JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 24
22 JUNE 2003
Electronic structures, vibrational spectra, and revised assignment
of aniline and its radical cation: Theoretical study
Piotr M. Wojciechowski, Wiktor Zierkiewicz, and Danuta Michalskaa)
Institute of Inorganic Chemistry, Wrocław University of Technology, Wybrzeże,
Wyspiaskiego 27, 50-370 Wrocław, Poland
Pavel Hobza
J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic and
Center for Complex Molecular Systems and Biomolecules, Dolejškova 3, 18223 Prague 8, Czech Republic
共Received 31 January 2003; accepted 25 March 2003兲
Comprehensive studies of the molecular and electronic structures, vibrational frequencies, and
infrared and Raman intensities of the aniline radical cation, C6 H5 NH⫹
2 have been performed by
using the unrestricted density functional 共UB3LYP兲 and second-order Møller–Plesset 共UMP2兲
methods with the extended 6-311⫹⫹G共df,pd兲 basis set. For comparison, analogous calculations
were carried out for the closed-shell neutral aniline. The studies provided detailed insight into the
bonding changes that take place in aniline upon ionization. The natural bond orbital 共NBO兲 analysis
has revealed that the p␲-radical conjugative interactions are of prime importance in stabilizing the
planar, quinoid-type structure of the aniline radical cation. It is shown that the natural charges
calculated for aniline are consistent with the chemical properties of this molecule 共an ortho- and
para-directing power of the NH2 group in electrophilic substitutions兲, whereas Mulliken charges are
not reliable. The theoretical vibrational frequencies of aniline, calculated by the B3LYP method,
show excellent agreement with the available experimental data. In contrast, the MP2 method is
deficient in predicting the frequencies of several modes in aniline, despite the use of the extended
basis set in calculations. The frequencies of aniline radical cation, calculated at the UB3LYP/
6-311⫹⫹G共df,pd兲 level, are in very good agreement with the recently reported experimental data
from zero kinetic energy photoelectron and infrared depletion spectroscopic studies. The clear- cut
assignment of the IR and Raman spectra of the investigated molecules has been made on the basis
of the calculated potential energy distributions. Several bands in the spectra have been reassigned.
It is shown that ionization of aniline can be easily identified by the appearance of the very strong
band at about 1490 cm⫺1 , in the Raman spectrum. The redshift of the N–H stretching frequencies
and the blueshift of the C–H stretching frequencies are observed in aniline, upon ionization. As
revealed by NBO analysis, the frequency shifts can be correlated with the increase of electron
* ) and decrease of ED on ␴ CH
* , respectively. These
density 共ED兲 on the antibonding orbitals ( ␴ NH
effects are associated with a weakening of N–H bonds and strengthening of C–H bonds in the
aniline radical cation. The simulated theoretical Raman and infrared spectra of aniline and its radical
cation, reported in this work, can be used in further spectroscopic studies of their van der Waals
clusters and hydrogen bonded complexes. © 2003 American Institute of Physics.
[DOI: 10.1063/1.1574788]
I. INTRODUCTION
Recent progress in the infrared spectroscopy of isolated
molecular clusters in a supersonic jet has made it possible to
provide detailed information on the nature of hydrogen bond
or van der Waals 共vdW兲 interactions between molecules.
Among the new spectroscopic methods, infrared depletion
spectroscopy, which combines the resonance enhanced multiphoton ionization spectroscopy with time-of-flight mass
spectrometry 共REMPI-TOF-MS兲 is especially useful technique for studying hydrogen bonding between closed-shell
systems in their ground electronic states.1 Aniline, the simplest aromatic amine, is a very good model system for studya兲
Author to whom correspondence should be addressed. Electronic mail:
michalska@ichn.ch.pwr.wroc.pl
0021-9606/2003/118(24)/10900/12/$20.00
ing molecular complexes by infrared depletion spectroscopy,
which exploits an aromatic system as a chromophore in the
infrared-ultraviolet 共IR-UV兲 double resonance technique.2
In the case of radical species, the high-resolution zero
kinetic energy 共ZEKE兲 photoelectron spectroscopy, recently
developed by Schlag and co-workers3 is of particular importance. This technique allows for the accurate determination
of the vibrational frequencies of radical ions and their molecular clusters.
In view of a broad occurrence of aromatic amines in
biological systems, knowledge of the nature of interactions
in the aniline complexes is indispensable. Nakanaga and
co-workers2,4 –7 performed extensive studies on intermolecular interactions in aniline complexes and its radical cations
by infrared depletion spectroscopy. These authors have
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© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
shown, for example, that ionization of the aniline–furan
complex leads to the changes in hydrogen bonding, from the
NH-␴ type in the neutral system to the NH-␲ type in the
cation cluster.5 Schmid et al.6 investigated the NH2
-stretching vibrations of different aniline-X van der Waals
clusters (X⫽N2 , CH4 , CHF3 and CO兲 and their radical cations, using infrared depletion spectroscopy. These authors
suggested that the main interaction force in the cation clusters is different from that in the neutral counterparts.
Aniline was also the first system for which the amino
group nonplanarity was proved.8 Excellent agreement between experimental and theoretical anharmonic inversiontorsion frequencies of fundamental, overtone, and combination modes in aniline has been obtained in the correlated ab
initio studies, which gives a confidence to the calculated potential energy surface, and the evidence to a rather high nonplanarity of aniline molecule.8,9 Sinclair and Pratt9 in their
detailed study of the rotationally resolved S 1 ←S 0 electronic
spectra of aniline, derived inertial parameters of the bare
aniline molecule and confirmed that it is pyramidally distorted at the NH2 group in S 0 , and quasi-planar in the S 1
state. These findings are of fundamental importance since
they have allowed to deduce that the amino groups in nucleic
acid bases are nonplanar.10
The aniline radical cation, C6 H5 NH⫹
2 is also a very attractive object of study. It has been reported that this radical
plays a key role in aniline oxidation polycondensation11 and
in the photoinduced electron transfer phenomena.12 Therefore, investigation of the structural and electronic changes in
aniline, upon its ionization, can help in elucidation of the
mechanism of these processes.
The ZEKE spectra of jet-cooled neutral aniline-Ar van
der Waals complex together with that of the aniline-Ar radical cation have been published by several authors.13–15 The
spectra have provided a number of well-resolved vibrational
bands of aniline cation. Piest et al.16 measured the infrared
absorption spectra of the jet-cooled neutral aniline-Ar and
aniline-Ar⫹ van der Waals complexes, in the range of frequencies 350–1700 cm⫺1 , by using mass-selective ion detection in two different IR-UV double resonance excitation
schemes. From the spectra, these authors inferred several frequencies of the gas-phase aniline radical cation. Recently,
Gée et al.17 reported the infrared spectra of aniline in lowtemperature argon matrix, in the spectral region from 500 to
4000 cm⫺1 . They have also observed five fundamental frequencies of aniline cation, formed inside the matrix by UV
laser irradiation.
Song et al.15 calculated vibrational frequencies of aniline
radical cation by using the unrestricted second-order Møller–
Plesset 共UMP2兲 method combined with a rather small 共631G*兲 basis set. However, one can notice quite large discrepancies between the experimental and the UMP2-calculated
frequencies of aniline cation obtained by these authors. In
our earlier studies on phenols18 –20 we have clearly demonstrated that the MP2 method fails in predicting the frequencies of some normal modes of aromatic ring 共in particular, of
those labeled 4 and 14 in Wilson’s notation for benzene兲. In
contrast, the B3LYP method gives excellent results for these
‘‘troublesome’’ modes in aromatic molecules.18 Therefore, it
Aniline and its radical cations
10901
is interesting to investigate the performance of the MP2
method in the reliable prediction of vibrational frequencies
of aniline.
Numerous theoretical calculations of the infrared spectrum of aniline have been carried out by many authors using
semiemprical, ab initio and DFT methods.15,16,21–28 Nevertheless, despite all the extensive theoretical studies, the assignment of several modes of aniline molecule remains uncertain, while that reported for aniline radical cation is very
ambiguous and contradictory. The reason of this situation is
that earlier vibrational assignments for aniline have been
made either by an approximate description of vibrations, or
by labeling the normal modes 共by analogy to the notations
used for benzene兲 or by plotting the calculated Cartesian displacements of the atoms. Unfortunately, all these approaches
turned out to be very misleading in making comparison between the corresponding normal modes in aniline and its
radical cation. To get the detailed information on the form of
the normal modes, it is indispensable to carry out the rigorous normal coordinate analysis and to calculate the potential
energy distribution 共PED兲 in terms of the internal coordinates.
