Measurements of ground-state OH rotational energy-transfer rates

Article abstract of DOI:10.1063/1.478073

We have studied rotational energy transfer (RET) in collisions of OH with the bath gases Ar, N₂, O₂, and H₂O at 293 K. Rotationally hot OH(X²Π_3/2,v^″=0,N ^″=1-12) was generated by photolysis of H₂O₂ at 266 nm, and collisional relaxation of the nascent rotational distribution was monitored by laser-induced fluorescence. The data are remarkably well described by an exponential-gap model for the matrix of state-to-state RET rate constants. For Ar, N₂, and O₂, RET rates are significantly faster at low N^″ than high N^″; for H₂O, RET is approximately an order of magnitude faster than for the other bath gases, and the rate is not as strongly dependent on N^″. The rates of rotationally inelastic energy transfer are similar in the X and A states, but the X-state depopulation rate constants (including nearly elastic, Λ-doublet-changing collisions) are faster than the A-state values. By comparing the depopulation rates derived from the present experiment with previous linewidth measurements, we conclude that RET is the dominant source of pressure broadening for OH microwave transitions and makes a significant contribution for ultraviolet A-X transitions. While generally good agreement is found between the present results and previous OH RET studies for both the ground and excited electronic states, some significant discrepancies are noted.

Full text of DOI:10.1063/1.478073

Measurements of ground-state OH rotational energy-transfer rates
Dahv A. V. Kliner and Roger L. Farrow
Citation: The Journal of Chemical Physics 110, 412 (1999); doi: 10.1063/1.478073
View online: http://dx.doi.org/10.1063/1.478073
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 1
1 JANUARY 1999
Measurements of ground-state OH rotational energy-transfer rates
Dahv A. V. Kliner and Roger L. Farrow
Sandia National Laboratories, Combustion Research Facility, Livermore, California 94551
͑Received 27 July 1998; accepted 25 September 1998͒
We have studied rotational energy transfer ͑RET͒ in collisions of OH with the bath gases Ar, N2,
2
O2, and H2O at 293 K. Rotationally hot OH(X ⌸3/2
,
ϭ0, N ϭ1–12) was generated by
v
Љ Љ
photolysis of H2O2 at 266 nm, and collisional relaxation of the nascent rotational distribution was
monitored by laser-induced fluorescence. The data are remarkably well described by an
exponential-gap model for the matrix of state-to-state RET rate constants. For Ar, N2, and O2, RET
rates are significantly faster at low N than high N ; for H O, RET is approximately an order of
Љ
Љ
2
magnitude faster than for the other bath gases, and the rate is not as strongly dependent on N . The
Љ
rates of rotationally inelastic energy transfer are similar in the X and A states, but the X-state
depopulation rate constants ͑including nearly elastic, ⌳-doublet-changing collisions͒ are faster than
the A-state values. By comparing the depopulation rates derived from the present experiment with
previous linewidth measurements, we conclude that RET is the dominant source of pressure
broadening for OH microwave transitions and makes a significant contribution for ultraviolet A–X
transitions. While generally good agreement is found between the present results and previous OH
RET studies for both the ground and excited electronic states, some significant discrepancies are
noted. © 1999 American Institute of Physics. ͓S0021-9606͑99͒01701-8͔
I. INTRODUCTION
of the OH rotational distribution in ϭ0–2. Rotational re-
v
Љ
laxation of the OH was found to occur at a gas-kinetic rate,
which was attributed to formation of a hydrogen-bonded
OH–H2O collision complex, and an average rate constant for
rotational relaxation was obtained. Holtzclaw et al.8 gener-
ated rotationally and vibrationally hot OH via the reaction of
O(1D) with H2 and observed collisional relaxation of the
Collisional processes profoundly influence the spectral
properties of molecules.1 Rotational energy transfer ͑RET͒ is
particularly important for determining molecular line shapes
and saturation behavior. Accurate knowledge of RET rates is
thus essential for quantitative application of spectroscopic
diagnostic methods such as absorption spectroscopy and
laser-induced fluorescence ͑LIF͒,2 and a large number of ex-
perimental and theoretical studies of RET have been
reported.3 Most experimental studies have been performed
using stable molecules and/or molecules prepared in an elec-
tronically excited state. Relatively few RET measurements
have been reported for transient species in the ground state.
rotational distribution by O at 100 K for ϭ1–3. The data
v
Љ
2
were well described by a model in which ⌬N was restricted
Љ
to be Ϯ1, with this assumption, state-to-state RET rate con-
stants for N ϭ8–25 were determined, and a local minimum
Љ
͑‘‘bottleneck’’͒ was found at N ϭ14.
Љ
In related work, Andresen et al.9 measured the total de-
population rate and the ⌳-doublet-changing collision rate for
OH( ϭ1, J ϭ1.5,4.5) in H . Copeland and Crosley10 ob-
In this paper, we report measurements of RET rates of OH in
v
Љ
Љ
2
2
the ground electronic and vibrational states ͑X ⌸3/2
ϭ0͒ for collisions with Ar, N2, O2, and H2O.
,
v
Љ
served a propensity for ⌳-doublet conservation in inelastic
(J ϭ1.5→2.5) collisions of OH( ϭ2) with H O, and
v
Љ
Љ
2
Wysong et al.11 observed a propensity for conservation of
total parity ͑not of ⌳-doublet state͒ in spin-orbit-changing
LIF detection of OH is widely used in a variety of ap-
plications, including laboratory studies, combustion mea-
surements, and atmospheric sensing. For applications in
which the temperature and/or composition are variable, e.g.,
combustion studies, knowledge of OH RET rates under the
relevant conditions is required for accurate determination of
OH densities and for OH thermometry.4,5 Several studies of
collisions of OH( ϭ2, J ϭ2.5) with He. Detailed crossed-
v
Љ
Љ
molecular-beam studies of ground-state OH RET have also
been reported.9,12–14
In the present experiment, rotationally hot
2
OH(X ⌸3/2
,
ϭ0,N ϭ1–12) was generated by photolysis
v
Љ Љ
2
RET in electronically excited OH A ⌺ϩ have been re-
of H2O2 at 266 nm. Collisional relaxation of the OH by the
bath gas ͑Ar, N2, O2, or H2O͒ was monitored by recording
LIF spectra at various times following photolysis. We find
that RET by H2O is approximately an order of magnitude
faster than for the other colliders. Moreover, for Ar, N2, and
O2, the OH rotational distribution at intermediate times is
ported, including measurements of both state-to-state transfer
rates and total depopulation rates ͑i.e., the sum of the state-
to-state rates out of a given level͒; this work has been re-
6
2
¨
viewed by Dagdigian and by Kohse-Hoinghaus.
