1. A DFT analysis of the vibrational spectra of nitrobenzene
John Clarkson*, W. Ewen Smith
Department of Pure and Applied Chemistry, Strathclyde University, Thomas Graham Building, 295 Cathedral Street,
Glasgow G1 1XL, Scotland, UK
Received 13 March 2003; accepted 23 April 2003
Abstract
Raman and FTIR, spectra of nitrobenzene, nb, and its isotopomers, nb-15
N, nb-13
C6 and nb-d5; were obtained and the
fundamental vibrational modes assigned with the aid of a B3LYP/6-311 þ G** calculation, without the need for scaling of the
force constants. The changes in vibrational coupling between the nitro and benzene groups upon certain isotopic substitutions
are well modelled by the calculation, which is able to reproduce the isotopic shifts in frequencies for the nitro vibrations, as well
as changes in IR intensities.
q 2003 Elsevier B.V. All rights reserved.
Keywords: Density functional theory; Isotopomers; Vibrational analysis
1. Introduction
Nitrobenzene, the simplest nitro aromatic com-
pound, is the parent molecule of a range of important
compounds, including explosives such as 2,4,6-
trinitrotoluene. It is also related to nitrophenols,
including the biologically important nitrotyrosine,
whose presence in proteins is often the result of
damage by peroxynitrite [1–3]. A full theoretical
understanding of the molecular properties of nitro-
benzene can therefore inform on the properties of
these other larger molecules.
This paper focuses on the use of modern density
functional theory (DFT), to fully account for the
experimental vibrational Raman and IR data from
nitrobenzene and its isotopomers. The vibrational
spectroscopy of nitrobenzene has been the subject of
numerous studies [4–15]. The exact nature of the
nitro vibrational modes, however, had been either
vague or contradictory. A thorough analysis of the
vibrational frequencies of the C–NO2 moiety on the
basis of a HF/6-31G* calculation, where the force
constants had been scaled, was published by Shlya-
pochnikov et al. [15]. This appeared to provide a clear
assignment of the nitro bands and seemed to fully
account for the isotopic shifts that occur for the
various isotopomers of nitrobenzene.
A vibrational analysis of 2-nitrophenol making use
of a B3LYP/6-31G* calculation also had to scale the
force constants to obtain a satisfactory fit of the
frequencies to the experimental data [16]. The scaling
0022-2860/03/$ - see front matter q 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0022-2860(03)00316-8
Journal of Molecular Structure 655 (2003) 413–422
www.elsevier.com/locate/molstruc
* Corresponding author. Tel.: þ44-141-552-4400; fax: þ44-141-
552-0876.
E-mail address: john.clarkson@strath.ac.uk (J. Clarkson).
Abbreviations: nb, nitrobenzene; nb-15
N, 15
N enriched
nitrobenzene; nb-d5, deuterium enriched nitrobenzene; nb-13
C6,
13
C enriched nitrobenzene.

2. of force constants for molecules such as nitrobenzene
and 2-nitrophenol was needed as it was thought that a
purely computational approach to the force field or
frequencies for such molecules was not possible.
Systematic calculation errors were compensated for
and good agreement with the observed experimental
frequencies was achieved by using a few empirical
scale factors for the calculated force constants
[15,16].
The present authors reported a recent successful
DFT analysis of the structure and vibrations of 2,4,6-
trinitrotoluene, TNT, using the hybrid density func-
tional B3LYP and the 6-311 þ G** basis set [17],
without the need to scale the force constants or
frequencies. The good fit between the theoretical and
experimental frequencies for TNT was only achieved
by use of the triple zeta, 6-311 þ G** basis set; A
B3LYP calculation of TNT with the double zeta, 6-
31G* basis set gave poor results. Following this, the
authors decided to re-examine the vibrational spectra
of nitrobenzene to test if a similar DFT analysis could
successfully model the vibrational spectra of nitro-
benzene and account for the isotopic shifts without the
need to rescale the force constants.
