Analyses of the infrared absorption bands of 15NO3 in the 1850 - 3150 cm-1 region

Article abstract of DOI:10.1021/jp908386n

We have observed the infrared spectrum of 15NO3 by a high resolution Fourier transform infrared (FT-IR) spectrometer using the reaction of F atoms with H15NO3. Five 2E' - 2A₂' bands are identified in the 1850 - 3150 cm-1 region. The rotational analyses indicate that these bands have the lower state in common, which coincides with the ground state of planar D_3h symmetry. The upper 2E' states more or less suffer from perturbations by close-lying dark states. Among them, those of the 2004, 2128, and 2492 cm-1 bands are analyzed to determine molecular parameters in these states by fixing the ground-state constants to those derived by a combination difference method. The spin - orbit and Coriolis coupling constants in the 2E' states are substantially different for different vibronic states. The vibrational assignments of NO₃ in the ground electronic state are discussed using experimental data heretof ore available, supplemented by those obtained by the present study.

Full text of DOI:10.1021/jp908386n

980
J. Phys. Chem. A 2010, 114, 980–986
15
Analyses of the Infrared Absorption Bands of NO3 in the 1850-3150 cm-1 Region
Takashi Ishiwata,*,† Yukio Nakano,† Kentarou Kawaguchi,‡ Eizi Hirota,§ and Ikuzo Tanaka¶
Graduate School of Information Sciences, Hiroshima City UniVersity, 3-4-1 Otsuka-Higashi, Hiroshima
731-3194, Japan, Faculty of Science, Okayama UniVersity, 3-1-1 Tsushima-Naka, Okayama 700-8530, Japan,
The Graduate UniVersity for AdVanced Studies, Hayama, Kanagawa 240-0193, Japan, and
Tokyo Institute of Technology, 2-12-1 Ohokayama, Tokyo 152-8550, Japan
ReceiVed: August 31, 2009; ReVised Manuscript ReceiVed: NoVember 9, 2009
We have observed the infrared spectrum of 15NO3 by a high resolution Fourier transform infrared (FT-IR)
spectrometer using the reaction of F atoms with H15NO3. Five 2E′-2A2′ bands are identified in the 1850-3150
cm-1 region. The rotational analyses indicate that these bands have the lower state in common, which coincides
with the ground state of planar D3h symmetry. The upper 2E′ states more or less suffer from perturbations by
close-lying dark states. Among them, those of the 2004, 2128, and 2492 cm-1 bands are analyzed to determine
molecular parameters in these states by fixing the ground-state constants to those derived by a combination
difference method. The spin-orbit and Coriolis coupling constants in the 2E′ states are substantially different
for different vibronic states. The vibrational assignments of NO3 in the ground electronic state are discussed
using experimental data heretofore available, supplemented by those obtained by the present study.
1. Introduction
symmetry in analyzing the dispersed fluorescence spectra,
whereas Nelson et al. supposed it to be of C2V. Ishiwata et al.
reported the frequencies of three vibrational modes in the ground
electronic state that are active in fluorescence: ν1 (a1′: symmetric
N-O stretch), ν3 (e′: degenerate N-O stretch), and ν4 (e′:
degenerate ONO deformation). Ishiwata et al.9 and Kawaguchi
et al.10 applied infrared diode laser spectroscopy to a band
around 1492 cm-1 and unambiguously assigned the ground
electronic state to be of 2A2′ symmetry with a planar D3h
structure from the rotational analysis. They also showed that
the upper state of the 1492 cm-1 band was an E′ vibronic state,
consistent with the assignment of the band to the ν3 fundamental.
The E′ vibronic state was subject to a few anomalies arising
The nitrate radical (NO3) is one of the chemical intermediates
that play important roles in chemical transformation in the
Earth’s atmosphere.1-3 Atmospheric NO3 is predominantly
formed by the reaction
NO2 + O3 f NO3 + O2
(1)
During the daytime, NO3 is rapidly photolyzed by sunlight and
is known to participate in the reaction system, which reduces
the ozone concentration in the stratosphere. On the other hand,
NO3 persists at night and works as the most important oxidizing
species in the troposphere, in place of OH during the daytime.
The NO3 radicals react with certain organic compounds,
typically by hydrogen abstraction or by addition to an unsatur-
ated bond, and contribute to the chemical processes giving acid
rain and toxic compounds in the atmosphere, i.e., to air pollution
by artificial NOx emissions.
2
˜
from the vibronic coupling with the B E′, which was discussed
by Hirota et al.11
Friedl and Sander12 confirmed our observation of the 1492
cm-1 band by Fourier transform infrared spectroscopy, and
newly found the ν2 (a2′′: out-of-plane bending) band at 762 cm-1.
