The dynamics of O(3P) + deuterated hydrocarbons: Influences on product rotation and fine-structure state partitioning

Article abstract of DOI:10.1039/b108699p

The dynamics of the reactions O(³P) + CH₄/CD₄ and O(³P) + cyclo-C₆H₁₂/C₆D₁₂ were experimentally studied. The novel dynamical experimental results confirmed the main fe

Full text of DOI:10.1039/b108699p

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3
The dynamics of O( P) 1 deuterated hydrocarbons: influences on
product rotation and fine-structure state partitioning
a
Florian Ausfelder, Hailey Kelso and Kenneth G. McKendrick*
b
b
a
Department of Chemistry, The University of Edinburgh, Edinburgh, UK EH9 3JJ
Department of Chemistry, Heriot-Watt University, Edinburgh, UK EH14 4AS
b
Received 24th September 2001, Accepted 20th November 2001
First published as an Advance Article on the web 3rd January 2002
3
3
The dynamics of the reactions O( P) þ CH
4
=CD
4
and O( P) þ cyclo-C
6
H
12=C
experimentally. Translationally hot O( P) atoms were generated by laser photolysis of NO
6
D
12 have been investigated
3
2
at 266 nm.
The rotational and fine-structure state distributions in the nascent product OH or OD radicals were determined
by laser-induced fluorescence. The deuterium-labelled reactants have provided confirmation of the main
0
features of the product-state partitioning observed previously for normal-hydrogen compounds. Only OH n ¼ 0
0
0
is detectable from CH
4
. CD
4
also produces predominantly OD n ¼ 0, with n ¼ 1 being just detectable with an
0
estimated branching ratio of ꢀ 0.06. Both cyclo-C H and C D produce significant yields of n ¼ 0 and 1
6
12
6
12
0
products. Despite the opposite trend in exothermicities, the n ¼ 0 products are rotationally hotter from methane
than from cyclohexane, indicative of a stereochemical effect. The absolute rotational energy release is in each
case found to be essentially independent of hydrogen isotope. It is argued that this supports the accepted
collinear abstraction mechanism for this class of reactions. The OH fine-structure state partitioning is not
influenced by hydrogen isotope, nor by product vibrational level despite distinct differences in the associated
rotational energy release. This appears consistent with a previously derived model involving selected non-
adiabatic coupling of adiabatic electronic fine-structure surfaces.
theory (see below). In the most recent work based on OH
Introduction
1
0
detection, Kajimoto and coworkers have taken the first steps
into stereodynamics by determining polarisation-sensitive
Doppler profiles for certain product channels of the reactions
with selected secondary and tertiary hydrocarbons. Essentially
the only dynamical study not based on OH detection is the
3
The reactions of O( P) atoms with saturated hydrocarbons are
of practical importance in high temperature combustion.
There have consequently been many conventional kinetic
1
–4
measurements of their rate constants.
They are also of
1
1
interest fundamentally, stimulating investigations of their
dynamics. Comparatively speaking, however, they have
received much less attention in this respect than their cousins,
single determination by Suzuki and Hirota of CH
3
3
umbrella
by
mode vibrational state distributions from O( P) þ CH
4
diode laser absorption spectroscopy.
1
12
the reactions of O( D) with hydrocarbons. This is primarily for
experimental reasons, because the relatively large barriers, first
established kinetically, require high collision energies and
On the theoretical side, Luntz and Andresen developed
model pseudo-triatomic semi-empirical LEPS surfaces. Quasi-
classical trajectory (QCT) calculations on these surfaces were
successful in modelling the main qualitative features of their
3
make product yields low. Nevertheless, the O( P) reactions are
an interesting class because they appear to be at the opposite
1
3
experimental results. Almost in parallel, Walch and Dunning
3
1
end of the dynamical spectrum from the O( D) reactions,
made the first rigorous ab initio prediction that O( P) þ CH
4
involving direct abstraction in contrast to transient insertion.
