Experimental and theoretical determination of the magnetic dipole transition moment for the Br(4p5)(2P1/2←2P3/2) fine-structure transition and the quantum yield of Br(2P1/2) from the 193 nm photolysis of BrCN

Article abstract of DOI:10.1063/1.478689

The integrated-absorption coefficients of several hyperfine lines of the magnetic dipole allowed transition of the bromine atom, Br, center at 3685.2 cm^-1 were measured, and a value for the square of the magnetic dipole transition moment of the Br atom was determined. A theoretical calculation for the magnetic dipole transition moment was also carried out using a relativistic ab initio atomic structure formulation. The theoretical value was in excellent agreement with the value predicted assuming pure LS coupling, and in reasonable agreement with experiment. The Br atom was generated in equal concentration with the cyano radical (CN) by the 193 nm photolysis of cyanogen bromine, BrCN. The CN radicals were titrated by the rapid reaction with C₃H₈ to generate HCN and a small amount of HNC. Both time-resolved and frequency-scanned infrared absorption spectroscopy were used to monitor the Br, HCN, and HNC species. The photolysis of BrCN at 193 nm produced both the ground state Br(²P_3/2) and the spin-orbit excited Br(²P_1/2) atoms, and the yield for the production of Br(²P_1/2) atoms was measured to be 0.31±0.01. The rate constants for the quenching of Br(²P_1/2) by BrCN and C₃H₈ at 293 K were also determined.

Full text of DOI:10.1063/1.478689

Experimental and theoretical determination of the magnetic dipole transition moment
for the Br (4p 5 )( 2 P 1/2 ← 2 P 3/2 ) fine-structure transition and the quantum yield of
Br ( 2 P 1/2 ) from the 193 nm photolysis of BrCN
G. He, Michael Seth, I. Tokue, and R. Glen Macdonald
Citation: The Journal of Chemical Physics 110, 7821 (1999); doi: 10.1063/1.478689
View online: http://dx.doi.org/10.1063/1.478689
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/110/16?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 16
22 APRIL 1999
Experimental and theoretical determination of the magnetic dipole
2
2
transition moment for the Br„4p5…„ P1/2— P3/2… fine-structure transition
2
and the quantum yield of Br„ P1/2… from the 193 nm photolysis of BrCN
G. He, Michael Seth, I. Tokue,a) and R. Glen Macdonald
Argonne National Laboratory, Chemistry Division, Argonne, Illinois 60439
͑Received 31 August 1998; accepted 28 January 1999͒
The integrated-absorption coefficients of several hyperfine lines of the magnetic dipole allowed
transition of the bromine atom, Br, center at 3685.2 cmϪ1 were measured, and a value for the square
of the magnetic dipole transition moment of the Br atom was determined. A theoretical calculation
for the magnetic dipole transition moment was also carried out using a relativistic ab initio atomic
structure formulation. The theoretical value was in excellent agreement with the value predicted
assuming pure LS coupling, and in reasonable agreement with experiment. The Br atom was
generated in equal concentration with the cyano radical ͑CN͒ by the 193 nm photolysis of cyanogen
bromine, BrCN. The CN radicals were titrated by the rapid reaction with C3H8 to generate HCN and
a small amount of HNC. Both time-resolved and frequency-scanned infrared absorption
spectroscopy were used to monitor the Br, HCN, and HNC species. The photolysis of BrCN at 193
nm produced both the ground state Br(2P3/2) and the spin-orbit excited Br(2P1/2) atoms, and the
yield for the production of Br(2P1/2) atoms was measured to be 0.31Ϯ0.01. The rate constants for
the quenching of Br(2P1/2) by BrCN and C3H8 at 293 K were also determined.
͓S0021-9606͑99͒01416-6͔
oms, X(np5), gives rise to two low lying fine-structure lev-
els, the ground state, P3/2 , and excited state, P1/2 , labeled
I. INTRODUCTION
2
2
The UV laser photodissociation of R–X and/or related
compounds, where R is an organic radical and X is a Br or I
atom, is a convenient method for generating the radical R,
without generating another reactive species. The radicals so
generated can be used to study radical–radical kinetics; how-
ever, being second-order processes, it is necessary to know
the radical’s concentration in order to determine a rate con-
stant. In some cases, the radical concentration can be inferred
from the UV absorption cross section of the parent R–X
molecule and the initial UV photolysis intensity; however,
the photochemistry of R–X must be well-established for this
to be a reliable technique. A more direct method of deter-
mining the initial concentration of the radical would be to
determine the concentration of the corresponding atom X.
This was the motivation of the present work, and the major
effort devoted to providing an experimental measurement of
the magnetic dipole transition moment between the two fine-
structure levels of the Br atom. Previously, Morter et al.1
used the 193 nm photolysis of C3H3Br to study the recombi-
nation reaction of C3H3 radicals. These workers calculated
the pure LS coupling value for the magnetic dipole transition
moment to determine the peak absorption coefficient for the
Br(2←3) atom hyperfine transition, and hence, deduced the
initial C3H3 radical concentration. This procedure enabled a
direct measurement of the important C3H3 self-
recombination rate constant.
*
X . The energy separation between these fine-structure lev-
els increases with atomic number of the halogen, and for Br
it is 3685.2 cmϪ1 3–6
Unfortunately, the radiative transition
.
rates between the spin-orbit states are relatively slow because
they are magnetic dipole-induced transitions.2,7 On the other
*
*
hand, the long radiative lifetimes of Br and I make them
excellent candidates for high power laser development,8 es-
pecially I . Interest in Br as a laser source9 has increased
by the development of a photolytic repetitive energy transfer
IR laser, based on efficient electronic-to-vibration, E–V, en-
ergy transfer processes.10 Detailed descriptions and laser de-
velopment would benefit from an accurate determination of
the magnetic dipole transition moment for the Br atom.
*
*
Recently, Ha et al.11 studied the I ←I transition to mea-
*
sure the magnetic dipole transition moment of the I atom.
These workers applied high-resolution absorption spectros-
copy to the hyperfine transitions in the I atom. The I atom
was created in several different environments, i.e., using in-
frared multi-photon dissociation of various fluorocarbon-
iodine compounds and the thermal dissociation of I2 in a
furnace. They also compared their measurements to ab initio
atomic structure calculations for the magnetic dipole transi-
tion moment of the I atom.
In the present work, Br atoms were created by the 193
nm laser photolysis of BrCN in the presence of C3H8 in Ar.
The CN radicals reacted rapidly with C3H8 to generate HCN
and a small quantity of HNC. All three species, HCN, HNC,
and Br, were monitored using infrared time-resolved and
frequency-scanned absorption spectroscopy. The concentra-
tion of the Br atoms was equal to the measured concentra-
The ground state electronic structure2 of the halogen at-
a͒
Department of Chemistry, Faculty of Science, Niigata University,
Niigata 950-21, Japan.
7821
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7822
J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
tions of HCN and HNC, and the integrated-absorption coef-
ficients of several hyperfine transitions of the Br atom were
determined. These data were used to calculate the magnetic
dipole transition moment of the Br atom. A theoretical cal-
culation of the magnetic dipole transition moment using a
relativistic formulation based on a Dirac–Fock–Breit ͑DFB͒
ab initio atomic structure calculation12 was also carried out,
and compared to the experimental measurement.
car signal averager, and was measured just before the exci-
mer laser was fired. The frequency-scanned data were re-
corded using two boxcar signal averagers, one to record the
absorption signal, ⌬IϭI0ϪI, and the other to record I0 . The
gate of the boxcar recording the signal was delayed so that
the probed species was monitored in a time regime where
internal relaxation was complete and the loss by diffusion
was minimal.
