CHAPTER FOUR BrO PRESSURE BROADENING
CHAPTER FOUR
PRESSURE BROADENING
STUDIES OF BrO
Ozone (O3) is a rare constituent of the Earth’s atmosphere. It is found in two
regions: over 90% of it exists in the stratosphere (between 10 and 50km altitude) and is
commonly referred to as the ‘Ozone Layer’, and the remainder is present in the
troposphere (0 to 10km). Reactions governing stratospheric O3 production and removal
were first proposed by Chapman in 1930 [1]:
O 2  h  2O
O  O2  M  O3  M
O 3  h  O  O 2
O 3  O  2O 2
The ‘Ozone Layer’ absorbs most of the biologically damaging UV-B radiation incident
on Earth from the Sun. These absorptions account for the characteristic heating of the
stratosphere and shield the Earth from UV-B radiation. In the troposphere O3 is toxic to
animal and plant life due to its high chemical reactivity. In contrast to stratospheric O3
most of the tropospheric O3 is not ‘naturally occurring’ but is formed from pollutants
concentrated in urban smog.
In the 1930’s discrepancies between observed atmospheric O3 concentrations [2]
and those predicted by Chapman’s reaction scheme indicated that other O3 depletion
processes were significant. The roles of Hydrogen (H, OH, HO2) [3] and Nitrogen (NO,
NO2) [4] in catalytic O3 destruction were identified. In 1974, Stolarski and Cicerone
suggested that Chlorine might also be significant to stratospheric O3 chemistry [5]. In the
same year Molina and Rowland pointed out that CFC’s emitted to the atmosphere could
be transported to the stratosphere, photodissociated, and provide a source of O3 depleting
Cl and ClO [6]. In 1985 Farman et al showed that stratospheric O3 concentrations in
Antarctica declined when solar illumination returned to the polar region during
107
CHAPTER FOUR BrO PRESSURE BROADENING
springtime [7]. This decline had been worsening throughout the 1970’s and 80’s and
currently around 70% of the total O3 concentration over Antarctica is lost during
September and early October [8]. This phenomenon is popularly referred to as the
‘Ozone Hole’. Subsequent studies of the stratosphere have highlighted the importance of
halogen radicals in O3 destruction cycles both in the gas phase and in heterogeneous
chemistry on Polar Stratospheric Clouds (PSC’s) [9, 10]. Ozone depletion in the Arctic
and mid-latitude regions has also been reported [10, 11].
The principal role of CFC’s in stratospheric O3 depletion and the planetary
consequences of an ‘Ozone Hole’ were recognised by the Montreal Protocol, banning the
production of CFC’s, halons, CCl4, and CH3CCl3. The Ozone Depletion Potential (ODP)
is used to compare the relative impact of different gases upon current and future O3
concentrations [12]. Policies governing the emission and production of O3 depleting
molecules are based on their ODP. The ODP of a molecule is a time integrated index
which quantifies the expected reduction in O3 concentration for a unit mass emission of
the trace species to the atmosphere relative to the expected O3 reduction for a unit mass
release of CFC-11. The stratospheric chemistry of the molecule, including its sources,
sinks, and interaction with reactive intermediates must be understood to evaluate the
ODP precisely. Accurate data pertaining to the atmospheric concentrations, lifetimes and
reaction rates of source molecules or reactive intermediates, as well as stratospheric
chemical and dynamical processes, are used to evaluate ODPs. This data is obtained
through atmospheric remote sensing and laboratory experiments.
In this Chapter the results of a laboratory pressure broadening study of BrO are
presented. BrO is a reactive intermediate in the lower stratosphere and troposphere. The
TuFIR spectra of BrO are used to determine a pressure-broadening coefficient that can
then be used to decipher atmospheric concentrations of the molecule. BrO is influential
in O3 depletion cycles, and these data are therefore directly relevant when determining
future ODP’s of bromine containing molecules.
4.1 The Significance of BrO in Atmospheric Chemistry
Free radicals play a central role in atmospheric chemistry. They are formed by
degradation of larger molecules, then initiate and propagate chain reactions in the
atmosphere, generating further radicals and removing species such as O3. They finally
108
CHAPTER FOUR BrO PRESSURE BROADENING
exit the cycle by reacting to form stable species. Bromine is transported to the
stratosphere by CH3Br, CHBr3, and halons, Brominated CFC’s. The latter are used
extensively in fire extinguishing systems and released into the atmosphere by leakage, or
discharge during disposal, fire prevention, and testing. Two of these Halons, CBrF3
(CFC-13B1) and CBrClF2 (CFC-12B1), have ODPs of 11.4 and 2.7 respectively [13]:
these values are greater than the cumulative ODP of all remaining O3 depletors! These
molecules have long atmospheric lifetimes, (29 to 112 years), and are only removed from
the atmosphere by photolysis or reacting with O(1D) or OH, releasing Br atoms. Br
subsequently reacts with O3 to form BrO and it is these free radicals that are the primary
source of inorganic Bromine in the atmosphere. BrO is also regenerated from reservoir
