γ(-ω; ω, 0,0) and γ(-2ω; ω, ω,0) represent static, dc-Kerr and EFSHG
DFWM
second hyperpolarizability coefficients, respectively. The γ
is used to calculate the quadratic
non-linear refractive index (n2).
2
-23
DFWM
n2
(cm /W)
=
8.28
×
10
γ
(au)…………………………………………………………..(4)
The n values of both compounds at different wavelength (532 nm and 1064 nm) are
2
2
7

summarized in Table 9 and graphically represented in Fig. 7. The spectral curves of n are
2
comparable to the dc-Kerr effect and ESHG effect those illustrate the dominant contribution of
both these effects in enhancing non-linear refractive index. The n values obtained for both
2
-17
2
-17
2
compounds 1 and 2 are 1.78×10 cm /W and 1.28×10 cm /W at ω = 532nm. These
-18
2
-18
2
compounds have n values in the range of 3.08×10 cm /W and 2.99×10 cm /W at ω = 1064
2
nm. The n values clearly indicate that the pronounced effect is observed at low wavelength (532
2
-17
2
nm) where the highest n value (1.78×10 cm /W) is observed for compound 1. These n values
2
2
confirmed the influence of different wavelengths on the amplitude of first hyperpolarizability
βo). Beside the different wavelengths, the structure of compounds also plays important role in
(
variation of non-linear optical response. The replacement of hydrogen of amine group by acetate
group results in amide group formation in 1. The further delocalization towards carbonyl may be
responsible for enhancement of NLO response in 1.
Table 9: The static, dc-Kerr effect, electric field-induced second harmonic generation
2
coefficients (in au) and quadratic non-linear refractive index (n = cm /W) at different
2
wavelength (in nm) of both compounds 1 and 2.
Compounds Frequency
γ(0; 0, 0, 0) γ(-ω; ω, ω, 0) γ(-2ω; ω, ω, 0) n2
0
31861.7
1
-
17
18
5
1
0
32
064
50712.4
35345.8
562631
44543.9
1.78×10
3.08×10
-
17797.6
-
17
18
2
532
064
25480.9
19314.9
121742
23084.8
1.28×10
2.99×10
-
1
2
8