Infrared spectrum and theoretical study of the dinitrogen pentoxide molecule (N2O5) in solid argon

Article abstract of DOI:10.1063/1.471500

Fourier Transform Infrared (FTIR) spectra of the covalent dinitrogen pentoxide molecule isolated in a solid argon matrix at 10 K are reported. The measured frequencies in the 200-4000 cm^-1 region are in close agreement with gas phase values previously reported. An accurate and sophisticated ab initio study showed that the stable equilibrium structure, C₂ symmetry, was in agreement with the structure previously determined by electron diffraction data.

Full text of DOI:10.1063/1.471500

Infrared spectrum and theoretical study of the dinitrogen pentoxide molecule (N2O5) in
solid argon
L. Bencivenni, N. Sanna, L. SchriverMazzuoli, and A. Schriver
Citation: The Journal of Chemical Physics 104, 7836 (1996); doi: 10.1063/1.471500
View online: http://dx.doi.org/10.1063/1.471500
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Infrared spectrum and theoretical study of the dinitrogen pentoxide
molecule (N2O5) in solid argon
L. Bencivenni
`
Universita di Roma ‘‘La Sapienza,’’ Dipartimento di Chimica, Ple Aldo Moro 5, 0185 Roma, Italy
N. Sanna
`
CASPUR Consorzio per le Applicazioni del Supercalcolo per Universita e Ricerca, Ple Aldo Moro 5, 00185
`
Roma (Italia), c/o CICS, Universita Roma, Italy
L. Schriver-Mazzuolia) and A. Schriver
´
´
Laboratoire de Physique Moleculaire et Applications, Laboratoire Propre du CNRS, Universite P. et M.
Curie. Tour 13 Case76, 4, Place Jussieu 75252 Paris Cedex 05, Franceb)
͑Received 3 August 1995; accepted 6 February 1996͒
Fourier Transform Infrared ͑FTIR͒ spectra of the covalent dinitrogen pentoxide molecule isolated in
a solid argon matrix at 10 K are reported. The measured frequencies in the 200–4000 cmϪ1 region
are in close agreement with gas phase values previously reported. An accurate and sophisticated ab
initio study showed that the stable equilibrium structure, C2 symmetry, was in agreement with the
structure previously determined by electron diffraction data. © 1996 American Institute of
Physics. ͓S0021-9606͑96͒01118-0͔
Ab initio calculations performed by Carpenter et al.10 indi-
I. INTRODUCTION
cated that the nitro groups were rotated out of the central
N-O-N plane ͑42°͒ in a contratory fashion. However, this
investigation was restricted to the C2 and C2v symmetry
structures of N2O5 accomplished by Hartree-Fock-Self Con-
sistent Field ͑HF-SCF͒ calculations using the STO-3G and
4-31G basis sets. Thus the effects of polarized basis sets and
even more important, electron correlation, have not been
taken into account so far. The desirability of ultimately de-
termining the structure of this molecule prompted us to rein-
vestigate the energy surface of N2O5 by taking the previous
theoretical study, one step further. Furthermore this analysis
is also intended as a means of calculating the vibrational
frequencies of the molecule in order to provide a basis for
the assignment of the experimental spectrum.
In this way, we have previously reinvestigated the vibra-
tional spectrum of N2O5 using a matrix isolation technique.
This technique is a convenient method for studying the IR
spectra of isolated molecules. The rotation of impurities is
hindered in the host lattice and the sharp vibrational bands
are characterized by small shifts relative to the gas phase
values. Spectra obtained in an argon matrix are compared
with those reported by Hisatsune for the gas phase3 and those
obtained recently by A.B. Horn from the condensation of a
solid amorphous film of N2O5 at 80 K.11 This paper presents
our results in two parts. The first section is devoted to the
FTIR spectral measurements of N2O5 trapped in argon ma-
trices. In the second section, the structure and vibrational
analysis for N2O5 using the harmonic approximation are cal-
culated by means of the GAUSSIAN 92 package.24
Stratospheric N2O5 was unambiguously detected for the
first time in the Atmos 47° sunrise spectra1 and may play an
important role in stratospheric ozone chemistry. On the one
hand, it is a significant reservoir for stratospheric nitrogen
oxides which have an influence on the destruction of atmo-
spheric ozone. On the other hand, heterogeneous reactions of
N2O5 with H2O and HCl on a surface of ice particles in polar
stratospheric clouds may be responsible for the formation of
nitric acid and the conversion of the stable HCl reservoir into
more active forms, which release chlorine atoms under solar
radiation.2 Infrared spectroscopy is a convenient method for
the measurement of N2O5 concentrations both in the atmo-
sphere and in the laboratory. Tentative full vibrational as-
signments of N2O5 in both gas phase and solid phase were
published forty years ago by Hisatsune et al.3 More recently
the far infrared spectrum of N2O5 at room temperature has
been described.4 Absolute cross sections for the strongest
bands of N2O5 have also been determinated from laboratory
measurements, and are discussed in regard to stratospheric
detection of gaseous N2O5.5–7
In its gas phase, the dinitrogen pentoxyde compound has
a covalent structure, which is preserved in the solid state for
several hours when the gas is condensed on a surface at
about 93 K. On warming, however, the molecule decom-
poses to form nitronium nitrate ͑NOϩ2 NO3Ϫ͒.8 The proposed
vibrational assignments given by Hitsasune et al.3 and sup-
ported by force field calculations, were based on a planar
C2v point group symmetry model. However from electron
diffraction experiments, Mc Clelland et al.9 fit their data in
terms of a molecule with C2 symmetry giving rise to larger
amplitude torsional motion of the NO2 groups and a low
energy minimum of 30° for each of the two torsion angles.