In this work we have performed comprehensive density
functional and ab initio 共MP2兲 studies of aniline and its radical cation. The results from natural bond orbital 共NBO兲
analysis have provided detailed insight into the bonding and
electronic changes that take place in aniline, upon ionization.
But the primary goal of this work was to obtain the
clear-cut assignment of the vibrational spectra of aniline and
its cation. The theoretical infrared and Raman spectra of both
the molecules are presented. Several bands are reassigned on
the basis of the calculated PED. The shifts of vibrational
frequencies, and the changes in intensities of the IR and Raman bands caused by the ionization of aniline, are thoroughly discussed. The results obtained in this work can be
useful in further studies of the vibrational spectra of hydrogen bonded complexes and van der Waals clusters of aniline
and its radical cation.
II. THEORETICAL METHODS
The optimized equilibrium structure, harmonic frequencies, infrared intensities, and Raman scattering activities of
aniline have been calculated by the density functional threeparameter hybrid model 共DFT/B3LYP兲 共Refs. 29, 30兲 and ab
initio MP2 method.31 For the radical cation, the corresponding unrestricted 共UB3LYP and UMP2兲 methods have been
used. The ground electronic state of the radical cation is 2 B 1 ,
therefore, a spin contamination of the UHF wave function
may occur in an unrestricted calculation. We have examined
the expectation value of the total spin, Ŝ 2 . In UB3LYP calculation the final Ŝ 2 is 0.7503, which is in excellent agreement with the expectation value of 0.7500 for the doublet
ground state. This confirms validity of the UB3LYP results
for radical cation. However, some amount of spin contamination 共about 11%兲 remains in the UMP2 calculations, as
indicated by the final value of Ŝ 2 , 0.8319.
A natural bond orbital 共NBO兲 analysis32,33 has been carried out for aniline and its radical cation using the B3LYP-
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10902
Wojciechowski et al.
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
density matrices. In the studies, the 6-311⫹⫹G共df, pd兲,
6-311G共df, pd兲 and 6-311⫹G共d, p兲 basis sets have been
employed.34 All calculations were performed with the
35
GAUSSIAN 98 package.
The normal coordinate analyses have been carried out
for both the molecules, according to the procedure described
in our earlier papers.36,37 The nonredundant set of 36 internal
coordinates has been used as recommended by Fogarasi and
Pulay.38 The frequencies of the CH and NH stretching vibrations were scaled by 0.958 共derived from the recently reported scaling factor for the valence A–H stretching force
constants39兲. The harmonic frequencies below 2000 cm⫺1
were scaled by the factor of 0.983 共determined in our previous study of similar systems20兲.
It should be noted that the symmetry point group of
aniline is Cs , whereas that of the radical cation is C2 v 共in
their ground electronic states兲. According to IUPAC recommendation for C2 v point group, ␴ XZ reflection plane should
be perpendicular to the ring plane. Thus, the normal modes
of A ⬘ symmetry in aniline correspond to A 1 and B 1 vibrations in cation, while modes of A ⬙ symmetry in aniline correspond to B 2 and A 2 modes in cation 共with A 2 being IR
inactive兲.
The theoretical Raman spectra of aniline and its radical
cation were calculated by using the B3LYP-calculated Raman scattering activities of the normal modes. It should be
emphasized that Gaussian program does not calculate the
Raman spectra 共as stated in Ref. 40兲 since it does not provide
the Raman intensities 共although it gives the infrared intensities兲. However, the Raman intensities can be derived from
the calculated Raman scattering activities of the normal
modes.
We have calculated the Raman spectra of the investigated molecules on the basis of the relation that the intensity
of a Stokes Raman band (I R ) is directly proportional to its
differential scattering cross section 共⳵␴/⳵⍀兲,41
I R ⬇ 关 ⳵␴ / ⳵ ⍀ 兴 i .
共1兲
Ozkabak et al.42 have shown that the theoretical differential
Raman scattering cross section of a Stokes band associated
with the normal mode Q i is given by
关 ⳵␴ / ⳵ ⍀ 兴 i ⫽D 共 ␯ 0 ⫺ ␯ i 兲 4 关 1⫺exp共 ⫺h ␯ i c/kT 兲兴 ⫺1S Ri , 共2兲
where ␯ 0 is the wave number of exciting laser radiation 共in
our calculations we have used ␯ 0 ⫽9398.5 cm⫺1 , which corresponds to the Nd-YAG laser radiation兲; ␯ i is the theoretical
wavenumber (cm⫺1 ) of the normal mode Q i ; k, h, c, and T
are Boltzmann and Planck constants, speed of light, and temperature in Kelvin 共298.15兲, respectively; S Ri is the theoretical Raman scattering activity of the normal mode
(Å4 amu⫺1 ); the constant D is equal 2.3975⫻10⫺15 in our
calculations. In the simulated Raman and IR spectra, the
band shape has been approached by a Lorentzian function
using the ‘‘half-width at half height’’ of 3 cm⫺1 .
TABLE I. Atom distances and bond angles of the neutral aniline 共A兲 and its
radical cation 共B兲 optimized by B3LYP and MP2 methods using the 6-311
⫹⫹G共df, pd兲 basis set, and the experimental data for aniline vapor.
Parametera
B3LYP 共UB3LYP兲
A
B
C1 –N
N–H13
C1 – C2
C2 – C3
C3 – C4
C2 – H8
C3 – H9
C4 – H10
C1 •••C4
C2 •••C6
C3 •••C5
C1 – C2 – C3
C2 – C3 – C4
C3 – C4 – C5
C2 – C1 – C6
C1 – C2 – H8
C4 – C3 – H9
C3 – C4 – H10
C1 – N– H13
H13 – N– H14
␾c
␥d
1.395
1.008
1.401
1.388
1.392
1.084
1.083
1.082
2.812
2.408
2.397
120.49
120.79
118.87
118.56
119.49
119.99
120.56
116.23
112.79
35.51
1.50
1.332
1.012
1.432
1.368
1.410
1.082
1.081
1.082
2.779
2.481
2.453
119.36
120.16
120.85
120.09
119.45
119.74
119.57
121.58
116.82
0.00
0.00
MP2 共UMP2兲
A
B
1.402
1.011
1.400
1.393
1.395
1.086
1.085
1.084
2.813
2.409
2.405
120.51
120.48
119.12
118.69
119.42
120.11
120.41
113.73
110.48
42.84
2.26
1.332
1.011
1.428
1.343
1.403
1.084
1.083
1.084
2.750
2.475
2.452
119.51
119.96
121.03
120.04
119.31
119.40
119.49
121.34
117.32
0.00
0.00
Expt. Anilineb
1.402⫾0.002
1.001⫾0.001
1.397⫾0.002
1.394⫾0.003
1.396⫾0.002
1.082⫾0.004
1.083⫾0.002
1.080⫾0.002
120.12⫾0.20
120.70⫾0.08
118.92⫾0.08
119.43⫾0.20
119.83⫾0.20
119.92⫾0.08
120.54⫾0.08
115.94
113.10⫾2
a
Atom distances in Å, bond angles in deg.
From the gas-phase microwave studies reported in Ref. 43.
c
Angle between the bisector of the HNH angle 共in the NH2 plane兲 and the
axis passing through the C1 and C4 atoms.
d
Angle between the C1 –N bond axis and the C1 – C4 axis.
b
III. RESULTS AND DISCUSSION
A. Geometrical structure
The optimized geometrical parameters of both the molecules are listed in Table I, together with the experimental
values for aniline obtained from the gas-phase microwave
studies.43 Figure 1 shows the numbering of atoms. The theoretical and experimental data indicate that the neutral
aniline in its ground electronic state ( 1 A 1 ) is nonplanar.8,9,43– 45 However, it should be noted, that the degree of
NH2 pyramidalization varies, depending on the experimental
method employed. The dihedral angle between the NH2
plane and the C6 H5 N plane has been determined as 37⫾2°,
by the microwave studies 共with the assumption that the C–N
bond is coplanar with the ring兲.43 This angle is slightly larger
共42⫾1°兲 when determined by resonance fluorescence44 or by
far infrared data.45
According to our calculations, at both levels of theory,
the C1 –N bond is slightly bent and it makes an angle ␥ of
about 1.5°–2.3° with the C1 –C4 axis 共Table I兲. It should be
noted that the bond lengths and angles of the neutral aniline
calculated at the MP2/6-311⫹⫹G共df, pd兲 level are in excellent agreement with the microwave data. For example, the
experimental C1 –N bond length as well as C–C distances in
the ring are almost reproduced at this level of theory. The
B3LYP calculated geometry of aniline is also in very good
agreement with experiment.