3
proceeds via a preferred collinear O–H–C saddle-point geo-
metry. This therefore supported the explanation arrived at
Previous work on the dynamics of the O( P) þ hydro-
1
2
carbons, and some related reactions, is the subject of a recent
independently by Luntz and Andresen for the cold OH
rotational distributions that are observed experimentally.
5
review and so only a concise summary will be given here.
1
4,15
From an experimental point of view, the first insight was
gained through the ground-breaking work of Andresen and
Following some sparse intermediate work,
something of an explosion of theoretical interest in the
there has been
6
Luntz. They first introduced the use of laser-induced fluor-
3
O( P) þ CH
4
system in recent years. Two separate full-
escence (LIF) detection to determine product state distribu-
tions in the product OH. A series of representative primary,
secondary and tertiary hydrocarbons was examined. Similar
dimensional ab initio potential energy surfaces (PESs) have
1
been developed by Truhlar and coworkers and by Gonzalez
´
6
1
and coworkers. The Truhlar PES and its subsequent mod-
7
7
,8
18
ifications have been exploited in reduced-dimensional quan-
studies followed in the groups of Whitehead and McKen-
9
3
19–22
drick, with the introduction of laser photolysis for O( P)
generation in place of the discharge methods used originally.
Significantly, this allowed the OH from parent reaction,
tum scattering calculations by the groups of Clary
2
and
Nyman. These studies have focussed primarily on the influ-
3
ence of selective excitation of CH vibrational modes on the
4
3
9
O( P) þ CH
4
, to be studied for the first time. This reaction
reaction cross-section and product energy disposal. In parallel,
1
7,24
requires the highest laboratory frame translational energies
because it has the highest activation barrier in conjunction
with the least favourable kinematics. Undoubtedly, however, it
is the most important of the class in terms of comparison with
Gonza
´
lez and coworkers
have carried out QCT calcula-
tions on a pseudo-triatomic fit to their full-dimensional PES.
They have been successful in reproducing the experimentally
1
7
observed OH rotational state distribution,
and more
DOI: 10.1039/b108699p
Phys. Chem. Chem. Phys., 2002, 4, 473–481
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473

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2
4
recently have made predictions of various as yet unobserved
features of the dynamics. Essentially all the theoretical work
supports the original basic conclusion of a direct abstraction
mechanism via a preferred collinear geometry.
first time, a complete characterisation for both OH vibrational
states produced in reaction (2). The intention is to establish
whether the factors that determine the fine-structure state
branching are independent of those controlling the nuclear
framework rotation. This will provide a test of theoretical
In the current work we aim to extend the experimental
knowledge base on this class of reactions in two ways. First, we
use isotope substitution to provide confirmation of the nuclear
framework dynamics of two representative reactions:
2
5
models based on selective couplings between adiabatic elec-
tronic fine-structure surfaces. Although none of the rigorous
3
theoretical work on O( P) þ CH has yet advanced to the
4
treatment of multiple fine-structure surfaces, this general topic
is currently the subject of intense theoretical
3
26,27
Oð PÞ þ CH4 ! OH þ CH3
ð1aÞ
ð1bÞ
and experi-
2
8–31
mental
interest in related systems.