The photolysis of BrCN at 193 nm yielded a significant
III. RESULTS
*
quantity of excited Br atoms, and the quantum yield for
A. Integrated and peak absorption coefficients
*
Br production determined by laser gain-vs-absorption spec-
troscopy described by Haugen et al.13 The quenching rate
Radiative transitions between the two fine-structure lev-
els of the Br atom are dominated by the allowed-magnetic
dipole transition moment. The allowed-electric quadrupole
transition rate between these levels is three orders of magni-
tude smaller.15 Unfortunately, the hyperfine interactions
complicate the situation. Bromine has two stable isotopes
79Br and 81Br with natural abundances of 50.52% and
49.48%, respectively, and each isotope has a nuclear dipole
moment, I, Iϭ3/2. The total angular momentum, F, of the
atom is given by FϭIϩJ, and the magnetic dipole selection
rules are ⌬Fϭ0,Ϯ1 with parity conserved, resulting in six
allowed-hyperfine transitions for each isotope.2,7
*
constants for Br with C3H8 and BrCN were also measured.
II. EXPERIMENT
The apparatus has been described14 in detail previously,
but for completeness a brief description is given here. The
transverse flow reactor ͑TFR͒ consists of a stainless steel
chamber containing a Teflon™ box of dimensions 100
ϫ100ϫ5 cm. The TFR is evacuated by a liquid-nitrogen
trapped mechanical pump to a pressure of a few mTorr, and
has a leak rate of less than 0.5 mTorr/min. The reactant gases
continuously flow through the chamber, and their partial
pressures determined from their known flow rates and total
pressure.
The photolysis laser was either a Lumonics model 740
or a Lamda Physik model 203 Compex excimer laser, both
operating in the power stabilization mode at a wavelength of
193 nm. The results were independent of the excimer laser
parameters. Most of the data were collected at a nominal
power density of 10–20 mJ cmϪ2 and a repetition rate of 5
Hz.
The probe laser was a single-mode Burleigh model 20
FCL color center laser. This laser is continuously tunable
from 2.6 to 3.4 microns with a bandwidth of ϳ2 MHz, which
is much narrower than the 293 K thermal Doppler line
widths of the probed species. All three species, Br, HNC,
and HCN, can be monitored using this single laser source.
The laser frequency was continuously monitored using the
appropriate etalons, and the absolute wavelength determined
by an evacuated Burleigh model 20IR wavemeter.
The infrared absorption path length was increased from
the nominal photolysis length of 1 m to 14 m using a White
cell to multi-pass the probe laser through the photolysis
zone. Both the infrared and excimer laser radiation were
overlapped using a UV-IR dichroic mirror mounted directly
on the White cell optical axis.
Shortley16 has discussed magnetic dipole-allowed radia-
tive transitions between fine-structure levels in the case of
Russell–Sanders, LS, coupling, and gives the square of the
magnetic dipole matrix element,
͉ J ͉␮ ͉J ͉
,2 as
Ј Љ
͗ ͘
m
2
͉
J
͉
␮
͉J ͉
Љ
͘
Ј
͗
m
JϪSϩLϩ1͒ JϩSϪLϩ1͒ JϩSϩLϩ2͒ SϩLϪJ͒
͑
͑
͑
͑
ϭ
4 Jϩ1͒
͑
2
eh
ϫ Ϫ
,
͑1͒
ͩ
ͪ
4␲mec
where h, c, e, and me have their usual meaning, S, L, and J
are the spin, orbital, and total angular momentum quantum
numbers (JϭSϩL), respectively. Note that for LS coupling,
the evaluation of the magnetic dipole matrix element in Eq.
͑1͒ is independent of the radial portion of the electronic wave
function, and is given by the Bohr magnetron, ␮
B
ϭeh/(4␲me2c). For the Br atom fine-structure transition,
͉
J ͉␮ ͉J ͉
equals 4/3␮2B. In an absorption experiment,
Ј Љ
͗ ͘
m
the magnetic dipole transition moment can be directly related
to the observed attenuation of the probing radiation through
Ј Љ
the integrated-absorption coefficient, S(J ,J ) given by17
3
2
8␲
͉ J ͉␮ ͉J ͉
Ј Љ
͗ ͘
m
S J ,J ͒ϭ
¯␯
,
͑2͒
͑
Ј Љ
3hc
gJ
Љ
Two types of absorption data were recorded, time-
resolved and frequency-scanned. The time-resolved data
were recorded using a LeCroy model 9410 digital oscillo-
scope. The passage of the excimer laser through the appara-
tus resulted in an undesirable background signal. To remove
this interference, the following procedure was adapted. A
signal-averaged trace was recorded with the infrared laser
tuned to the peak of an absorption feature, and then, the laser
was detuned several line widths and a signal-averaged back-
ground trace recorded. Both traces were transferred to a labo-
ratory PC, and subtracted to obtain the unperturbed signal
trace. The initial laser intensity, I0 , was recorded by a box-
where gJ is the degeneracy of the lower fine-structure level,
Љ
2J ϩ1.
Љ
For the Br atom, the influence of hyperfine structure
must be taken into account and Eq. ͑2͒ modified accordingly.
Morter et al.1 have described the evaluation of the
integrated-absorption coefficients taking into account the hy-
perfine interaction using angular momentum algebra. The
method used here was taken from Sobel’man,7 who provides
a convenient table of normalized coefficients for the straight-
forward evaluation of the appropriate matrix elements. Zuev
et al.18 have also summarized the evaluation of the hyperfine
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J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
7823
TABLE I. Summary of the theoretical LS coupling integrated-absorption
duces to the normal Beer–Lambert Law expression. Further-
more, the energy separations among the hyperfine states
within a spin-orbit manifold are very small compared to kT
so that they can be considered to be nearly isoenergetic, and
thus, populated according to their degeneracies. Hence,
coefficients for the hyperfine lines of the Br atom. At 293 K and for ␯
0
ϭ3685.2 cmϪ1, the value of g(␷0) is 185.9 ͑cm͒ so that the peak absorption
coefficient can be calculated according to Eq. ͑4͒. The integrated-absorption
coefficients for the hyperfine transitions in individual isotopes are obtained
by multiplying the S(J IF ;J IF ) by the relative isotopic abundance of
Ј
Ј
Љ
Љ
79Br and 81Br.
N
, the concentration in a hyperfine level F, is given by
͔
͓
F
gF N /⌺ (2Fϩ1), where ͓N͔ is the total concentration of
the appropriate species in a spin-orbit manifold.
͓
͔
F
S(J IF ;J IF )
Ј
Ј
Љ
Љ
(10Ϫ21 cm1 moleculeϪ1
Br
)
Transition
The integrated-absorption coefficient, S(␯ J ;␯ J ), for
Ј Ј Љ Љ
Br(F ←F )
Ј
Љ
a fundamental rovibrational transition in a linear polyatomic
molecule in a ⌺ electronic state is given by
19.24
6.87
6.87
1.37
6.87
2.75
2←3
2←2
1←2
2←1
1←1
1←0
19,20
1
3
8␲
2
S 1,J ;0J ͒ϭ
␷
͉
1
͉
␮
͉0
1
͉
͘
HW
͑
Ј
Љ
͗
ji
3hc
eϪE /kT
i
ϫAji
1Ϫeh␯/kT͒FIA,
͑6͒
͑
QrQ
␯
where S(1J ;0J ) has units cm moleculeϪ1, j is the upper
Ј
Љ
matrix elements following the procedure outlined by
Sobel’man. The integrated-absorption coefficient between
hyperfine levels, F ←F , is given by
state (␯ϭ1, J ), and i the lower (␯ϭ0, J ), ␯ is the tran-
Ј
Љ
ji
sition frequency in cmϪ1
,
͉
1
͉
␮
͉
0
͉ the vibrational transi-
͘
͗
Ј
Љ
1
tion dipole moment, HW, the Herman–Wallis factor, ac-
counts for rotation-vibration interaction, Aji the Honl–
London factor, Jϩ1 for an R branch and J for a P branch
3
2
8␲
J FI
F J 1
Љ Љ
Ј
2
S J IF ;J IF ͒ϭ
¯
␯ 2Fϩ1͒
͉ J ͉␮ ͉J ͉ ,
Ј Љ
͗ ͘
m
͑
͑
Ј
Ј Љ
Љ
ͭ
ͮ
3hc
͑3͒
transition, Ei is the energy of the initial state, Qr and Q are
␯
where S(J IF ;J IF ) has units cm moleculeϪ1, the term in
the rotational and vibrational partition functions, respec-
tively, and FIA is the fractional isotopic abundance of the
absorbing species.