According to calculations with both the unrestricted
methods 共UB3LYP and UMP2兲, the aniline radical cation in
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
FIG. 1. The numbering of atoms in aniline 共A兲 and its radical cation 共B兲,
and the natural charges from NBO analysis 关B3LYP/6-311⫹⫹G共df, pd兲 calculations兴.
its ground electronic state ( 2 B 1 ) is planar (C2 v symmetry兲.
The C1 –N bond is shortened to 1.332 Å, in comparison to
the neutral aniline. This indicates the formation of a partial
double CN bond upon ionization. It is interesting to note that
the calculated N7 –H bond lengths are slightly longer in cation than in the neutral aniline, as revealed by density functional method, while they remain unchanged in MP2 calculations. The former result is in agreement with the
experimental data from the IR spectra,7 as will be shown
later.
It follows from Table I that both the C1 NH and HNH
bond angles considerably increase in cation, as compared to
the neutral molecule. Furthermore, significant geometrical
changes are noticed in the ring. In cation, the C1 –C2 共and
equivalent C1 – C6 ) distances are elongated by 0.031 Å, the
C2 – C3 共and C5 – C6 ) bond lengths are shortened by 0.020 Å,
and C3 – C4 共and C4 – C5 ) bond lengths are elongated by
0.018 Å 共B3LYP results兲. It should be noted that the unrestricted MP2 method slightly exaggerates the quinoid-type
structure of the ring in aniline cation, since the calculated
C2 – C3 共and C5 – C6 ) bond lengths are shortened by as much
as about 0.05 Å.
The distances between the nonbonded carbon atoms in
the ring also change in cation, in comparison to those in
aniline. According to the B3LYP results, the distances
C2 •••C6 and C3 •••C5 increase by 0.073 Å and 0.056 Å,
respectively 共Table I兲. This is accompanied by a shortening
of the C1 •••C4 distance by 0.033 Å 共versus 0.063 Å in MP2
calculations!兲. The UMP2 results can be affected by some
spin contamination, as noted earlier.
Aniline and its radical cations
10903
FIG. 2. The differences between the natural charges on the corresponding
atoms in aniline radical cation and in the neutral aniline (⌬q⫽q cation
⫺q neutral) calculated by the MP2 and B3LYP methods using 6-311
⫹⫹G共df, pd兲 basis set. Due to the presence of the reflection plane (C s
symmetry兲 the results for the half of the molecule are shown.
are illustrated in Fig. 2. As follows from this figure, the MP2
method predicts the largest difference on the C4 carbon atom,
since the natural charge on C4 increases by 0.263 e 共from
⫺0.219 e in aniline to 0.044 e in cation兲. According to
B3LYP calculation, the positive charge is delocalized mainly
between the C4 and N7 atoms, the charge on C4 increases by
0.210 e, while that on nitrogen increases by 0.228 e. Furthermore, the B3LYP method shows an increase of charge 共by
about 0.1 e兲 on the carbon atoms in the ortho-position, C2
and C6 , in cation.
It should be stressed that in the case of aniline, the net
atomic charges obtained from Mulliken population analysis
show extremely strong basis set dependence and they vary
considerably with the method employed in calculations. For
example, the Mulliken charge on the C1 atom in aniline varies from ⫺0.57 e 共MP2兲 to ⫺0.91 e 共B3LYP兲 when the 6-311
⫹⫹G共df,pd兲 basis set is used in calculations, and it increases
to about ⫹0.10 e 共MP2 and B3LYP兲 when the diffuse functions are excluded from the above basis sets. Figure 3 illustrates comparison between the natural and Mulliken charges
on the corresponding atoms of the neutral aniline 关calculations performed at the B3LYP/6-311⫹⫹G共df, pd兲 level兴. One
B. Natural charges „NBO population versus Mulliken
population analysis…
Figure 1 compares the natural charges of aniline 共A兲 and
its radical cation 共B兲 calculated by density functional method
using 6-311⫹⫹G共df, pd兲 basis set. It is evident from this
comparison that the total charge 共⫹1兲 of the aniline radical
cation is not localized, but is distributed among all atoms.
The differences between natural charges on the corresponding atoms in aniline radical cation and the neutral molecule
FIG. 3. Comparison of atomic charges in the neutral aniline obtained from
the NBO and Mulliken population analyses 关calculations performed at the
B3LYP/6-311⫹⫹G共df, pd兲 level of theory兴.
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10904
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
TABLE II. Occupancies of natural orbitals 共NBOs兲a in the ␣ and ␤ spin system of aniline radical cation
calculated at the UB3LYP/6-311⫹⫹G共df,pd兲 level
Donor
Lewis-type
NBOs
␴C1N
␴NH
␴C2H
␴C3H
␴C4H
␴C1C2
␴C2C3
␴C3C4
␲C2C3
␲C1N
LPN
p C4
␣
␤
⌬b
0.9968
0.9949
0.9895
0.9894
0.9909
0.9871
0.9904
0.9911
0.8494
0.9965
0.9950
0.9896
0.9894
0.9908
0.9866
0.9904
0.9908
0.8566
0.9286
⫺0.0015
⫺0.0011
⫺0.0004
⫺0.0017
⫺0.0012
⫺0.0018
⫺0.0039
⫺0.0037
0.9135
0.5832
⫺0.9373
Acceptor
non-Lewis
NBOs
␴C*1N
*
␴NH
␴C*2H
␴C*3H
␴C*4H
␴C*1C2
␴C*2C3
␴C*3C4
␲C*2C3
␲C*1N
p C⬘ 1
p C⬘
4
␣
␤
⌬b
0.0087
0.0042
0.0060
0.0064
0.0052
0.0119
0.0062
0.0071
0.1546
0.0085
0.0044
0.0062
0.0064
0.0054
0.0120
0.0064
0.0073
0.0308
0.0529
⫺0.0024
⫺0.0011
⫺0.0016
⫺0.0007
⫺0.0032
⫺0.0002
⫺0.0016
⫺0.0019
0.4881
0.2409
a
The core and Rydberg NBOs are omitted, for clarity. LPN is a valence lone pair orbital on nitrogen, p C is a
valence p-type orbital on carbon, starred label 共*兲 denotes antibonding orbital and ‘‘prime’’ label 共⬘兲 identifies
a non-Lewis 共formally empty兲 orbital.
b
⌬ is the difference between the total 共␣⫹␤兲 occupancy of the NBO in the radical cation and the occupancy of
the corresponding NBO in aniline.
can notice quite large discrepancies between these results.
According to NBO analysis, the ortho-carbon atoms (C2 and
C6 ) and the para-carbon atom C4 have the largest negative
charges among all carbon atoms in aniline ring. This is in
accordance with the well known fact that the amine substituent in the benzene ring has a strong ortho- and paradirecting power for the electrophilic substitution. However,
the opposite result has been obtained by Mulliken population
analysis. As follows from Fig. 3, the meta-carbon atoms (C3
and C5 ) have much higher negative charges than ortho- and
para-carbons. Moreover, both the C2 and C6 atoms are positively charged 共⫹0.38 e兲 which precludes the electrophilic
substitution at the ortho-position in aniline. Thus, it can be
concluded that natural atomic charges can be used for reliable description of the chemical properties of aniline,
whereas the Mulliken charges have unrealistic values for this
molecule.
C. NBO analysis
The natural bond orbital 共NBO兲 analyses of aniline and
its radical cation have revealed very interesting and valuable
details on the electronic structures of these molecules.