We present FTIR and Raman data for liquid
nitrobenzene, nb, nb-d5; nb-15
N, and nb-13
C6 and
assign the spectra on the basis of a B3LYP/6-
311 þ G** calculation. The changes in the
vibrational mode coupling between the nitro group
and the benzene ring for the various isotopomers are
well modelled by the B3LYP/6-311 þ G** calcu-
lation and previous assignments of the vibrational
spectra are revised. The present analysis represents a
reappraisal of the analysis of Shlyapochnikov et al.
[15], presenting new vibrational data for nb-13
C6 and
new insights into the coupling of the nitro and
benzene modes.
2. Methods
Nitrobenzene and d5-nitrobenzene were obtained
from Aldrich. 15
N (98%) enriched nitrobenzene and
13
C6 (99%) enriched nitrobenzene, were obtained
from Cambridge Isotope Laboratories.
Raman spectra were obtained using a Renishaw
micro-Raman system 1000 spectrometer with 785 nm
excitation. FTIR spectra were obtained using a
Nicolet Impact 400D.
Geometry optimisation and frequency analysis of
nitrobenzene was performed using GAUSSIAN 98 [18]
with the B3LYP hybrid density functional [19,20]
using the 6-31G* [21–23] and 6-311 þ G** [24,25]
basis sets.
3. Results and discussion
Computed bond lengths and angles for nitroben-
zene together with the electron diffraction and
microwave data (Fig. 1) are shown in Table 1.
Previous MP2 calculations showed the C–C bonds as
getting longer the farther away from the NO2 group
attachment point, in contrast to the HF calculation
[15]. The present B3LYP calculations is in agreement
with the HF calculation in that only the farthest away
CC bond length is notably longer, the other two being
near equal. There is a large difference in the CN and
NO bond lengths modelled by the B3LYP calculations
compared to previous HF and MP2 calculations. The
improvement in the MP2 NO2 bond lengths over the
HF values is in increasing the CN bond length,
however, it overestimates the NO bond length [15].
The B3LYP calculations increase further the CN bond
length, but decreases the NO bond length. The effect
of the 6-311 þ G** basis set on the B3LYP
functional, compared to the B3LYP/6-31G* structure
Fig. 1. Labelling of the atoms of nitrobenzene.
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422414

3. is to further increase the length of the CN bond and
decrease the NO bond length.
Raman and FTIR spectra for nb, nb-15
N, nb-13
C6
and nb-d5 are shown on Fig. 2 and assignments based
on the B3LYP/6-311 þ G** calculation are presented
on Table 2. The calculated B3LYP/6-31G* frequen-
cies, the IR intensities and their changes for the
various isotopomers of nitrobenzene were found to be
inaccurate. A similar result was found in the TNT
study [17]. The assignments on Table 2 are based on a
visual inspection of the calculated eigenvectors and
the benzene ring modes are numbered after the Wilson
[26] notation as recommended by Varsanyi [27].