Fewer measurements of RET rates for ground-state OH
X ⌸3/2 have been reported. Gericke and Comes7 used the
reaction of O(1D) with H2O to generate rotationally and vi-
brationally excited OH in the presence of excess H2O; ab-
sorption spectroscopy was used to follow the time evolution
‘‘kinked,’’ indicating more efficient RET for low N than
2
Љ
high N ; in contrast, H O does not exhibit such a pro-
Љ
2
nounced variation of RET rate with N . To extract RET rate
Љ
constants from the observed time evolution of the OH rota-
0021-9606/99/110(1)/412/11/$15.00
412
© 1999 American Institute of Physics
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J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
413
tional distribution, the data were fit using various models for
the state-to-state RET rate matrix. An exponential-gap model
is remarkably successful in reproducing the measured distri-
butions for all four bath gases. We compare the derived
state-to-state and depopulation rate constants with previous
measurements of OH RET rates for both the ground and
excited electronic states and with OH pressure-broadening
studies. While generally good agreement is found, some sig-
nificant discrepancies are noted.
continuously over this spectral region: slow scans were per-
formed over the regions of interest, and the laser was
scanned quickly between these regions. The wavelength of
the DFDL was measured with a wavemeter ͑New Focus
Model 7711, 0.001-nm resolution͒ and recorded at each
point in a spectral scan; transmission of the DFDL output
through an etalon ͑1.0-cmϪ1 free-spectral range͒ was also
recorded to linearize the scan ͑i.e., to interpolate between
wavemeter readings͒.
Each laser beam was collimated to a diameter of ϳ4 mm
prior to entering the flow cell. The copropagating beams
were crossed near the center of the cell, providing a several-
cm-long overlap region. The delay between the photolysis
and probe pulses was electronically variable over a wide
range ͑Ͼ20 ␮s͒ with a jitter of at most Ϯ1 ns. The pulse
energies of the two lasers were monitored with pyroelectric
detectors ͑Molectron J3͒.
II. EXPERIMENT
A. Overview
Photolysis of H2O2 at 266 nm produced rotationally hot
OH( ϭ0) in a flow cell in the presence of excess bath gas
v
Љ
͑Ar, N2, O2, or H2O͒, which collisionally relaxed the OH.
The time evolution of the OH rotational population distribu-
tion was monitored by laser-induced fluorescence ͑LIF͒ us-
ing a variably delayed probe laser ͑ϳ282 nm͒. The main
components of the apparatus were: ͑i͒ the photolysis laser,
͑ii͒ the probe laser, ͑iii͒ the H2O2 source and flow cell, and
͑iv͒ the LIF collection and detection system. Each compo-
nent and other experimental details are presented below.
C. H2O2 source and flow cell
Hydrogen peroxide was obtained by flowing the bath gas
through a bubbler ͑10–20-␮m pore size͒ containing 50 wt. %
aqueous H2O2 ͑Aldrich͒. The flow rate of the bath gas was
1–5 standard cm3 sϪ1. The concentration of the H2O2 solu-
tion was verified prior to and following the experiments by
measuring its density and its absorption spectrum in the
300–400-nm region. Comparison with literature values15,16
indicated a composition of 48Ϯ1 wt. % at the beginning of
these experiments and 55Ϯ1 wt. % at the end ͑i.e., the H2O2
solution had partially distilled during the course of the ex-
periments͒. For the experiments with Ar, N2, and O2, the
bubbler pressure was maintained at ϳ750 Torr, correspond-
ing to a gas-phase composition of 99% bath gas, 0.82% H2O,
and 0.069% H2O2 ͑the vapor pressure of 50 wt. % H2O2 at
20 °C is 6.68 Torr, with 92.3% H2O͒.15 For experiments with
H2O as the bath gas, the boil-off from the bubbler was used
directly ͑i.e., no additional flow was provided͒. The flow
from the bubbler passed through a Teflon metering valve and
a short length of PFA tubing before entering the cell.
The flow cell was a Pyrex cross with fused-silica win-
dows terminating each arm. The laser beams propagated
along the long axis of the cell, and the LIF was collected
along one of the perpendicular arms. The cell could be
evacuated to ϳ25 mTorr. For the present experiments, the
cell pressure was regulated using a needle valve on the out-
put port to within Ϯ0.1 Torr ͑Ϯ0.05 Torr for a single scan͒
at ϳ1–8 Torr ͑depending on the bath gas͒. The pressures in
the bubbler and flow cell were measured with capacitance
manometers ͑MKS Baratron͒. The residence time in the
ϳ300-cm3 cell was typically ϳ30 s.
B. Laser systems
The photolysis laser produced 266-nm pulses of 100-ps
duration and 30 mJ of energy at a repetition rate of 20 Hz. In
this system, selected pulses from a diode-pumped, mode-
locked Nd:YAG laser ͑Lightwave Model 131, 100-ps pulse
duration͒ were amplified in a Nd:YAG regenerative amplifier
followed by two single-pass Nd:YAG amplification stages
͑Positive Light͒. The output of the final amplifier stage, con-
sisting of 200-mJ pulses at 1064 nm, was frequency qua-
*
drupled using KD P crystals. The 266-nm pulse energy was
reduced to ϳ1 mJ incident at the photolysis cell using two
beam splitters followed by a half-wave plate and MgF2
Rochon polarizer ͑Halbo Optics͒. The photolysis beam was
split into two beams of approximately equal intensity, which
were crossed at a small angle in the flow cell. This geometry
was a remnant of previous four-wave mixing experiments
and was not required for the present study; it was advanta-
geous, however, for reducing optical damage to the cell win-
dows.
The probe laser produced tunable ϳ282-nm pulses of
ϳ90-ps duration and 0.5 mJ of energy at a repetition rate of
20 Hz. A Nd:YAG laser ͑Coherent Infinity͒ pumped a
distributed-feedback dye laser ͑DFDL͒, tunable from ϳ562
to 565 nm. The DFDL produced nearly transform-limited
pulses of ϳ90-ps duration and 0.15-cmϪ1 linewidth, which
were frequency doubled in an angle-tuned BBO crystal ͑In-
rad Autotracker II͒. The probe laser was attenuated to ϳ50
␮J using a half-wave plate and polarizer to avoid saturation
of the LIF transitions ͑see below͒. This arrangement also
allowed the relative polarizations of the photolysis and probe
lasers to be varied; in most experiments, these polarizations
were parallel.