Ј
Ј Љ
Љ
braces is the Wigner 6-j symbol, the degeneracy of the
lower level (2F ϩ1) has been included, and the squared
Љ
There have been several experimental determinations of
magnetic dipole matrix element is given by Eq. ͑1͒.
The integrated-absorption coefficient is related to the ob-
served quantity, the absorption coefficient at a frequency ␷,
␴͑␷͒, through the normalized line shape function, g(␷), ac-
cording to
the ␷ H–C stretch vibrational transition moment and the
3
Herman–Wallis parameters for HCN.21–23 For the present
experiments, these quantities were taken from Smith et al.22
For 293 K the H12C14N(000) P(8) transition, the peak-
absorption coefficient was calculated to be 3.84
ϫ10Ϫ17 cm2 moleculeϪ1. The fundamental vibrational transi-
␴ ␷͒ϭS J IF ;J IF ͒g ␷͒,
͑4͒
͑
͑
͑
Ј
Ј Љ
Љ
where ␴͑␷͒ has units cm2 moleculeϪ1. In the present experi-
ments, g(␷) is well-described by a thermal Doppler profile
for Tϭ293Ϯ1 K, and at line center, ␷0 ,g(␷0) is given by
ln(2)/␲ 1/2/3.581ϫ10Ϫ7␯0(T/M)1/2, where ␯ is the wave
tion moment of the ␷ H–N stretch vibration and an estimate
1
of the first order Herman–Wallis parameter has recently
been measured in this laboratory.24 The peak-absorption co-
efficient for the H14N12C(000)R(9) transition was calculated
to be 9.69ϫ10Ϫ17 cm2 moleculeϪ1 at Tϭ293 K.
͕
͖
0
number at line center, T is the temperature, and M the mass
of the absorbing species. For Tϭ293 K, the calculated hy-
perfine integrated-absorption coefficients for the Br atom,
based on pure LS coupling, are summarized in Table I.
In the present experiments, a nonequilibrium distribution
of fine-structure states was initially created by the photolysis
laser pulse so that stimulated emission from the excited spin-
orbit manifold must also be considered. This effect manifests
itself as a correction to the population used to describe the
time dependent absorption signal, with the population given
by NF ϪgF /gF NF , where NF and NF are the popula-
B. Determination of the Br atom magnetic dipole
transition moment
The following series of reactions occur following the
193 nm photolysis of BrCN in a mixture of BrCN, C3H8,
and Ar:
193 nm
2
BrCN —— Br P ͒ϩCN,
͑7a͒
͑7b͒
→
͑
3/2
193 nm
2
BrCN —— Br P ͒ϩCN,
→
͑
Љ
Љ
Ј
Ј
Љ
Ј
1/2
tions in the corresponding hyperfine state of the lower and
upper spin-orbit manifolds, respectively. The time dependent
absorbance, A(t)ϭln(I0 /I(t)), is given by a modified Beer–
Lambert Law as19
k
8a
2
2
Br P ͒ϩC H —— Br P ͒ϩC3H8,
͑8a͒
͑8b͒
͑9͒
͑
→
͑
1/2
3
8
3/2
k
8b
2
2
Br P ͒ϩBrCN —— Br P ͒ϩBrCN,
͑
→
͑
1/2
3/2
ln I /I t͒͒ϭ␴ ␷͒l
N
t͒ Ϫg /gF
N
t͒ ͒, ͑5͒
͑ ͔
F
Ј
͑
͑
͑
͓͑
͑
͔
͓
0
F
F
Љ
Ј
Љ
k
9
where l is the path length in cm, gF and gF are the degen-
Љ
Ј
CNϩC3H8→HCNϩC3H7,
eracies in the lower and upper levels, respectively, and the
square brackets, ͓ ͔, indicate concentration units
molecules cmϪ3. At long times or equilibrium Eq. ͑5͒ re-
k
10
CNϩC H —— HNCϩC H ,
͑10͒
→
3
8
3
7
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7824
J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
k
11
XϩY ——
,
͑11͒
͑12͒
→
k
diff
Z ——
,
→
where reaction ͑11͒ stands for any removal process involving
atoms and radicals, Br or C3H7, such as recombination, i.e.,
Ϫk11 Y X , and reaction ͑12͒ stands for the removal of all
͓ ͔͓ ͔
species by diffusion.
The concentration of Br atoms created in the initial pho-
tolysis of BrCN was small, Ͻ3ϫ1012 atoms cmϪ3, and the
only possible loss processes for Br atoms were recombina-
tion with Br or C3H7 and diffusion. At a maximum total
pressure of 4 Torr, the self-recombination25 of Br atoms oc-
curs through a three body process with a rate constant esti-
mated to be 3ϫ10Ϫ34 cm6 moleculesϪ2 sϪ1, resulting in a
completely negligible first-order decay of Ͻ10Ϫ4 sϪ1. The
BrϩC3H7 atom-radical recombination process has not been
investigated experimentally, but the rate constant should be
similar to that for IϩC3H7, which has been measured26 to be
5ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1 at 298 K. Even if k11 were gas
kinetic, the time scale for the recombination reaction would
still be several orders of magnitude longer than the measure-
ment time scale, i.e., the time scale for the relaxation of the
excited Br(2P1/2) spin-orbit state, and would be the same
order of magnitude as the removal rate by diffusion ͑ϳ150
sϪ1͒.27 Reaction ͑10͒ was included to account for the ob-
served production of HNC.
As is evident from the above reaction sequence, all of
the CN reacted with C3H8 to form HCN and HNC, and the
only removal process for these molecules was by diffusion
so that the total concentration of Br atoms is given by
͓Br͔ϭ͓HCN͔ϩ͓HNC͔. Typical time-resolved absorption
profiles for HCN, HNC, and Br are shown in Fig. 1. With
C3H8 as the CN radical titrant, not only was reaction ͑9͒
rapid28 (k9ϭ2.6ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1 at 297 K͒, but
the vibrational relaxation of all the vibrational modes of both
HCN and HNC were also rapid and vibrational equilibration
was complete in several hundred microseconds, as is evident
by the nearly constant absorption region for HCN and HNC
in Fig. 1. Some excited vibrational levels for both HCN and
HNC were directly monitored, and observed to decay rapidly
back to the baseline. Not shown is the decay of HCN or
HNC on long time scales, but at 4 Torr total pressure these
molecules were removed from the observation region by
diffusion,27 with the fast diffusion component having a rate
constant of about 150 sϪ1. Note that the decay of the Br
atom, Fig. 1͑c͒, appears slightly faster than either HCN or
HNC. This was attributed to the atom-radical recombination
process, reaction ͑11͒.
FIG. 1. ͑a͒ Typical time-resolved absorption profile for HCN͑000͒ P(8).
The initial negative signal indicates a degeneracy-weighted population in-
version, Eq. ͑5͒. Vibrational relaxation was complete after 200 ␮s. On this
time scale, removal by diffusion is barely detectable. ͑b͒ Same as ͑a͒ except
for HNC͑000͒ R(9). ͑c͒ Same as ͑a͒ except for the Br(2←3) hyperfine
transition. The conditions of the experiment were PArϭ3.66, PC H ϭ0.280
3
8
and PBrCNϭ0.0795 Torr at 293 K.
of BrCN produces CN radicals that are highly rotationally
excited,29–32 with a rotational state distribution peaking near
Jϭ60.5 for CN(␯ϭ0) and with considerable translational
energy,
E
ϭ43 kcal moleϪ1. The rapid decrease in the
͘
T
͗
yield of HNC with decreasing PC H suggests that the excess
3
8
translational energy may be primarily responsible for gener-
ating the HNC channel. Generally, very high rotational states
are difficult to relax in collisions with spherically symmetric
collision partners.33 As a further investigation into this effect,
some experiments were carried out with (CN)2 as a CN radi-
cal source because the CN radicals are produced with much
less translational and rotational energy.34 No HNC produc-
tion was detected at all in these experiments indicating that
k10 was small for thermal CN radicals.