The C2v symmetry of nitrobenzene classifies the
normal vibrations into 13 A1, 12 B2, 7 B1 and 4 A2
modes. Following the analysis of Shlyapochinkov
et al. [15], seven of these modes are identified with the
C–NO2 moiety; three A1, (ns NO2, n CN and d ONO),
two B2, (nas NO2 and t NO2), one B1 (v NO2), and
one A2 (x NO2) modes. Eight NO2 modes were
selected by Shlyapochinkov et al. [15] due to the fact
that the v NO2 out-of-plane deformation takes part
nearly to the same extent in both n25 and n26; *5 and
*6, respectively. The greater isotopic shift for *6 in
nb-15
N, Table 3, suggests this fundamental as
predominantly the NO2 out of plane deformation
mode. The present analysis, however, shows that this
Table 1
Computed B3LYP/6-311 þ G** bond lengths and angles for nitrobenzene
HF 6-31G*a
MP2 6-31G*a
MP2 6-31G**a
B3LYP 6-31G* B3LYP 6-311 þ G** Microwavea
C1–C3 1.3833 1.3911 1.3905 1.3936 1.3915 1.3748
C3–C4 1.3833 1.3934 1.3928 1.3934 1.3914 1.4026
C2–C4 1.3867 1.3960 1.3953 1.3976 1.3952 1.3958
C–N 1.4588 1.4700 1.4699 1.4734 1.4807 1.4916
N–O 1.1938 1.2413 1.2412 1.2308 1.2243 1.2272
C3–C1–C5 122.32 122.77 122.76 122.35 122.28 124.99
C1–C3–C4 118.51 118.11 118.12 118.47 118.51 117.11
C2–C4–C3 120.10 120.33 120.50 120.19 120.20 120.30
C4–C2–C6 120.46 120.01 120.01 120.33 120.31 120.18
C–N–O 117.70 117.66 117.62 117.70 117.67 117.82
O–N–O 124.61 124.69 124.77 124.60 124.65 124.35
C3–H10 1.0709 1.0839 1.0787 1.0829 1.0811 1.080
C4–H9 1.0742 1.0866 1.0812 1.0859 1.0834 1.0829
C2–H8 1.0750 1.0867 1.0813 1.0863 1.0839 1.0803
C1–C3–H10 120.02 119.93 119.80 119.52 119.63 120.7
C2–C4–H9 120.24 120.10 120.07 120.19 120.18 120.05
C4–C2–H8 119.77 120.00 120.00 119.84 119.85 119.91
a
From Ref. [15].
Fig. 2. Raman and FTIR spectra of nitrobenzenes, (A) nb-15
N, solid
line, (B) nb-13
C6, (C) nb-d5. Dotted lines in (A) and (B) are
nitrobenzene, nb spectra.
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422 415

4. Table 2
Vibrational assignment of nitrobenzene, nb and nb-15
N, nb-13
C6 and nb-d5
n no. nb IR nb
Raman
nb Theory nb-15
N IR nb-15
N
Raman
nb-15
N
Theory
Assignments
1 3107 3223.4 A1 3223.4 A1 2 C–H str.
2 3107 3223.1 B2 3223.1 B2 20b C–H str.
3 3076 3082 3197.0 A1 3197.0 A1 20a C–H str.
4 3076 3188.3 B2 3188.3 B2 7b C–H str.
5 3049 3175.6 A1 3175.6 A1 13 C–H str.
6 1620 1651.8 B2 1619 1647.2 B2 8b ring str. þ NO2 as. str.
6 1606 1604 n29 þ n20, Fermi resonance
7 1588 1588 1627.9 A1 1588 1588 1627.8 A1 8a ring str.
1526 n27 þ n23
8 (*1) 1523 1524 1584.1 B2 1496 1497 1553.7 B2 NO2 as. str. þ 8b ring str.
9 1479 1479 1508.5 A1 1478 1478 1508.4 A1 19a ring str.
1463 n28 þ n25
10 1455 1486.5 B2 1452 1453 1485.4 B2 19b ring str.
1383 1380 1391 n21 þ n33, n23 þ n30
1372 n33 þ n22, n30 þ n23
1364 1363 1363 1366 2£n27, n34 þ n16
1348 1348 2£n28
11 (*2) 1347 1347 1371.9 A1 1324 1322 1348.9 A1 NO2 s. str.
1325 n30 þ n25
12 1316 1353.1 B2 1315 1353.1 B2 14 ring str.