II. ANALYSIS OF THE N2O5 VIBRATIONAL SPECTRUM
A. Experiment
a͒
N2O5 was prepared by the reaction of NO2 with O3.
Ozone was obtained by silent electrical discharge through
To whom correspondence should be addressed.
b͒
´
´
Laboratoire associe aux Universites Paris Sud et Pierre et Marie Curie.
7836
J. Chem. Phys. 104 (20), 22 May 1996
0021-9606/96/104(20)/7836/11/$10.00
© 1996 American Institute of Physics
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Bencivenni et al.: IR spectrum of N2O5 in Ar
7837
oxygen in a closed system isolated with liquid nitrogen using
N45 purity oxygen from Air Liquide. The synthesis of small
quantities of N2O5 was obtained directly using a vacuum line
through a mixture of pure O3 and NO2. After reaction, the
final product was trapped in bulk and degased at 120K to
remove any excess of O2 and O3. Then it was diluted with
argon and directly deposited. After many attempts12 the most
best mixture contained 10 Torr of NO2 and 20 Torr of O3,
leading to a matrix mixture of N2O5/Ar ͑1/800͒, which was
nearly free of NO2 ͓except for the amount in equilibrium
with N2O5 ͑Refs. 13 and 14͔͒ and nitric acid.
Isotopic N2O5 species were also synthesized in a similar
manner. The O2N-18O-NO2 molecule was obtained through
the reaction between NO2 and 18O3, while O125N-O-15NO2
was synthesized from a mixture containing 15NO/O2, in a
similar way.
N2O5/Ar mixtures were deposited onto a gold mirror
cooled to 18 K with a deposition rate of 6–8 m mol hϪ1. The
cryostat was an Air Product Displex model 202A closed
cycle helium refrigerator. It was equipped with a silicon di-
ode for temperature determination and with a resistor heater.
A Fourier transform infrared spectrometer ͑Bruker IRTF
113 v͒ was used for product analysis. The spectra were re-
corded at a temperature of 11 K by reflection with a resolu-
tion of 0.5 cmϪ1 over the 200–4000 cmϪ1 spectral region.
FIG. 1. Infrared spectra of ͑a͒ 14N2O5 and ͑b͒ 15N2O5 isolated in argon
matrix ͑M/RϷ1/800͒ in the 1800-1650 cmϪ1 region. Recording temperature,
10 K.
spectra of compounds containing either the NO2 ͑Refs. 15–
19͒ or the O-NϭO ͑O-NO2͒ ͑Refs. 19–21͒ groups reported
in the literature.
B. Results and discussion
Fifteen vibrations are expected for the N2O5 molecule:
six stretching modes, five in plane bending modes and four
out of plane bending modes. If the molecule belongs to the
C2v group, only thirteen bands can be observed ͑note that the
two out plane bending modes for the A2 symmetry are IR
inactive͒. Furthermore the two NO2 groups may be assumed
to be weakly coupled in this molecule and consequently
some NO2 modes can be degerate. In Figs. 1 to 5 we show
examples of the spectral absorption characteristics of the in-
frared vibrational bands of N2O5 diluted in argon, which
were obtained from our Fourier Transform Spectroscopy
͑FTS͒ laboratory experiments. These figures also show the
isotopic shifts observed in some regions for 15N2O5 and a
mixture of O2N-18O-NO2/O2N-16O-NO2 ͑ratio 1:1͒. All of
the observed bands can be assigned to the covalent N2O5
molecule. No bands belonging to the ionic structure were
observed. When the N2O5 concentration in argon was raised
from 1/1000 to 1/200, only the band widths increased with-
out the appearance of any new features. The spectrum ob-
tained in the argon matrix showed the same absorptions fea-
tures that were observed by Hisatsune in the gas phase,3 with
the exception of one new band ͑bringing the total number of
measured absorption bands to eleven in the 200–2000 cmϪ1
spectral range͒. Table I summarizes the positions of the
bands obtained from this study and their relative intensities.
