Microwave spectroscopy of the NBr radical in the X3Σ- state

Article abstract of DOI:10.1063/1.477354

The pure rotational spectrum of N⁷⁹Br and N⁸¹Br in the electronic ground state was measured. The measurement was carried out using a source-modulated microwave spectrometer with a 2 m free space discharge cell in the frequency region from 213 GHz to 381 GHz. The precise molecular constants including the rotational and the centrifugal distortion constants, the spin-spin and the spin-orbit interaction constants, and the hyperfine coupling constants were accurately determined.

Full text of DOI:10.1063/1.477354

Microwave spectroscopy of the NBr radical in the X 3 Σ − state
Toru Sakamaki, Toshiaki Okabayashi, and Mitsutoshi Tanimoto
Citation: The Journal of Chemical Physics 109, 7169 (1998); doi: 10.1063/1.477354
View online: http://dx.doi.org/10.1063/1.477354
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 109, NUMBER 17
1 NOVEMBER 1998
Microwave spectroscopy of the NBr radical in the X 3⌺؊ state
Toru Sakamaki,a) Toshiaki Okabayashi, and Mitsutoshi Tanimoto
Department of Chemistry, Faculty of Science, Shizuoka University, 836 Ohya, Shizuoka 422-8529, Japan
͑Received 15 June 1998; accepted 29 July 1998͒
The microwave spectrum of the NBr radical in the X 3⌺Ϫ ground electronic state has been observed
by a source modulated spectrometer. The NBr radical was generated in a free space cell by a dc
glow discharge in a mixture of N2 , Br2 , and He. The spectrum with three spin components of both
two isotopomers, N79Br and N81Br, was observed. The spectrum showed complicated splitting by
the hyperfine interactions due to both bromine and nitrogen nuclei. The molecular constants
including the magnetic hyperfine and nuclear quadrupolar hyperfine interaction constants were
determined by analyzing the observed spectrum. The spin density of the unpaired electrons was
estimated from the observed hyperfine coupling constants to be 73.4% and 22.4% on the nitrogen
and the bromine atoms, respectively. © 1998 American Institute of Physics.
͓S0021-9606͑98͒01141-6͔
are scarce. Milton et al.15 observed the rotationally resolved
spectrum of NBr produced by the same method as that used
by Elliott. They assigned the spectrum to the b 1⌺ϩ –X 3⌺Ϫ
transition from the rotational analysis by the combination
differences for the upper and lower electronic states of indi-
vidual bands. Although only the transitions terminating on
the F1 spin component (JϭNϩ1) of the X 3⌺Ϫ state (QP
I. INTRODUCTION
The nitrogen monohalides NX ͑XϭF, Cl, Br, and I͒,
which are iso͑valence͒electronic with O2 , have the X 3⌺Ϫ
ground electronic state and the two low-lying electronically
excited states, a 1⌬ and b 1⌺ϩ. These molecules have exten-
sively been studied through their electronic transitions. High
resolution spectroscopic studies of these molecules, how-
ever, were reported only for fluoride1–8 and chloride9–13
(X 3⌺Ϫ,a 1⌬,b 1⌺ϩ). Since the NX radical has two atoms
with nonzero nuclear spins, its rotational spectrum shows
complicated structure by the fine and the hyperfine interac-
tions. The information concerning the distribution of un-
paired electrons will be obtained through the analysis of the
hyperfine splittings.
S
and R branches͒ were observed, they succeeded in deriving
two probable sets of the rotational (B), the spin-spin (␭) and
the spin-rotation (␥) constants in the ground state as well as
the rotational constant in the excited state.
More recently Pritt et al. reported on the low-resolution,
visible and near-infrared transitions of NBr generated in the
F/BrϩHN3 flame.16 This method of production populated the
lower vibrational levels of NBr (b 1⌺ϩ) and thus allowed
them to detect the 0–0 band. They compared the observed
low-resolution spectrum with the synthesized one and found
a good fit for a second set of the molecular constants re-
ported by Milton et al.15 Subsequently Pritt19 observed rota-
tionally resolved emission spectra of the 0–0 band of the
b 1⌺ϩ –X 3⌺Ϫ transition in NBr produced by the reaction of
atomic fluorine with molecular bromine and hydrogen azide.