13 1308 1337.5 B2 1308 1337.5 B2 3 C–H i.p. bend
1248 1248 1240 1240 n33 þ n23
14 1174 1172 1195.8 A1 1174 1173 1195.8 A1 9a C–H i.p. bend
15 1162 1162 1184.9 B2 1162 1162 1184.9 B2 9b C–H i.p. bend
1127 n31 þ n27
16 (*3) 1108 1107 1115.7 A1 1107 1106 1114.9 A1 C–N str. þ 1 ring breathing
1095 1092 n33 þ n26, n34 þ n24
17 1070 1074 1099.6 B2 1069 1072 1099.6 B2 18b C–H i.p. bend
18 1042.2 A1 1042.2 A1 18a C–H i.p. bend
19 1021 1021 1018.6 B1 1021 1021 1018.5 B1 10b C–H o.o.p. bend
20 1004 1003 1018.5 A1 1003 1003 1018.4 A1 12 C–C–C trigonal bending
21 990 1000.7 A2 990 1000.7 A2 17a C–H o.o.p. bend
22 975 959.5 B1 975 959.3 B1 17b C–H o.o.p. bend
935 934 n27 þ n34
873 n35 þ n26
23 (*4) 852 852 868.6 A1 846 846 861.5 A1 ONO s. bend þ 12/1ring str.
24 840 855.6 A2 843 840 855.6 A2 5 C–H o.o.p. bend
25 (*5) 793 793 789.0 B1 786 787 784.4 B1 11 C–H o.o.p. bend þ v NO2
710 710 700 701 n35 þ n30
26 (*6) 702 703 705.0 B1 694 692.5 B1 11 C–H o.o.p bend þ v NO2
27 681 681 696.2 A1 681 681 696.0 A1 6a C–C–C i.p bend
28 676 684.9 B1 675 684.5 B1 5 C–H o.o.p.bend
29 611 611 626.3 B2 610 610 626.4 B2 6b C–C–C i.p bend
30 (*7) 532 529 526.6 B2 529 527 524.1 B2 NO2 as. bend, 9b C–H in
plane bend
31 436 439.6 B1 438.6 B1 16b C–C–C o.o.p. bend
32 417 414.9 A2 414.9 A2 16a C–C–C o.o.p. bend
33 392 396 394.7 A1 394 393.1 A1 Ring i.p bend þ CN st.
34 255 254 256.1 B2 254 256.0 B2 9b C–H i.p. bend
35 182 176 168.2 B1 176 168.2 B1 Ring tors.
36 (*8) 51 45.8 A2 45.8 A2 NO2 tors.
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422416

5. Table 2 (continued)
n no. Nb-13
C6 IR Nb-13
C6
Raman
Nb-13
C6
Theory
Assignments
1 3104 3212.8 A1 2 C–H str.
2 3104 3212.6 B2 20b C–H str.
3 3087
3063
3087
3065
3186.3 A1 20a C–H str.
4 3178.1 B2 7b C–H str.
5 3047 3044 3166.0 A1 13 C–H str.
1595 n34 þ n11
6 1568 1612.5 B2 NO2 as. str. þ 8b ring str.
n29 þ n21
1553 Fermi resonance
7 1535 1534 1571.6 A1 8a ring str.
8 (*1) 1513 1514 1563.1 B2 8b ring str. þ NO2 as. str.
1490 n30 þ n21
1473 n33 þ n16
9 1447 1447 1476.2 A1 19a ring str.
10 1426 1454.0 B2 19b ring str.
1384 n33 þ n18
1364 n33 þ n20
11 (*2) 1345 1345 1370.8 A1 NO2 s. str.
1324 1325 2 £ n27
12 1297 1322.9 B2 3 C–H i.p. bend
13 1274 1304.5 B2 14 ring str.
1237 n33 þ n23
1180 2£n29
14 1166 1166 1187.4 A1 9a C–H i.p. bend
15 1154 1157 1178.7 B2 9b C–H i.p. bend
1117 n30 þ n29
16 (*3) 1082 1081 1086.4 A1 C–N st. þ 1 ring breathing, n34 þ n24
1073 1072 Fermi Resonance
17 1047 1047 1083.5 B2 18b C–H i.p. bend
18 1016.2 A1 18a C–H i.p. bend
19 996 996 1009.1 B1 10b C–H o.o.p. bend
20 977 989.7 A2 17a C–H o.o.p. bend
21 967 967 981.6 A1 12 C–C–C trigonal bending
22 963 949.6 B1 17b C–H o.o.p. bend
925 n32 þ n30
872 n35 þ n26
23 (*4) 846 846 862.8 A1 O–N–O s. bend þ 12/1ring str.