It was not discovered until most of the data had been
collected that HNC was produced in this system. Thus the
total CN concentration was corrected for the small produc-
tion of HNC using the linear relationship between the yield
of HNC and the mole fraction of C3H8 shown in Fig. 2 in
order to interpolate to other conditions.
Figure 1͑b͒ shows that HNC was produced directly by
reaction ͑10͒; however, this reaction was not initiated by
thermal CN radicals. Although the exothermicity of the
CNϩC3H8 reaction is sufficient to produce HNC, the yield of
HNC decreased with the decreasing partial pressure of C3H8,
PC H , indicating that the HNC product was not from the
As shown by Eq. ͑5͒, an absorption experiment monitors
the degeneracy-weighted population difference between the
two levels connected by the radiative transition. Thus the
population in the upper level must be completely equili-
brated in order to infer a total population. As will be dis-
3
8
reaction of thermalized CN radicals. This is shown in Fig. 2
where the mole fraction of C3H8 is plotted against the yield
of HNC at a total pressure of 4 Torr. The 193 nm photolysis
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J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
7825
FIG. 2. The yield of HNC from reaction of CN with C3H8 following the 193
nm photolysis of BrCN. The linear relationship between the yield of HNC
and the C3H8 mole fraction, indicated by the least-squares fit solid line, was
used to correct the results of experiments in which HNC was not monitored.
FIG. 3. ͑a͒ Frequency-scanned absorption profile for HCN͑000͒ P(8) for
the same experimental run as in Fig. 1. The absorption signal was taken
from a boxcar gate delayed to sample in the constant absorbance region of
Fig. 1͑a͒. The solid line is a nonlinear least-squares fit to the experimental
points, ᭹, and the difference between the experimental and calculated
points, x. The FWHM of the Doppler profile has the expected value of 230
MHz. ͑b͒ Same as ͑a͒ except for HNC͑000͒ R(9). ͑c͒ Same as ͑a͒ except for
the Br(2←3) hyperfine transition. The 79Br and 81Br peaks were fit inde-
pendently in the nonlinear least-squares analysis. The 81Br peak is at zero
frequency.
cussed in Sec. III D, the 193 nm photolysis of BrCN pro-
duced a significant population of excited Br(2P1/2) atoms;
however, the relaxation of the excited spin-orbit state, reac-
tions ͑8a͒ and ͑8b͒, was fast, as evident by the rapid rise to
the nearly constant absorbance region in Fig. 1͑c͒. The ki-
netics of this relaxation process will be discussed further in
Sec. III E.
form, and the FWHM were in agreement ͑Ϯ5%͒ with the
expected thermal Doppler widths at 293 K. Unfortunately,
the scatter in the measurements of the line widths was large
enough to prevent a determination of pressure broadening
parameters. Over the 2–4 Torr pressure range of the experi-
ment, pressure broadening effects are small, and for HCN,
with Ar as the collision partner, can be calculated to decrease
the peak absorption cross section from the pure Doppler
broadened value by a factor of 0.97–0.94, respectively.35 To
a first-order approximation, pressure broadening is propor-
tional to the collision frequency so that the effects of colli-
sion broadening on the Br atom transitions should be about
75% of those on HCN. Thus the effects of pressure broaden-
ing should be similar for each species and almost cancel out.
As a result, no pressure broadening correction was applied to
the data.
As is evident from Fig. 3͑c͒, the Br(2←3) transition
consists of two overlapping peaks both of which should have
very nearly the same line width; however, to obtain a com-
pletely independent measurement of the maximum absor-
bance for the two Br isotopes, the absorbance traces for the
Br(2←3) hyperfine transition were fit to two independent
Gaussian functions. This introduced extra uncertainty into
The Br(2←3) hyperfine transition is the most intense
spectral feature of the six allowed transitions ͑see Table I͒;
however, because the two Br atom isotopes have slightly
different transition frequencies3–6 this transition consists of
two lines separated by 154 MHz, almost the Br atom thermal
FWHM ͑full width half maximum͒ Doppler width at 293 K.
For accurate measurements, it was necessary to scan this
absorption feature as a function of frequency in order to de-
termine the actual line profile. Furthermore, a frequency-
scanned absorption profile eliminates the uncertainty in
manually tuning the probe laser frequency to the peak of an
absorption line. Typical frequency-scanned absorption pro-
files for HCN, HNC, and Br are shown in Fig. 3 for the same
experimental conditions as the time-resolved traces shown in
Fig. 1. The frequency-scanned line profiles were recorded
with the boxcar gate delayed to sample the absorption signal
in the nearly constant absorbance region for the species be-
ing probed.
The peak absorbance for each species was determined by
a nonlinear least-squares fit to the line profiles assuming a
Gaussian line shape function. As is evident from Fig. 3, the
line shapes were well-represented by a Gaussian functional
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7826
J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
FIG. 5. Results of the measurements of the integrated-absorption coeffi-
cients for hyperfine transitions of individual Br isotopes, open symbols 79Br
and closed symbols 81Br, as a function of the ͓CN͔. The approximate total
pressure is indicated by the shape of the symbol, ᭺ ͑2 Torr͒, ᭝ ͑3 Torr͒, and
ᮀ ͑4 Torr͒. The lines indicate the average value for the indicated isotope. ͑a͒
For the Br(2←3) hyperfine transition. ͑b͒ For the Br(2←2) transition.
FIG. 4. ͑a͒ Frequency-scanned absorption profile for HCN͑000͒ P(8).
Similar to Fig. 3͑a͒ except PArϭ1.75, and PBrCNϭ0.083 Torr at 293 K. ͑b͒
Frequency-scanned absorption profile for the Br(2←2) hyperfine transition.
the nonlinear least-squares determination of the fitted-peak
height because of increased scatter in the determination of
the Gaussian widths. To overcome this difficulty, another
transition was also probed, the Br(2←2) hyperfine transi-
tion. For this transition, the frequencies of the two isotopic
species are well-separated, but the integrated-absorption co-
efficient is a factor of 2.8 less than for the Br(2←3) transi-
tion, Table I. Typical frequency-scanned profiles for
HCN͑000͒ P(8) and Br(2←2) are shown in Fig. 4. The
fitted FWHM widths for the Br(2←2) transition were well-
described by the expected thermal Doppler width for Br at-
oms at Tϭ293 K.
As noted, the concentration of Br atoms was equal to the
concentration of HCN and HNC. This enabled the peak-
absorption coefficient of the probed-hyperfine transition,
␴(␷0), to be evaluated according to Eq. ͑5͒, from which the
integrated-absorption coefficient was calculated using Eq.
͑4͒. The measured ␴(␷0) depends only on the ratio of the
absorbances for Br and HCN and is independent of path
length. The results of these measurements are plotted in Fig.
5 and summarized in Table II. Figure 5 is shown to illustrate
the scatter in the data; however, the ͓CN͔ is only a nominal
concentration, calculated from the observed absorbances us-
ing a path length of 1400 cm.
second is provided by the ratio of cross sections for the two
hyperfine transitions for the same isotope. According to Eq.
͑3͒ and given in Table I, the ratio for LS coupling should be
2.800 and depends only on angular momenta coupling coef-
ficients. The measurements give 2.68 and 2.92 for the 79Br
and 81Br isotopes, respectively, and an average of 2.80 if all
the data are combined. The agreement between the expected
value and the measurements is good, and indicates that ran-
dom errors dominate the scatter in the measurements.