He observed weaker OP and QR branches besides the QP and
SR branches observed by Milton et al.15 and obtained the
The spectrum of NBr was first reported by Elliott14 in
1938. He photographed an orange flame produced by admit-
ting molecular bromine into a stream of active nitrogen and
observed banded structures. He analyzed the vibrational
structure of the emission spectrum and attributed it to a tran-
sition between two unknown electronic states of NBr on the
basis of the vibrational frequency and its isotope effect as
well as of a detrimental effect of added oxygen on the pro-
duction of the orange bands. This emission band was later
assigned to the ⌺ϩ –3⌺Ϫ transition.15
1
Up to the present time the electronic transitions of NBr
(a 1⌬–X 3⌺Ϫ and b 1⌺ϩ –X 3⌺Ϫ) have been studied both in
the gas phase14–16 and in rare gas matrices.17 These studies
revealed the energy intervals of the bϪX and the aϪX
states, vibrational frequencies in these electronic states and
radiative lifetimes in the upper states. The vibrational funda-
mental of NBr in the ground state was observed in an inert
rigid matrix18 and corresponded well with that from the elec-
tronic spectrum. There is no infrared study in the gas phase
yet.
Though the extensive spectroscopic studies have been
carried out, the data on the rotational energy structure of NBr
FIG. 1. A typical spectral line of N81Br in the 378.68 GHz region, Nϭ14
Ϫ13 and Jϭ15Ϫ14. The vertical lines in the lower part of the figure show
the calculated hyperfine components.
a͒
Present Address: JASCO Corporation, Hachioji, Tokyo, Japan
0021-9606/98/109(17)/7169/7/$15.00
7169
© 1998 American Institute of Physics
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7170
J. Chem. Phys., Vol. 109, No. 17, 1 November 1998
Sakamaki, Okabayashi, and Tanimoto
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J. Chem. Phys., Vol. 109, No. 17, 1 November 1998
Sakamaki, Okabayashi, and Tanimoto
7171
rotational and the fine structure constants of NBr in the
paramagnetic lines around the frequency region just below
217.1 GHz. These lines became much stronger when O2 gas
was introduced into the cell, and we supposed that this spec-
trum was due to an oxygen-containing radical, BrO. Since
this spectrum of BrO was strong even when only a small
amount of O2 remained in the cell, we had to be careful not
to leak air. As we proceeded to search toward the lower
frequency side from the predicted region, we found three
paramagnetic lines with a few MHz intervals around 214.0
GHz. The central line had intensity twice as strong as the
other two lines and it apparently gained its intensity from the
overlapping of two lines. We thought that these lines were
split by the hyperfine interaction due to the bromine nucleus.
If these lines were to be ascribed to the NBr radical, an
almost equally intense spectrum should appear for another
bromine isotopomer at the corresponding frequency, since
bromine has two isotopes (79Br and 81Br͒ with nearly equal
natural abundance. We calculated the frequency from the
ratio of the reduced masses of N79Br and N81Br and found
four paramagnetic lines with almost the same intensity as the
previous ones at the calculated frequency ͑about 213.2 GHz͒.
Thus the spectrum at the higher frequency was definitely due
to N79Br and that at the lower frequency was due to N81Br.
By using these frequencies, other F2 transitions were pre-
dicted and observed.
X 3⌺Ϫ state: B0ϭ0.4529 cmϪ1, ␭ϭ12.38 cmϪ1 and ␥
ϭϪ0.023 cmϪ1
.
In the present study, we have observed the pure rota-
tional spectrum of N79Br and N81Br in the electronic ground
state and determined their precise molecular constants: the
rotational and the centrifugal distortion constants, the spin-
spin and the spin-orbit interaction constants, and the hyper-
fine coupling constants for the N and Br nuclei.
II. EXPERIMENT
The measurement was carried out using a source-
modulated microwave spectrometer20 with a 2 m free space
discharge cell in the frequency region from 213 GHz to 381
GHz.