24 831 848.7 A2 5 C–H o.o.p. bend
25 (*5) 784 784 780.5 B1 11 C–H o.o.p. bend þ NO2
707 707 n35 þ n30
26 (*6) 700 703.0 B1 11 C–H o.o.p bend þ NO2
27 661 661 674.9 A1 6a C–C–C i.p. bend
28 665.4 B1 5 C–H o.o.p. bend
29 589 589 603.6 B2 6b C–C–C i.p. bend
30 (*7) 525 523 521.1 B2 NO2 as. bend, 9b C–H i.p bend
31 427.3 B1 16b C–C–C o.o.p bend
32 402.9 A2 16a C–C–C o.o.p. bend
33 389 388.3 A1 Ring i.p bend þ CN st.
34 247 251.6 B2 9b C–H i.p. bend
35 172 163.4 B1 Ring tors.
(continued on next page)
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422 417

6. Table 2 (continued)
36 (*8) 45.2 A2 NO2 tors.
n no. nb-d5 IR nb-d5 Raman nb-d5 Theory Assignments
1 2309 2309 2386.4 A1 2 C–D str.
2 2303 2384.9 B2 20b C–D str.
3 2289 2367.2 A1 20a C–D str.
4 2283 2356.1 B2 7b C–D str.
5 2342.9 A1 13 C–D str.
6 1593 1627.6 B2 8b ring str. þ NO2 as. str.
6 1584 n34 þ n11, n30 þ n13
7 1556 1591.6 A1 8a ring str.
1545 1545 n30 þ n14, n28 þ n15
8 (*1) 1518 1518 1574.7 B2 NO2 as. str. þ 8b ring str.
1466 1467 n35 þ n12, n30 þ n15, n25 þ n20
1439 2£n24
9 (*2) 1360 1361 1377.1 A1 19a ring str. þ NO2 s. str
10 1349 1350 1370.1 B2 19b ring str.
11 (*2) 1341 1341 1369.3 A1 NO2 s. str. þ 19a ring str.
1331 1332 n27 þ n24
1310 2£n25
12 1299 1300 1340.8 B2 14 ring str.
1260 1260 n32 þ n16
1173 2£n28
1151 n29 þ n27
13 (*3) 1076 1076 1082.5 A1 C–N str. þ 1 ring breathing
14 1037 1039 1053.6 B2 3 C–D i.p.bend
974 n32 þ n28
15 960 960 974.9 A1 12 C–C–C trigonal bending
16 872 872 885.3 A1 18a C–D i.p. bend
17 (*4) 846 845 861.4 A1 ONO s. bend, 9a C–D i.p. bend
18 859.3 B2 9b C–D i.p. bend
19 834 845.5 B1 5 C–D o.o.p. trigonal
20 815 815 827.6 B2 18b C–D i.p. bend
21 801 814.6 A1 18a C–D i.p. bend
22 812.9 A2 17a C–D o.o.p. bend
23 796.6 B1 17b C–D o.o.p. bend
24 (*5) 720 720 723.6 B1 11 C–D o.o.p. bend þ v NO2
25 655 654 667.7 A1 6a C–C–C i.p. bend þ ONO s. bend
26 665.3 A2 10a C–D o.o.p. bend
27 (*6) 612 612 614.3 B1 11 C–D o.o.p bend þ v NO2
28 586 6b C–C–C i.p. bend
29 539 541 548.3 B1 5 C–D o.o.p. bend
30 (*7) 510 508 512.8 B2 NO2 as. bend, 9b C–D i.p. bend
31 393.9 B1 16b C–C–C o.o.p. bend
32 387 387.2 A1 Ring i.p bend þ CN s.
33 361.3 A2 16a C–C–C o.o.p bend
34 241 245.2 B2 9b C–D i.p. bend
35 168 158.5 B1 Ring tors.