The frequencies are compared to those previously reported
for the gas phase and the solid phase
The two strongest bands are centered at 1742.7 and
1702.7 cmϪ1 ͑Fig. 1͒, and are characterized by full width
half maximum ͑FWHH͒ values of 2 and 1.6 cmϪ1 respec-
tively. These bands are assigned unambiguously to the two
asymmetric NO2 stretching modes in phase and out of phase.
No isotopic shift due to 18O was observed, but when the 15
N
substitution was made the two bands shifted to 1701.8 cmϪ1
and 1663 cmϪ1 respectively. This large observed shift ͑Ϸ40
cmϪ1͒ is consistent with that measured for the dinitrogen
dioxide dimer.15 At lower frequency, the very weak band at
1338 cmϪ1 ͑FWHHϭ7 cmϪ1͒ and the medium band at 1241
cmϪ1 ͑FWHHϭ3.5 cmϪ1͒ ͑Fig. 2͒ are assigned to the sym-
metric NO2 stretching modes in phase and out of phase,
which is in agreement with the corresponding stretching fre-
quencies reported for N2O4 by Mellen et al.18 When the 18O
isotopic substitution was made the two bands shifted to the
red by Ϸ10 cmϪ1 to 1328 and 1227.5 cmϪ1, respectively,
indicating that they are mixed with the stretching or bending
modes belonging to the N-O-N central group. Thus for this
vibrational mode the two nitro groups appear to be depen-
dent on each other, and this coupling explains why the fre-
quency separation between the two symmetric stretchings is
stronger than that between the two antisymmetric stretch-
ings. When the 15N isotopic substitution is made, the pair of
the bands shows a red shift of about 7 cmϪ1
.
As seen in Fig. 2 a resolved shoulder which does not
seem to belong to an impurity, is observed at 1246 cmϪ1 on
the high frequency side of the 1243 cmϪ1 absorption.
Assignments for the other vibrational modes of the NO2
Tentative assignments were made in a similar manner to
Hisatsune’s work. Our assignments are based on characteris-
tic frequencies, isotopic shifts and a comparison with the
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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7838
Bencivenni et al.: IR spectrum of N2O5 in Ar
FIG. 2. Infrared spectra of ͑a͒ 14N2O5 , ͑b͒ 18O 14N2O4/14N2O5 mixture, and ͑c͒ 15N2O5 in argon matrices recorded at 10 K in the 1360-1200 cmϪ1 region. The
dashed lines correspond to the same spectra with expanded vertical scale.
groups is less straightforward because the frequencies of the
rocking and wagging modes are close together.17–19 In addi-
tion the bending modes should occur fairly close in fre-
quency to the vibrational stretching modes of the N-O-N
group.19 Bands at 860, 743, 614 and 577 cmϪ1 observed in
the gas phase were assigned by Hisatsune to the N-O-N a
stretching, NO2 s bending, NO2 rocking ͑in phase͒ and NO2
wagging ͑out of phase͒ whereas Stirling et al. from their
calculations22 associated the 860, 743 and 577 cmϪ1 bands
with the NO2 s bending, NO2 a bending and NO2 a rocking
modes. The N-O-N stretching mode is expected to occur at
about 800 cmϪ1, and in the sym O-N-OЈ-N-O species, the
symmetric and the antisymmetric N-OЈ stretchings are ob-
served at 973 and 704 cmϪ1 ͑or 877 cmϪ1͒, respectively.19 In
FIG. 3. Infrared spectra of 14N2O5 ͑a͒, 18O 14N2O4/14N2O5 mixture ͑b͒, and 15N2O5 ͑c͒ in argon matrices recorded at 10 K with expanded vertical scale in the
880-600 cmϪ1 region.
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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Bencivenni et al.: IR spectrum of N2O5 in Ar
7839
our spectra the weak feature at 863 cmϪ1 ͑Fig. 3͒ is substan-
tially shifted when both 18O and 15N isotopic substitutions
are made, and its assignment to the N-O-N asymmetric
stretching as given by Hisatsune, seems the most reasonable.
However, a careful search of the frequency region where one
might expect the corresponding symmetric N-O-N stretching
mode to occur revealed nothing, and the weak band at 1033
cmϪ1 reported by Hisatsune was not observed in our spectra.
The intense 737 cmϪ1 band can be assigned to the s bending
NO2 mode in agreement with the NO2 group frequencies of
other compounds reported in the literature.17–19 However it is
very sensitive to the isotopic substitution, as illustrated Fig.
4, and the shift observed in the 18ON2O4 species shows that it
is mixed with the N-O-N skeletal modes. The very weak
band at 639.7 cmϪ1 ͑Fig. 3͒, and the medium absorption at
569.4 cmϪ1 ͑Fig. 5͒ are associated with the nitro group, but
their precise assignment either to the rocking mode or to the
wagging mode, cannot be predicted from experimental data.