In this method, delocalization of electron density between occupied Lewis-type 共bonding or lone pair兲 orbitals
and formally unoccupied 共antibonding or Rydberg兲 nonLewis NBOs corresponds to a stabilizing donor–acceptor interaction. The strength of this interaction can be estimated by
the second order perturbation theory.32
The results of the NBO analysis performed for the
closed-shell ground state of aniline indicate that the electronic interactions in the ring are dominated by strong conjugation allowing each localized ␲ bond orbital to delocalize
into two adjacent ␲* antibonding NBOs ( ␲ i → ␲ *j ). These
interactions are similar to those calculated for benzene.46
Also, very important in the neutral aniline is the electron
donation from the nitrogen lone pair orbital, LPN , to the
* orbitals in the ring. The LPN orantibonding acceptor ␲ CC
bital has 90.6% p-character and is occupied by 1.8508 electrons 共this is consistent with a delocalization of electron density from the idealized occupancy of 2.0 e兲. A strong LPN
* interaction decreases pyramidalization of the NH2
→ ␲ CC
group in aniline molecule and flattens the molecule.
In the case of aniline radical cation, the NBO procedure
has been applied separately to ␣ and ␤ spin density matrices,
according to the method of ‘‘different hybrids for different
spins’’ 共DHDS NBO兲 described by Carpenter and Weinhold
for open-shell species.33
Table II collects the calculated occupancies in NBOs of
aniline radical cation 共for ␣ and ␤ spin systems兲. In addition,
the calculated differences 共⌬兲 between the corresponding
NBO occupancies in radical and neutral aniline, are also included. The Rydberg NBOs 共extra-valence orbitals兲 have
relatively small occupancies, therefore, they are omitted
from this table.
It should be emphasized that gain 共or loss兲 of occupancy
in antibonding acceptor orbital can be directly correlated
with a weakening 共or strengthening兲 of the bond associated
with this orbital. As follows from Table II, in the radical
cation, the total occupancy in the C1 – N sigma antibonding
* ) decreases by 0.0024 e, in comparison to the
orbital ( ␴ CN
neutral aniline. This implies that upon ionization, the C1 – N
bond becomes stronger, which is consistent with experimental data. From Table II it is further evident that electron density at nitrogen lone pair LPN , decreases 共by 0.9373 e兲 which
gives clear evidence on planarization of amino group when
going from the neutral aniline to the radical cation.
On the other hand, the NBO analysis of aniline radical
cation predicts an increase in occupancy of the NH antibond* ), by about 0.0011 e, which is associated
ing orbitals ( ␴ NH
with a weakening of the N–H bonds. This prediction is also
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
supported by the reported experimental data showing the
redshift of the N–H stretching frequencies in the radical cation, in comparison to aniline.7
This finding is, however, unexpected since in the case of
guanine, planarizaton of amino group is connected with a
contraction of the NH bond and a blueshift of the respective
stretching frequency.47 Decrease of electron density at the
amino nitrogen lone electron pair of guanine 共occurring as
the result of dimerization of guanine兲 yields planarization of
amino group and a significant blueshift of the N–H stretching frequency. According to the NBO results obtained in this
work, the N–H hybridization changes when going from the
neutral aniline (s p 2.82) to the cation (s p 2.43). Decrease of
p-character and simultaneous increase of the s-character
共upon ionization兲 should be related to contraction of the NH
bond length in the system. However, in the aniline radical
cation, the N–H stretching frequency is shifted to the red,
*
which is due to an increase of electron density on the ␴ NH
orbital. Evidently, the two mentioned processes 共change in
hybridization and electron density transfer to the antibonding
orbital兲 compete, and the latter one is more pronounced.
It is also interesting to note that the occupancies of all
* ) are smaller in cation than in the neutral
CH antibonds ( ␴ CH
molecule. This indicates a strengthening of the CH bonds
upon ionization. In accordance with this prediction, all the
calculated frequencies of the C–H stretching vibrations are
blueshifted in the radical cation, as compared to the neutral
aniline 共these results will be shown later in the discussion of
vibrational spectra兲.
The results obtained for aniline radical reveal the presence of two ␲ CC orbitals 共␲ C2C3 and ␲ C5C6兲 and one ␲ C1N
orbital, which is consistent with the quinod-type structure.
The ␣ spin 共majority兲 electrons seem to be more delocalized
than ␤ spin electrons. As is seen in Table II, a striking feature
of the ␣ spin system is the occupancy of only 0.5832 e in the
valence pure p-orbital on C4 carbon atom, p C4 共orthogonal to
the molecular plane兲. It should be mentioned that in the idealized Lewis structure of aniline radical cation, this p-orbital
is singly occupied by the ‘‘unpaired’’ electron. The loss of ␣
spin electron density from this orbital is undoubtedly caused
by the radical conjugation. Examination of the donor–
acceptor interaction energies has revealed that this effect is a
direct result of a strong donation of density from the p C4
orbital to two acceptor antibonding NBOs (p C4 → ␲ C* C and
2 3
p C4 → ␲ C* C ) in accord with the usual chemical picture of the
5 6
radical conjugation. The other dominant interaction in the
aniline radical cation involves donation of ␣ spin electron
density from the nitrogen lone pair orbital, LPN 共which has
99.97% p-character兲 to the empty valence p orbital on the C1
atom, p C⬘ . 共In the Lewis structure of the ␣ spin system this
1
p-orbital is formally empty, therefore, it is labeled by
‘‘prim.’’兲 The latter interaction builds a partial double bond
between N and C1 atoms. Furthermore, in the ␣ spin system
one can note the conjugative interactions: ␲ CC→p C⬘ and
1
* 共the formally empty orbital p C⬘ is acting as the
p C⬘ → ␲ CC
1
1
acceptor in the former, and as the donor orbital in the latter
Aniline and its radical cations
10905
transition兲. The resulting occupancy of the p C⬘ orbital is
1
quite high, 0.4881 e.
In the ␤ spin system, the bonding ␲ C1N is formed by an
overlap of two pure p-type valence orbitals 共on carbon C1
and N atoms兲, and is occupied by 0.9286 electrons. The examination of the estimated energies of the donor–acceptor
interactions in the ␤ spin system has revealed a great importance of the ␲ CC→p C⬘ interactions, i.e., donation of electron
4
density from two bonding ␲ CC NBOs to the valence p-orbital
on the C4 atom, p C⬘ .A large occupancy 共0.2409 e兲 of this
4
non-Lewis orbital reflects a high delocalization of ␤ spin
* and
⬘ → ␲ CC
electrons. The other conjugative interactions, p C4
␲ CC→ ␲ C*1N , lead to an increase in occupancies of ␲ * antibonds in the ␤ spin system.
Thus, it can be concluded that strong conjugation effects
extend over all aniline radical cation, and stabilize the planar
geometry of this species. It also follows from calculations,
that ionization of aniline leads to the quinoidlike distortion of
the ring and, consequently, to significant double bond character of the exocyclic CN bond. The ‘‘unpaired’’ electron is
not localized on the C4 atom, but is diffused to the ring.
It is worth noticing that the results presented in Table II
have been obtained from density matrices calculated by the
unrestricted B3LYP method with the 6-311⫹⫹G共df,pd兲 basis
set, however, the NBO analysis performed with a smaller
basis set 共without the diffuse functions兲 has yielded very
similar results.
D. Vibrational spectra and their assignment
Table III lists the theoretical frequencies, infrared intensities and Raman scattering activities of the neutral aniline
and its radical cation, obtained from the B3LYP 共UB3LYP兲
calculations using the extended 6-311⫹⫹G共df, pd兲 basis set.
These data are compared with the recently reported experimental frequencies of aniline in low-temperature argon
matrix,17 and with the gas-phase frequencies of aniline radical cation.16 Some experimental frequencies from the earlier
studies on aniline48,49 have also been employed for comparison with the theoretical values. The calculated potential energy distribution 共PED兲 for the cation is shown in the table
共the different PED obtained for the neutral aniline is indicated under the table兲. According to the results obtained, the
two modes in aniline radical cation, Q25 (B 2 ) and Q26 (A 1 )
have entirely different character than the other two modes
共Q25⬘ and Q26⬘兲 in the neutral aniline, therefore, the PED
elements of these four normal modes are explicitly shown in
Table III. To facilitate comparison of our results with those
reported by other authors13–17,21–28 the normal modes of
aniline are labeled in Table III, according to the convention
used by Varsányi50 for substituted benzenes.