36 (*8) 44.1 A2 NO2 tors.
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422418

7. NO2 mode mixes with benzene mode 11, yielding the
two *5 and *6 modes. This NO2 mode also mixes with
benzene mode 11 in nb-d5 giving the largest isotopic
shift in Table 3, due to the large contribution from C–
H/D out of plane bending in these modes. Shlyapo-
chinkov et al. calculate þ19.7 and 213.4 cm21
shifts
for nb-d5 modes *5 and *6, respectively, which
the present analysis suggests are incorrectly assigned
[15]. The present calculation predicts that of all the
isotopomers of nitrobenzene, except for nb-d5, the *6
mode has the highest contribution from the NO2 of-of-
plane deformation mode. It appears that the *5 band of
nb-d5 was mistaken for the nitrobenzene *6 band by
Shlyapochinkov et al. [15].
There is very good agreement between our
calculated isotopic shifts and those observed exper-
imentally, Tables 2 and 3, giving extra confidence in
the modelled vibrations. Table 4 shows our calculated
frequencies for all of the isotopomers of nitrobenzene
studied to date, including nb-18
O16
O, nb-18
O2 and nb-
p-d1.
The asymmetric nitro vibration *1, is calculated
to couple to the benzene mode 8b, (n6 and n8 for nb
and nb-13
C6, Fig. 3). The degree of this mixing
dramatically changes in nb-13
C6, where the highest
non-C–H stretching mod, (n6; Fig. 3) is predicted to
have the second highest IR intensity, Fig. 4. The
benzene 8b mode of nitrobenzene is involved in Fermi
resonance with the combination mode 12 þ 6b,
(1004 þ 611 cm21
), resulting in two IR bands at
1620 and 1606 cm21
. Identical Fermi resonance is
observed for nb-15
N and also for nb-13
C6, were two
strong bands, at 1568 and 1553 cm21
, are observed.
The increased contribution of the nb-13
C6 asymmetric
nitro stretch to the highest non C–H stretching mode,
modelled by the calculation, is shown by the large
increase in IR absorption for these Fermi resonance
bands, Fig. 4.
The 1620 and 1606 cm21
IR bands were correctly
identified as a Fermi resonance pair by Kuewae and
Machida, though the benzene mode combination band
was wrongly identified as 1 þ 6b [13]. These bands,
however, were incorrectly assigned to fundamentals
by Shlyapochinkov et al. [15]. There are many
combinations and overtones present in the Raman
and IR spectra of the nitrobenzene above 1650 cm21
,
which we have not assigned. Combinations and
overtones below 1650 cm21
have been assigned to
fully account for all bands in the fundamental region
of the spectra, Table 2.
Table 3
List of observed and calculated isotopic frequency shifts for the C–NO2 moiety for nitrobenzene. Values in parenthesis calculated by
Shlyapochinkov et al [15].
No. Vibration nb-13
C6
a
nb-15
Na
nb-d5
a
Nb-16
O,18
O [15] Nb-18
O2 [15] Para-d-nb [15]
Obs. Calc. Obs. Calc Obs. Calc. Obs. Calc. Obs. Calc. Obs. Calc.
*1 nas NO2 210 221.0 228 230.4
(227.9)
26 29.4
(213.7)
213 210.8
(25.1)
221 223.7
(220.1)
24 23.5
(26.0)
*2 23 21.1 223 222.9
(225.7)
þ14, 26 þ5.2
(þ7.7), 22.7
214 216.9
(28.3), 220.9
227 235.2
(229.2)
21 0.0
(20.1)
*3 n CN 227 229.3 21 20.8
(20.2)
231 233.3
(240.3)
24 22.3
(22.3)
24.6
(28.8)
0 20.1
(20.1)
*4 d ONO 26 25.8 26 27.1
(26.0)
27 27.1
(23.1)
212 27.2
(27.3)
226 229.1
(28.4)
0 20.7
(20.6)
*5 v NO2 29 28.5 26 24.6
(25.5)
273 265.4
(þ15.5)
0 20.6
(20.4)
22 21.3
(21.6)
230 236.4
(233.9)
*6 23 22.0 28 212.5
(210.8)
290 290.7
(219.7)
0 22.1
(21.0)
22 24.3
(23.7)
214 25.1
(214.2)
*7 t NO2 26 25.5 22 22.5
(22.3)
219 213.8
(213.4)
212 28.2
(24.3)
224 216.5
(216.2)
22 21.2
(21.3)
*8 x NO2 20.6 0.0
(0.0)
21.7
(21.2)
20.8
(20.5)
21.5
(22.0)
0.0
(0.0)
Notation: n; d; v; t; and x-stretching, bending, wagging, rocking and tortional vibrations, respectively; a, as-symmetric and antisymmetric.