The remaining major band at 343.9 cmϪ1 ͑Fig. 5͒ has been
previously assigned either to the NO2 rocking mode ͑out of
3
phase͒ or to the N-O-N symmetric stretching mode.22 The
assignment of the 343.9 cmϪ1 absorption to the N-O-N
stretching mode appears unlikely because of its low fre-
quency and we prefer to assign it to the NO2 rocking mode.
A feature not observed by Hisatsune et al. in the gas phase
can be seen in our measurements at 715 cmϪ1 after expand-
ing the absorption scale by a large amount ͑Fig. 3͒. In addi-
tion we found that the spectral feature shifted to 697.8 cmϪ1
after 15N substitution ͑Fig. 3͒. This weak absorption could
correspond either to the symmetric out of phase bending
mode or to the in phase wagging mode, suggesting, in this
case, that the N2O5 molecule does not belong to the C2v
symmetry group for which this mode ͑symmetry A2͒ is in-
frared inactive. Unfortunately neither this present investiga-
FIG. 4. Infrared spectra of ͑a͒ 14N2O5 , ͑b͒ 18O 14N2O4/14N2O5 mixture, and
͑c͒ 15N2O5 in argon matrices recorded at 10 K in the 760-700 cmϪ1 region.
FIG. 5. Infrared spectra of ͑a͒ 14N2O5 , ͑b͒ 18O 14N2O4/14N2O5 mixture, and ͑c͒ 15N2O5 in argon matrices recorded at 10 K in the 600-300 cmϪ1 region.
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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7840
Bencivenni et al.: IR spectrum of N2O5 in Ar
TABLE I. Comparison of observed frequencies ͑cmϪ1͒ for N2O5 isolated in argon with those reported in the literature for gas and solid states. Relative
integrated intensities for our results are given in brackets.
Ar matrix
͑This work͒
Gas
͑2͒
Solid 80 K
͑12͒
N2O5
NO2-18O-NO2
15N2O5
Tentative assignment
a
1728
1728
1338
1247
860
743
743
614
577
1764
1705
1340
1258
864
760
•••
•••
•••
•••
1742.4͑1͒
1742.4
1702.7
1328.0
1227.5
857.4
730.2
715
639.7
567.0
343.9
1701.8
1663.0
1321.3
1235.0
853.0
728.5
697.8
625
␯
␯
␯
␯
␯
␦
␦
out of phase
in phase
out of phase
in phase
NO
2
a
1702.7͑0.5͒
1339.8͑0.07͒
1243.0͑0.35͒
863.1͑0.02͒
737 ͑0.5͒
715 ͑0.02͒
639.7͑0.015͒
569.4͑0.3͒
343.9͑0.3͒
NO
2
S
NO
2
S
NO
2
a
͑NON͒
NO
s
out of phase
in phase or ␻
NO
s
2
NO
NO
2
2
rNO
2
567.1
333.6
wNO
353
rNO 2 or ␦NON
2
tion nor others previously reported can give conclusive as-
signments for all of the bands, and further calculations are
needed to resolve this problem.
harmonic frequency calculations. The whole ab initio study
was carried out by means of the GAUSSIAN-92 package24
adopting the Hartree-Fock ͑HF͒, Density-Functional ͑DF͒
and the second order Mo”ller-Plesset ͑MP2͒ levels employing
the Dunning-Huzinaga double-zeta basis set of contracted
Gaussians25,26 augmented with a set of six d-like functions
for each of the atoms. The complete double-zeta plus polar-
ization ͑DZϩP͒ basis set is designated (9s5p1d/4s2p1d)
for the nitrogen atom and (9s5p1d/3s2p1d) for the oxygen
atom. The polarization function exponents are ␣dϭ0.80 for
nitrogen and ␣dϭ0.85 for oxygen.25,26
Preliminar HF-SCF calculations were accomplished with
the less extended DZ basis set, which does not includes po-
larization d-functions, however the influence of the polariza-
tion functions was found to be remarkable, on the values of
the calculated molecular parameters and vibrational frequen-
cies. In particular, the polarized basis set DZϩP shortens all
the bond lengths and overestimates the harmonic vibrational
frequencies with respect to the DZ basis set. These conclu-
sions may be easily inferred from the data reported in Table
II where the main results of the study are summarized.
The HF/DZϩP calculations were useful for making an
estimate of the stability of the four structures of the molecule
and it was established that the Cs symmetry structure 1a has
the lowest energy stationary point. Each of the remaining
structures i.e., the nonplanar C2 symmetry 1b, the planar
C2v symmetry 1c and the nonplanar C2v symmetry 1d struc-
tures are less stable by approximately 1, 20 and 33 kJ/mol,
respectively. In addition, the frequency calculations indicate
that Cs symmetry structure (1a), is a stable minimum of the
energy surface since all the harmonic frequencies of vibra-
tion have positive values. The other structures show at least
one imaginary frequency and are therefore saddle-points.