In addition, we have also performed calculations of the
vibrational spectra of aniline by the MP2 method using two
basis sets, 6-311⫹G共d,p兲 and 6-311⫹⫹G共df, pd兲. The detailed examination of the PED calculated at different theoretical levels has revealed deficiencies of the MP2 method in
predicting frequencies of aniline, which will be discussed
later.
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10906
Wojciechowski et al.
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
TABLE III. Comparison of the experimental wave numbers (cm⫺1 ) and theoretical harmonic frequencies 共␻, cm⫺1 ), infrared intensities (A IR, km/mol兲 and
Raman scattering activities, (S R , Å4 /amu兲 of aniline and its radical cation calculated by the B3LYP 共UB3LYP兲 method using 6-311⫹⫹G共df, pd兲 basis set.
Vibrational assignment is based on the calculated potential energy distribution 共PED兲.
Aniline-B3LYP/6- 311⫹⫹G共df, pd兲
No.
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
Q20
Q21
Q22
Q23
Q24
Q25
Q26
Q25⬘
Q26⬘
Q27
Q28
Q29
Q30
Q31
Q32
Q33
Q34
Q35
Q36
Sym. 共label兲 Expt.
a
A⬘
A⬙
A⬙
A⬙
A⬘
A⬘
A⬘
A⬙
A⬘
A⬘
A⬙
A⬘
A⬘
A⬙
A⬘
A⬘
A⬘
A⬙
A⬙
A⬙
A⬘
A⬘
A⬙
A⬙
A⬘
A⬙
A⬙
A⬘
A⬘
A⬘
A⬙
A⬘
A⬙
A⬘
A⬘
A⬙
共16a兲
共16b兲
共6a兲
共6b兲
共4兲
共11兲
共10a兲
共1兲
共17b兲
共17a兲
共5兲
共12兲
共18a兲
共18b兲
共9b兲
共9a兲
共20a兲
共14兲
共3兲
共19a兲
共8b兲
共19b兲
共8a兲
共13兲
共7b兲
共7a兲
共20b兲
共2兲
217e
277g
390h
415h
501h
526h
共541兲i
619h
688
755
812
822
875
957h
968h
996
1028
1054h
1115h
1152h
1176
1282
1324h
1340h
1503
1594
1470h
1608
1618
3025h
3037h
3050h
3072h
3422o
3508o
␻
b
A
IR
217
5.6
289 16.8
377
0.3
410
0.2
489 166.0
525 48.7
541 107.0
626
0.3
689 27.6
752 69.2
816
0.0
819
4.9
873
6.9
951
0.0
966
0.1
996
2.7
1031 3.5
1043 2.6
1115
5.0
1163
2.1
1183 11.3
1280 72.6
1323 7.2
1349 0.0
Cation radical-UB3LYP/6-311⫹⫹G共df, pd兲
SR
0.8
0.3
0.6
0.0
1.0
1.5
7.9
4.5
0.2
1.4
0.2
21.8
0.1
0.0
0.2
34.9
18.2
0.1
2.3
4.1
2.8
13.3
1.6
0.3
1508 66.5
5.4
1599 1.4
3.7
1477 1.4
1.2
1617 24.1 16.7
1632 160.9 30.3
3021 17.1 16.7
3022 3.6 108.8
3038 4.1 166.8
3044 33.0 23.4
3060 11.7 247.9
3430 20.3 194.9
3526 17.1 56.0
c
Sym. Expt.
B1
A2
B2
A2
B1
A1
B1
B2
B1
B1
A2
A1
B1
A2
B1
A1
A1
B2
B2
B2
A1
A1
B2
B2
B2
A1
B2
A1
A1
A1
B2
A1
B2
A1
A1
B2
179f
386
442
519
652
582f
622
785
814f
913
982f
993
1107
1188f
1385f
1360
1434
1483
1515
1594f
1635
3395o
3488o
␻
b
A
IR
SR
PED 共%兲d
␶ 3 ring 共53兲, ␥ C1 N 共19兲, ␶ 2 ring 共17兲
tors NH2 共90兲
␤ C1 N 共79兲, ␤ 3 ring 共10兲
␶ 2 ring 共72兲, ␶ 3 ring 共24兲
␶ 1 ring 共36兲, ␥ C1 N 共33兲, ␶ 3 ring 共28兲
␤ 2 ring 共82兲
wag NH2 共85兲
␤ 3 ring 共76兲
␶ 1 ring 共50兲, ␥ C1 N 共⫹13兲, ␥NH2 共⫺12兲, ␥ C4 H 共⫹10兲j
␥ C1 N 共⫹27兲, ␶ 1 ring 共23兲, ␥ C4 H 共⫺21兲
␥ C2 H 共⫹33兲, ␥ C6 H 共⫺33兲, ␥ C3 H 共⫹14兲, ␥ C5 H 共⫺14兲
␯(C1 –C2 ) 共⫹28兲, ␯(C1 –C6 ) 共⫹28兲, ␯(C1 –N兲 共⫹18兲
␥C4 H 共⫹37兲, ␥C2 H 共⫺28兲, ␥C6 H 共⫺28兲
␥C3 H 共⫹35兲, ␥C5 H 共⫺35兲, ␥C2 H 共⫺15兲, ␥C6 H 共⫹15兲
␥C3 H 共⫹32兲, ␥C5 H 共⫹32兲, ␥C4 H 共⫺26兲
␤ 1 ring 共63兲, ␯共C–C兲 共31兲
␯(C3 – C4 ) 共⫹31兲, ␯(C4 – C5 ) 共⫹31兲, ␤CH 共16兲
rock NH2 共59兲, ␯(C1 – C2 ) 共⫹13兲, ␯(C1 – C6 ) 共⫺13兲
␤C4 H 共⫹21兲, ␯(C4 – C5 ) 共⫺16兲, ␯(C3 – C4 ) 共⫹16兲k
␤C3 H 共⫹21兲, ␤C5 H 共⫹21兲, ␤C4 H 共⫺19兲, ␯共C-C兲 共20兲
␤C2 H 共⫹21兲, ␤C6 H 共⫺21兲, ␤C3 H 共⫺16兲, ␤C5 H 共⫹16兲
␯(C1 –N兲 共⫹42兲, ␤C3 H 共⫺10兲, ␤C5 H 共⫹10兲
␯共C–C兲 共76兲tot
␤C4 H 共⫹23兲, ␤C2 H 共⫹21兲, ␤C6 H 共⫹21兲
␤C3 H 共16兲, ␤C5 H 共16兲, ␯(C1 – C2 ) 共⫺13兲, ␯(C1 – C6 ) 共13兲
␯(C1 –N兲 共⫹23兲, ␤C3 H 共⫹13兲, ␤C5 H 共⫺13兲
␤C3 H 共⫹16兲, ␤C5 H 共⫺16兲, ␤C2 H 共⫹13兲, ␤C6 H 共⫺13兲l
␯(C3 –C4兲共18兲,␯共C4 –C5兲共⫺18兲,␯共C1 –C2兲共⫺17兲,␯共C1 –C6兲共17兲m
1524 12.9
1.6 ␤C4 H 共⫹28兲, ␯(C2 –C3 ) 共⫺15兲, ␯(C5 –C6 ) 共⫹15兲
1604 28.0 68.6 ␯(C2 – C3 ) 共⫹25兲, ␯(C5 – C6 ) 共⫹25兲, ␤CH 共24兲n
1646 114.9 12.0 sciss NH2 共86兲, ␯(C1 –N兲 共12兲
3056 0.0
42.3 ␯(C2 –H兲 共⫹40兲, ␯(C6 –H兲 共⫹40兲
3057 1.4
62.2 ␯(C2 –H兲 共⫹46兲, ␯(C6 –H兲 共⫺46兲
3066 0.0
71.9 ␯(C4 –H兲 共⫹64兲, ␯(C3 –H兲 共⫺10兲, ␯(C5 –H兲 共⫺10兲
3076 3.8
40.2 ␯(C3 –H兲 共⫹46兲, ␯(C5 –H兲 共⫺46兲
3080 2.4 260.0 ␯(C3 –H兲 共⫹32兲, ␯(C5 –H兲 共⫹32兲, ␯(C4 –H兲 共⫹31兲
3391 257.7 120.0 ␯s NH2 共100兲
3498 95.0 48.5 ␯ as NH2 共100兲
181
555
383
361
444
524
639
585
626
785
804
811
928
995
1004
979
992
1010
1113
1171
1193
1375
1361
1351
1449
1491
7.3
0.0
2.7
0.0
10.5
1.0
82.8
0.6
119.6
70.6
0.0
0.3
5.2
0.0
1.0
0.4
8.6
0.0
12.3
0.2
0.1
1.4
10.6
1.4
5.4
76.7
0.2
0.3
1.3
0.0
0.1
17.3
0.6
2.9
0.2
0.5
0.2
23.0
0.4
0.1
0.0
12.4
26.5
0.1
2.0
0.0
21.6
35.9
1.5
1.1
9.0
129.8
a
Experimental wave numbers for aniline from Ref. 17 or otherwise, as indicated.