CHBr3
CH 3 Br
Halons
OH, O( P), h 
3
NO, O
3
OH, O( P)
HBr
3
Br
BrO
h, O( 3P)
HO2 , HCHO
OH
h, O( 3P)
HO 2
HOBr
h
NO 2
BrONO
h, O( 3P)
ClO
BrCl
Figure 4.1: Atmospheric Bromine Photochemistry. (Adapted from reference [20])
109
CHAPTER FOUR BrO PRESSURE BROADENING
species such as HBr, HOBr, or BrONO2 [14], (figure 4.1). Transport of the most stable
Br-containing compounds to the troposphere acts as a sink. Although the amounts of
Bromine released to the stratosphere in this way are about two orders of magnitude less
than Chlorine, they are predominantly in reactive forms and therefore can be up to 100
times more effective at destroying O3.
Wofsy et al first suggested that Bromine could destroy stratospheric O3 in 1975
[15]. Following the discovery of the ‘Ozone Hole’ in 1985 three possible catalytic cycles
emerged to explain O3 depletion [9, 16, 17]. Only one of these cycles involved Bromine
in a ClO + BrO coupled reaction releasing Cl and Br atoms to react with O3 [17]. This
mechanism (I) is outlined below:
(a)
I. ClO  BrO  Cl  Br  O 2
 Br  OClO
(b)
 BrCl  O 2
(c)
BrCl  h  Br  Cl
Br  O 3  BrO  O 2
Cl  O 3  ClO  O 2
Net  2O 3  3O 2
With the exception of pathway (b) all the reactions lead to O3 loss. This cycle is most
effective in the lower stratosphere where Br and BrO concentrations are around 18ppt
and 10ppt respectively [18]. It dominates Bromine-catalysed O3 loss in the polar regions
(Arctic and Antarctic) where ClO production is enhanced by heterogeneous reactions on
PSCs. Two additional Bromine-catalysed cycles for O3 loss emerged (II & III) [18-20]:
II. BrO  HO 2  HOBr  O 2
HOBr  h  OH  Br
Br  O 3  BrO  O 2
OH  O 3  HO 2  O 2
III. BrO  NO2  M  BrONO2  M
BrONO2  M  Br  NO3
NO3  h  NO  O 2
Br  O 3  BrO  O 2
NO  O 3  NO2  O 2
Both mechanisms contribute to O3 loss in the polar regions, where mechanism III is also
relevant in heterogeneous Bromine chemistry [21]. Mechanism II is significant near the
110
CHAPTER FOUR BrO PRESSURE BROADENING
tropopause when ClO concentrations are negligible. In the Arctic, low concentrations of
ClO make Br-catalysed O3 loss even more significant. Together with mechanism I, II is
important to O3 loss at mid-latitudes [18]. The BrO self-reaction may also be of
significance in tropospheric O3 depletion [22].
Evidence to support these reaction mechanisms is obtained from direct
observations of the Br-intermediates in the stratosphere. In-situ detection of ppt levels of
BrO had been made prior to the discovery of the Antarctic ‘Ozone Hole’ [23]. A flowing
air sample was extracted from the atmosphere and mixed with NO; any BrO present
underwent a rapid bimolecular reaction yielding Br atoms. The Br concentration was
determined by atomic resonance fluorescence in the vacuum ultraviolet and indirectly
used to determine the BrO concentration. Large errors are associated with this method,
(up to  25%): it is however still widely used to determine ppt BrO levels in Arctic,
Antarctic and mid-latitude conditions [e.g. 9, 24-26]. The presence of BrO was also
inferred by ground based observations of OClO, (mechanism I). The low steady state
concentration (5x108 molec/cm3) and short atmospheric lifetime (a few seconds to an
hour) of BrO in the stratosphere hinder direct spectroscopic observations. Ground based
Differential Optical Absorption Spectroscopy (DOAS) was first used by Carroll et al to
detect BrO directly in the Antarctic stratosphere [26]. Platt et al detected BrO for the first
time in the troposphere [27]. They monitored BrO absorption at 338nm with a sensitivity
of 106 to 107 molec/cm3; calculated mixing ratios were between 4 and 17ppt. The first
satellite measurements of BrO were recently made using UV-visible spectroscopy [28]
and are being used to build up a global map of the stratospheric BrO distribution.
Currently, the total stratospheric BrO concentration is estimated at 16ppt. Observing BrO
in other spectral regions is now feasible e.g. pure rotational spectra in the submillimetre.
In the next few years a number of satellite missions will be operational around 300GHz
to 1THz and will be equipped with heterodyne receivers at around 640 and 700GHz for
BrO observation by remote sensing [11]. It is envisaged that altitude profiles of the BrO
concentrations will be obtained between 22 and 45km providing a clearer picture of the
role of this molecule in stratospheric chemistry.
4.2 The Rotational Spectroscopy of BrO
The simplest model describing the rotation of a diatomic molecule is the
‘dumbbell model’, i.e. a system of two point masses, m1 and m2, connected by a massless
111
CHAPTER FOUR BrO PRESSURE BROADENING
rod of length r. The rigid body has only two rotational degrees of freedom perpendicular
to the line between the two masses. Classically, the rotational energy of such a molecule
is purely kinetic:
E rot 
1
I 2
2
(4.1)
where  is the angular velocity and I is the moment of inertia of the molecule about the
rotational axis given by:
I   m i ri2  r 2
(4.2)
i
where  is the reduced mass. In terms of the total angular momentum of the molecule, P,
the rotational energy can be rewritten as:
E rot
P2