To detect NO3 in an ambient air and laboratories, it is usual
to use the visible electronic transition which has been known
since the 19th century. This system consists of about 20 diffuse
bands in the 480-680 nm range, and its strong absorption
centered at ∼662 nm is ascribed to the (0-0) band.4,5 This
-
Weaver et al.13 reported the photoelectron spectra of NO3 . Their
analysis indicated that the ground electronic state of NO3 had a
D3h equilibrium geometry and was vibronically coupled to the
2
˜
B E′ state through the ν4 mode. We extended the analysis from
1500 to 3000 cm-1 by infrared diode laser spectroscopy and
Fourier transform infrared spectroscopy and identified about 10
bands.14-16 Some of them were too complicated to analyze,
perhaps because of perturbations by close-lying dark states. The
bands analyzed were all found to be due to perpendicular
2
2
˜
˜
electronic transition is historically labeled as B E′-X A2′ in
accord with the Walsh diagram,6 originating from qualitative
theoretical consideration, but this assignment was not based on
experimental evidence even for the ground state until recently.
The spectroscopic studies on NO3 were initiated with the laser
spectroscopic observations carried out about a quarter century
ago; Ishiwata et al.7 and Nelson et al.8 succeeded independently
in observing laser induced fluorescence and dispersed fluores-
2
˜
transitions of the E-A type with the X A2′ state as the lower
state in common. We noticed that the E′ vibronic levels in the
region between 2000 and 3000 cm-1 were difficult to simply
represent in terms of overtone and/or combination states of the
four normal modes, and thus only tentative assignments have
been given for the observed bands.
2
2
˜
˜
cence spectra of the B E′-X A2′ transition. The spectral data
obtained by the two groups were almost identical, but Ishiwata
et al. supposed the ground-state structure of NO3 to be of D3h
A number of ab initio calculation studies have been carried
out on NO3 concerning the equilibrium geometry and harmonic
* Corresponding author. E-mail: ishiwata@hiroshima-cu.ac.jp.
† Hiroshima City University.
2
17
˜
frequencies for the X A2′ ground state. However, the results
‡ Okayama University.
§ The Graduate University for Advanced Studies.
¶ Tokyo Institute of Technology.
so far obtained were not conclusive as to the explanation for
2
˜
anomalies in the vibronic energy levels in the X A2′ state. In
10.1021/jp908386n  2010 American Chemical Society
Published on Web 12/21/2009

Analyses of Infrared Absorption Bands of 15NO3
J. Phys. Chem. A, Vol. 114, No. 2, 2010 981
relation to this problem, Stanton18 recently proposed a reas-
signment of the vibrational state lying at 1492 cm-1 to ν1 + ν4
using the model Hamiltonian approach developed by Ko¨ppel
et al.,19 and interpreted the bands in the fluorescence spectrum
-
and the photoelectron spectra of NO3 on the basis of a new
assignment of ν3 to be ∼1000 cm-1
.
More recently, Jacox and Thompson20 observed the infrared
spectra of NO3 and its isotopic species trapped in sold neon in
the 700-3000 cm-1 range. Their study confirmed the bands
observed in the gas phase and, in addition, identified some weak
ones that were not detected in previous studies. A weak band
thus found at 1412.5 cm-1 was more reasonable to assign to ν1
+ ν4 in view of the observed intensities and isotope shifts, and
the 1492 cm-1 band to ν3 + ν4.21 Beckers et al.22 observed the
ν4 fundamental band in Ne matrix and gave a tentative
assignment of the vibronic bands on the basis of ν3∼1100 cm-1
by following the reassignment of the 1492 cm-1 band. Stanton23
studied the infrared spectrum of NO3 by using the equation-
of-motion coupled-cluster method, and the ν3 fundamental mode
Figure 1. R branch side of the spectrum of the 2004 cm-1 band of
15NO3.
was calculated to lie at 1067 cm-1
.
Under these circumstances, we have restarted a program of
the study on the NO3 radical using high-resolution spectroscopy,
by focusing attention to the effects of vibronic interactions on
the ground state, including primarily the vibrational reassign-
ment of ν3 proposed by Stanton. The present paper describes
the first report of such study on the 15N isotopic species of
NO3.
2. Experimental Section
The infrared absorption spectra of 15NO3 were recorded at
0.008 cm-1 resolution using a Fourier- transform spectrometer
(Bruker IFS 120 HR) at Okayama University. An absorption
cell equipped with a White-type multireflection mirror system,
14.2 cm in inner diameter and 150 cm in length, was employed,
and the effective path length was set to be 24 m.