The scaling factor for frequencies was 0.983, except for modes Q30–Q36 scaled by 0.958, see text.
c
Experimental wave numbers for radical cation from Ref. 16 or otherwise, as indicated.
d
PED calculated for cation 共predominant values兲. Different PED for neutral aniline is indicated in the last column, and under the table. Abbreviations: ␯,
stretching; ␤, in-plane bending; ␥, out-of-plane bending; ␶, torsional vibration; sciss, scissoring; rock, rocking; wag, wagging; tors, torsion; tot, total. The
phases of internal coordinates are indicated by signs: The plus sign corresponds to the clockwise in-plane bending, or the in-phase stretching 共or the
out-of-plane bending兲 vibrations; the minus sign has the opposite meaning.
e
Reference 49.
f
Reference 15.
g
Reference 45.
h
Reference 48.
i
Reference 24.
j
Different PED for aniline共A兲: ␶ 1 ring 共87%兲.
k
A:⫹rock NH2 共27%兲.
l
PED for Aniline.
m
PED for A.
n
A:⫹NH2 sciss 共26%兲.
o
Reference 7.
b
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
Aniline and its radical cations
10907
FIG. 4. Theoretical infrared spectra of the neutral aniline 共A兲 and its radical
cation 共B兲, calculated at the B3LYP/6-311⫹⫹G共df, pd兲 level.
Figure 4 illustrates the theoretical infrared spectra of
aniline 共A兲 and its radical cation 共B兲, calculated with the
B3LYP method. The theoretical Raman spectra of these molecules are shown in Figs. 5 and 6. It follows from these
figures that the Raman spectra have revealed significant
changes in the relative intensity pattern of the corresponding
bands in aniline and its radical cation, particularly, in the
range of frequencies of 0–2000 cm⫺1 .
FIG. 6. Theoretical Raman spectra of the neutral aniline 共A兲 and its radical
cation 共B兲, in the range of frequencies 2800–3600 cm⫺1 , calculated at the
B3LYP/6- 311⫹⫹G共df, pd兲 level.
1. NH 2 vibrations
FIG. 5. Theoretical Raman spectra of the neutral aniline 共A兲 and its radical
cation 共B兲, in the range of frequencies 0–2000 cm⫺1 , calculated at the
B3LYP/6-311⫹⫹G共df, pd兲 level.
The NH2 stretching frequencies of aniline and its cation
have been accurately determined by Nakanaga et al.7 using
the infrared depletion spectroscopy. For the neutral aniline
these authors observed two absorption bands, of approximately equal infrared intensities, positioned at 3508 and
3422 cm⫺1 . They assigned these bands to the NH2 antisymmetric and symmetric stretching vibrations, respectively. As
is seen in Table III, the theoretically predicted frequencies
and IR intensities of the corresponding modes in aniline,
Q36 and Q35, are in very good agreement with the experimental data. In the case of radical cation, the agreement is
excellent, the experimentally determined frequencies, 3488
and 3395 cm⫺1 共Ref. 7兲 are almost reproduced by our calculations. Nakanaga et al.7 noticed that N–H absorption bands
in the IR spectrum of cation are much stronger, in comparison to aniline. This effect is also confirmed by the B3LYP
results. It is clear from Fig. 4 that the calculated infrared
intensities of the N–H stretching vibrations in radical cation
共B兲 are several times larger than those in aniline 共A兲. The
redshift of their frequencies, by about 20–30 cm⫺1 共Figs. 4
and 6兲 indicates a weakening of the N–H bond in aniline,
upon ionization. This is supported by the results from NBO
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10908
Wojciechowski et al.
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
analysis, which have shown an increase of electron density
* ) in the radical cation.
on the NH antibonding orbital 共␴ NH
The calculated PED has revealed that the NH2 scissoring
vibration in the neutral aniline contributes to two modes,
Q28 共8a兲 and Q29 共with the predominant contribution to the
latter mode兲. These modes have been assigned to the bands
at 1608 and 1618 cm⫺1 , respectively, in the IR spectrum of
aniline in argon matrix.17. In radical cation, mode Q29 corresponds to almost pure NH2 scissoring vibration and its
frequency shifts to 1635 cm⫺1 in the experimental
spectrum.16,17
Evans,48 in the IR spectroscopic studies of aniline in the
gas phase and inert solvents, suggested that the two bands, at
1054 and 1115 cm⫺1 , involve NH2 deformation vibration.
Our calculation for aniline clearly indicates that Q18 and
Q19 modes involve considerable contribution from the NH2
rocking vibration, 43% and 27%, respectively. Furthermore,
the calculated frequencies of these modes, 1043 and 1115
cm⫺1 , are in excellent agreement with the corresponding experimental values. It should be noted that several
authors17,23,26 misassigned the mode Q19 共18b兲 to the band
observed at about 1090 cm⫺1 . The latter band arises probably from an overtone of the NH2 wagging mode, as suggested by Rauhut and Pulay.24
According to our calculations for radical cation, the Q18
mode (NH2 rocking vibration兲 shifts to a lower frequency 共to
about 1010 cm⫺1 ), while both its IR and Raman intensities
drop to almost zero. Therefore, this vibration may not be
observed in the spectra. On the contrary, quite significant IR
intensity has been predicted for the Q19 mode in cation.
Thus, the latter mode can be assigned to the band at 1107
cm⫺1 , observed by Piest et al.16 in the IR spectrum of
aniline cation. It should be noted that the calculated frequency of this mode, 1113 cm⫺1 is in very good agreement
with the experimental.
The NH2 wagging vibration in aniline 共which corresponds to the ammonia inversion兲 is so strongly anharmonic
that it is impossible to predict its frequency within harmonic
approximation. It can be described by a symmetric double
minimum potential, with a barrier to inversion of 526
cm⫺1 . 8,49 Absorptions observed in the far IR spectrum of
aniline vapor, 40.8 and 423.8 cm⫺1 , have been assigned to
the fundamental and the first overtone transitions,
respectively.45,49 These frequencies were very well reproduced in correlated ab initio studies using the anharmonic
potential for inversion motion in aniline.8 Niu et al.21 and
Rauhut and Pulay24 in their calculations have derived the
frequency of 541 cm⫺1 共from the average of the two transitions, 1→3 and 0→2兲 as the harmonic approximation of the
frequency of the inversion mode in aniline. 共This value is
quoted in Table III for the mode Q7.兲 It is interesting to note
that our calculated frequency 共541 cm⫺1 ) reproduced their
estimate.
The aniline radical cation is planar, therefore the frequency of the NH2 wagging vibration (B 1 ) is much higher.
Moreover, this frequency is quite well predicted within the
harmonic approximation, as shown in Table III 共mode Q7兲.
Piest et al.16 assigned this vibration at 652 cm⫺1 , and other
authors assigned this mode at similar frequency, 656 – 658
cm⫺1 . 14,15,17 Our calculated frequency, 639 cm⫺1 , confirms
their assignment. It should be noted that the UMP2/6-31G*
calculation for aniline radical cation yielded much too low
frequency for this mode, 532 cm⫺1 . 15
Of particular interest is the assignment of the NH2 torsional vibration in aniline, since the frequency of this mode
has been used in calculations of the torsional barrier, V t2 .