The theoretical integrated-absorption coefficients for
pure LS coupling in the Br atom at 293 K have been sum-
marized in Table I. A comparison with the experimental
TABLE II. Summary of the experimental data for the determination of the
peak-absorption coefficient and integrated-absorption coefficients for the
Br(2←3) and Br(2←2) hyperfine transitions. The measurements were
made at total pressures of 2–4 Torr, with PC H ranging from 0.03 to 1.5
3
8
Torr, and PBrCN from 0.03 to 0.08 Torr, at Tϭ293Ϯ1 K.
␴(␷0)
S(1/2,3/2,2;3/2,3/2,F )
Љ
(10Ϫ18 cm2 moleculeϪ1
)
(10Ϫ21 cm1 moleculeϪ1
)
Br
(F ←F )
79Br
81Br
1.97Ϯ0.20
79Br
81Br
Ј
Љ
The measurements provide several internal checks on
their consistency. The first is provided by the relative isoto-
pic abundance. The ratio of the cross sections for 81Br/79Br
should be 0.9794; unfortunately, the experimental scatter,
one standard deviation from the mean ͑Ϯ1␴͒, was up to 10%
in some cases. Nevertheless, the ratio is 1.06 for the Br(2
←3) transition and 0.98 for the Br(2←2) transition. The
1.85Ϯ0.16a
9.95Ϯ0.86 10.6Ϯ1.1
2←3
b
͑18͒
2←2
0.691Ϯ0.024 0.675Ϯ0.048 3.72Ϯ0.13
͑9͒
3.63Ϯ0.26
aThe uncertainty is one standard deviation ͑Ϯ1␴͒ from the average of the
indicated number of independent measurements.
bNumber in parenthesis is the number of independent measurements.
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J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
7827
TABLE III. Results of the relativistic wave function calculations compared
where the orbitals are represented by the principle quantum
number n, ␬ is the relativistic angular quantum number, ␬
ϭϮ(jϩ1/2) for 1ϭjϮ1/2, and a,b represent the orbitals
comprising a configuration. In atomic units, these matrix el-
ements have the form
to the LS coupling and the experimental measurement of the present work
2
for A1/2 3/2 and
͉
1/2
͉
␮
͉
3/2
͉
.
͗
͘
m
2
Fine-structure
A1/2 3/2
͑sϪ1
͉ 1/2͉␮ ͉3/2 ͉
͗ ͘
m
Method
splitting ͑cmϪ1
͒
͒
(10Ϫ40 erg2/G2)
DF
DFϩBQ
LS
Experiment
͑This work͒
3758.3
3682.2
3685.2
3685.2
0.953
0.897
1.145
1.146
j ϩ1͒␻
͑
b
j Ϫ1/2
a
n ␬bʈ
␮
mʈna␬
ϭ
͘
ͱ
Ϫ1͒
͑
͗
b
a
0.899
1.147
␲c
0.96Ϯ0.09a
1.23Ϯ0.11a
ja
1
0
jb
ϫ
M
,
͑14͒
ͩ
ͪ
ab
1/2
Ϫ1/2
aThe uncertainty includes Ϯ1␴ of 7% from the experimental scatter and an
estimate of 2% in the HCN and HNC absorption coefficients.
where the magnetic radiative transition integral, Mab, is de-
fined by
integrated-absorption coefficients shows that the experimen-
tal measurements are 6.1% and 7.6% higher for the Br(2
←3) and Br(2←2) transitions, respectively. This difference
is within one standard deviation, ␴ϭϮ7.4%, of the com-
bined measurements. The absolute uncertainty is slightly
larger than this because the uncertainty in the HCN and HNC
infrared cross sections must be included, and was estimated
to be about Ϯ2%. Thus the overall uncertainty in the experi-
mental was estimated to be Ϯ9%.
3
M
abϭ
␬ ϩ␬ ͒Iϩ
͑15͒
͑16͒
͑
a
b
1
&
with
Iϩϭ
ϱ
P
r͒Q
r͒
͑
͑
͑
͵
n ␬
n ␬
1
a
a
b
b
0
ϩQn ␬ r͒P
͑
n ␬
b b
r͒͒j ␻r/c͒dr.
͑
1
͑
a
a
The magnetic dipole transition moment defined by Eq.
͑1͒ was evaluated from the experimental measurement of the
integrated-absorption coefficient and the numerical factors
appearing in Eq. ͑3͒. The results are summarized in Table III
and will be discussed in the next section.
The energy separation between the spin-orbit states is given
by ␻, P, and Q are the large and small component of the
orbital wave function divided by r and ir, respectively, r is
the radial distance of the electron, and j1(␻r/c) is the first-
order spherical Bessel function of the first kind.
The necessary wave functions and matrix elements for
C. Relativistic calculation of the magnetic dipole
transition moment for Br
the Br(2P1/2
) atom were evaluated using the GRASP
program.37 The calculation was at the averaged level ͑AL͒
type including only the configuration state functions ͑CSFs͒
corresponding to the p21/2p33/2 and p11/2p43/2 electron configura-
tions. The influence of the Breit interaction was included
perturbatively as was an approximate treatment of higher-
order QED effects. The use of an AL wave function has the
drawback that the same set of orbitals are used to describe
As noted in Sec. III A, in pure LS coupling
2
͉
1/2
͉
␮
͉
3/2
͉
2ϭ4/3␮ for the Br atom, and in this approxi-
͗
͘
m
B
mation, the matrix element is completely independent of the
radial electronic wave functions in the two fine-structure lev-
els. For the heavier I atom, Ha et al.11 found that the experi-
2
mentally determined
͉
J
͉
␮
͉
J
͉
Љ
͘
was 13% smaller than
Ј
͗
m
2
2
both the P1/2 and P3/2 states. It has been found, however,
that AL calculations give fine-structure splittings of similar
quality to those derived using optimized level ͑OL͒ calcula-
tions where the orbitals used to describe each state are opti-
mized separately.39 To the authors’ knowledge a similar
comparison of magnetic dipole transition rates has not been
made, but the accuracy of the AL method should be suffi-
cient for the purposes of the present calculation. A second
drawback of the method used is the neglect of electron cor-
relation. This should not cause significant errors due to the
similarity of the two fine-structure states causing correlation
effects to be suppressed.40 The fine-structure splitting and
spontaneous emission rate constant were calculated using
both the Dirac–Fock ͑DF͒ and Dirac-FockϩBreit and QED
(DFϩBQ) wave functions.
the LS coupling prediction. They also evaluated this matrix
element for several configuration interaction wave functions
using ab initio atomic structure theory, and found close
agreement with the LS coupling value. However, a relativis-
tic calculation of the magnetic dipole transition matrix ele-
ment gave a value that was substantially too low. In order to
explore some of these effects, a relativistic calculation of the
2
͉
J
͉
␮
͉
J
͉
Љ
͘
for the Br atom was carried out.
Ј
͗
m
In light of the results of Ha et al.11 and the fact that the
2
2
Br atom P1/2 and P3/2 electronic wave functions must be
quite similar, it was felt that the best procedure was to use a
relativistic formulation using jj coupled four-component
wave functions.12 Equations for the matrix elements between
states described by four-component wave functions arising in
multipole transitions have been derived by Grant,12,36 Dyall
et al.,37 and Rosner and Bhalla.38 The magnetic dipole ma-
trix element can be written in terms of single-electron tran-
sition integrals as
The magnetic dipole transition matrix element was used
to calculate the spontaneous emission rate constant, AJ , j
,
Ј Љ
for the Br fine-structure transition16
4
3
64␲
␯
2
AJ J
Ј Љ
ϭ
͉
J
͉
␮
͉
J
͉
Љ
͘
.
͑17͒
Ј
͗
J
͉
␮
͉
J
ϭ
Љ
͘
d
n ␬bʈ
␮
mʈna␬
,
͘
a
͑13͒
Ј
͗
͗
m
3hc3 gJ
͚
m
a,b
b
a,b
Ј
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7828
J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
The results of the calculation are summarized in Table III.