We generated 15NO3 by the reaction of F + H15NO3. Fluorine
atoms were generated by a microwave discharge in F2 diluted
to 1% by He. We produced H15NO3 by the reaction of Na15NO3
(99.8% 15N, obtained from Shoko Co. Ltd.) with H2SO4 and
purified it by vacuum distillation. The experimental conditions
were typically 70 mTorr of H15NO3 at a total pressure of 1.5
Torr.
Figure 2. Spectrum near the origin of the 2004 cm-1 band of 15NO3.
for 14NO3 in the 2200-2400 cm-1 region, either are too weak
or are missing due to the overlap of absorption bands of N2O5
and HNO3.
Figure 1 shows an example of the spectra observed for the
R-branch side of the 2004 cm-1 band. The observed lines appear
with K numbers equal to 0, 3, 6, 9, 12, ...; i.e., K ) 3n (n )
integer) levels only occur. This observation indicates that three
oxygen atoms with zero nuclear spin are equivalent in the
molecule, supporting the presence of a 3-fold axis. On the other
hand, as shown in Figure 2, the rQ0(N) transitions observed near
the band origin show that the N quantum number is limited to
1, 3, 5, ...; that is, only odd N levels occur. Two oxygen atoms
are therefore equivalent with respect to a 2-fold axis, which is
perpendicular to the 3-fold axis. These observations establish a
planar D3h structure of 15NO3 and show that the ground state is
3. Results
a. Spectral Features. We identify five vibrational bands of
15NO3 in the 1850-3150 cm-1 range. They are all perpendicular
transitions of the 2E-2A type, and their features resemble those
previously observed for 14NO3.9,10,14-16 The spectra clearly show
a characteristic series of doublets attributed to the rQ0(N) branch
p
transitions lying near the band origin, and much stronger P
2
the A2′ electronic state as is the case with 14NO3 reported
r
and R branch transitions at lower and higher frequencies than
previously.9
rQ0(N), respectively. Among the observed five bands, three at
2004, 2128, and 2492 cm-1 are rotationally analyzed in detail
(all the transition frequencies observed for the three bands are
listed in the tables in the Supporting Information), while the
remaining two bands at 1900 and 2868 cm-1 suffer from strong
perturbations in the upper states, preventing us from carrying
out rotational analyses. The rotational lines of these two bands
are partly assigned for some smaller K and N levels, but it is
difficult to extend the assignment to larger K and N levels. For
the rest of the bands, we use a Hamiltonian for D3h molecules
without explicitly taking account of perturbations in the upper
state. Some other bands, which correspond to those observed
b. Ground State. In analyzing the vibrational bands, we fix
the molecular constants of the ground state determined from
r
the combination differences, which are formed either from R
r
p
p
and Q branch transitions or from Q and P transitions, as
described below:
∆′′(N, K) ) F′′(N+1,K) - F′′(N,K)
r
)
rRK(N) - QK(N+1)
(2)
p
)
pQK(N) - PK(N+1)
There are several reasons for carrying out such an analysis.
First, the upper E′ vibronic states more or less suffer from

982 J. Phys. Chem. A, Vol. 114, No. 2, 2010
Ishiwata et al.
2
species containing 14N.10,16 The rotational constants are es-
sentially invariant between the two species, since the nitrogen
atom sits at the center of the molecule. The substitution of the
nitrogen atom with its isotope will not change the moment of
inertia of the radical much, as is actually found. The N-O bond
length r0 is calculated to be 1.2381 Å from the ground-state
rotational constant of 15NO3.
TABLE 1: Molecular Constants of NO3 in the A2′ Ground
a
State (cm-1
)
15NO3
14NO3
b
c
B
0.4586150(68)
1.093(13) × 10-6
-2.063(40) × 10-6
-0.01640(14)
0.4585485(63)
1.113(12) × 10-6
-2.121(27) × 10-6
-0.01649(13)
DN
DNK
εbb
The observed ground-state spin-rotation interaction constant
is found to be consistent with the electronic structure of NO3;
a Values in parentheses denote one standard deviation. The
planarity condition is assumed: C ) B/2 and DK ) -(2DN
+
ε
bb is determined to be -0.016 cm-1, in good accord with that
3DNK)/4. b Present study. c Reference 16.
estimated using the following theoretical expression:24
perturbations by close-lying dark states. These perturbations
make it difficult to fit the observed spectral line frequencies
within the experimental accuracy without taking into account
the effects of perturbations. Furthermore, the perturbations in
the upper E′ states occur in different ways for different vibronic
states, which may make the molecular constants of the ground
state inconsistent among band-by-band analyses. Under these
circumstances, it is quite useful to analyze the lower state only
without being affected by perturbations in the upper states.