This is the case for the C2 symmetry (1b) and the planar C2v
symmetry (1c) models ͑which predict imaginary frequencies
at 27i cmϪ1 and 89i cmϪ1, respectively͒ while the nonplanar
C2v symmetry (1d) structure has a second order saddle point
͑with imaginary frequencies at 74i and 34i cmϪ1͒.
III. THE THEORETICAL STUDY OF THE N2O5
MOLECULE
Ab initio calculations were carried out to determine the
stable equilibrium structure and the vibrational spectrum of
the N2O5 molecule. The starting point for this investigation
was the optimization of the molecular parameters of the
structures of N2O5 shown in Fig. 6. These four structures
were selected within a restricted number of suitable models
͑which are represented as symmetries 1a, 1b, 1c and 1d in
the calculations presented in Table II. The corresponding
symmetry models are 1a ͑nonplanar Cs symmetry model͒,
1b ͑nonplanar C2 symmetry model͒, 1c ͑planar C2v symme-
try model͒ and 1d ͑nonplanar C2v symmetry model͒. These
structures were fully optimized and were characterized by
FIG. 6. Structures considered for the N2O5 molecule: 1a- Cs symmetry, 1b-
C2 symmetry, 1c- C2v symmetry planar structure and 1d- C2v symmetry
nonplanar structure.
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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Bencivenni et al.: IR spectrum of N2O5 in Ar
7841
TABLE II. Geometries,a vibrational frequencies and relative stabilityb,c of the N2O5 molecule.
Cs symmetry 1a
HF/DZ
HF/DZϩP
DF/DZϩP
MP2/DZϩP
Bond lengths
N2O5
1.221
1.212
1.203
1.442
1.449
1.1785
1.173
1.170
1.384
1.4065
1.231
1.215
1.227
1.4985
1.6435
1.228
1.204
1.222
1.446
1.657
N3O4/N3O6
N2O7
N2O1
N3O1
Bond angles
N2O1N3
113.1
116.6
114.25
111.65
114.2
131.7
131.4
112.2
117.0
114.05
111.4
114.0
131.6
131.9
109.5
117.7
112.6
110.3
112.6
132.0
134.8
106.9
117.4
111.8
111.5
111.8
131.1
136.5
O5N2O1
O4N3O1
O7N2O1
O6N3O1
O5N2O7
O4N3O6
Torsional angles
O4N3O1N2
O5N2O1N3
O6N3O1N2
O7N2O1N3
90.0
90.0
90.0
90.0
0.0
0.0
0.0
0.0
Ϫ90.0
180.0
Ϫ90.0
180.0
Ϫ90.0
180.0
Ϫ90.0
180.0
C2 symmetry 1b
Bond lengths
HF/DZ
1.446
1.218
1.205
HF/DZϩP
1.395
DF/DZϩP
1.571
MP2/DZϩP
1.532
E.D. ͓9͔
N2O1/N3O1
1.492
1.183
N2O5/N3O6
1.176
1.220
1.2145
N3O4/N2O7
1.171
1.2215
1.214
Bond angles
N2O1N3
113.9
115.9
112.5
131.6
113.9
116.2
112.0
131.7
116.8
117.7
108.8
133.4
112.7
116.4
109.9
133.6
111.8
O5N2O1/O1N3O4
O1N3O6/O1N2O7
O4N3O6/O5N2O7
Torsional angles
O4N3O1N2/O5N2O1N3
O6N3O4N2/O7N2O5N3
133.2
30.0
43.2
41.0
23.1
31.3
162.2
163.7
172.1
167.4
C2v symmetry 1c
Bond lengths
N3O6/N2O7
HF/DZ
1.213
1.208
1.454
HF/DZϩP
1.170
DF/DZϩP
1.2185
1.222
MP2/DZϩP
1.212
N2O5/N3O4
1.173
1.212
N2O1/N3O1
1.405
1.580
1.550
Bond angles
N2O1N3
123.4
109.0
120.0
131.1
122.6
108.6
120.1
131.2
119.9
107.4
119.2
133.4
119.3
107.3
118.8
133.9
O5N2O1/O1N3O4
O1N3O6/O1N2O7
O4N3O6/O5N2O7
C2v symmetry 1d
Bond lengths
HF/DZ
1.456
1.213
HF/DZϩP
1.400
DF/DFϩP
1.588
N2O1/N3O1
N2O5/N3O4
1.174
1.222
N3O4/N2O7
Bond angles
N2O1N3
111.3
114.4
109.6
114.3
106.2
113.5
O5N2O1/O1N3O4
O1N3O6/O1N2O7
O4N3O6/O5N2O7
Torsional angles
O4N3O1N2/O5N2O1N3
O6N3O4N1/O7N2O5N3
131.4
131.4
133.0
91.3
91.1
91.3
Ϫ91.3
Ϫ91.1
Ϫ91.3
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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7842
Bencivenni et al.: IR spectrum of N2O5 in Ar