D. LIF collection and detection system
The LIF emitted perpendicular to the propagation axis of
the laser beams was collected with an f/2 lens and focused
with an f/4 lens onto the entrance slit of a 0.25-m monochro-
mator ͑Oriel͒. A wide monochromator bandpass ͓ϳ20 nm
full width at half maximum ͑FWHM͔͒ was used to allow
The probe laser was scanned from 281.2 to 282.1 nm,
allowing detection of N ϭ1–12 ͑Sec. II F͒. Because of the
collection of fluorescence originating from both ϭ0 and
v
Ј
Љ
large line spacings at high N , the laser was not scanned
ϭ1. The spectrally filtered fluorescence was attenuated
v
Љ
Ј
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414
J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
with neutral density filters, as needed, before detection by a
photomultiplier tube ͑PMT, Hamamatsu R955͒. The PMT
pulses were amplified with a charge-integrating amplifier
͑EG&G Model 142͒, whose output was digitized using a
12-bit A/D converter. Similar A/D converters digitized the
outputs of the pyroelectric detectors and of the photodiode
that monitored the etalon transmission.
The digitized signals were recorded with a computer,
which also controlled and recorded the DFDL wavelength.
The LIF signal was normalized by the photolysis-and probe-
laser energies on each shot before being averaged. Typically
20 shots were averaged at each wavelength, with a DFDL
step size of 9ϫ10Ϫ4 nm ͑corresponding to 0.05 cmϪ1 in the
UV͒.
2
ϩ
2
FIG. 1. OH A
⌺
(
ϭ1)ϪX
⌸
(
ϭ0) LIF spectrum ͑points͒ and the
vЉ
vЈ
3/2
least-squares fit ͑line͒; the residuals are shown below the spectrum. Each
point represents an average of 20 laser shots, corrected for the photolysis
and probe powers on a shot-by-shot basis. Line assignments are given above
the spectrum. The bath gas was Ar, the pressure was 7.7 Torr, and the delay
between the photolysis and probe laser pulses was 10 ns. Note the scale
discontinuities on the abscissa.
E. H2O2 photolysis and the initial OH rotational
distribution
Gericke et al.17 studied in detail the scalar and vector
properties of the OH produced by 266-nm photolysis of
H2O2. In this process, 10% of the 20 700 cmϪ1 of available
energy is partitioned into OH rotation and 90% is partitioned
into relative translation of the fragments ͑Ͻ0.2% appears as
OH vibrational energy͒; the nascent OH is well characterized
by a rotational temperature of 1530Ϯ150 K. The OH spin-
orbit states are statistically populated, and there is a small
lowing subsequent rotational relaxation to be monitored
without the complication of continued OH production.
F. Determination of OH„␯ ؍0,N … populations from
Љ
Љ
preference for the ⌸(A ) ͑or f ͒ ⌳ doublet.18 The photodis-
Љ
the LIF spectra
sociation process is rapid ͑i.e., instantaneous on the time
scale of the present experiment͒: the lifetime of the electroni-
cally excited H2O2 is Ͻ60 fs.17
The probe laser was tuned over the R1 and R21 branches
2
2
of the A ⌺ϩ(␯ ϭ1)ϪX ⌸ (␯ ϭ0) transition with N
Ј
Љ
Љ
3/2
ϭ1–12. For these branches, the total angular momentum
(J ) is N ϩ1/2 and N is equal to N ϩ1; both branches
Translational relaxation of the nascent OH occurred
more rapidly than rotational relaxation, as evidenced by the
temporal evolution of the LIF line shapes ͑see Sec. II F͒.
Moreover, for the bath gases Ar, N2, and O2, the OH rota-
tional distribution measured at the earliest time ͑i.e., the
smallest pressure-time product͒ was in good agreement with
the expected nascent distribution17 ͑Sec. III A͒. Thus, for
these bath gases, translational relaxation of the nascent OH
allowed RET to be monitored without the complication of
distorted ͑broadened͒ line shapes and, more importantly, en-
sured that the measured RET rates correspond to thermally
equilibrated collisions. For H2O, RET was faster, and some
rotational relaxation had occurred even at the earliest time.
This result is in accord with a previous measurement7 of the
rate constant for OH translational relaxation by H2O at 300
K of Ͼ2.3ϫ10Ϫ10 cm3 molϪ1 sϪ1, corresponding to a relax-
ation time of Ͻ130 ns at 1 Torr. The H2O RET data in the
present experiment may therefore have a contribution from
superthermal collisions, particularly at the earliest times.
The rate constant for ⌳-doublet-changing collisions is
comparable to that for translational relaxation;9,10 the
⌳-doublet states were therefore thermally equilibrated under
our experimental conditions. The transitions accessed in the
Љ
Љ
Ј
Љ
originate in the ⌸(A ) ͑or e͒ ⌳ doublet.18,19 N ϭ11 was not
Ј
Љ
recorded because of a spectral overlap with the R2(9) line.
Nonlinear least-squares fits to the LIF spectra were used
to extract relative populations of the OH(␯ ϭ0,N ) levels.
Љ
Љ
Line positions were taken from Dieke and Crosswhite,19 and
B coefficients were calculated using the line strengths given
in LIFBASE.20 Each spectrum was modeled as a sum of
Gaussian profiles whose widths were varied in the fitting
procedure to account for variations in the laser linewidth and
in the OH Doppler width following photolysis ͑important
only at the earliest times͒. The line positions were also al-
lowed to vary ͑slightly͒ to account for nonlinearities in the
scanning rate of the DFDL. The integrated line intensity of
each N level was determined from a weighted average of
Љ
the integrated line intensities for the corresponding main
(R1) and satellite (R21) branches. A representative OH LIF
spectrum and the corresponding fit are shown in Fig. 1; Fig.
2 shows spectra at various pressure-time products for two
bath gases.
To obtain relative populations, the integrated line inten-
sities from the spectral fits were corrected for variations in
the fluorescence quantum yield ͑⌽͒ with N according to
Ј
LIF detection scheme ͑Sec. II F͒ probed only the ⌸(A )
Ј
state.18,19
A
⌽ϭ
,
͑1͒
An advantage of the use of photolysis rather than chemi-
cal reaction for generating rotationally excited OH is the
separation of time scales between OH production and RET:
generation of OH occurred only during the laser pulse, al-
AϩkB B ϩk
͓ ͔
H O
͔
2
͓
H O
2
where A is the spontaneous emission rate, kX is the OH col-
lisional quenching rate for molecule X, ͓X͔ is the density of
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J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
415
corded at a second pressure. The measured distributions
at different pressures but the same pressure-time product
were identical within experimental uncertainty, verifying
that the results are independent of the residence time in
the flow cell.
͑3͒ The polarization of the probe laser was rotated by 90°
͑perpendicular photolysis and probe͒ to check for align-
ment or orientation effects; no difference in the mea-
sured OH rotational distributions was observed.