Second, the analyses using combination differences lead to
unambiguous assignment for the two spin components; the
spectral lines of NO3 are split into two spin components and it
is not always obvious to assign which component to F1 or F2
transitions. The transitions of these spin components are
sometimes inverted in energies, and the spectra show different
appearance. Third, what is more important is that the analysis
based on the combination differences establishes an accurate
assignment of the rotational quantum number N. Since spectral
εbb ) 4A ∑ 0|L |n n|BL |0 /(E - E )
(6)
〈
〉〈
〉
SO
n
b
b
n
0
In this expression, |0〉 and |n〉 denote the ground and electroni-
cally excited states, respectively, Lb represents the b component
of the electronic orbital angular momentum, and En and E0 stand
for the energies of the nth excited and the ground states,
respectively. Because La and Lb belong to E′′ symmetry, the
ground state of A2′ symmetry will interact with excited states
2
˜
of E′′ symmetry. NO3 has the first excited state, A E′′, at 7000
cm-1 above the ground state,13,25,26 and the observed εbb constant
leads to the spin-orbit interaction constant ASO of about 60
cm-1, which is comparable to the corresponding value of O
atom, 160 cm-1, and is consistent with the theoretical prediction
that an unpaired electron in the ground state lies in the p orbital
of the O atom lying on the molecular plane.27
The εcc constant arises from the interactions of the ground
electronic state with excited states of A1′′ symmetry. An ab initio
calculation predicts such states lying far apart, more than 60 000
cm-1 above the ground electronic state.27 Therefore, εcc will be
negligibly small, and in fact, it is not necessary to introduce
this parameter in the present analysis.
p
r
lines are congested in the energy region where the Q and Q
transitions appeared, the relation shown in eq 2 is quite useful
to assign these series of transitions. We thus derive 412
combination differences for the lower state from the five infrared
bands under the study: 31 in the 1900 cm-1 band, 132 in the
2004 cm-1 band, 99 in the 2128 cm-1, 97 in the 2492 cm-1
band, and 53 in the 2868 cm-1 band. These data are all
consistent within the accuracy of the measurements, and five
infrared bands observed in the present study are confirmed to
It should be pointed out that the molecular parameters for
the ground state of 15NO3 shown in Table 1 are different from
those reported in our first paper on 14NO3.9 The spin-rotation
interaction constants, εbb and εcc reported in ref 9, in particular,
differ much from the present results. The discrepancies primarily
stem from our failure in analyzing the upper E′ vibronic state
of the 1472 cm-1 band of 15NO3; the previous analysis took
into account the εcc spin-rotation interaction constant. But we
later noticed that this εcc constant was too large compared with
a theoretically expected value and should be replaced by a
spin-orbit interaction term in the upper E′ state, as described
in the second paper on 14NO3.10 In the previous analysis by diode
laser spectroscopy, we derived 22 combination differences for
the lower state of the 1472 cm-1 band of 15NO3. These data
spanned the ranges of K′′ ) 3-15 and N′′ ) 6-18 and were
consistent with those derived in the present study from other
bands. We thus confirmed that the 1472 cm-1 band of 15NO3
2
have the A2′ ground state as the common lower state.
The expression for the rotational energy levels of the ground
state is
〈N,k,l|Hvr|N,k,l〉 ) BN(N+1) +
(C - B)k2 - DNN2(N+1)2 - DNKN(N+1)k2 - DKk4
(3)
where C ) B/2 is assumed, in accord with a D3h molecular
structure. The planarity relation for the centrifugal distortion
terms, 2DN + 3DNK + 4DK ) 0, is also employed. The spin-
rotation interaction is included in both the diagonal and off-
diagonal blocks as follows:
2
˜
also originated from a transition with the X A2′ ground state as
the lower state.