Also included in Table III are the LS and experimental val-
ues for the A(1/2)(3/2) factor and squared magnetic dipole tran-
sition matrix elements. The spontaneous emission rate con-
stant was calculated according to Eq. ͑17͒, using the
2
appropriate
͉
J
͉
␮
͉
J
͉
Љ
͘
matrix element. As is evident
Ј
͗
m
from Table III, the DF calculated fine-structure splitting is
2% larger than the observed value, and at the DFϩBQ level
it is, perhaps fortuitously, in excellent agreement. The calcu-
lated relativistic dipole matrix elements were both in excel-
lent agreement with the pure LS value. Although the experi-
2
mental value for
͉
J
͉
␮
͉
J
͉
Љ
͘
is slightly larger than the
Ј
͗
m
theoretical predictions, the agreement is well within the esti-
mated uncertainty ͑scatter and systematic error͒ of the mea-
surement, and the best value to use may still be the theoret-
ical LS prediction, Table III.
2
D. Yield of Br„ P1/2… from the photolysis of BrCN
The bond dissociation energy41 of BrCN is 86.9
kcal moleϪ1 so that there is an excess energy of 61.3
kcal moleϪ1 available to the products in the photolysis of
BrCN at 193 nm. This is more than sufficient energy to pro-
duce excited Br atoms in the photolysis process. Further-
more, there has been much interest in elucidating the photo-
dissociation dynamics of cyanogen halides, especially ICN,
to which BrCN is closely related.
*
FIG. 6. Determination of the quantum yield of Br from the 193 nm pho-
tolysis of BrCN. ͑a͒ The laser frequency was tuned near the peak of the
Br(2←3) transition. The insert shows the absorption of the final ͓Br͔ after
The use of time-resolved absorption spectroscopy to
monitor the Br atom spin-orbit populations is particularly
useful for this task because the degeneracy weighted differ-
ence in population is monitored directly ͓see Eq. ͑5͔͒. As
long as the detection electronics is fast enough to resolve
rapid changes in absorption that may occur due to relaxation
processes, the absorption signal is internally calibrated from
the initial difference created in the photodissociation step to
the final equilibration stage, where the upper level has been
removed by relaxation. Haugen et al.13 have used this el-
egant laser gain-vs-absorption technique to completely map
out the yield of Br(2P1/2) as a function of photolysis wave-
length for Br2 and IBr.
*
complete quenching of Br . ͑b͒ The very long time decay of the Br atom is
shown. Diffusion was assumed to dominate, but reaction ͑11͒ may contrib-
ute. The conditions of the experiment were
PArϭ2.94 and PBrCN
ϭ0.050 Torr at 293 K.
hyperfine levels, according to Eq. ͑5͒. The population in in-
dividual hyperfine levels, Br F , has been discussed in Sec.
III A, and the observed absorbance from a hyperfine transi-
tion can be expressed in terms of the total atom population in
a spin-orbit manifold. The initial Ai measured at a particular
frequency, ␷, in terms of total populations is given by
͓
͔
The yield of excited Br(2P1/2), ␾ , from the photodis-
gF
Br
*
Љ
2
2
A ϭl␴ ␷͒ Br P ͒ Ϫ
Br P
͒
,
͑19a͒
͑
͓
͑
͔
͓
͑
͔
ͩ
ͩ ͪ
ͪ
i
3/2
i
1/2
i
sociation of BrCN at 193 nm is defined by
gF
Ј
2
Br P
͒
͔
i
͓
͑
1/2
and the final absorbance is given by
␾
ϭ
,
͑18͒
Br
*
2
2
Br P ͒ ϩ Br P
͒
͔
i
͓
͑
͔
͓
͑
1/2
i
3/2
gF
where the Br(2P
Љ
2
*
is the initial concentration of the Br ,
͓
͔
1/2 i
A ϭl␴ ␷͒
Br P
͒
͔
.
3/2 f
͑19b͒
͑
͓
͑
f
16
and the total concentration of Br, ͓Br͔, created in the pho-
tolysis laser pulse is Br ϭ Br(2P ) ϩ Br(2P
)
͔
3/2
i . At
͓
͔
͓
͔
͓
1/2
i
*
An expression for the yield of Br can be obtained by divid-
ing Eq. 19͑a͒ by 19͑b͒ and rearranging the terms. For the
Br(2←3) hyperfine transition, the result is
thermal equilibrium for 293 K, the Br(2P
) is virtually
͔
͓
1/2
zero, and the final absorbance, Af , determines the total con-
centration of Br atoms created in the photolysis step pro-
vided no Br atoms are lost from the system. The determina-
1
3
Ai
Af
tion of ␾
was carried out in mixtures where either PC H
␾
ϭ
1Ϫ
.
͑20͒
Br
*
ͭ
ͮ
Br
*
3 8
was zero or small, PC H Ͻ0.06 Torr, so that the only signifi-
3
8
cant loss process for Br atoms was diffusion, and this oc-
curred on a time scale long compared to the time scale for
relaxation, reaction ͑8͒: see Fig. 6͑b͒.
At tϭ0, the initial absorbance, Ai , is proportional to the
degeneracy weighted population difference between the two
It is important to note that ␾
does not depend explicitly
Br
*
on the probe laser frequency as long as thermalization of the
translation motion of the Br atoms occurs more rapidly than
spin-orbit relaxation. Similarly, as long as equilibration
within a hyperfine manifold proceeds faster than spin-orbit
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J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
7829
TABLE IV. Summary of measurement of ␾
at 193 nm.
from the photolysis of BrCN
Br
*
PC H
PAr
͑Torr͒
PBrCN
͑Torr͒
3
͑Torr8͒
␾
Br
*
2.9–3.9
2.9
0.0
0.015–0.06
0.03–0.08
0.045
0.304Ϯ0.0026
a
͑4͒
0.308Ϯ0.0047
͑4͒
Summary
0.306Ϯ0.0042
aNumber of independent experiments.
relaxation, only a single hyperfine transition needs to be
monitored. Both these conditions are satisfied in the present
experiments.
Typical temporal absorption profiles for the Br atom,
following photolysis of BrCN at 193 nm, are shown in Fig.
6. Figure 6͑a͒ shows the initial time dependence, and Fig.
6͑b͒ the long time dependence. It is clear from Fig. 6͑b͒ that
the loss of Br atoms occurs on a much longer time scale than
*
that for the quenching of Br , shown in the insert in Fig.
6͑a͒. The Ai values were determined by simply extrapolating
the early time dependence of the difference curve to the t
ϭ0 intercept, as indicated in Fig. 6͑a͒. The frequency re-
sponse of the detection electronics was better than 5 MHz,
and at 4 Torr total pressure translational and hyperfine relax-
ation should be complete over a time scale of less than a
microsecond. No evidence for any rapid transients was ob-
served. The results of several experiments with and without
C3H8 are given in Table IV. The average of the eight inde-
FIG. 7. Determination of the quenching rate constant for
*
Br ϩC3H8→BrϩC3H8.
A linear least-squares fit to kϭk8a C H
͓ ͔
3 8
ϩk8a BrCN for fixed ͓BrCN͔ gives k8a . As expected, the quenching rate
͓
͔
constant was independent of which Br atom hyperfine level was monitored.
the large slope-to-intercept ratio ͑a factor of 20͒. A small
change in slope results in a large change in the intercept;
furthermore the PBrCN was not completely constant but var-
ied, with the average value being PBrCNϭ0.06Ϯ0.02 Torr. A
better estimate of k8b was provided from an analysis of the
experiments with PC H ϭ0.0. The removal rate was a sensi-
pendent measurements gives ␾ ϭ0.306Ϯ0.0041 so that a
Br
*
significant amount of the Br atoms are formed in the excited
spin-orbit state in the 193 nm photolysis of BrCN.