͑4͒ The photolysis and probe power dependences were re-
corded several times throughout the course of these ex-
periments to ensure that the LIF signal was linear in both
the photolysis and probe powers, i.e., that neither the
photolysis nor the LIF transitions were saturated.
III. RESULTS
A. Measured OH rotational distributions
Figure 2͑a͒ shows OH LIF spectra recorded at various
times following H2O2 photolysis in N2; Fig. 2͑b͒ shows a
similar set of spectra, but with H2O as the bath gas. The
dramatically faster RET rate of H2O is evident from these
figures; for example, the OH rotational distribution is nearly
thermal by 190 ns•Torr for H2O, while significant population
is observed in N ϭ7–12 at 980 ns•Torr for N .
Љ
2
The time evolution of the OH( ϭ0) rotational distri-
v
Љ
FIG. 2. OH( ϭ0) LIF spectra at the indicated pressure-time products
vЉ
following 266-nm photolysis of H2O2 for the bath gases ͑a͒ N2 ͑6.3 Torr͒
and ͑b͒ H2O ͑0.98 Torr͒. Note the scale discontinuities on the abscissa.
bution is most conveniently presented as a Boltzmann plot
͓i.e., a plot of the population of each N level divided by the
Љ
level degeneracy (2N ϩ2) versus the rotational energy͔ at
Љ
various pressure-time products. Such plots are shown in
Figs. 3–6 for the bath gases Ar, N2, O2, and H2O, respec-
tively. The OH rotational distributions for Ar, N2 and O2
have qualitatively similar behavior: the lowest rotational lev-
X, and B denotes the bath gas. Both A and kX are functions of
N . A values were obtained from LIFBASE.20 kX values were
Ј
determined from Gaussian fits to literature values21–25 of kX
vs N ͑these fits were required to interpolate and extrapolate
Ј
els (N Ͻ6) attain thermal equilibrium relatively quickly,
Љ
the reported quenching rates to unmeasured N ͒. For the
range of conditions in the present experiment, ⌽ varied be-
tween 0.015 and 0.54, the variation with bath gas was more
Ј
while the higher levels relax on a slower time scale, resulting
in a kinked rotational distribution at intermediate times. OH
in H2O behaves differently, however: in addition to having
an overall faster relaxation rate, the difference in relaxation
pronounced than that with N ͑less than Ϯ27% variation for
Ј
a given bath gas͒.
rates between high and low N is not as pronounced, leading
Љ
At early times, the spectral lines were broadened due to
the large translational energy imparted to the OH fragments
by the photodissociation ͓e.g., the bottom spectra in Figs.
2͑a͒ and 2͑b͔͒. Because OH translational relaxation is faster
than rotational relaxation for Ar, N2, and O2, the spectral
lines sharpened prior to substantial cooling of the nascent
rotational distribution for these bath gases; for H2O, some
RET had occurred before translational equilibration was
complete ͑Sec. II E͒.
to only slight curvature of the Boltzmann plot; the rotational
relaxation is primarily characterized by a monotonic increase
in the slope with time. These observations will be made more
quantitative in Sec. IV A, in which modeling of the OH ro-
tational relaxation is discussed.
For Ar, N2, and O2, the initial OH rotational distribution
is well characterized by a temperature of 1660Ϯ120 K,
in
good
agreement
with
previous
experiments
(1530Ϯ150 K).17 Moreover, the OH linewidths had nar-
rowed to their room-temperature values by ϳ200 ns•Torr,
before significant rotational relaxation had occurred. This re-
sult confirms that translational relaxation of the nascent OH
occurs on a time scale faster than RET for these bath gases.
For H2O, some rotational relaxation had occurred at the ear-
liest time, as seen in Fig. 6 ͑and as mentioned in Sec. II E͒.
The measured rotational distributions have a small con-
tribution from OH produced by H2O2 photolysis by the probe
laser. This contribution, which was most significant for high
G. Experimental checks
A number of experimental checks were performed:
͑1͒ As discussed in Sec. II C the composition of the aqueous
H2O2 solution was checked by measuring its density and
UV absorption spectrum.
͑2͒ In most of the experiments, OH rotational distributions
were measured at a fixed pressure with various time de-
lays between the photolysis and probe lasers. For the
bath gases N2 and H2O, rotational distributions were re-
N
at late times, was measured to be generally Ͻ1% and
Љ
always Ͻ3%. Because this interference was minor, no cor-
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416
J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
FIG. 5. Same as Fig. 3, but for O2 bath gas at 2.8 Torr.
FIG. 3. Boltzmann plots of the OH( ϭ0) rotational distribution at the
vЉ
indicated pressure-time products following 266-nm photolysis of H2O2 in Ar
at 7.9 Torr. The points are the experimental data; the lines are the corre-
sponding distributions from the best-fit exponential-gap model ͑Model 1,
Sec. III B͒. Data at the different times have been offset for clarity.
͑3͒ mJ-scrambling exponential gap:
k ϭ␣(2N ϩ2)exp Ϫ␤(E ϪE )/k T , and
͕
͖
B
fi
f
f
i
͑4͒ ⌬N ϭϮ1: k ϭ␣ ␦(N ,N ϩ1).
Љ
fi
i
f
i
rection was applied to the data. Similarly, the small amount
͑Ͻ1%͒ of H2O present in the Ar, N2, and O2 ͑from the aque-
ous H2O2 solution͒ contributed to the measured RET rates
for these bath gases. Quantification of the H2O contribution
requires knowledge of the form of the RET rate matrix ͑see
below͒ and is discussed in Sec. IV A.
In these formulas, ␣, ␤, and ␥ are adjustable parameters, Ef
and Ei denote the rotational energies of levels Nf and Ni ,
respectively, kB is Boltzmann’s constant, and T is the abso-
lute temperature ͑293 K for the present experiment͒; kfi rep-
resents an upward rate (NfϾNi), and the downward rates
were determined by microscopic reversibility.
Model 1 is the standard exponential-gap form, which has
often been found to provide a good description of RET
rates.26,27 The modified exponential-gap formulas, 2a and 2b,
allow a first-order dependence of ␣ or ␤ on Ni . Model 3
weights kfi by the degeneracy of the final state, (2Nfϩ2).
Model 4 allows transitions only between adjacent rotational
levels ͑␣i may be different for each Ni͒; this model was used
by Holtzclaw et al.8 to fit their OH RET data.
B. RET models
The present measurements do not provide a unique de-
termination of the matrix of state-to-state RET rate constants,
k. The elements of k are denoted kfi , where f and i corre-
spond to the final and initial rotational states ͑Nf and Ni ,
respectively͒. By assuming a functional form for the depen-
dence of kfi on Nf and Ni , however, k can be determined
from a fit to the measured rotational population distributions.