a
Observed values from our own data shown on Fig. 2, Table 2.
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422 419

8. The symmetric nitro vibration, *2, does not shift
much in energy for nb-13
C6, revealing the lack of
involvement of the benzene ring in this mode.
The principle CN mode *3, does however show a
large shift in frequency for nb-13
C6, which is
tentatively assigned to be involved in Fermi resonance
with the combination mode n34 þ n24; to give two
bands at 1082 and 1073 cm21
.
The most notable change to the vibrational spectra
of nb-d5 are the two intense bands at 1360 and
1341 cm21
, which are both assigned to the symmetric
nitro stretch, *2. This nitro mode mixes with the
benzene mode 19a, giving two modes, (nb-d5n9 and
n11; Fig. 3), with differing contributions from the
nitro group; they also differ in the phases of the
benzene and nitro group contributions. These two
intense nitro bands are amongst a group of four bands
found between 1390 and 1310 cm21
, Fig. 5. The
calculation predicts the negatively shifted isotopic
band to have the greatest contribution from the nitro
Table 4
B3LYP/6-311 þ G** frequencies for nitrobenzene isotopomers
C6H5NO2
13
C6H5NO2 C6H5
15
NO2 C6H5N18
O2 C6H5N16
O18
O d5-C6H5NO2 p-d1-C6H4NO2
A1 3223.4 3212.8 3223.4 3224.4 3223.4 A00
2386.4 3223.3
3197.0 3186.3 3197.0 3197.0 3197.0 A0
2367.2 3188.0
3175.6 3166.0 3175.6 3175.6 3175.6 A0
2342.9 2355.2
1627.9 1571.6 1627.8 1627.7 1627.8 A0
1591.6 1622.3
1508.5 1476.2 1508.5 1508.2 1508.3 A0
1377.1 (*2) 1503.0
*2 1371.9 1370.8 1348.9 1336.7 1355.0/1351.0 A0
1369.3 1371.9
1195.8 1187.4 1195.8 1195.1 1195.5 A0
1082.5 (*3) 1195.8
*3 1115.7 1086.4 1114.9 1111.1 1113.5 A0
974.9 1115.6
1042.2 1016.2 1042.2 1042.0 1042.1 A0
885.3 1039.3
1018.5 981.6 1018.5 1018.4 1018.5 A0
861.4 (*4) 1001.8
*4 868.6 862.8 861.5 839.4 854.1 A0
814.6 867.9
696.2 674.9 696.0 689.0 692.9 A0
667.7 691.6
394.7 388.3 393.1 384.5 389.5 A0
387.3 392.2
A2 1000.7 989.7 1000.7 1000.7 1000.7 A00
812.9 1000.7
855.6 848.7 855.6 855.6 855.6 A00
665.3 855.6
414.9 402.9 414.9 414.8 414.9 A00
361.3 414.9
*8 45.8 45.2 45.8 44.3 45.0 A00
44.1 45.8
B1 1018.6 1009.1 1018.6 1018.6 1018.6 A00
845.5 992.2
959.5 949.6 959.3 959.5 959.5 A00
796.6 893.0
*5 789.0 780.5 784.4 787.6 788.3 A00
723.6 752.3
*6 705.0 703.0 692.5 700.8 702.9 A00
614.3 699.9
684.9 665.4 684.5 684.9 684.9 A00
548.3 614.9
439.6 427.3 438.6 438.8 439.2 A00
393.9 426.6
168.2 163.4 168.2 166.6 167.4 A00
158.5 162.4
B2 3223.1 3212.6 3223.1 3223.1 3223.1 A0
2384.9 3223.1
3188.3 3178.1 3188.3 3188.3 3188.3 A0
2356.1 3188.2
1651.8 1612.5 (*1) 1647.2 1649.3 1650.4 A0
1627.6 1647.3
*1 1584.1 1563.1 1553.7 1560.4 1573.3 A0
1574.7 1580.6
1486.5 1454.0 1485.4 1485.2 1485.7 A0
1370.1 1439.8
1353.1 1304.5 1353.1 1352.6 1355.0/1351.0 A0
1340.8 1351.7
1337.5 1322.9 1337.5 1336.7 1337.2 A0