Larsen et al.45 examined the far infrared spectrum of aniline
vapor and assigned this mode at 277.3 cm⫺1 . However, other
authors tentatively assigned this vibration at 216 cm⫺1 . 21,23
Our calculated frequency, 289 cm⫺1 for the mode Q2, supports the assignment given in Ref. 45.
As follows from Table III, in the planar radical cation,
the theoretically predicted frequency of the NH2 torsional
vibration, 555 cm⫺1 共mode Q2兲, is almost twice as large as
that in the neutral aniline. Moreover, this mode becomes IR
inactive (A 2 symmetry兲. This indicates that the earlier assignment of the band at 356 cm⫺1 to the NH2 torsional vibration in aniline radical cation, reported by other
authors,15,16 is wrong.
2. C – N vibrations
Upon ionization of aniline, the C1 – N bond significantly
shortens due to an increased conjugation between the planar
NH2 group and the ring, as discussed earlier. The structural
changes and redistribution of electron density in the C1 – N
bond are clearly demonstrated in the IR and Raman spectra
of aniline radical cation 共B兲.
In the IR spectrum of cation the new band arises at 1483
cm⫺1 . 16,17 According to calculations, this band can be assigned to the mode Q26 (A 1 symmetry兲 which is the coupled
vibration involving the C1 – N stretching 共23%兲 and the inplane CH bending vibrations, as shown in Table III. The
theoretical frequency of this mode, 1491 cm⫺1 , is very close
to the experimental value. It should be emphasized that this
mode gives rise to the strongest band in the Raman spectrum
of radical cation, as predicted by the calculated Raman intensities 关Fig. 5共B兲兴.
As revealed by the PED obtained for the neutral aniline,
the stretching ( ␯ C1 – N) vibration has predominant contribution 共51%兲 to the mode Q22. This vibration has been assigned at 1282 cm⫺1 in the IR spectrum of aniline in the Ar
matrix.17. Our calculated frequency, 1280 cm⫺1 , is in excellent agreement with the experimental. In the case of radical
cation, the predicted frequency of mode Q22 increases to
1375 cm⫺1 , while the theoretical IR intensity of this mode
dramatically decreases, as is seen in Fig. 4共B兲. On the other
hand, the Raman intensity of this mode in cation 共B兲 is
nearly three times higher than that in the neutral aniline 共A兲,
as shown in Fig. 5. On the basis of these results, we have
assigned the weak infrared band at 1385 cm⫺1 , reported by
Song et al.,15 to the mode Q22 in radical cation. It should be
noted that the frequency of this mode 共1456 cm⫺1 ) reported
from the UMP2/6-31G* calculations15 was overestimated by
about 70 cm⫺1 , in comparison to experiment.
As is seen from Table III, mode Q12 also involves significant contribution from the C1 – N stretching vibration. In
the IR spectrum of aniline in argon matrix this vibration has
been attributed to the band at 822 cm⫺1 , 17 which is sup-
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
ported by our calculations. Thus, the earlier assignment of
the two bands, at 812 and 822 cm⫺1 , to the modes Q12 共1兲
and Q11 共10a兲, respectively, reported by Evans48 and followed by other authors,23 should be reversed.
According to calculations, the in-plane C1 – N bending
vibration in aniline cation 共mode Q3兲 has the theoretical frequency of 383 cm⫺1 共Table III兲. This is in very good agreement with the experimental frequency, 386 cm⫺1 , reported
by Piest et al.,16 and rules out the earlier assignment of this
vibration to the band at 550 cm⫺1 . 15
The C1 – N out-of-plane bending vibration is coupled
with ring torsions and contributes mainly to the modes Q1,
Q5, and Q10. For the neutral aniline, the calculated frequencies of these modes are: 217, 489, and 752 cm⫺1 , respectively, and are very similar to the experimental frequencies:
217, 501,48 and 755 cm⫺1 , 17 respectively. In the case of radical cation, our calculated frequency of the mode Q1 共181
cm⫺1 ) agrees very well with the experimental frequency of
179 cm⫺1 . 15 The calculated frequencies of the remaining
modes, Q5 and Q10 共444 and 785 cm⫺1 ) almost reproduce
the experimental frequencies, 442 and 785 cm⫺1 ,
respectively.16 It should be noted that the earlier assignment
of the mode Q10 to the band at 577 cm⫺1 , in the spectrum of
aniline cation,15 is obviously wrong.
3. Phenyl ring vibrations
Detailed examination of the theoretical results obtained
for aniline and its radical cation has revealed remarkable
differences between the frequencies as well as the IR 共Raman兲 intensities of the bands corresponding to ring vibrations in these molecules. This is caused by significant
changes of the geometrical and electronic structures of the
radical cation, in comparison to the neutral aniline.
According to our results for aniline, mode Q9 corresponds to almost pure ring puckering vibration and the
B3LYP-calculated frequency of this mode, 689 cm⫺1 , is in
perfect agreement with the experimental, 688 cm⫺1 . 17 In the
case of radical cation, the calculated frequency of this mode,
626 cm⫺1 , is also in excellent agreement with the reported
frequency, 622 cm⫺1 . 16 However, one can notice several discrepancies in the assignment of the latter frequency, reported
by other authors. Takahashi et al.13 in the spectrum of aniline
cation, erroneously attributed the band at 628 cm⫺1 to the
first overtone of the NH2 wagging mode. Song et al.15 assigned the bands at 445 and 629 cm⫺1 , to the modes labeled
4 共Q9兲 and 16b 共Q5兲, respectively. This assignment should
be reversed, according to our calculations.
The mode Q16 in aniline can be described as the trigonal
ring ‘‘breathing’’ vibration derived from the benzene vibration No. 12, whereas mode Q17 originates from the CC
stretching vibrations coupled with the C–H in-plane bending
vibrations 共18a兲. These modes were assigned at 996 and
1028 cm⫺1 , respectively, in the spectrum of aniline in argon
matrix.17 Both the modes are very weak in infrared but
strong in the Raman spectrum, as predicted by calculations
and illustrated in Figs. 4 and 5. In the IR spectrum of cation,
the modes Q16 and Q17 can be assigned to the bands observed at 982 cm⫺1 共Ref. 15兲 and 993 cm⫺1 , 16 respectively.
It should be emphasized that the corresponding theoretical
Aniline and its radical cations
10909
frequencies, 979 and 992 cm⫺1 , are in excellent agreement
with experiment. It is interesting to note, that the relative
Raman intensities of the modes Q16 and Q17 in cation are
opposite to those in aniline, as follows from Fig. 5 共and Table
III兲.
The mode Q23 in aniline can be described as the
Kekulé-type vibration 共the coupled C–C stretching vibrations of the benzene ring兲. The B3LYP-calculated frequency
of this mode, 1323 cm⫺1 , is in perfect agreement with the
experimental, 1324 cm⫺1 reported by Evans for aniline.48
The corresponding frequency calculated for cation, 1361
cm⫺1 , almost reproduces the experimental value of 1360
cm⫺1 . 16
The strong band at 1594 cm⫺1 , in the Raman spectrum
of cation 关Fig. 5共B兲兴 can be assigned to the mode Q28 共8a兲.
This band is about 4 times more intense than the corresponding Raman band 共at 1608 cm⫺1 ) in the spectrum of neutral
aniline 共A兲.
The assignment of the C–H stretching frequencies in
aniline, has been very uncertain. We demonstrated in our
earlier studies on phenol18 that the frequencies of C–H
stretching vibrations calculated at the B3LYP/6-311
⫹⫹G共df, pd兲 level, and scaled by the factor of 0.958 共derived from Ref. 39兲 almost reproduced the experimental anharmonic C–H stretching frequencies. The same procedure
has been used in this study, and the frequencies of the C–H
stretching vibrations 共Q30–Q34兲 are completely reassigned,
as shown in Table III.
According to calculations, mode Q34 共denoted as 2 in
Wilson’ notation兲 has the largest Raman scattering activity.