We investigated several functional forms for k, including,
The best-fit parameters for each model and bath gas
were determined by minimizing the function
͑1͒ exponential gap: k ϭ␣ exp Ϫ␤(E ϪE )/k T ,
͕
͖
T
12
fi
f
i
B
2
f
Pmeas t ;N ͒ϪP
t ,N ͒
Љ
j
͑
͑
Љ
j
calc
␹ϭ
,
͑2͒
͑2a͒ modified exponential gap:
ͩ
ͪ
͚ ͚
Pmeas t ,N ͒
͑
Љ
jϭ1
j
N ϭ1
Љ
k ϭ␣(1ϩ␥N )exp Ϫ␤(E ϪE )/k T ,
͕
͖
fi
i
f
i
B
where j, the time index, runs from 1 ͑the initial time͒ to Tf
͑the final time͒, Pmeas(t ,N ) is the measured population of
͑2b͒ modified exponential gap:
k ϭ␣ exp Ϫ␤(1ϩ␥N )(E ϪE )/k T ,
Љ
j
͕
͖
B
fi
i
f
i
FIG. 4. Same as Fig. 3, but for N2 bath gas at 6.2 Torr.
FIG. 6. Same as Fig. 3, but for H2O bath gas at 0.98 Torr.
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J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
417
TABLE I. Best-fit parametersa for the exponential-gap and modified
exponential-gap RET models.
time evolution of the OH rotational population distributions:
this model is able to reproduce the kinked rotational distri-
butions at intermediate times for Ar, N2, and O2 as well as
the less-pronounced curvature of the Boltzmann plots for
H2O. These fits were obtained with only two adjustable pa-
rameters ͑␣ and ␤͒ for each bath gas.
Bath gas
Ar
Model
␣
␤
␥
1
1.0
1.73
1.34
1.28
2.06
1.67
1.42
1.40
1.21
¯
Ϫ0.062
0.019
¯
2a
2b
1
0.44
0.38
4.0
By allowing a first-order dependence of ␣ or ␤ on N
Љ
N2
O2
1
1.3
¯
͑Models 2a and 2b͒, a somewhat better fit was obtained for
the bath gases Ar and O2 ͑␹ was decreased by 35% and 15%,
respectively, compared to Model 1͒; this improvement was
comparable for Models 2a and 2b, i.e., the data do not allow
us to distinguish between these two models. For interpolation
or extrapolation of the measured distributions, we recom-
mend using the parameters from Model 2a or 2b for Ar and
O2. The modified exponential-gap models did not provide a
significantly better fit for N2 or H2O.
The mJ-scrambling exponential-gap model ͑Model 3͒
was not as successful in fitting the observed distributions as
the standard exponential-gap model for all bath gases: the
values of ␹ were 4%–20% larger for Model 3 than for Model
1. Similarly, Chandler and Farrow29 found close agreement
with an exponential-gap model but unsatisfactory agreement
with an mJ-scrambling exponential-gap model for their mea-
2a
2b
1
0.82
0.73
4.2
Ϫ0.041
0.0093
¯
H2O
aUnits of ␣ are 10Ϫ10 cm3 sϪ1; ␤ and ␥ are unitless.
level N at time tj , and Pcalc(t ,N ) is the corresponding
Љ
Љ
j
calculated population. The calculated populations were de-
termined by evaluating the expression
Pcalc t ͒ϭexp k t Ϫt ͒ P
t ͒,
͑
meas 1
͑3͒
͑
͑
͕
͖
j
j
1
where Pcalc(t ) is the vector of populations, P (t ,N ) ,
͕
Љ
͖
j
calc
j
at time tj , and Pmeas(tj) is the corresponding measured
population vector. Note that the calculation was initialized
with the rotational distribution measured at t1 ͑i.e., at the
smallest pressure-time product͒. In evaluating ␹, we omitted
levels that were not measured because their populations were
sured RET rates for HD( ϭ1) colliding with thermal HD
v
Љ
at 296 K. Sitz and Farrow30,31 measured state-to-state RET
and alignment-transfer rates for N ( ϭ1) in collisions with
too small ͑high N at large t͒ or because of spectral interfer-
Љ
v
Љ
2
ence (N ϭ11). Minimization of ␹ was performed using the
Љ
thermal N2; this work showed directly that the rate of
mJ-changing collisions is slower than that of J-changing col-
lisions and that alignment ͑i.e., a nonstatistical mJ-state dis-
tribution͒ is preserved in J-changing collisions. Although the
present OH RET results are consistent with this observation,
they do not allow an explicit determination of the effect of
collisions on the mJ-state distribution.
software STEPIT.28
To ensure conservation of population in the measured
rotational distributions, the ͑unmeasured͒ populations of N
Љ
ϭ11, 13, and 14 were filled in by interpolating/extrapolating
the measured populations of N ϭ10 and 12: the ‘‘tempera-
Љ
ture’’ corresponding to the Pmeas(tj,10)/Pmeas(tj,12) ratio
was determined for each j, and the corresponding popula-
Model 4 (⌬N ϭϮ1) provided a better fit to the data
Љ
tions of N ϭ11, 13, and 14 at this temperature were then
Љ
than Model 1 ͑␹ was reduced by 20%–40%͒. This result was
expected because Model 4 has 12 adjustable parameters ͑one
calculated. This procedure ensured proper normalization of
the measured population distributions ͑for comparison with
the calculated distributions͒ and did not significantly influ-
ence the analysis. The populations of the interpolated and
extrapolated levels were not included in the determination
of ␹.
The best-fit parameters for the exponential-gap model
for the four bath gases are listed in Table I; the correspond-
ing calculated rotational distributions are shown by the solid
lines in Figs. 3–6. For Ar and O2, the best-fit parameters for
Models 2a and 2b are also given in Table I. These RET
models are discussed further in the following section. We
estimate the uncertainty of the model parameters to be ap-
proximately Ϯ15% for ␣, Ϯ5% for ␤, and Ϯ5% for ␥; these
uncertainties are based on the results of multiple fits to each
data set ͑i.e., they reflect the nonindependence of the param-
eters͒ and on fits to comparable data sets recorded on differ-
ent days.
for each N ͒ while Model 1 has two parameters. Given this
Љ
large increase in the number of adjustable parameters, the
reduction in ␹ for Model 4 is minimal. Previous RET
measurements2,29,30,32 for both polar and nonpolar diatomic
molecules have shown that ⌬N is not restricted to Ϯ1, par-
Љ
ticularly at low N , where the energy gaps are small ͑B
Љ
e
ϭ18.9 cmϪ1 for OH͒.33 The exponential-gap results ͑Table I͒
indicate the importance of multiple-quantum transitions: kfi
is reduced by a factor of two from its maximum value when
EfϪEi is 67–120 cmϪ1 ͑depending on bath gas͒. We there-
fore conclude that Model 4 is unlikely to provide an accurate
representation of the state-to-state RET rate matrix.