The NBr radical was generated in the cell by a dc glow
discharge in a mixture of N2 , Br2 , and He. The optimum
condition was 5–10 mTorr of Br2 , 15–20 mTorr of N2 , and
30–40 mTorr of He with the discharge current of 300–400
mA. The cell was cooled to about 0 °C, for bromine vapor
condensed below this temperature. We first searched for the
Nϭ8Ϫ7, Jϭ8Ϫ7 transition (F2 spin component͒ which
was expected to appear around 217.2 GHz from the molecu-
lar constants reported by Pritt.19 As the predicted frequency
seemed to have relatively large uncertainty, we needed to
scan a wide region centering at the predicted frequency. As
soon as we started the observation, we found four strong
We searched then for the Nϭ9Ϫ8, Jϭ10Ϫ9 transition
(F1 spin component͒. The frequency of the F1 component
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7172
J. Chem. Phys., Vol. 109, No. 17, 1 November 1998
Sakamaki, Okabayashi, and Tanimoto
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J. Chem. Phys., Vol. 109, No. 17, 1 November 1998
Sakamaki, Okabayashi, and Tanimoto
7173
menta. The nuclear spin of both the 79Br and 81Br nuclei is
3/2, and that of the 14N nucleus is 1. The matrix elements of
the Hamiltonian were given by Yamada et al.9 The energy
matrix was numerically diagonalized and used in a least-
squares analysis.
was dependent on the spin-spin and spin-rotation interaction
constants. As these constants had been determined with mar-
ginal uncertainties, the prediction of the transition frequency
was rather crude. We observed nine paramagnetic lines
around 250.3 GHz and assigned these lines to the spectrum
of N79Br. The corresponding transition of N81Br was found
around 249.4 GHz. By using these data, the molecular con-
stants were refined to make the prediction more reliable.
Other transitions of the F1 and F3 spin components were
thus easily detected. In contrast to the F2 component the
spectrum of the F1 and F3 spin components showed splitting
into many hyperfine components due to both the nitrogen
and bromine nuclei. Figure 1 shows the Nϭ14Ϫ13, Jϭ15
Ϫ14 transition of N81Br. Finally, fine and hyperfine compo-
nents of the rotational transitions of Nϭ8Ϫ7, Nϭ9Ϫ8, N
ϭ10Ϫ9 and Nϭ14Ϫ13 were observed for both bromine
isotopomers. Tables I and II list the transition frequencies
observed in the present study.
The preliminary values of the rotational, centrifugal dis-
tortion and fine structure constants were first determined
from the data obtained by averaging the frequencies of the
hyperfine components. These parameters were used as initial
parameters in the subsequent analysis. The Br hyperfine cou-
pling constants b͑Br͒, c͑Br͒, and eQq͑Br͒ were estimated
from those of BrO ͑Ref. 21͒ and the ratio of the chlorine
hyperfine constants of NCl to those of ClO.22 The nitrogen
hyperfine constants of NCl were used as the initial values of
the b͑N͒, c͑N͒, and eQq͑N͒. As shown in Tables I and II,
many hyperfine components were not resolved. For these
transitions the frequencies were calculated by averaging
those of component lines weighted in proportion to their
relative intensities. Table III lists the molecular constants
obtained by the least squares fit to the microwave transitions,
together with the constants reported by Pritt.19 The nitrogen
eQq constant was found to be smaller than its standard de-
viation and was thus fixed to zero in the analysis. The stan-
dard deviations of the fit were 30 and 29 kHz, respectively,
for N79Br and N81Br.
III. ANALYSIS
The Hamiltonian used in the present analysis is given as
follows:
HϭHrotϩHssϩHsrϩHhfs͑N͒ϩHhfs͑Br͒,
͑1͒
where Hrot represents the rotational energy of the molecule,
Hss the spin-spin interaction, Hsr the spin-rotation interac-
tion, Hhfs͑N͒ the hyperfine interaction of the nitrogen
nucleus, and Hhfs͑Br͒ the hyperfine interaction of the bro-
mine nucleus including the nuclear spin-rotation interaction.