TABLE II. ͑Continued.͒
Vibrational frequencies ͑cmϪ1
Cs symmetry 1a
͒
HF/DZ
20
HF/DZϩP
41
DF/DZϩP
13 i
80
MP2/DZϩP
39
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Љ
Љ
Ј
Ј
Љ
Ј
Љ
Ј
Ј
Ј
Ј
Ј
Ј
Ј
Љ
87
102
86
221
449
584
619
745
758
859
910
954
1296
1395
1624
1365
253
161
187
502
292
215
658
453
466
702
458
523
840
563
601
858
667
715
964
703
716
1018
1080
1493
1614
1944
1958
C2 symmetry 1b
HF/DZϩP
27 i
730
759
825
858
1217
1316
1656
1738
1267
1366
1888
2018
HF/DZ
9 i
DF/DZϩP
62
MP2/DZϩP
42
B
524
583
258
205
742
831
475
520
759
857
652
690
914
1020
1493
1928
89
698
719
1295
1607
84
1222
1679
48
1262
1941
61
A
232
273
197
220
457
571
336
348
672
771
630
645
853
954
717
766
951
1076
1612
1976
820
834
1389
1653
1315
1725
1346
1958
C2v symmetry 1c
HF/DZ
85 i
13
DF/DZϩP
89 i
75
DF/DZϩP
44 i
87
MP2/DZϩP
53 i
90
A2
B1
A1
B2
A1
B1
A2
B2
A1
B2
A1
B2
A1
B2
A1
260
301
194
221
402
456
189
109i
330
433
482
330
735
850
645
677
753
869
659
696
759
846
472
508
805
907
694
730
909
1001
1040
1486
1592
1897
2003
694
713
921
818
827
1282
1366
1543
1663
1226
1317
1678
1733
1273
1355
1942
1969
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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Bencivenni et al.: IR spectrum of N2O5 in Ar
7843
TABLE II. ͑Continued.͒
C2v symmetry 1d
HF/DZϩP
HF/DZ
DF/DZϩP
A2
B1
A1
A2
A1
B1
B2
B2
B2
A1
A1
B2
A1
A2
B1
89 i
62 i
232
74 i
34 i
211
67 i
95 i
148
534
476
401
643
570
439
721
643
500
769
690
398
848
760
643
968
873
702
990
881
762
1074
1493
1610
1902
1968
951
804
1308
1401
1565
1646
1221
1306
1675
1700
Relative stabilityb,c
⌬1
0
ϩ1
ϩ20
ϩ33
⌬2
ϩ4
0
ϩ1
ϩ33
⌬3
ϩ57
0
⌬4
ϩ36
0
⌬5
ϩ1
0
ϩ4
⌬6
ϩ23
0
ϩ6
ϩ248
Cs symmetry 1a
C2 symmetry 1b
C2v symmetry 1c
C2v symmetry 1d
ϩ5
ϩ4
ϩ302
aBond lengths are given in Å and bond angles in degrees.
bThe ⌬E ͑kJ/mol͒ values refers to the lowest energy structure and are indicated as ⌬i ͑iϭ1,2,3,4,5,6͒ calculations.
c⌬1 is HF/DZϩP//HF/DZϩP, ⌬2 is DF/DZϩP//DF/DZϩP, ⌬3 is MP2/DZϩP//HF/DZϩP, ⌬4 is MP2/DZϩ2P//HF/DZϩP, ⌬5 is MP2/DZϩP//MP2/DZϩP,
⌬6 is MP2/DZϩ3P//MP2/DZϩP.
We will restrict our discussion to the calculations for the
structures 1a, 1b and 1c, because the nonplanar C2v sym-
metry model 1d is indeed predicted from the HF-SCF, DF
and MP2 calculations to lie in the high energy region of the
energy surface explored by us and it is an unstable configu-
ration ͑see the ⌬E values reported in Table II͒. A more so-
phisticated study of the stability of the structures of the N2O5
molecule was undertaken by considering electron correlation
at the MP2/DZϩP level. These calculations were carried out
using the all orbital active approximation for the HF/DZϩP
optimized geometries. The stability order determined from
these calculations does not confirm that of the HF-SCF and
DF levels since the C2 and the planar C2v symmetry struc-
tures 1b and 1c are the most stable ones. In particular, the
C2 structure occurs at the lowest energy value and the planar
C2v structure is just 5 kJ/mol less stable than the C2 station-
ary point. The most surprising result of the single point MP2/
DZϩP//HF/DZϩP calculation ͑indicated in Table II as ⌬3͒
is that the Cs symmetry structure 1a is unstable by 57 kJ/mol
with regard to the C2 and the planar C2v symmetry forms.