We used the calculated rate matrices to investigate the
contribution of RET by H2O to the other bath gases ͑Sec.
III A͒. Specifically, subtracting k for H2O ͑weighted by its
mole fraction͒ from k derived for another bath gas measured
in the presence of water yields k for the bath gas alone. For
Ar ͑the bath gas with the slowest RET rate͒, removing the
H2O contribution to the exponential-gap rate matrix reduces
␣ by 3.7% and ␤ by 1.7%; for the N2 and O2, the effect is
even smaller. We therefore conclude that the effect of the
residual H2O in the other bath gases is insignificant.
IV. DISCUSSION
A. RET models
As seen in Figs. 3–6, the exponential-gap model ͑Model
1͒ provides a remarkably good description of the observed
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418
J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
FIG. 7. Total depopulation rates, ki ͑diagonal elements of k͒, calculated
using the indicated RET models for ͑a͒ Ar and ͑b͒ H2O.
FIG. 8. Ensemble average of the OH( ϭ0) rotational energy versus
vЉ
pressure-time product for Ar, N , O , and H O: ͑a͒ N ϭ1–14, ͑b͒ N
Љ
Љ
2
2
2
ϭ1–5. The points are the data, and the lines are single-exponential fits
corresponding to the average RET ‘‘rate constants’’ shown in parentheses
͑units of 10Ϫ10 cm3 sϪ1͒. The ensemble-average rotational energy at time tj
B. Total depopulation rates
is given by ⌺Pmeas(t ,N )E /⌺Pmeas(t ,N ), where the summations run
Љ
Љ
j
N
j
Љ
For spectroscopic applications ͑e.g., determination of
linewidths͒,30 a particularly important parameter is the rate
of population transfer out of a given level, i. These depopu-
lation rates, denoted ki , correspond to the diagonal matrix
elements of k, i.e., kiϭ⌺fkfi , where fÞi but f can be
greater or less than i. Although the values of ki are somewhat
dependent on the assumed form of the rate matrix, they are
better determined in the present experiment than are the in-
dividual state-to-state rate constants, kfi .
over the relevant range of N .
Љ
tional distributions for Ar, N2, and O2͒ and the differences
between H2O and the other bath gases.
C. Average relaxation rates
RET has often been characterized by a single ‘‘rate’’;34
Figure 7 shows the total depopulation rate as a function
such an approach was taken by Gericke and Comes7 to de-
of N for the bath gases Ar and H2O. The results of the
Љ
scribe their measurements of OH( ϭ0) RET in collisions
v
Љ
exponential-gap and modified exponential-gap models are
shown to indicate the model dependence of ki . For Ar at low
with H2O. We have extracted ‘‘average RET rate constants’’
from our measured OH rotational distributions by calculating
N , Models 2a and 2b yield k values as much as 50%
Љ
i
the ensemble average of the OH( ϭ0) rotational energy as
v
Љ
smaller than Model 1; this difference is generally diminished
a function of time ͑Fig. 8͒. To illustrate the N -dependence
Љ
at higher N , where k is dominated by downward, single-
Љ
i
of this rotational-relaxation ‘‘rate,’’ we compared the effect
of including all of the levels in calculating the rotational
energy ͓Fig. 8͑a͔͒ with including only the lowest five levels
͓Fig. 8͑b͔͒. In all cases, the data are reasonably well de-
scribed by single exponential decays, from which the aver-
age RET rate constants given in Fig. 8 are obtained. The rate
constants for Ar, N2, and O2 are a factor of ϳ2 smaller for
quantum transitions ͑i.e., where the energy gaps are large͒.
For H2O, the differences between the models are smaller
͑ϳ15%͒, as expected from the ␹ values ͑Sec. IV A͒. We
conclude that the present experiment is likely able to deter-
mine k values to an accuracy of ϳϮ50%. Plots of k vs N
Љ
i
i
for N2 and O2 ͑not shown͒ are similar to that for Ar ͓Fig.
7͑a͔͒ in both shape and magnitude. In contrast, for H2O ͓Fig.
7͑b͔͒, the ki values are approximately an order of magnitude
N ϭ1–5 than for N ϭ1–14. In contrast, the average RET
Љ
Љ
rate constant for H2O is not strongly dependent on the num-
ber of levels included in the analysis.
larger and depend less strongly on N , consistent with stron-
Љ
ger attractive forces for this bath gas.21 Note that the differ-
ences between H2O and the other bath gases are significantly
larger than the uncertainties in ki .
D. Comparison with previous results
The results shown in Fig. 7 are in accord with the quali-
tative RET observations presented in Sec. III A concerning
We can compare our results with several previous RET
studies of both ground-state and electronically excited OH.
the dependence of the RET rate on N ͑i.e., the kinked rota-
Љ
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J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
419
FIG. 9. Comparison of measured state-to-state RET rate constants ͑symbols,
A state͒ ͑Refs. 35 and 36͒ with those derived from modeling of the present
data ͑lines, X state͒ for the indicated bath gases. Noted in each panel are the
initial rotational state (Ni) and the vibrational level of the state-to-state
FIG. 10. Comparison of measured depopulation rate constants for the A
state ͑symbols͒ with the present, X-state values ͑lines͒. Filled symbols de-
measurements ( ); the abscissa corresponds to the final rotational state
v
(Nf). For Ar, the lines correspond to Model 2b ͑which best reproduced the
experimental results͒; for N2 and H2O, the lines correspond to Model 1
͑which gave results indistinguishable from Model 2b͒. The A-state data refer
to symmetry-preserving transitions within the F2 manifold.
note ϭ0 and open symbols denote ϭ1; triangles are from Ref. 39,
vЈ vЈ
squares are from Ref. 36, filled circles are from Ref. 38, and open circles are
from Ref. 23. The values from the present experiment include a correction
for the contribution of nearly elastic, ⌳-doublet-changing collisions (4.5
ϫ10Ϫ10 cm3 sϪ1).
2. Depopulation rate constants
1. State-to-state rate constants
Depopulation rate constants, ki , have been reported for
both the A and X states. Care must be taken in comparing our
ki values ͑the diagonal matrix elements͒ with other measure-
ments because we detected only one of the ⌳ doublets ͑Sec.
II F͒. Previous studies have shown that nearly elastic,
⌳-doublet-changing collisions (⌬N ϭ0,⌬J ϭ0) are rapid:
2
We first compare the OH(X ⌸3/2
,
ϭ0) k values de-
v
Љ
fi
rived from the present experiment with measured
OH(A ⌺ϩ, ϭ0,1) state-to-state rate constants35,36 ͑Fig.