The coupling scheme of the angular momenta based on the
Hund’s case b␤ basis is written as J؍NϩS, F1ϭJ؉I͑Br͒,
F؍F1ϩI͑N͒ with the standard notation for the angular mo-
IV. DISCUSSION
Molecular constants including the hyperfine constants of
NBr in the X 3⌺Ϫ ground state have precisely been obtained
for the first time. As shown in Table III, the molecular con-
stants reported by Pritt differ from those determined in the
present work by more than their standard deviations. In his
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7174
J. Chem. Phys., Vol. 109, No. 17, 1 November 1998
Sakamaki, Okabayashi, and Tanimoto
TABLE IV. Spin density and ␲ electron transfer (⌬p).
TABLE III. Molecular constants of NBr ͑MHz͒.a
N79Br
Prittb
Spin density͑%͒
Backdonation
N81Br
on halogen
⌬
Reference
p
B0
D0
␭
13380.46783͑83͒
0.0226722͑26͒
346635.8͑17͒
Ϫ2.6980͑11͒
Ϫ517.100͑48͒
80.60͑23͒
Ϫ274.7͑14͒
505.9͑57͒
0.0631͑86͒
42.01͑26͒
Ϫ61.1͑16͒
13330.79426͑64͒
0.0225004͑20͒
346642.8͑15͒
Ϫ2.68803͑90͒
Ϫ515.244͑42͒
86.63͑27͒
Ϫ296.9͑19͒
428.6͑50͒
0.0735͑81͒
42.02͑23͒
Ϫ61.9͑16͒
13580͑110͒
N35Cl
N79Br
O35Cl
O79Br
21.9
22.4
35.1
36.7
0.44
0.45
0.35
0.37
9
This work
22
371100͑3300͒
Ϫ690͑540͒
␭
D
24
␥
b͑Br͒
c͑Br͒
eQq͑Br͒
CI͑Br͒
b͑N͒
c͑N͒
is also valid in the oxygen compounds, ClO ͑Ref. 22͒ and
BrO.24
The electron configuration of NBr in the X 3⌺Ϫ state is
1␴22␴2...10␴24␲45␲2. If we assume that the 4␲ and 5␲
orbitals are expressed by a linear combination of the 2p
orbital of the nitrogen atom and the 4p orbital of the bromine
atom, the ␲ electrons transferred from Br to N ͑back dona-
tion͒ are given by ⌬pϭ(4Ϫn)␳, where n represents the
number of electrons that occupy the 5␲ orbital and ␳ repre-
sents the spin density on the Br atom. The amount of ⌬p is
calculated to be 0.45 for N79Br͑transfer from Br to N͒. The
backdonated ␲ electron ⌬p in NBr is compared in Table IV
with the values for N35Cl,35ClO,and 79BrO.The values of ⌬p
in the nitrogen compounds are slightly larger than those in
the oxygen compounds.
In a diatomic molecule, the quadrupole coupling eQq is
related to the electronegativity difference of the two atoms.
Table V lists eQq͑Br͒ of four second-row bromides (79Br͒.
The entry eQq͑corr͒ denotes the value corrected for the
transfer of ␲ electrons described above. Since the transfer of
one ␲-electron corresponds to the correction of ϪeQq/2,
the correction is made by adding Ϫ(⌬p/2͒ (eQq410) to the
observed eQq value. In Fig. 2, observed and corrected val-
ues are plotted against the electronegativity difference. The
solid curve represents the empirical relation proposed by
Gordy and Cook.27 The corrected values can be fitted by
shifting down the curve slightly. This relation is similar to
the case of the second-row chlorides.9
aValues in parentheses denote one standard deviations in units of the last
digits.
bReference 19.
work the branches terminating on the F2 spin component
were not observed, which might explain the difference. From
the observed B0 and D0 constants, the frequencies of the
fundamental N–Br stretching vibration for N79Br and N81Br
were estimated to be 686 and 685 cmϪ1, respectively, using
the relation, Dϭ4B3/␻2. These frequencies agree with those
reported by Milton et al.15 ͑691.75 and 690.45 cmϪ1), which
confirms their assignment of the lower state of the electronic
transition to the ground state.