1053.7 1324.5
1184.9 1178.7 1184.9 1184.9 1184.9 A0
859.3 1125.9
1099.6 1083.5 1099.6 1099.5 1099.5 A0
827.6 887.6
626.3 603.6 626.4 626.3 626.3 A0
600.4 621.5
*7 526.6 521.1 524.1 510.1 518.4 A0
512.8 525.3
256.1 251.6 256.0 248.8 252.3 A0
245.2 254.4
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422420

9. group and the greatest IR absorption, Fig. 4, whereas,
experimentally they are of near equal intensity.
Kuewae and Machida also assign the 1360
and 1341 cm21
features to symmetric nitro modes
and their calculated force field correctly predicts the
positive and negative isotopic shifts [13].
The assignment of *4 for nb-d5 is assigned to the
band at 846 cm21
in agreement with Shlyapochinkov
et al. [15] and Laposa [14]. The intense Raman band
at 872 cm21
, which may be mistaken for *4, is
assigned to a C–D in plane bending mode, with a very
small contribution from ONO bending.
Interestingly the calculation predicts that the
reduction in molecular symmetry to Cs upon substi-
tution of one of the nitro group oxygen atoms with
18
O, nb-16
O18
O, results in the symmetric nitro stretch
Fig. 3. The B3LYP/6-311 þ G** eigenvectors for selected nitro
modes of nitrobenzene isotopomers. The differing lengths of arrow
show relative differences in amplitude of the vibrating atom.
Fig. 4. Comparison of the predicted B3LYP/6-311 þ G** and
experimental IR data for nb, nb-14
N, nb-13
C6 and nb-d5.
Fig. 5. Raman and IR spectra for nb-d5 between 1390 and
1310 cm21
; the two largest fitted curves are assigned to nitro
symmetric stretch modes, n9 and n11; coupled to benzene mode
19a.
J. Clarkson, W. Ewen Smith / Journal of Molecular Structure 655 (2003) 413–422 421

10. mixing with benzene mode 14, Fig. 3. This gives rise
to two symmetric nitro stretch modes, *2, that are
predicted to have near identical IR intensity, near half
of that for the *2 mode of nb, separated by 4 cm21
.
The experimental data only shows one intense IR
band for 16
O18
O-nb [10], however, symmetric nitro IR
bands are generally broad features and any possible
splitting of this band may be obscured. It is also
possible that experimentally the two symmetric nitro
stretch modes are degenerate, with both contributing
to the observed peak.
4. Conclusions
The use of the B3LYP functional with the triple
zeta, 6-311 þ G** basis set gives accurate frequen-
cies and IR intensities for nitrobenzene and accounts
for the isotopic shifts observed for the isotopomers,
without the need to rescale the force constants. The
present analysis improves the previous analysis by
Shlyapochinkov et al. [15], accounting for all the
observed fundamentals, plus Fermi resonance, com-
binations and overtones below 1650 cm21
, with the
new data from nb-13
C6 helping in the assignment of
the spectra.
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