2
v
Ј
9͒. Although there is no a priori reason to expect comparable
RET rates in the X and A states, Zizak et al.37 found them to
be similar; specifically, by modeling saturated OH LIF mea-
surements, they concluded that RET is 30% faster in the X
state than in the A state. Similarly, comparison of the present
ϭ0 measurements with A-state data for both ϭ0 and
Љ
Љ
2
for OH(X ⌸3/2
,
ϭ2,J ϭ1.5) colliding with H O, the rate
v
Љ Љ
2
constant for such e↔f transfer is 4ϫ10Ϫ10 cm3 sϪ1 ͑Ref.
2
10͒; for OH(X ⌸3/2
,
ϭ1, J ϭ1.5) colliding with H , the
v
Љ Љ
2
v
v
v
rate constant is (5.1Ϯ1.1)ϫ10Ϫ10 cm3 sϪ1 ͑Ref. 9͒. For
comparison with previous measurements, we therefore added
4.5ϫ10Ϫ10 cm3 sϪ1 ͑the average of the two e↔f rate-
constant measurements͒ to the ki values derived from the
RET models; this procedure is reasonable because ͑i͒ the
e↔f rate does not appear to have a strong dependence on
Љ
Ј
Ј
ϭ1 is justified because the RET rates in these two vibra-
tional levels are nearly equal.23,35,36,38 As shown in Fig. 9,
the agreement between the previously measured and our de-
rived kfi values is surprisingly good, both for the magnitude
of the rate constants and for their dependence on ⌬N and
bath gas. The main area of disagreement is for H2O, which
shows a stronger dependence on ⌬N ͑i.e., a stronger prefer-
ence for ⌬NϭϪ1͒ in the state-to-state measurements. We
cannot determine if this result reflects a real difference be-
tween the X and A states or is an artifact of the RET model
used to analyze the present data.
v
Љ
or bath gas, and ͑ii͒ for the range of N under consideration,
Љ
the ⌳-doublet splitting is Ͻ2 cmϪ1, i.e., we do not anticipate
a strong dependence of the rate on N .
Љ
Copeland and Crosley10 measured ki to be
9
2
ϫ10Ϫ10 cm3 sϪ1 for OH(X ⌸3/2
,
ϭ2,J ϭ1.5) colliding
v
Љ Љ
with H2O, in excellent agreement with the present value of
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420
J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
FIG. 11. Comparison of the OH de-
population rate constants derived from
the present experiment ͑293 K, ϭ0͒
vЉ
to those of Holtzclaw et al. ͑Ref. 8͒
͑100 K, ϭ1–3͒ for collisions with
vЉ
O2.
8.9ϫ10Ϫ10 cm3 sϪ1 for OH( ϭ0,J ϭ1.5). Andresen
while that of Holtzclaw et al. was performed at 100 K. The
former difference is unlikely to account for a factor of 5–10
v
Љ
Љ
et al.9 obtained a similar value of (5Ϫ9)ϫ10Ϫ10 cm3 sϪ1
for collisions of OH( ϭ1,J ϭ4.5) with H O .
because the RET rates are not strongly dependent on
v
Љ
Љ
2
2
8,23,36,38
.
Although a rapid increase in the RET rate with
v
Љ
Figure 10 shows a comparison of previously measured
depopulation rate constants for the A state23,36,38,39 with our
calculated, X-state values for all four bath gases. The A-state
rates are generally larger than the present rates, in accord
with the conclusion of Zizak et al.37 For Ar, N2, and O2, the
X-state rates are larger by factors of ϳ2–7; this difference is
almost wholly accounted for by the contribution of e↔f
exchange to ki , i.e., rotationally inelastic energy-transfer
rates are nearly equal in the two electronic states ͑as indi-
cated in Fig. 9͒. For H2O, the e↔f rate constant is a smaller
fraction of ki , and the X-state and A-state depopulation rate
constants are therefore nearly equal. For Ar, N2, and O2, ki is
not strongly dependent on Ni in either the A or X state for the
range Niϭ1–6.
decreasing temperature could account for the discrepancy,
OH pressure-broadening measurements40,41 indicate that this
increase would have to occur at temperatures below 200 K
͑see below͒.
3. Pressure-broadening coefficients
The width of absorption lines is often determined by
collisional processes. If elastic dephasing collisions are as-
sumed to make an insignificant contribution to the linewidth,
the pressure-broadening coefficient for the transition be-
tween levels Ni and Nf(␥if , FWHM͒ is related to the total
depopulation rates of these levels ͑ktiot and ktfot , respectively͒
by:42
Holtzclaw et al.8 reported RET rate constants for the
process OH( ,N )ϩO →OH( ,N Ϫ1)ϩO for
v
v
v
Љ
Љ
Љ
Љ
Љ
2
2
ktiotϩktfot
ϭ1–3 at 100 K. Because the data analysis assumed no
␥ifϭ
,
͑4͒
multiple-quantum transitions ͑Model 4, ⌬N ϭϮ1͒, these
Љ
2␲c
rate constants correspond to depopulation rates, ki ͑for the
where ktiot and ktfot include RET and, where relevant, vibra-
tional energy transfer and electronic quenching.
range of N under consideration, the correction for transi-
Љ
tions with ⌬N ϭϩ1 is insignificant͒. Moreover, these rate
Љ
Table II compares measured pressure-broadening coeffi-
cients of several OH lines with values calculated using Eq.
constants are directly comparable to our depopulation rate
constants because both experiments were characterized by an
equilibrium distribution between the ⌳-doublet levels. Our
results are compared to those of Holtzclaw et al. in Fig. 11.
͑4͒. The first five entries refer to microwave transitions
2
within ϭ0 of the X ⌸ state, and the remaining entries
v
Љ
3/2
refer to the P (2)UVA( ϭ0)–X( ϭ0) transition. For
v
v
Љ
Where the data sets overlap (N ϭ8–12), our k values are a
Ј
Љ
1
i
the X state, only RET contributes to the depopulation rates
(ktjotϭkj), and we used the kj values obtained from the
present experiment ͑e.g., Fig. 10͒. For the A state, we used
measured depopulation rates ͑ktfot including RET and
quenching͒ for N2 and O238; for Ar, we used the kf value
factor of ϳ10 smaller than the previous values. This discrep-
ancy is puzzling. It is likely partially attributable to the as-
sumption of ⌬N ϭϮ1 in the data analysis procedure of
Љ
Holtzclaw et al.: Model 4 yields consistently larger ki values
than any of the other models ͑although it is able to fit both
our data set and that of Holtzclaw et al.͒; this result, how-
͑RET only͒ for F (5) in v ϭ1 of Kienle et al.36 ͑this ap-
Ј
2
ever, accounts for no more than a factor of two for N
proximation is justified because electronic quenching by Ar
Љ
ϭ8–12. The main differences between the two experiments
were ͑i͒ we detected ϭ0 while Holtzclaw et al. detected
is insignificant and ␥if for this transition is dominated by
RET in the ground state͒. Note that for A–X transitions with
v
Љ
Ͼ0, vibrational energy transfer will contribute to ktot
.