N,k, l,J|H |N,k,l,J )
〈
〉
sr
c. Vibrationally Excited States. The analyses of the rota-
tional structure in the upper vibrational states were performed
using a Hamiltonian appropriate for the states of vibronic E′
symmetry. The diagonal term of the vibration and rotation
energy is given by
{εbb - (εbb - εcc)k2/[N(N+1)]} ×
{[J(J+1) - N(N+1) - S(S+1)]/2}
(4)
(5)
and
N-1, k,l,J|H |N,k,l,J )
〈
〉
sr
N,k,l|H |N,k,l ) T + BN(N+1) + (C - B)k2 -
(1/2)(εbb - εcc)(k/2N)[N2 - k2]1/2
〈
〉
vr
v
2Cꢀkl + ηNN(N+1)kl + ηKk3l - DNN2(N+1)2 -
The molecular constants of the ground state thus derived are
D
NKN(N+1)k2 - DKk4
(7)
summarized in Table 1. The standard deviation of fitting is
0.001 36 cm-1. The molecular constants of the 15N substituted
species of NO3 are consistent with those derived in the normal
The off-diagonal term

Analyses of Infrared Absorption Bands of 15NO3
J. Phys. Chem. A, Vol. 114, No. 2, 2010 983
TABLE 2: Molecular Constants of 15NO3 in the E′ Vibronic
N,k+1,l)1|H |N,k-1,l)-1 ) (1/2)[q +
〈
〉
vr
a
States (cm-1
)
qNN(N+1)] × {[N(N+1) - k(k-1)][N(N+1) -
k(k+1)]}1/2
2004 cm-1
2128 cm-1
2492 cm-1
(8)
ν00
B
C
DN
DNK
DK
Cꢀ
ηN
ηK
q
qN
aeff
εbb
εbb- εaa
σfit
2003.9849(4)
2128.5244(10)
0.454139(26)
2492.9587(6)
0.4534443(50)
0.2264397(43)
0.454279(15)
0.2265752(67)
is included to account for the (2, 2) vibration-rotation interac-
tion. The matrix elements of the spin-rotation interaction are
identical to those of eqs 4 and 5. Furthermore, as in the case of
14NO3 reported previously,10 the Hamiltonian includes the
spin-orbit interaction matrix elements as follows:
0.226500(14)
0.816(13) × 10-6
-1.811(27) × 10-6
0.980(19) × 10-6
-0.004217(19)
1.24(18) × 10-6
-2.85(28) × 10-6
1.29(28) × 10-6
-0.022250(57)
-4.60(12) × 10-5
4.29(11) × 10-5
0.00884(27)
1.152(82) × 10-6
-2.14(17) × 10-6
0.969(85) × 10-6
0.018005(28)
-0.834(17) × 10-5
0.704(18) × 10-5
0.0037649(75)
0.289(51) × 10-5
-0.323(50) × 10-5
0.000522(35)
N,k,F |H |N,k,F ) a k/2(N+1)
(9)
〈
〉
1
SO
1
eff
-4.44(19) × 10-5
0.01805(39)
-0.018317(27)
-0.01356(40)
0.00243
0.06518(84)
0.10306(52)
-0.017031(57)
-0.00917(51)
0.00258
N,k,F |H |N,k,F ) a k/2N
(10)
〈
〉
2
SO
2
eff
-0.01705(11)
N-1,k,F |H |N,k,F ) a (N2 - k2)/2N
(11)
〈
〉
1
SO
2
eff
0.00362
where aeff ) 〈Eev|aLz|Eev〉 denotes an effective spin-orbit
coupling constant in the upper vibrational state.
a Values in parentheses denote one standard deviation. The
ground-state constants were fixed to those in Table 1.
The subband analyses for each of the K sublevels were carried
out iteratively to assign the transitions in the observed spectra
with fixing the molecular constants of the ground state. Since
the ground-state parameters were initially unknown, assignments
were facilitated by a set of constants derived for 14NO3
previously.16 As expected, the substitution of 15N isotope in the
normal 14NO3 species did not affect the molecular parameters
in the ground state, and the spectra were reasonably assigned
in lower K and N levels. This analysis provided combination
differences for the ground state that were sufficient enough to
give its molecular constants, and we used them to calculate the
ground-state constants for 15NO3 by a least-squares method. The
subband analyses continued to extend the assignments by using
this new set of constants, and additional data thus obtained
provided new combination differences of the ground state to
improve its molecular constants. By repeating this cycle several
times, we finally assigned 651 transitions for the 2004 cm-1
band, 498 for the 2128 cm-1 band, and 511 for the 2492 cm-1
band.
The observed lines thus assigned were fed to a total fitting
program, where the ground-state constants were fixed to those
listed in Table 1. In the 2000 cm-1 energy region, there are
several overtone or combination states that come close to the
upper E′ states under the study. The perturbing states were not
necessarily evident by the occurrence of additional lines and/
or the level crossing, but the spectra showed apparent energy
shifts in the E′ upper states. The shifts generally depend largely
on N, which suggests the perturbation is inhomogeneous.
However, the data were in most cases insufficient to specify
which lines should be included in the fit. To describe the upper
states, we fitted the data using an effective Hamitonian for a
degenerate vibrational state without explicitly taking into account
the perturbations. The resulting parameters obviously depend
on our choice of lines included but are good enough to limit
the residual to 0.008 cm-1, which is close to the spectral
resolution of the present study.
TABLE 3: Isotope Shift of Band Origin (cm-1
isotope shift (∆E)b
)
a
band
15NO3
14NO3
gasa
matrixc
1492
1927
2024
2155
2200
2240
2380
2518
2585
2900
1472.8331(13)d
1492.3936(5)e
N.G.
2024.3230(8)
2155.1885(7)
N.G.
N.G.
N.G.