3
8
tive function to PBrCN , but no systematic variation in PBrCN
*
E. Relaxation of Br by BrCN and C3H8
was possible. From these experiments, it was estimated that
k8b was 4.1Ϯ3.0ϫ10Ϫ12 cm3 moleculesϪ1 sϪ1
.
As shown in the previous section, 30.6% of the Br atoms
are initially formed in the excited spin-orbit state, and the
increase in the Br atom absorbance, as illustrated in Figs.
IV. DISCUSSION
*
1͑c͒ and 6͑b͒, is due to the removal of the Br atoms by
There have only been two reported measurements of the
magnetic dipole transition moment for the Br atom.44,45
C3H8 and BrCN, reactions 8͑a͒ and 8͑b͒, respectively. The
exponential rate constant describing these relaxation pro-
cesses is given by kϭk8a C H ϩk BrCN , and can be
*
These have relied on using Br laser radiation as a probe of
͓
͔
͓
8b
͔
Br atoms in photolyzed IBr samples or in thermal equilib-
3
8
determined by fitting the temporal absorbance profiles to a
series of exponential terms, i.e., A(t)ϭAf exp(Ϫkdifft)
ϪAr exp(Ϫkt) using a nonlinear least-squares fitting proce-
dure based on Marquardt’s method.42 If the ͓BrCN͔ is kept
*
rium with Br2. The Br laser operates only on the strongest
hyperfine Br(2←3) transition, which has a complicated line
shape ͓see Fig. 3͑b͔͒, making the precise lasing and hence
absorption frequency uncertain. The interpretation of the
data of Efimenko et al.45 used integrated-absorption coeffi-
constant and the C H varied, then a plot of k against
͓
͔
3
8
C H gives a straight line with slope k8a and intercept
͓
͔
*
cient data for the I (4←3) transition, and hence has extra
3
8
k8b BrCN . This procedure is valid as long as the contribu-
͓
͔
uncertainty associated with it. The direct determination by
Boriev et al.44 gives the square of the magnetic dipole tran-
sition moment for the Br atom that is a factor of 1.42 larger
than the LS prediction of 4/3␮2B, with an uncertainty of
Ϯ37%. Again, the LS coupling value is within the experi-
mental scatter of the measurement although this measure-
ment has considerably more uncertainty associated with it
than the measurements of the present work.
*
tion from the quenching of Br by Ar is small, which is the
*
case here as the rate constant for the removal of Br by Ar
has been measured43 to be 2.5ϫ10Ϫ16 cm3 moleculeϪ1 sϪ1 at
295 K.
A plot of k as a function of PC H is shown in Fig. 7 for
3
8
293 K. A least-squares analysis gives k8a to be 1.99Ϯ0.052
ϫ10Ϫ11 cm3 moleculesϪ1 sϪ1 and the intercept to be 3.85
Ϯ0.96ϫ104 sϪ1. In these experiments the intercept only pro-
vides a crude order of magnitude estimate of k8b because of
Garstang15 carried out a large number of calculations on
forbidden transitions in atomic spectra, and suggested that
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7830
J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
the deviation between the LS coupling predictions and the
actual magnetic dipole transition moments could differ by as
much as 20%. The processes that are ignored in arriving at
Eq. ͑1͒ are the neglect of intermediate coupling, configura-
tional mixing, relativistic effects, and the contribution of the
magnetic moment of the nucleus. Garstang46 has recently
addressed the effects of these contributions to the electronic
wave function in discussing radiative hyperfine transitions,
and concludes that they will contribute only a few percent
from the pure LS coupling predictions for the lighter ele-
ments. Indeed, these conclusions are borne out for the I
atom. Ha et al.11 compared their experimental measurement
for the magnetic dipole transition moment for the I atom
using several different configurational atomic wave functions
as well as a relativistic calculation. The configuration inter-
action calculations gave only a slight deviation from the LS
value. This is to be expected because Lilenfeld et al.47 have
measured the Lande g value for the I(2P1/2) atom, and found
it to be within Ϯ0.2% of the pure LS value. Ha et al.11 found
that the relativistic calculation improved the energy separa-
tion between the I atom fine-structure levels, but the
calculated-magnetic dipole transition moment was in consid-
erable disagreement with experiment. In comparison with the
I atom, the lower atomic number Br atom, with even a
smaller spin-orbit interaction and more energetic excited
electronic configurations, should behave even more as a pure
LS coupling case.
smooth function of J, and it is not possible to infer the quan-
*
tum yield of Br from such measurements.
For BrCN, the 193 nm photolysis wavelength is slightly
to the blue of the peak of the A continuum, and value of ␾
Br
*
was found to be ␾ ϭ0.31; Table IV. For ICN, the quan-
Br
*
*
tum yield of I was found to be ␾ ϭ0.44 near the peak in
I
*
the A continuum.49 Both quantum yields for the production
of the corresponding spin-orbit states are substantial, and in-
dicate that similar mechanisms for their production may be
operative in both cases.
Wannenmacher et al.51 have investigated the photodisso-
ciation dynamics of BrCN as a function of wavelength to the
red of the peak wavelength of the A band continuum, ͑202
nm͒.52 These workers used a detailed Doppler analysis of the
rotational lines of the CN fragment to deduce ␾
as a func-
Br
*
tion of the both photolysis wavelength and CN(␯ϭ0,J) ro-
tational state. Near the peak of the BrCN A band continuum,
they found that ␾ ϭ1 for J’sϽ50.5 and decreased with
Br
*
increasing J, resulting in a total ␾ ϭ0.87 for a photolysis
Br
*
wavelength of 209 nm. The results of this work, Table IV,
*
indicate that the production of Br must decrease rapidly as
the photolysis wavelength shifts to the blue of the peak A
band absorption.
The electronic-to-vibrational ͑E–V͒ energy transfer pro-
cesses represented by reactions 8͑a͒ and 8͑b͒ were found to
be efficient, Fig. 7. Generally, an E–V transfer process is
rapid if there is a near resonant vibrational energy level in
the quenching molecule involving the transfer of a small
number of vibrational quanta.9,10,43 For both C3H8 and BrCN,
the energy transfer step must involve multi-quanta of vibra-
tional energy; however, the measured rate constants are still
large. Perhaps, the rather dense rotational state density of
each molecule could act as another near-resonant energy res-
ervoir not available to smaller and lighter quenching partners
to enhance the collisional efficiency of the E–V process.
This expectation was borne out in the relativistic calcu-
lations of the Br atom magnetic dipole transition moment
reported in Table III. The more refined relativistic calcula-
tion was in perfect agreement with the LS coupling value for
2
͉
J
͉
␮
͉
J
͉, and any variation in the radiative spontaneous
͘
Ј
Љ
͗
m
emission rate constant arose from differences in the calcu-
lated fine-structure splitting. More accurate experiments,
with less scatter, will be necessary in order to determine if
there is a real difference between the LS predictions and
experiments. It appears that the best values for the
integrated-absorption cross sections for the hyperfine transi-
tions in the Br atom are still based on the LS model, as listed
in Table I.
ACKNOWLEDGMENT
This work supported by the U.S. Department of Energy,
Office of Basic Energy Sciences, Division of Chemical Sci-
ences under Contract No. W-31-109-ENG-38.
The first absorption feature in the UV spectra of the
cyanogen halides is the A band continuum absorption, and it
is attributed to transitions to similar electronic states in
ClCN, BrCN, and ICN.41 For various technical reasons, the
photodissociation dynamics of ICN have played an important
part in elucidating the interplay among the processes that can
occur on excited state potential energy surfaces.48 Among
these are the nonadiabatic couplings on the excited potential
energy surfaces that lead to the production of the excited
atomic states. Hess and Leone49 have studied the photodis-
1 C. L. Morter, S. K. Farhat, J. D. Adamson, G. P. Glass, and R. F. Curl, J.
Phys. Chem. 98, 7029 ͑1994͒.