3
Oð PÞ þ CD4 ! OD þ CD3
and
Experimental
3
Oð PÞ þ cyclo-C6H12 ! OH þ cyclo-C6H11
ð2aÞ
ð2bÞ
The basis of the experimental method was essentially the same
9
as that described previously, so only the main features are
3
3
summarised here. The O( P) atoms were generated by photo-
Oð PÞ þ cyclo-C6D12 ! OD þ cyclo-C6D11
2
lysis of NO and the OH products probed by LIF. Experiments
were carried out in a stainless steel vacuum chamber, con-
structed around a central six-way cross. The chamber was
evacuated by a diffusion pump, backed by a rotary pump, with a
(
where cyclo-C H indicates cyclohexane). The energetics of
6 12
the two reactions are represented in Fig. 1, which emphasises
the lower barrier and greater exothermicity for abstraction
from a secondary H–C bond in reaction (2). This is the first
systematic investigation of isotope effects in these reactions
and we shall consider whether the results agree with the
accepted picture of the dynamics. It also provides valuable
À6
base pressure of better than 1 Â 10 Torr. During experimental
2
runs, NO precursor and hydrocarbon reactant gases were flo-
wed in via separate needle valves. This was designed to prevent
their mixing prior to entering the chamber and minimise the
undesired photolytic production of OH identified in several
experimental corroboration of the OH product state parti-
3
5
previous studies. In particular, it was successful in preventing
tioning for the parent O( P) þ CH reaction, (1a). As we have
4
9
isotope exchange between deuterium-labelled hydrocarbons
and the contaminant responsible for the photolytic OH. We
found virtually no measurable prompt OD signal. The total
pressure in the chamber was controlled by partially throttling
the diffusion pump. It was typically in the range 100–250 mTorr,
stressed above, this has only been reported once previously
yet remains the benchmark for comparison with rigorous
4
theory. The use of CD eliminates a significant source of
experimental interference as will be explained further below.
A second aim of the current work is to shed further light on
electronic aspects of the reaction. It has been widely noted
previously that the electronic fine-structure states of the open-
2
shell OH(X P) product are unequally populated. We have
carried out a systematic study of this branching for both iso-
topomers of both reactions (1) and (2). This includes, for the
2
made up of a 50:50 mixture of NO and hydrocarbon reactant.
9
The photolysis and probe laser beams counter-propagated
through the chamber. The entrance and exit arms were fitted
with Brewster-angle windows and internal baffles to reduce
scattered laser light. One of the main technical changes was
that the photolysis light was provided by the 4th harmonic of a
Nd:YAG laser (Continuum SLII-10) at 266 nm. Typical
photolysis pulse energies were around 40 mJ.
9
In previous work we had used either shorter (248 nm) or
longer (308 nm, 337 nm) excimer or N laser wavelengths. The
2
implications of 266 nm photolysis for the collision energy
distributions are shown in Fig. 1. These must necessarily be
estimated because, as far as we are aware, there have been no
direct measurements of the kinetic energy release for photo-
2
lysis of NO at this wavelength, nor indirectly of the internal
state partitioning in the co-product NO. For the purposes of
presentation in Fig. 1, we have assumed two scenarios for this
NO distribution. In one, we have assumed that it is similar to
3
2
that which has been measured at 248 nm, but curtailed by the
reduction in the total energy available in the photolysis. The
measured distribution at 248 nm apparently has a secondary
maximum at NO n ¼ 0, corresponding to a component of
3
relatively fast O( P) atoms. This component is not observed at
3
3
longer photolysis wavelengths in the same band. Since it is
not clear whether it would be present at 266 nm, we have also
presented an alternative distribution in which a relatively low
NO n ¼ 0 population was imposed by extrapolating smoothly
the populations in the higher levels. Having defined the NO
vibrational populations, the corresponding centre-of-mass
Fig. 1 Reaction energetics. The bold lines in the centre of the figure
3
are schematic reaction coordinates for O( P) þ CH
4 4
=CD (solid lines)
12 (dashed lines). Individual OH and OD pro-
rotational manifold in each
and cyclo-C
6
H12=C
6
D
3
0
duct N levels are indicated for the F
1
O( P) þ hydrocarbon collision energy distributions were
product vibrational level. Spin-orbit and L-doublet splittings are not
shown. The distributions to the left, referred to the top axis, illustrate
the centre-of-mass collision energy distributions following 266 nm
obtained using standard expressions which account for the
2
kinematics and the thermal motions of the NO precursor and
34
hydrocarbon reactants.
photolysis of NO
are made about the distribution in the co-product NO. O( P) þ CH
with (solid line) and without (dotted line) a peak at NO n ¼ 0.