2518.7130(5)
2585.0935(10)
N.G.
19.561
19.4
28.1
20.2
26.8
24.3
23.4
N.G.f
2003.9849(4)
2128.5244(10)
N.M.g
N.M.
N.M.
2492.9587(7)
N.G.
20.338
26.664
25.754
25.6
33.6
27.9
N.G.
a Present study. b Relative to 15NO3: ∆E
)
Ev(14NO3)
-
Ev(15NO3). c Reference 20. In Ne matrix. d Reference 9. e Reference
10. f Not given. g Not measured.
us to determine molecular constants of the upper E′ states, as
summarized in Table 2.
d. Isotope Effect. Table 3 summarizes the origins of the
vibrational bands observed for 15NO3, to be compared with those
of 14NO3, where the correspondence of the bands between the
two isotopic species is made by assuming the isotope shifts to
be in the range of 20-30 cm-1. In addition, the band intensities
give further information on the correspondence. For 15NO3, the
relative intensities of the four dominant bands at 1900, 2004,
2128, and 2492 cm-1 are roughly 1:0.5:0.6:0.6, as estimated
r
from the absorbance of the R6(6) transition, which are very
close to those of the bands of 14NO3, each lying 20-30 cm-1
higher than the 15NO3 band.16 Jacox and Tompson20 reported
the absorption bands of 14NO3 and its isotopic species in Ne
matrices. Although the absorption bands are shifted by matrix
effects to lower frequencies by about 1 cm-1, the isotope shifts
agree within 0.2 cm-1 with the present results in the gas phase.
This observation confirms that the vibrational bands observed
in the present study are all cold bands; i.e., their lower states
are common: the ground vibrational state, as already established
by our analyses.
The upper state of the 2004 cm-1 band was less perturbed
than those of the other two bands at 2128 and 2492 cm-1. Even
in this case, however, we could include only 441 transitions in
the analysis, which corresponded to only 64.9% of the total
assigned lines in the subband analysis. The situations were much
worse in the other bands: 146 transitions (29.1%), and 217
transitions (39.2%) for the 2128 and 2492 cm-1 bands,
respectively. The transition frequencies employed for the
determination of molecular constants are almost free from the
perturbations, as certified by the ground-state combination
differences (see the paragraph right after eqs 9-11), and allowed
Table 4 compares the Coriolis coupling and the effective
spin-orbit interaction constant, ꢀ and aeff, derived for the E′
upper vibrational states for the two isotopic species, 14NO3 and
15NO3. These two parameters, both magnitude and sign, will
reflect characteristic features of the upper E′ states, and it is
interesting to note that both the parameters behave in parallel
to some extent but still exhibit sizable variations between the
two species. From the results of the present study, we may add

984 J. Phys. Chem. A, Vol. 114, No. 2, 2010
Ishiwata et al.
TABLE 4: Summary of the Molecular Constants of the E′ States
14NO3
15NO3
assignment
a
a
band
ꢀ
aeff
ꢀ
aeff
∆Ea (cm-1
)
Ib
IIc
1492
1927
2024
2155
2518
2585
0.194
-0.20
-0.011
-0.108
0.103
0.173
-0.09
-0.013
0.093
0.139
-0.034
19.561d
(28.1)
20.338
26.664
25.754
(33.6)
ν3
ν3 + ν4
ν3 +2ν4
5ν4
ν1 + ν3
ν1 +4ν4
2ν3+ ν4
ν3 + ν4
5ν4
-0.019
-0.098
0.079
0.018
0.065
0.103
ν1 +3ν4
ν1 + ν3
2ν1+ ν4
0.116
a In cm-1. ∆E ) Ev(14NO3) - Ev(15NO3). b Reference 16. c References 18, 20, and 22. d References 9 and 10.
two more terms to this list: the l-type doubling constant q and
the anisotropic term of the spin-rotation interaction εbb - εaa.
These findings not only give the basis for the correspondence
of the bands of the two isotopic species as listed in Table 4 but
also provide us with invaluable information on the characteristics
of the upper vibrational states leading to the vibrational
assignments of these states.
assignments I and II using experimental data other than the
isotope shifts of the vibrational frequencies on which Beckers
et al.’s discussion is mainly based. As Kawaguchi et al.10
reported, two prominent anomalies appear in this band: the
spin-orbit coupling term and the first-order Coriolis coupling
constant. The rotational analysis of this band requires a small,
but definite, spin-orbit coupling term to be included, in spite
of the fact that the ground electronic state is of electronically
nondegenerate A2′ symmetry. The Coriolis constant may be
calculated from a conventional force field to be ꢀ ≈ 0.7, which
differs much from the observed value of ꢀ ≈ 0.2.