2I
(4.3)
To find the rotational energy levels of the molecule from this classical picture it is
necessary to quantise the angular momentum. The square of the total angular momentum
of the molecule, P2, is quantised in units of J(J+1)h2/42, where J, the rotational
quantum number, is an integer. Equation 4.3 becomes:
E rot
J ( J  1)h 2

8 2 I
(4.4)
This result may also be obtained by solving Schrödinger’s Equation for the rigid rotor
[29]. The rotational constant of the molecule (Hz) is defined as:
B
h
8 2 I
(4.5)
The term values of the rotational energy levels of a diatomic molecule are therefore
given by:
F ( J )  BJ ( J  1)
(4.6)
Each J-level also has (2J+1) MJ-levels, corresponding to different possible projections of
J onto a space fixed axis and this degeneracy is lifted in Stark or Zeeman spectroscopy.
Since the molecule is not completely rigid some stretching of the bond will occur during
rotation due to centrifugal forces acting on the nuclei. Classically, this effect increases
with the angular velocity and therefore, quantum mechanically, with J. Consequently, the
term values given in (4.6) are modified giving [30]:
Fv ( J )  Bv J ( J  1)  Dv J 2 ( J  1) 2  H v J 3 ( J  1) 3  
112
(4.7)
CHAPTER FOUR BrO PRESSURE BROADENING
where D is the centrifugal distortion constant. The higher order terms in equation 4.7
arise because molecular vibration is better described as that of an anharmonic rather than
harmonic oscillator.
The spectra of free radicals such as BrO are more complex than simple diatomic
molecular spectra. The interactions between all the angular momenta of the system must
be considered, i.e. orbital, electron spin, molecular rotation, and nuclear spin angular
momentum. BrO has one unpaired electron in a p antibonding molecular orbital. The
total orbital angular momentum, , of the molecule is 1, (in units h/2): the electronic
ground state is therefore 2 [31]. This electronic state is doubly degenerate as there are
two possible orientations of  along the internuclear axis. The presence of this unpaired
electron implies that the moment of inertia about the internuclear axis, Ia, is non-zero.
The molecule is therefore analogous to a prolate symmetric top molecule with one small
and two equal principal moments of inertia. The term values from equation 4.6 are
rewritten as [31]:

Fv ( J )  Bv J ( J  1)  2

(4.8)
The first rotational level is no longer J=0 but J=. Coupling between the molecular
rotation and the orbital motion of the electrons splits the degeneracy of the electronic
states where 0. This splitting is called -doubling and increases with J. For every
value of J there are two rotational energy levels, one with positive and one with negative
parity.
Another splitting originates from the coupling between the total electron spin of
the molecule, S, and the orbital angular momentum. S is the sum of all the individual
spins of all the electrons in the molecule. However, S is only non-zero if there are
unpaired electrons in the molecule. Therefore, all electronic states with 0 are split into
2S+1 components. The resultant angular momentum, has a total magnitude h/2, given
by:

(4.9)
where  has values from S, S-1, …-S …-S. The energy, Te, of each multiplet component
is given by [31]:
Te  To  A
(4.10)
113
CHAPTER FOUR BrO PRESSURE BROADENING
where A is the spin-orbit parameter and To the energy of the non-degenerate state. The
electronic ground state of BrO is therefore split into two states 21/2 and 23/2. BrO is
actually an example of an inverted 2 molecule, with a large, negative A value. In fact A
is greater than , the vibrational constant [32].
The order in which these two couplings occur dictates the pattern of the rotational
energy levels. BrO is a Hund’s case (a) molecule in which the electron spin-orbit
coupling is large, whilst the coupling of the molecular rotation with the electronic motion
is weak. Consequently, the angular momentum about the internuclear axis is represented
by the ‘good’ quantum number  rather than . The vector diagram of this coupling
scheme is shown in figure 4.2. The first rotational energy level has J=. It is also
important to note that J is now the total angular momentum quantum number, can have
non-integer values, and is fixed in space. The term values for the rotational energy levels
given in equation 4.7 still hold, with the ‘new’ J replacing the ‘old’ value. The molecular
rotational quantum number is now represented as R. Since 0, -type doubling also
occurs, lifting the degeneracy of the + and – states. The overall parity of each level is
determined from the symmetry properties of the wavefunction [31]. In absorption, the
selection rules for the pure rotational transitions of such a molecule, determined from the
transition moment, are [31]:
J  1

(4.11)
J
R



S
L
Figure 4.2: Vector diagram for Hund’s case (a). (Adapted from ref. [31])
114
CHAPTER FOUR BrO PRESSURE BROADENING
The nuclear spin angular momentum is quantised in units of (I(I+1)1/2)h/2,
where I, the nuclear spin, can be zero, integral, or half integral. Coupling between the
total angular momentum and nuclear spin angular momentum is significant when I is
non-zero for any of the atoms in a molecule. The resultant total angular momentum of
the molecule, F, is found by vector addition of J and I according to a Clebsch-Gordan
series, i.e. F has values J+I, J+I-1…J-I. If J>I then the lowest value of F is |J-I| but if
J<I the lowest value of F is |I-J| [29]. For atoms such as
79
Br and 81Br where I=3/2, the
nucleus also possess an electric quadrupole moment, Q, which further modifies the
energy levels from Erot to Erot+EQ. The quadrupole moment arises from an asymmetry of
the nuclear charge, due to either an elongating, (+Q value), or flattening, (-Q value), of
the nucleus along its spin axis. The interaction between the quadrupole moment and
electric field gradient surrounding the nucleus, , is given by EQ [29]:
 3

  C (C  1)  I ( I  1)  J ( J  1) 
(4.12)
4

E Q  eqQ 
2 I (2 I  1)( 2J  1)( 2J  3) 



where e is the charge on the electron, q is the field gradient along the internuclear axis
and C is given by:
C  F ( F  1)  I ( I  1)  J ( J  1)
(4.13)
The function in brackets in equation 4.12 is known as Casimir’s Function. The selection
rule governing transitions between nuclear hyperfine levels in pure rotational spectra is:
F  0,1
(4.14)
Figure 4.3 illustrates the arrangement of energy levels and allowed transitions in BrO.
The rotational transition intensities are governed by the populations of the energy
levels according to the Boltzmann distribution and the relative rates at which absorption
and stimulated emission are occurring. The fraction of molecules occupying each
rotational energy level in a diatomic molecule is given by [29]:

 E rot

( 2J  1) exp

kT
N J 



N
q rot
where qrot the rotational partition function is defined as:
(4.15)

 E rot

q rot   g J exp

kT


J 0
(4.16)
115
CHAPTER FOUR BrO PRESSURE BROADENING
F
4
+
3
J
2
1
5/2
1
2
3
4
-
3
2
-
1
0
3/2
0
1
2
3
+
F=-1
F=0
F=+1
Figure 4.3: Energy level diagram for the rotational line J=5/23/2 in the 23/2 ground
electronic state of BrO. On the left are the rotational energy levels after spin –orbit
coupling (21/2 state not shown), followed by the introduction of -type doubling and
nuclear hyperfine structure. These two splittings have been exaggerated for clarity. The
allowed transitions (18 in all) are indicated by the arrows, and follow the selection
rules mentioned in the text.
116
CHAPTER FOUR BrO PRESSURE BROADENING
The quantity gJ accounts for the multiplicity of each J-level. Emission as well as
absorption processes must be considered as many rotational energy levels are
significantly populated at room temperature. For a transition between two levels, i and j,
the net absorption is given by [29]:
(N j  Ni )
Bij  ( ij )h ij
(4.17)
N
where Nx is the fraction of molecules in state x, Bij the Einstein B coefficient, (ij) the
I abs 
radiation density of frequency , the transition frequency J+1J. Bij itself depends upon
the dipole moment matrix element for the transition, |Rij|2. For the rotational spectrum of
a diatomic molecule this is given by [29]:
( J  1)
(4.18)
( 2J  1)
where  is the permanent dipole moment of the molecule. The absorption intensity for
R ij
2
 2
each molecular rotational transition is found by combining equations 4.15, 4.17, and
4.18:

 2 ij 2
8 3
  E rot 
I abs   ( ij )
 ij R  exp

(4.19)
 kT 
 3(4 0 )q rot 
The 2 factor in equation 4.19 means that the maximum in the absorption spectrum
occurs at a higher J value than Jmax, the maximum populated energy level. For a simple
rotational transition equation 4.19 describes the transition intensity accurately. In the
case of BrO each transition is split into 18 components, due to -type doubling and
nuclear hyperfine structure. If only -type doubling was observed, the two transitions
would be almost equal in intensity. The relative intensities of the nuclear hyperfine
components depend upon the angular momentum quantum numbers associated with each
transition, i.e. [30]:
(4.20)
B( J  F  I  1)( J  F  1)( J  F  I  1)
F
B( J  F  I  1)( J  F  I )( J  F  1)( J  F  I  1)( 2F  1)

(4.21)
F ( F  1)
I abs( F 1 F ) 
I abs( F  F )
I abs( F 1 F ) 
B( J  F  I )( J  F  I  1)( J  F  I  1)( J  F  I  2)
F 1
(4.22)
The sum of the intensities of all the hyperfine components is equal to the intensity of the
rotational transition had no splitting occurred. For J>10 the most intense hyperfine
transitions occur when F=J. The relative intensities of these transitions are
approximately proportional to F. For F=0 and F=-1 the relative intensity is a small
117
CHAPTER FOUR BrO PRESSURE BROADENING
fraction of the entire transition. In the TuFIR BrO spectra the F=+1 components are
most intense but the F=0, -1 transitions are often too weak to be observed.
BrO rotational spectra are intense as the radical possesses a large dipole moment,
=1.794D [11]. Many previous studies of BrO have been made in the UV-visible [3336], IR [37-40] and millimetre regions [32, 41-44]. BrO was first observed by electronic
emission [33] and absorption [34] around 300nm. In both cases, a reliable vibrational and
rotational analysis was precluded by the diffuseness of the observed bands. The first
microwave studies were made in 1969 by Powell et al [41]. They studied the J=5/23/2
transition of both isotopic forms in the =0 vibrational level of the 23/2 ground
electronic state. From an Electron Paramagnetic Resonance (EPR) study of the same
transition, Carrington et al [42] determined the effective hyperfine and quadrupole
coupling constants, and estimated the spin-orbit coupling. Brown et al [44] extended the
EPR work to the J= 7/25/2 transition. Rotational transitions in the vibrationally excited
=1 state were first observed by Amano et al [43]. The most extensive millimetre and
sub-millimetre study to date was undertaken by Cohen et al [32] in 1981. Around the
same time McKellar studied the rotational transitions of the magnetic dipole allowed
2
1/2 23/2 band by IR-Laser Magnetic Resonance (LMR) [38]. He made the first direct
observations of the 21/2 state and was able to determine an accurate value for A, the
spin-orbit splitting parameter. In addition, he determined a number of rotational
parameters for the 21/2 state, including the rotational constant B, and -type doubling
parameter, q. Cohen et al measured the =0 and =1 rotational spectra of
81
79
BrO and
BrO in the 23/2 state from 60 to 400GHz. Using the spin-orbit parameter, A,
determined by McKellar, they were able to fit all their experimental data accurately. A
complete set of constants was derived for the 23/2 state and used to estimate the
vibrational frequency e, and anharmonic term ee. These constants have been
amended by later IR studies [39,40]. Reliable predictions of higher frequency transitions
were made from Cohen et al’s data. These are currently held on the JPL Submillimetre,
Millimetre, and Microwave Spectral Line Catalogue [45-47]. BrO transition frequencies
and intensities for this study were taken directly from the JPL Catalogue which is
regularly updated, occasionally using parameters derived from unpublished work, e.g.
Cohen has now studied the BrO spectrum to 600GHz and amended the molecular
constants accordingly [48].
118