This results was confirmed from the single-point MP2/DZ
ϩ2P//HF/DZϩP calculation ͑indicated in Table II as ⌬4͒,
where the DZ basis set was augmented with two ͑␣dϭ1.60,
0.40 for N and ␣dϭ1.70, 0.425 for O͒ polarization
d-functions. We noted that the MP2 level strongly destabi-
lizes structure 1d with respect to the HF-SCF and DF meth-
ods and it was for this reason that we did not persue this
structure any further. Additional information concerning the
relative stability of the structures 1a, 1b and 1c was ob-
tained from using MP2/DZϩP//MP2/DZϩP optimizations
and single-point MP2/DZϩ3P//MP2/DZϩP calculations.
These calculations confirmed our preference for the C2
symmetry structure, although, the MP2/DZϩP//MP2/DZϩP
level calculations indicate that the Cs and C2v symmetry
structures ͑1a and 1c͒ have comparable stability, being
separated by 1 and 4 kJ/mol, respectively, from the lowest
energy structure 1b. The MP2/DZϩ3P//MP2/DZϩP level
calculations, where three polarization d-functions ͑␣dϭ3.20,
0.80, 0.20 for N and ␣dϭ3.40, 0.85, 0.2125 for O͒ were
added to the DZ basis set, increased the energy separation of
the less stable forms ͑1a and 1c͒ from the lowest energy
structure 1b, but largely destabilized the structure 1a ͑see
Table II͒. It therefore seems likely that electron correlation
and the use of multiple polarization d-functions will destabi-
lize structure 1a with respect to the other two forms. This
appears to imply that the description of the energy surface
for this molecule is greatly influenced by the computational
level. However, higher level geometry, vibrational frequency
and relative stability calculations are not feasible for this
molecule. To demonstrate this, we attempted to evaluate the
relative stability of the C2, Cs and C2v structures at the all
orbital active MP2 level, using the DZ basis set augmented
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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7844
Bencivenni et al.: IR spectrum of N2O5 in Ar
FIG. 7. Theoretical IR spectra of the N2O5 molecule calculated by two different methods for each symmetry. Cs symmetry: ͑a͒ DF/DZϩP and ͑b͒
MP2/DZϩP; C2 symmetry: ͑c͒ DF/DZϩP and ͑d͒ MP2/DZϩP; C2v symmetry planar structure: ͑e͒ DF/DZϩP and ͑f͒ MP2/DZϩP.
with three d and one f polarization functions on all the at-
oms. This proved to be unsuccessful, however, owing to the
computational limits of the available computer facilities.
The vibrational frequency calculations reflect the consid-
erations just reported above. The comparison between the
DF/DZϩP//DF/DZϩP and MP2/DZϩP//MP2/DZϩP results
is interesting since the DF and MP2 frequencies given in
Table II are much more realistic than the HF-SCF ones. First
of all, the main discrepancies between the two methods can
be explained by the fact that the MP2 level removes the
instability present at the DF level for the Cs symmetry struc-
ture, but on the other hand, increases the number of imagi-
nary frequencies in case of the C2v symmetry structure 1c.
Apart from this, both the DF and MP2 methods are in agree-
ment concerning the nature of the stationary point 1b. It is
helpful to remark once again that if the MP2 calculations
were carried out employing a multipolarized DZ basis set
they might produce different conclusions. Examples of simu-
lated IR spectra for the three main structures of the N2O5
molecule are presented in Fig. 7, where the DF and MP2
spectra for the Cs , C2 and C2v structures have been grouped
together for comparative purposes. It may be argued, that
neglecting the numerical differences which exist between the
DF and MP2 calculations ͑which might be corrected by force
constant matrix scaling procedure͒,27 the two computational
methods appear to predict comparable IR spectra for the
same structure, with relative band intensity ratios fairly close
to each other. This actually occurs for the bands lying in the
higher frequency range. Apart these considerations, the IR
spectral calculations might be helpful to decide whether the
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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Bencivenni et al.: IR spectrum of N2O5 in Ar
7845
TABLE III. Potential energy distribution ͑P.E.D.͒ of the MP2/DZϩP vibra-
tional frequencies of the C2 symmetry N2O5 molecule.