4. Discussion
As mentioned in the Introduction, the vibrational assignment
for NO3 in the ground electronic state has not been established.
Stanton18 proposed a new assignment for the ν3 fundamental
band at around 1000 cm-1, at variance with the earlier and
The presence of a small spin-orbit interaction constant in
the upper state of the 1492 cm-1 band is obviously ascribed to
mixing of the excited electronic states of E′ symmetry with this
state. Hirota et al.11 in fact showed that the first-order vibronic
interaction term containing the q3 coordinate linearly accounted
for the small spin-orbit coupling constant. This treatment is
of course based upon the assignment I, and the first-order
vibronic interaction matrix element of about 1139 cm-1 was
required to explain the small spin-orbit interaction constant of
0.173 cm-1, where the upper electronic state responsible for
the interaction is mainly the ground vibrational state associated
widely accepted position of 1492 cm-1 7,9-12
We have carefully
.
scanned the region from 800 to 1400 cm-1 by Fourier transform
infrared spectroscopy to detect the “ν3” band but did not observe
any band stronger than 0.1 of the 1492 cm-1 band. Stanton21,23
later calculated the intensity of the “ν3” band to be extremely
small (∼1/600).
Stanton’s proposal, if correct, requires revision of the
vibrational assignment for overtone and combination bands
observed in the 1500-3150 cm-1 region, which was tentatively
made by Kawaguchi et al.16 some years ago. In fact, Beckers et
al.22 recently reported an alternative assignment mainly based
on the isotope shifts of the vibrational frequencies calculated
by Stanton,23 claiming that this assignment resolved all “con-
flicting observations”. However, the isotope shifts in vibrational
frequency are certainly insufficiently by themselves to fully
endorse Stanton’s proposal. Table 4 compares the two assign-
ments: I (Kawaguchi et al.) and II (Beckers et al.) for the six
most prominent bands in the 1400-2600 cm-1, where one
modification is made for I, namely the 1927 cm-1 band is
assigned to ν3 + ν4.
2
˜
with the B E′ electronic state, the extent of mixing being only
0.58%, provided that the spin-orbit constant ASO is assumed
to be 30 cm-1. When we adopt assignment II, ν3 + ν4 assigned
to 1492 cm-1, we may employ a more or less similar procedure,
except for the vibrational states interacting with the upper state
of the band.
The vibronic Hamiltonian of ref 11 was extended to include
the contribution of the ν4 mode, i.e., H′ ) H1-3 + H1-4
+
H2-33 + H2-44 + H2-34, where the first two represent the
first-order terms linear in the normal coordinates q3 and q4,
respectively, and the last three the second-order terms
2
2
proportional to q3 , q4 , and q3q4, respectively. The ν3 state
There are two major difficulties in making vibrational
assignment for NO3 in the ground electronic state: vibronic
interaction and vibration-rotation interaction including an-
harmonicity resonance. The two factors are obviously cor-
related to some extent. Hirota et al.11 attempted to explain
anomalies observed for the 1492 cm-1 band in terms of
vibronic interaction. One of the important findings they
reported is that, when they treated the first-order and second-
order vibronic interaction terms by perturbation, they found
cubic anharmonic potential terms to result in the vibrational
potential function. For example, when the ν3 normal coor-
dinate is active in the vibronic interaction, the perturbation
contributes to the k333 cubic constant, which has been known
to play an important role in the l-type doubling constant, a
result of the vibration-rotation interaction.
˜
˜
in X will vibronically interact with the B state (ν3′, ν4′) )
(0,0), (2,0) [H1-3], (1,1) [H1-4], (3,0) [H2-33], (1,2) [H2-44],
and (0,1), (2,1) [H2-34], whereas the ν3 + ν4 state in X with
˜
(0,1), (2,1) [H1-3], (1,0), (1,2) [H1-4], (3,1) [H2-33], (1,3)
[H2-44], and (0,0), (2,0), (0,2), (2,2) [H2-34], where the
Hamiltonian in square brackets yields the matrix elements.
We should perhaps take into account the Franck-Condon
type overlap integral and should also pay attention to the
different nature of the ν3 mode in the two assignments.
Unfortunately, little has been known on the vibrational states
2
˜
in the B E′. We thus concluded that it is still quite difficult
at the present to put the argument on a quantitative basis
and to compare the extent of mixing of the vibrational states
2
˜
of the B E′ with the ν3 state for assignment I and with the ν3
It would be natural to presume that the higher the vibrational
state is, the more extensive the anharmonicity mixing is, and
we have thus decided to focus attention mainly to the 1492 cm-1
band in the present study and have critically examined the two
+ ν4 state for assignment II.