6
H12: with (dashed line) and without (dot-dashed line)
2
. As discussed in the text, two different assumptions
3
The tuneable probe laser light was provided by a Nd:YAG-
laser pumped dye laser system (Spectron Laser Systems,
SL803S þ SL400G þ SL400EX). It was not necessary to avoid
optical saturation because of the comparative method used to
4
:
3
O( P) þ cyclo-C
a peak at NO n ¼ 0.
4
74 Phys. Chem. Chem. Phys., 2002, 4, 473–481

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calibrate the effective linestrengths described below, so pulse
energies up to 2–3 mJ were used to maximise LIF signals.
Fluorescence was collected by a short focal length fused
silica lens mounted perpendicular to the mutual laser axis.
There were several sources of undesired background signals. In
addition to scattered light from the photolysis and probe laser
beams, there was a strong photolysis-laser induced signal from
the NO2 precursor. This was most probably caused by an
accidental double-resonance process in which vibrationally
excited NO formed in the photolysis step was excited by
absorption of a second 266 nm photon on the NO A–X (1,5)
longer delay. The timing of the second spectrum was chosen to
be as early as possible consistent with achieving adequate
signal-to-noise. Values of 150 ns and 300 ns were used for
cyclo-C H
6
and CH , respectively, in conjunction with
4
12
respective total pressures of 100 and 200 mTorr. In each case
the 50 ns spectrum was subtracted from the later spectrum,
leaving only the OH formed bimolecularly in the intervening
period of 100 or 250 ns, respectively. As a check, spectra were
recorded for cyclo-C H12 with the slightly higher pressures and
6
longer delays used for CH . The OH populations were found
4
to be not significantly degraded from their more assuredly
nascent values at shorter times.
0
0
band. This resulted in strong emission on the NO A–X (1, n )
bands. The most inconvenient of these are the (1,8) and (1,9)
bands that happen to fall in the same region as the OH diag-
onal bands. Two different methods were attempted to isolate
the desired probe-laser induced fluorescence signal from the
background signals. At the expense of lower throughput but
with greater discrimination, the fluorescence was collimated
and refocused on the entrance slit of a monochromator (Hilger
and Watts, Monospek 1000, 1m focal length). Alternatively,
0
For OH(n ¼ 1), there was further interference from a LIF
signal excited accidentally by the probe laser from nascent NO
2
produced in the NO photolysis. The NO B-X (0,7) and (0,8)
bands partially obscure the longer wavelength region of the
OH A-X (2,1) band, restricting the lines that could be used in
the analysis.
In contrast, the OD LIF signal was found to be effectively
free from any photolytic contributions. It was therefore suffi-
9
more similar to our previous work but with a new custom
6 4
cient for cyclo-C D12 and CD to record spectra at respective
filter designed to optimise discrimination between signal and
background, the collimated light was passed through an
interference filter before being refocused and detected.
photolysis-probe delays of 100 and 200 ns and total pressures
of 100 and 250 mTorr. These contained essentially only reac-
tively produced OD.
In either case the transmitted light was detected by a pho-
tomultiplier tube and the signal captured by a transient digi-
tiser (100 MHz, DSP 2001A). The digitiser was part of an
integrated data-collection and control system (CAMAC, IEE
For both OH and OD, a further spectrum was recorded in
parallel at a relatively long photolysis-probe delay of 20 ms.
Examples of the typical time evolution of the OD LIF spec-
4 6
trum are shown for CD and cyclo-C D12 in Fig. 2. We believe
5
83) under the control of a microcomputer. The most impor-
that under the long-time conditions, corresponding to several
tens of gas-kinetic collisions, the OH or OD rotational dis-
tribution is essentially completely thermalised. The nascent
distributions are generally not very substantially rotationally
excited and therefore only a modest amount of rotational
energy has to be transferred in collisions to achieve thermali-
sation. Rotational relaxation of OH is particularly efficient in
collisions with polyatomic partners such as methane or
cyclohexane, and so we believe several tens of gas-kinetic
collisions will be more than adequate. We are confident that
the majority of the OH has been present for a substantial
fraction of the total delay time because the reactivity of the
tant feature of this system was that it provided active control
of the delay between photolysis and probe lasers, which could
be cycled on a shotwise basis. This allowed, in particular, LIF
excitation spectra for different delays to be recorded in par-
allel, as discussed further below.