The equilibrium bond length is estimated from the iso-
topically invariant Dunham constant U01 . This constant can
be estimated from the ground state rotational constants of
two isoptopic species, provided that the anharmonicity in the
vibrational potential function negligibly affects the lower-
order Dunham constants. The equilibrium bond length is cal-
culated to be 1.77799͑11͒ Å, the uncertainty being three
standard deviations.
Fermi contact interaction arises when an unpaired elec-
tron resides on the nucleus with nuclear spin. This interac-
tion thus results from the s-character of the unpaired elec-
tron. The contact value bFϭbϩc/3 is calculated to be
Ϫ10.97 ͑52͒ MHz in N79Br. The negative interaction con-
stant reflects the spin-polarization. If this value is compared
with the atomic value of 32 070 MHz for the 79Br atom,23 the
s-character is only 0.034%, which shows that the orbital of
the unpaired electron is not mixed with s-orbital. The same is
true also for nitrogen with the s-character of 1.20%.
Using the hyperfine interaction constants, we have esti-
mated the spin density of the unpaired electron. Although
gsgN␤␤N 1/r3 cannot be calculated directly from hyperfine
It is thought that the observed spin-spin constant in a
molecule bearing a heavy atom is dominated by the second-
order spin-orbit contribution. The main second-order contri-
bution comes from the b 1⌺ϩ electronic state, the lowest
state among many states capable of interaction. Lefebvre-
Brion and Field28 have presented a method to estimate this
contribution,
͗
͘
TABLE V. Bromine (79Br͒ nuclear quadrupole coupling constant of XBr
͑MHz͒.
constants obtained, it is estimated from the hyperfine con-
stant c by assuming the angular part 3 cos2 ␪Ϫ1 to be
͗
͘
s
a
Ϫ2/5. Through the comparison with the corresponding
atomic value (79Br: 2044 MHz, N: 138.8 MHz͒,23 the spin
density in N79Br is calculated to be 22.4% and 73.4% on the
bromine and the nitrogen nuclei, respectively. First column
of Table IV shows the spin density on the halogen atom of
the NX and OX ͑X ϭ Cl and Br͒ molecules in the X 3⌺Ϫ
state. As seen in the table, the spin density of NBr is nearly
the same as that of the NCl radical,9 but the bromide has
slightly larger spin density than the chloride. This tendency
Molecule
eQq
eQq͑corr͒
⌬␹
BBrb
NBr
133.2
505.9
650.0
–
Ϫ0.8
0.2
0.7
677.6
791.3
–
OBrc
FBrd
1086.9
1.2
aElectronegativity difference, ␹͑X͒Ϫ␹͑Br͒.
bReference 25.
cReference 21.
dReference 26.
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J. Chem. Phys., Vol. 109, No. 17, 1 November 1998
Sakamaki, Okabayashi, and Tanimoto
7175
ACKNOWLEDGMENTS
The present study was supported by a Grant-in-Aid from
the Ministry of Education, Science, Sports, and Culture
͑Nos. 07217209, 07454150, 07740456, and 08740457͒.
1 A. H. Curran, R. G. MacDonald, A. J. Stone, and B. A. Thrush, Chem.
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FIG. 2. Relation between the electronegativity difference of two constituent
atoms and eQq values. The open circles represent the observed values and
the closed circles the values corrected for the backdonation. The solid line
shows the empirical relation.
3 P. B. Davies, P. A. Hamilton, and M. Okumura, J. Chem. Phys. 75, 4294
͑1981͒.