Hirota et al.11 tried to explain why the first-order Coriolis
coupling constant of the 1492 cm-1 band is observed to be
much smaller than the force-field value, in terms of the

Analyses of Infrared Absorption Bands of 15NO3
J. Phys. Chem. A, Vol. 114, No. 2, 2010 985
average angular momentum induced by the degenerate
vibrational mode, ν3. However, they had to assume a quite
large value 2440 cm-1 for the second-order vibronic matrix
element. This finding indicates that the mechanism they
proposed is by no means a dominant one. On the other hand,
Kawaguchi et al.10 examined the effect of anharmonicity
resonance between ν3 and ν1 + ν4 on the first-order Coriolis
coupling constant; they transferred necessary molecular
parameters from the data on a molecule BF3 closely
resembling the structure of NO3. Because of a famous sum
rule for the Coriolis coupling constants of the two degenerate
normal modes of a planar D3h XY3 molecule28
The molecular constants of 15NO3 obtained in the present
study will be of great use in future for establishing the
vibrational assignment for NO3 in the ground electronic state,
although at present lack of some important information makes
it for us unpractical to analyze the isotopic data. One
important example of such data is those on the ν4 degenerate
mode in the gas phase. These data are indispensable to clarify
the details of the vibronic and vibration-rotation interactions
and to solve most important pending problems in NO3,
including the assignment of the 1492 cm-1 band as one of
the most central themes.
5. Conclusion
ꢀ3 + ꢀ4 ) 0
(12)
The present study reports the observation and analysis of a
few vibration-rotation bands of 15NO3 in the gas phase using
high-resolution Fourier transform infrared spectroscopy. The
results thus obtained are combined with those on 14NO3 and
others to critically examine the vibrational assignment of NO3
in the ground electronic state. We demonstrate, on the basis of
our gas-phase data, that both assignments I and II involve some
problems to be clarified further. To solve these important
problems, we need detailed and precise data on NO3, including
the ν4 fundamental band in the ground electronic state and the
observation and analysis of rovibronic transitions among the
X, A, and B states.
the effective value of the Coriolis coupling constant in the ν3
state reduces to
ꢀeff ) (δE)ꢀ3/2r
(13)
where δE denotes the unperturbed energy difference between
the ν3 and ν1 + ν4 states, i.e., the difference not affected by the
anharmonic resonance, whereas
2r ) [(δE)2 + 4W2]1/2
(14)
stands for the perturbed difference. The anharmonic resonance
is induced by the cubic anharmonic k134 term, which gives the
interaction matrix element W:
Acknowledgment. This work was partially supported by
JSPS Grant-in-Aid for Scientific Research (C) No. 21550009.
W ) k134/81/2
(15)
Supporting Information Available: Tables list all the
transition frequencies observed for the 2004, 2128, and 2492
cm-1 bands. This material is available free of charge via the
Internet at http://pubs.acs.org.
Kawaguchi et al. thus arrived at a value of ꢀeff ) 0.568, which
is still much larger than the observed value. It should, however,
be pointed out that, if we increase the BF3 value of k134 ) 67
to 107 cm-1, we may reproduce the observed data. This k134
value may look too large, but the vibronic interaction is likely
to substantially affect the ν4 vibration, in particular, and such
an increase of k134 is highly probable. On the other hand,
assignment II ascribes the 1492 cm-1 band to a “pure” ν3+ ν4
state, in which ꢀ3 + ꢀ4 ) 0.0 is expected, while the observed
value was ꢀ3 + ꢀ4 ) -0.2. Although it is still not easy to explain
the difference between the observed and calculated ꢀ3 + ꢀ4
values in terms of anharmonicity resonance, because no ap-
propriate candidates for the interacting states are found near
the ν3 + ν4 state, the discrepancy is smaller than that in the
case of assignment I, and some additional mechanisms such as
that discussed by Hirota et al.11 (partial quenching of vibrational
angular momentum by vibronic interaction) may explain this
discrepancy.
As stated above, assignment II ascribes the upper state of
the 1492 cm-1 band to the e′ substate of ν3 + ν4, for which the
vibrational angular momentum quantum number l ) (2.
Therefore, we expect that the rotational structure, in particular
of K′ ) 1 leading to l-type doubling, will differ considerably
from that of the fundamental band for which l ) (1, as is, in
fact, the case for a molecule closely related to NO3, i.e., SO3
studied in detail by Maki et al.29 Following Maki we have
performed the analysis based on assignment II and have
achieved fitting as good as for assignment I, although we
introduced more parameters for additional interactions such as
those among the e’ substate and the other two substates. As is
expected, the main l-type doubling parameter p34 was found to
take a value almost equal to q in assignment I. We are planning
to continue studying l-type doubling and other related phenom-
ena, which will play crucial roles in clarifying the vibrational
assignment.
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