species. However, if we exclude the Cs symmetry model
because of the stability considerations already discussed, the
theoretical spectra for the C2 and C2v symmetry structures
1b and 1c, exhibit large differences in their peak intensities
for the highest frequency band. However our measured FTIR
spectrum is in better agreement with the calculated spectrum
for the C2 symmetry structure 1b. Indeed, the IR pattern
Frequency ͑cmϪ1
͒
Potential energy distributiona,b
1958 (A)
1941 (B)
1346 (A)
1262 (B)
834 (A)
766 (A)
719 (B)
690 (B)
644 (A)
520 (B)
348 (A)
220 (A)
205 (B)
61 (A)
(0.24)(S3ϩS5)ϩ(0.23)(S4ϩS6)
(0.23)(S3ϩS5)ϩ(0.24)(S4ϩS6)
(0.20)(S3ϩS5)ϩ(0.23)(S4ϩS6)
(0.25)(S3ϩS5)ϩ(0.22)(S4ϩS6)
͑0.33͒(S7ϩS8)
3
observed for gaseous N2O5 and for a low temperature
crystal3 seem to confirm our structural proposal. Finally, the
theoretical spectra presented here were assigned from an
analysis of the potential energy distribution ͑P.E.D.͒ calcula-
tions carried out for the DF and MP2 frequencies ͑see Table
III͒. The assignments obtained for the vibrational spectra us-
ing both of the calculation procedures were to be identical
and therefore Table III only summarizes the study performed
at the MP2 level for the C2 symmetry structure. It goes with-
out saying that the theoretical assignments given in Table IV
provide a sound basis for the measured FTIR frequencies.
All of the experimental frequencies fit the calculated results
with the exception of the two N-O-N stretching modes. For
this case the values of the ab initio frequencies might be
influenced by strong couplings between other vibrations.
(0.24)(S11)ϩ(0.21)(S12ϩS13
͑0.49͒(S7ϩS8)
)
͑0.47͒(S12ϩS13
)
(0.18)(S9ϩS10)ϩ(0.24)(S12ϩS13
)
(0.13)(S1ϩS2)ϩ(0.31)(S9ϩS10
(0.35)(S1ϩS2)ϩ(0.12)(S9ϩS10
)
)
͑0.80͒(S11
͒
͑0.33͒(S1ϩS2)
(0.36)(S11)ϩ(0.23)(S14ϩS15
)
42 (B)
(0.11)(S1ϩS2)ϩ(0.33)(S14ϩS15)
aInternal coordinate definition ͓see Figure 1͑b͔͒. stretching: S1ϭ⌬͑N3O1͒,
S2ϭ⌬͑N2O1͒, S3ϭ⌬͑N2O5͒, S4ϭ⌬͑N2O7͒, S5ϭ⌬͑N3O4͒, S6ϭ⌬͑N3O6͒;
bending: S7ϭ⌬͑O7N2O5͒Ϫ⌬͑O1N2O5͒Ϫ⌬͑O1N2O7͒, S8ϭ⌬͑O6N3O4͒Ϫ
⌬͑O1N3O6͒Ϫ⌬͑O1N3O4͒,
⌬͑O6N3O1͒Ϫ⌬͑O1N3O4͒,
S9ϭ⌬͑O1N2O5͒Ϫ⌬͑O1N2O7͒,
11ϭ⌬͑N2O1N3͒; wagging:
S
10ϭ
S12
S
ϭ⌬͑O1N3O4O6͒, S13ϭ⌬͑O1N2O5O7͒, torsion: S14ϭ⌬͑O1N3O4O6͒, S15
ϭ⌬͑O1N2O5O7͒
bThe P.E.D. contributions lower than 10% are omitted.
IV. CONCLUSION
measured FTIR spectrum of the matrix isolated molecule
corresponds to that expected for structure 1a, 1b or 1c. For
this purpose, one has to observe that the two highest fre-
quency doublets may play a diagnostic role. In fact, these
doublets are calculated to have a very small frequency sepa-
ration for the 1b and 1d structures, whereas the two compo-
nents are more widely separated in the spectrum of the 1a
The calculations and measurements presented here
strongly suggest that the most likely ͑and most stable͒ struc-
ture for the N2O5 molecule is that of the C2 symmetry. This
conclusion is in agreement with the electron diffraction mea-
surements by MC Clelland et al.9 Unfortunately the calcula-
tions do not fit all the experimental frequencies measured in
an argon matrix and which compares favorably with other IR
TABLE IV. Assignment of the experimental frequencies ͑cmϪ1͒ of the N2O5 molecule based on the C2
symmetry DF and MP2 theoretical results.
Approximate description
Gas phasea
Matrixb
DF/DZϩP
MP2/DZϩP
of the vibrational modec
Stretching modes
1728
1728
1338
1247
860
1742.4
1702.7
1339.8
1243.0
863.1
1725
1679
1315
1222
258
1958
1941
1346
1262
205
(A) NO2 stretching
(B)
(A) NO2 stretching
(B)
(B) NON stretching
(A)
353
336
348
In plane bending modes
743
743
614
353
85
737
715
639.7
343.9
820
698
630
475
197
834
719
645
520
220
(A) NO2 bending
(B)
(A) NO2 bending
(B)
(A) NON bending
Out of plane bending modes
717
652
48
766
690
61
(A) NO2 wagging
(B)
(A) NO2 rocking
(B)
577
50
569.4
62
42
aTaken from Ref. 7.
bArgon matrix, this work.
cSee Table II for details.
J. Chem. Phys., Vol. 104, No. 20, 22 May 1996
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7846
Bencivenni et al.: IR spectrum of N2O5 in Ar
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