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Ϫ
0
ϩ
0
3
␭
SOϭ
⌺
͉
HSO 1
͉
⌺
2/2 E 1⌺ϩ͒ϪE 3⌺Ϫ͒
͓ ͑ ͔
0
͓
͔
͘
͑
͗
Ӎ C2 ␨ p͒ϩC2 ␨ p͒ 2/2 E 1⌺ϩ͒ϪE 3⌺Ϫ͒ ,
7 S. Yamamoto and S. Saito, J. Chem. Phys. 86, 102 ͑1987͒.
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12 K. Kobayashi, M. Goto, S. Yamamoto, and S. Saito, J. Chem. Phys. 104,
8865 ͑1996͒.
͓
͑
N
͑
Br
͔
͓ ͑
͑
͔
1
N
Br
͑2͒
E
1⌺ϩ͒ϪE 3⌺Ϫ͒ϭE 1⌺ϩ͒ϪE 3⌺Ϫ͒Ϫ2␭
,
obs
͑3͒
͑
͑
͑
͑
1
0
where HSO is the spin-orbit interaction Hamiltonian, CX is
the atomic orbital mixing coefficient, and ␨X(p) is the
atomic spin-orbit value. We use the spin density on N and Br
atoms, namely, 0.734 and 0.224, as C2N and CB2 r , respec-
tively. The 1⌺ϩϪ3⌺0Ϫ energy interval is 14787.3 cmϪ1 from
13 K. Kobayashi and S. Saito, J. Phys. Chem. A 101, 1068 ͑1997͒.
14 A. Elliott, Proc. R. Soc. London, Ser. A 169, 469 ͑1938͒.
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1202 ͑1961͒.
16 A. T. Pritt, Jr., D. Patel, and R. D. Coombe, J. Mol. Spectrosc. 87, 401
͑1981͒.
Ref. 16 and ␨ ͑p͒ϭ73.3 cmϪ1 from Ref. 28. Two different
N
values of ␨ ͑p͒ for 79Br are listed in Ref. 28, 2457 cmϪ1 and
17 J. C. Miller and L. Andrews, J. Chem. Phys. 71, 5276 ͑1979͒.
18 D. E. Milligan and M. E. Jacox, J. Chem. Phys. 40, 2461 ͑1964͒.
19 A. T. Pritt, Jr., J. Mol. Spectrosc. 130, 54 ͑1988͒.
20 T. Okabayashi and M. Tanimoto, J. Chem. Phys. 99, 3268 ͑1993͒.
21 A. R. W. Mckellar, J. Mol. Spectrosc. 86, 43 ͑1981͒.
22 E. A. Cohen, H. M. Pickett, and M. Geller, J. Mol. Spectrosc. 106, 430
͑1984͒.
Br
2215 cmϪ1, from which ␭SO is calculated to be 371 GHz for
the former and 307 GHz for the latter. The observed ␭ value
͑347 GHz͒ is intermediate between the two calculated val-
ues.
As Endo et al.9,29 have pointed out, the Br nuclear spin-
rotation interaction may be estimated from an approximate
formula,
23 J. R. Morton and K. F. Preston, J. Magn. Reson. 30, 577 ͑1978͒.
24 E. A. Cohen, H. M. Pickett, and M. Geller, J. Mol. Spectrosc. 87, 459
͑1981͒.
25 M. Nomoto, T. Okabayashi, Th. Klaus, and M. Tanimoto, J. Mol. Struct.
͉
CI /␥
͉
ϭ
͉
a/ASO
͉
.
͑4͒
413–414, 471 ͑1997͒.
For N79Br,ASO is estimated to be 550 or 604 cmϪ1 from the
relation ASOϭCN2 ␨NϩCB2 r␨Br , as discussed above and the
atomic value of a is taken to be 2044 MHz.23 The calculated
value of CI was 64.1 or 58.4 kHz, which was well compared
with the observed value, 63.1 kHz.
26
¨
H. S. P. Muller and M. C. L. Gerry, J. Chem. Phys. 103, 577 ͑1995͒.
27 W. Gordy and R. L. Cook, Microwave Molecular Spectra, 3rd ed. ͑Wiley,
New York, 1984͒.
28 H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Di-
atomic Molecules ͑Academic, Orlando, 1986͒.
29 Y. Endo, S. Saito, and E. Hirota, J. Mol. Spectrosc. 97, 204 ͑1983͒.
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