25
ϭ1–3, and ͑ii͒ our experiment was performed at 293 K
v
v
Ј
Љ
f
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J. Chem. Phys., Vol. 110, No. 1, 1 January 1999
D. A. V. Kliner and R. L. Farrow
421
TABLE II. Calculated and measured OH pressure-broadening coefficients
͑␥if , FWHM͒ at ϳ300 K.
V. CONCLUSIONS
From measurements of the collisional relaxation of a hot
OH(2⌸3/2
ϭ0) rotational distribution, we have derived
Calculated
Bath coefficientb
gas ͑cmϪ1 atmϪ1
Measured
coefficient
,
v
Љ
OH(N ϭ1–12) RET rate constants at 293 K for the bath
Љ
Transitiona
X; J ϭ1.5→J ϭ2.5
͒
͑cmϪ1 atmϪ1
͒
Ref.
gases Ar, N2, O2, and H2O. These and previous measure-
ments show that:
Ar
N2
O2
N2
O2
Ar
N2
O2
0.13
0.19
0.14
0.20
0.15
0.094
0.20
0.10
0.0999Ϯ0.0004 43
Љ
Љ
0.194Ϯ0.003
0.134Ϯ0.004
0.182Ϯ0.003
0.096Ϯ0.012
0.141Ϯ0.002
0.217Ϯ0.005
0.143Ϯ0.005
41
41
40
40
44
44
44
͑1͒ RET rates for H2O are approximately an order of mag-
nitude faster than for the other bath gases;
͑2͒ For Ar, N2, and O2, RET rates are significantly faster at
X; J ϭ2.5→J ϭ3.5
Љ
Љ
X, J ϭ2.5→A, J ϭ1.5
Љ
Ј
low N than high N ; for H O, the RET rate is not as
Љ
Љ
2
strongly dependent on N ;
Љ
͑3͒ For Ar, N2, and O2, the total depopulation rate of a given
level is dominated by nearly elastic, ⌳-doublet-changing
aX denotes the
bUsing Eq. ͑4͒.
⌸
(
ϭ0) state; A denotes the
⌺
(
ϭ0) state.
vЈ
2
2
ϩ
vЉ
3/2
collisions (⌬N ϭ0,⌬J ϭ0); for H O, rotationally in-
Љ
Љ
2
elastic collisions (⌬N Þ0) are comparably important;
Љ
͑4͒ RET is the dominant source of pressure broadening for
OH microwave transitions;
͑5͒ RET makes a significant contribution to pressure broad-
ening for OH UV A–X transitions;
͑6͒ Rotationally inelastic energy-transfer rates are similar in
the X and A states, but total RET rates ͑including
⌳-doublet-changing collisions͒ are faster in the X state
than the A state; and
͑7͒ Multiple-quantum transitions make a significant contri-
bution to OH rotational relaxation.
The agreement between the measured and calculated ␥if
values is remarkably good. In particular, Eq. ͑4͒ correctly
predicts the dependence of the linewidth on bath gas for both
the microwave and the UV transitions (ArрO2ϽN2). The
calculated pressure-broadening coefficients for the A–X
transition are ϳ30% too small for O2 and Ar, presumably
because of the neglect of collisional dephasing; a calculation
of ␥if that includes only RET in the X and A states shows
that RET accounts for over half of the pressure broadening
for this transition for all three bath gases. These results indi-
cate that RET dominates pressure broadening for the OH
microwave transitions and makes a significant contribution
to broadening of the UV transitions. Note that nearly elastic,
⌳-doublet-changing collisions are the dominant contributor
to the X-state depopulation rates, and hence to the pressure-
broadening coefficients, for Ar, N2, and O2; however, the
calculated dependence on bath gas derives from variations in
the rate of rotationally inelastic collisions.
The microwave pressure-broadening measurements pro-
vide information on the temperature dependence of OH
ground-state RET rates. Chance et al.40 and Park et al.41
measured a change of Ͻ30% in ␥if for O2 upon decreasing
the temperature from 296 to ϳ200 K. If the discrepancy
discussed above between the present results and those of
Holtzclaw et al.8 is caused by an increase in the RET rate
with decreasing temperature, this increase must therefore oc-
cur between 200 and 100 K.
We find generally good agreement with previous OH
RET and pressure-broadening measurements. One exception
is the study of Holtzclaw et al.,8 who obtained RET rate
constants for collisions with O2 at 100 K that are a factor of
ϳ10 larger than the present values. This previous experiment
predicts a microwave pressure-broadening coefficient at 100
K that is an order of magnitude larger than the measured
values at 300 and 200 K.40,41 Holtzclaw et al. reported that
OH RET is a factor of Ͼ100 faster for O2 than for Ar; the
present study yielded a factor of Ͻ2.
The present data are well described by an exponential-
gap model for the state-to-state RET rate matrix. This obser-
vation does not permit the conclusion that the actual rate
matrix is characterized by an exponential-gap law. State-to-
state measurements are required to gain a detailed under-
standing of OH RET, to resolve the remaining discrepancies,
and to investigate more quantitatively the conclusions out-
lined above.
ACKNOWLEDGMENTS
4. Other comparisons
This work was supported by the U.S. Department of En-
ergy, Office of Basic Energy Sciences, Division of Chemical
Sciences. We acknowledge the expert technical assistance of
P. Schrader. We thank D. R. Crosley and G. E. Caledonia for
helpful discussions.
Gericke and Comes17 reported an ‘‘RET rate constant’’
of (2.2Ϯ0.5)ϫ10Ϫ10 cm3 sϪ1 for OH( ϭ0) colliding with
v
Љ
H2O. This value is in reasonably good agreement with our
‘‘average RET rate constant’’ for H2O of
3.8ϫ10Ϫ10 cm3 sϪ1 ͓Sec. IV C, Fig. 8͑b͔͒.
1 A. C. Eckbreth, Laser Diagnostics for Combustion Species and Tempera-
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two orders of magnitude slower than RET by O2.8 Although
our results also show Ar to be slower than O2, we found this
difference to be no more than a factor of two ͑e.g., Fig. 8͒.
Similarly, Ar and O2 have comparable depopulation rate con-
stants for A-state OH ͓Figs. 10͑a͒ and 10͑c͔͒.
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