2 H. G. Kuhn, Atomic Structure ͑Academic, New York, 1962͒, Chap. 5.
3 P. B. Davies, B. A. Thrush, A. J. Stone, and F. D. Wayne, Chem. Phys.
Lett. 17, 19 ͑1972͒.
4 E. Luc-Koenig, C. Morillon, and J. Verges, Physica, 70, 175 ͑1973͒.
5 J. V. V. Kasper, C. R. Pollock, R. F. Curl, Jr., and F. K. Tittel, Chem.
Phys. Lett. 77, 211 ͑1981͒.
6 D. D. Nelson Jr., A. Schiffman, K. R. Lykke, and D. J. Nesbitt, Chem.
Phys. Lett. 153, 105 ͑1988͒.
7 I. I. Sobel’man, Introduction to the Theory of Atomic Spectra ͑Pergamon,
Oxford, 1972͒, Chap. 9.
8 K. Hohla and K. L. Kompa, in Handbook of Chemical Lasers, edited by
R. W. F. Gross and J. F. Bott ͑Wiley, New York, 1976͒.
9 R. O. Johnson, G. P. Perram, and W. B. Roh, Appl. Phys. B: Lasers Opt.
65, 5 ͑1997͒.
*
sociation of ICN, and measured the quantum yield of I as a
function of photolysis wavelength. They found that the peak
*
wavelength for I production was shifted to the red of the
10 R. L. Pastel, G. D. Hager, H. C. Miller, and S. R. Leone, Chem. Phys.
Lett. 183, 565 ͑1991͒.
peak in the A band absorption for ICN. Their quantum yields
were in good agreement with the those deduced from the
rotational state distribution of the CN fragment.50 Such mea-
surements cannot be made for BrCN. The 193 nm photolysis
of BrCN, produces a CN rotational distribution29–31 that is a
11 T.-K. Ha, Y. He, J. Pochert, M. Quack, R. Ranz, G. Seyfang, and I.
Thanopoulos, Ber. Bunsenges. Phys. Chem. 99, 384 ͑1995͒.
12 I. P. Grant, Adv. Phys. 19, 747 ͑1970͒.
13 H. K. Haugen, E. Weitz, and S. R. Leone, J. Chem. Phys. 83, 3402 ͑1985͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
137.149.200.5 On: Sun, 23 Nov 2014 14:15:14

J. Chem. Phys., Vol. 110, No. 16, 22 April 1999
He et al.
7831
14 G. A. Bethardy, F. J. Northrup, and R. G. Macdonald, J. Chem. Phys. 102,
7966 ͑1995͒.
35 G. A. Bethardy and R. G. Macdonald, J. Chem. Phys. 103, 2863 ͑1995͒.
36 I. P. Grant, J. Phys. B 7, 1485 ͑1974͒.
15 R. H. Garstang, J. Res. Natl. Bur. Stand., Sect. A 68A, 61 ͑1964͒.
16 G. H. Shortley, Phys. Rev. 57, 225 ͑1940͒.
37 K. G. Dyall, I. P. Grant, F. A. Parpia, and E. P. Plummer, Comput. Phys.
Commun. 55, 425 ͑1989͒.
17 G. Herzberg, Molecular Spectra and Molecular Spectra, Vol. I Spectra of
Diatomic Molecules ͑Van Nostrand, Princeton, 1950͒, Chap. 2.
18 V. S. Zuev, V. A. Katulin, V. Y. Nosach, and O. Y. Nosach, Sov. Phys.
JETP 35, 870 ͑1972͒.
38 H. R. Rosner and C. P. Bhalla, Z. Phys. 231, 347 ͑1970͒.
39 N. C. Pyper, J. Phys. B 16, L211 ͑1983͒.
40 S. M. O’Malley and D. R. Beck, Phys. Rev. A 57, 1743 ͑1998͒.
41 W. S. Felps, K. Rupnik, and S. P. McGlynn, J. Phys. Chem. 95, 639
͑1991͒.
19 H. W. Kroto, Molecular Rotational Spectra ͑Dover, New York, 1992͒.
20 M. A. H. Smith, C. P. Rinsland, B. Fridovich, and K. N. Rao, in Molecu-
lar Spectroscopy: Modern Research, Vol. III, edited by K. N. Rao ͑Aca-
demic, London, 1985͒, Chap. 3.
42 W. H. Press, B. P. Flannery, S. A. Teukosky, and W. T. Vetterling, Nu-
merical Recipes: The Art of Scientific Computing ͑Cambridge University
Press, Cambridge, 1988͒.
21 I. W. M. Smith, J. Chem. Soc., Faraday Trans. 2 77, 2357 ͑1981͒.
22 M. A. H. Smith, G. A. Harvey, G. L. Pellet, A. Goldman, and D. J.
Richardson, J. Mol. Spectrosc. 105, 105 ͑1984͒.
43 R. O. Johnson, G. P. Perram, and W. B. Roh, J. Chem. Phys. 104, 7052
͑1996͒.
44 I. A. Boriev, E. B. Gordon, A. I. Nadkhin, and S. A. Sotnichenko, Opt.
Spectrosc. 54, 233 ͑1983͒.
23 P. L. Varghese and R. K. Hanson, J. Quant. Spectrosc. Radiat. Transf. 31,
545 ͑1984͒.
45 A. A. Efimenko, I. A. Boriev, and E. B. Gordon, Sov. J. Quantum Elec-
tron. 15, 1127 ͑1985͒.
24 G. He and R. G. Macdonald, Chem. Phys. Lett. 301, 175 ͑1999͒.
25 B. A. DeGraff and K. J. Lang, J. Phys. Chem. 74, 4181 ͑1970͒.
26 D. M. Hayes and R. L. Strong, J. Phys. Chem. 90, 6305 ͑1986͒.
27 G. He, I. Tokue, and R. G. Macdonald, J. Phys. Chem. 102, 4585 ͑1998͒.
28 L. R. Copeland, F. Mohammad, M. Zahedi, D. H. Volman, and W. M.
Jackson, J. Chem. Phys. 96, 5817 ͑1992͒.
46 R. H. Garstang, Astrophys. J. 447, 962 ͑1995͒.
47 H. V. Lilenfeld, R. J. Richardson, and F. E. Hovis, J. Chem. Phys. 74,
2129 ͑1981͒.
48 J. F. Black, J. R. Waldeck, and R. N. Zare, J. Chem. Phys. 92, 3519
͑1989͒.
29 R. Lu, J. B. Halpern, and W. M. Jackson, J. Phys. Chem. 88, 3419 ͑1984͒.
30 W. H. Fisher, R. Eng, T. Carrington, C. H. Dugan, S. V. Filseth, and C. M.
Sadowski, Chem. Phys. 89, 457 ͑1984͒.
49 W. P. Hess and S. R. Leone, J. Chem. Phys. 86, 3773 ͑1987͒.
50 W. J. Marinelli, N. Sivakumar, and P. L. Houston, J. Phys. Chem. 88,
6685 ͑1984͒.
31 S. Hay, F. Shokoohi, S. Callister, and C. Wittig, Chem. Phys. Lett. 118, 6
͑1985͒.
51 E. A. J. Wannenmacher, H. Lin, W. H. Fink, A. J. Paul, and W. M.
Jackson, J. Chem. Phys. 95, 3431 ͑1991͒.
32 S. A. Wright and P. J. Dagdigian, J. Chem. Phys. 103, 6479 ͑1995͒.
33 T. A. Brunner and D. E. Pritchard, Adv. Chem. Phys. 50, 589 ͑1982͒.
34 S. W. North and G. E. Hall, J. Chem. Phys. 106, 60 ͑1997͒.
52 J. A. Russell, I. A. McLaren, W. M. Jackson, and J. B. Halpern, J. Phys.
Chem. 91, 3248 ͑1987͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
137.149.200.5 On: Sun, 23 Nov 2014 14:15:14