Furthermore, of all the calculated C–H stretching vibrations
in aniline, this mode has the highest frequency. Thus, the
strong polarized Raman band at 3072 cm⫺1 共liquid aniline兲,
reported by Evans48 should be assigned to mode Q34. This
implies that the two bands in the IR spectrum, at 3094 and
3084 cm⫺1 , assigned to various fundamentals in earlier
works,21–28,48 should be attributed to some combination
tones. The IR intensities of these combinations are enhanced
via Fermi resonance with the C–H stretching fundamentals.
It should be noted that very similar effect has been observed
in our previous study of the IR spectrum of phenol.18 We
have shown that the weak band at 3095 cm⫺1 is not a fundamental, but a combination tone.
The calculated frequencies of the modes Q30 and Q31
共3021 and 3022 cm⫺1 , respectively兲 indicate that the corresponding bands can overlap in vibrational spectra of aniline.
The medium intensity band positioned at 3025 cm⫺1 , in the
IR spectrum of aniline48 corresponds very well to these theoretical frequencies. It follows from Table III that the calculated frequencies of the C–H stretching vibrations are in very
good agreement with the experiment. This implies that the
presented new assignment of the C–H stretching vibrations
in aniline should be correct.
In the case of radical cation, the calculated frequencies
of the corresponding modes Q30–Q34 show a small blueshift, by about 30 cm⫺1 , relative to their counterparts in the
neutral aniline, whereas their infrared intensities dramatically
decrease, as illustrated in Fig. 4. However, all these modes
should be clearly seen in the Raman spectrum of the radical
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10910
Wojciechowski et al.
J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
TABLE IV. Comparison of the experimental wave numbers (cm⫺1 ) and
theoretical harmonic frequencies 共␻, cm⫺1 ) and infrared intensities (A IR,
km/mol兲 of aniline calculated by the MP2 and B3LYP methods using various basis sets 共selected values兲.
MP2/Ia
MP2/IIb
B3LYP/IIb
No.
Sym.
共label兲
Expt.
␻
A IR
␻
A IR
␻
A IR
Q9
Q10
Q13
Q14
Q15
Q23
A⬘共4兲
A⬘共11兲
A⬘共17b兲
A⬙共17a兲
A⬘共5兲
A⬙共14兲
688
755
875
957
968
1324
445
727
828
887
884
1433
12.6
249.5
8.3
0.5
1.1
6.2
682
752
846
906
967
1437
98.2
102.5
14.2
2.1
1.0
6.2
689
752
873
951
966
1323
27.6
69.2
6.9
0.0
0.1
7.2
a
I⫽6-311⫹G共d,p兲 basis set.
II⫽6-311⫹⫹G共df,pd兲 basis set.
b
cation 共Fig. 6兲. The blueshift in the frequencies of the C–H
stretching vibrations in radical cation, indicates a strengthening of the C–H bonds. This is confirmed by the NBO results,
which have shown a decrease of electron density on all C–H
* upon ionization of aniline.
antibonding orbitals ␴ CH
4. The MP2 and B3LYP predictions
of the ‘‘troublesome’’ modes in aniline
Finally, we shall discuss the performance of the MP2
method in predicting the frequencies of normal modes in
aniline. These modes which show the largest differences between the MP2- calculated frequencies and experimental
data are collected in Table IV.51
It is evident from this comparison that the MP2 method
is deficient in predicting the frequencies of several normal
modes in aniline. The most striking differences are observed
for the modes Q9 and Q23. The former mode can be described as the alternate out-of-plane motion of the aniline
carbon atoms 共which is analogous to the ring puckering
mode number 4 in benzene兲. Calculation at the MP2/6-311
⫹G共d, p兲 level yields the frequency of this mode dramatically too low, by about 240 cm⫺1 , in comparison to experiment. The use of the large basis set 关6-311⫹⫹G共df, pd兲兴
improves the agreement between the MP2-calculated and experimental frequencies, but the theoretical IR intensity of this
mode is significantly too high. In contrast, the B3LYP
method almost reproduces the experimental frequency 关even,
with the use of a smaller basis set, 6-311⫹G共d, p兲, our data兴.
The most ‘‘problematical’’ is mode Q23. It corresponds
to the benzene mode 14, which can described as an alternate
stretching and shrinking of CC bonds towards one of the two
Kekulé structures of the aromatic ring. As follows from
Table IV, the frequency of mode Q23 calculated by the MP2
method with the large basis set is still overestimated by more
than 110 cm⫺1 , whereas that predicted by B3LYP is in excellent agreement with experiment. Thus, the MP2 method
fails in predicting the frequency of this mode, regardless of
the basis set used.
Handy and co-workers52 demonstrated a similar deficiency of the MP2 method in the calculation of the modes
labeled 4 and 14 in benzene. In our earlier study18 we have
shown that MP2 method also fails in predicting the frequencies of the analogous ‘‘problematical modes’’ in phenol.
Thus, it is remarkable, indeed, that calculation with the
B3LYP method almost reproduces the experimental frequencies of all the ring vibrations in aniline and its radical cation.
IV. CONCLUDING REMARKS
The most important findings of this study are the following:
共1兲 For the aniline radical cation, the calculations with the
unrestricted B3LYP method indicates a planar,
quinoidal-type structure of the molecule. The UMP2
method with the large basis set, 6-311⫹⫹G共df, pd兲 overestimates the quinoid character of the ring.
共2兲 According to B3LYP results, ionization of aniline leads
to a delocalization of the positive charge to the phenol
fragment, and to an almost equal increase of a charge on
the nitrogen atom, and on the C4 carbon atom in the ring.
In contrast, the UMP2/6-311⫹⫹G共df, pd兲 calculation
predicts the biggest accommodation of the positive
charge on the C4 atom.
共3兲 The natural 共NBO兲 charges calculated for aniline well
describe its chemical properties 共the ortho- and paradirecting power of the NH2 group in electrophilic substitutions兲, while the calculated Mulliken charges for
aniline are not reliable.
共4兲 The results from NBO analysis have provided interesting
data on the electronic interactions in aniline and its radical cation. It is evident that the unpaired electron is delocalized to the ring, due to the p␲-radical character of
this molecule. The strong radical conjugation involves
the p␲ orbital of an unpaired electron and ␲ orbitals of
the ring, as well as p␲ orbitals of the C1 and N atoms.
This conjugation stabilizes the planar structure of an
aniline radical cation.
共5兲 The redshift of the N–H stretching frequencies and the
blueshift of the C–H stretching frequencies in the ionized aniline can be related to an increase of electron
* ) and dedensity 共ED兲 on the antibonding orbitals ( ␴ NH
* , respectively, as revealed by NBO
crease of ED on ␴ CH
analysis. These effects are associated with a weakening
of the N–H bonds and strengthening of the C–H bonds
in aniline radical cation.
共6兲 Excellent agreement has been obtained between the experimental and theoretical frequencies of aniline and its
radical cation, calculated at the B3LYP/6-311
⫹⫹G共df, pd兲 level. This gives strong evidence that the
revised vibrational assignment, presented in this study, is
correct. Moreover, it confirms the adequacy of the
UB3LYP method for describing the radical species.
共7兲 The clear-cut assignment of all the bands in the spectra
of aniline and its radical cation has been made on the
basis of the calculated potential energy distribution
共PED兲 for these molecules. Several discrepancies in the
previous vibrational assignments have been clarified, in
this work. For the neutral aniline, the C–H stretching
frequencies are completely reassigned.
共8兲 Aniline radical cation can be easily identified in the Raman spectrum by the presence of extremely strong band
near 1490 cm⫺1 .
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J. Chem. Phys., Vol. 118, No. 24, 22 June 2003
共9兲 The MP2 method is deficient in calculations of vibrational frequencies of aniline. In particular, the MP2
method fails in prediction of the ‘‘troublesome modes,’’
which are analogous to the modes labeled 4 and 14 in
benzene.
共10兲 The results presented in this work can help in further
studies of the vibrational spectra of van der Waals clusters and hydrogen bonded complexes of aniline and its
radical cation.
ACKNOWLEDGMENTS
The authors thank Professor Frank Weinhold from the
University of Wisconsin, Madison, for helpful suggestions.
The generous computer time from the Poznań Supercomputer and Networking Center as well as Wrocław Supercomputer and Networking Center is acknowledged. This study
was supported in part by the Polish Committee for Scientific
Research 共Grant No. KBN 4T09A 11922兲.
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