Reactants and the precursor were used as supplied, other
than the usual freeze–thaw cycling to removed dissolved air
from liquid samples. The manufacturers and stated purities
2 4 4
were NO (BOC, 98.3%); CH (BOC, 99.995%); CD (Eur-
isotop, isotopic purity 99.99%); cyclo-C H (BDH, 99%);
6
cyclo-C
12
6
D12 (Goss, isotopic purity 99.5%).
3
O( P) atoms declines rapidly as they lose translational energy
through collisions. The peak in the OH density, due to the
balance between production and fly-out and other loss
Results
The primary raw data were LIF excitation spectra excited on
the OH or OD –X off-diagonal (1,0) and (2,1) bands around
2
90 nm. Fluorescence was collected on the diagonal (1,1) and
2,2) bands in the region of 320 nm, isolated by either an
(
interference filter or a monochromator. For the significantly
populated ground-state N levels, the corresponding levels
2
accessed in the A
sociation for both vibrational levels of OD.
although the A S n ¼ 1 level state is unpredissociated below
N ꢀ 14, all rotational levels of n ¼ 2 are subject to predis-
sociation. This means that the (2,1) band would not normally
be considered ideal for determining OH ground state popula-
tions. The fluorescence quantum yield is reduced significantly
and in an N-dependent fashion, varying by a factor of ꢀ 2 over
the levels relevant to this study. However, because of the
relative method we have used to calibrate the effective line-
strengths (see below), this effect is automatically accounted for
in the analysis. We therefore persisted with the OH (2,1) band
0
þ
S
state lie below the onset of predis-
3
5–38
For OH,
2
þ
0
because of the convenience of collecting spectra for OH n ¼ 1
in the same region as the other product levels.
5
,9
Fig. 2 Representative time-evolution of OD A-X (1,0) LIF excitation
0
As noted above and seen in previous work, the photolysis
laser generates a significant prompt OH concentration which
3
spectra from the OD n ¼ 0 products of O( P) þ CD
4
(right panel, total
D12 (left panel, total pres-
3
pressure 400 mTorr) and O( P) þ cyclo-C
6
partially obscures the desired reactive product from CH
cyclo-C H . The photolytic contribution was eliminated
4
and
sure 80 mTorr). In each case, a sequence of three spectra are shown
with photolysis-probe delays of 50 ns (lower trace), 200 ns (middle
trace) and 20 ms (upper trace), respectively. The spectra have been
artificially offset for the sake of clarity.
6
12
operationally by recording a spectrum at a very short photo-
lysis-probe delay of 50 ns in parallel with one at a slightly
Phys. Chem. Chem. Phys., 2002, 4, 473–481
475

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processes, is correspondingly observed at a time considerably
earlier than that at which the thermal spectrum is measured.
Therefore, the ratio of prompt reactive to long-time thermal
signals provides a method of calibrating the effective line-
0
strengths as a function of N . It eliminates the need to rely on
calculated or previously measured linestrengths. No correc-
tions are required for the wavelength dependence of the
detection system in emission, differential optical saturation of
lines with different linestrengths, differential rates of collisional
2
þ
quenching, and, in the case of OH A S n ¼ 2, differential
rates of predissociation (see above). Because of deliberate
heavy optical saturation, the effect of any potential differential
alignment of the nascent population relative to the isotropic
thermal distribution would be substantially suppressed. In
addition, because the spectra were recorded in parallel on an
alternating shotwise basis, reactive product populations are
automatically corrected for drifts in the experimental condi-
tions such as photolysis and probe laser powers, gas compo-
sition and pressure, optical alignment, etc.
0
Fig. 3 Distributions as a function of rotational quantum number, N ,
0
3
in the F
1
manifold of OD reaction products. O( P) þ CD
4
! OD n ¼ 0
In practice, populations were extracted by using the program
3
0
0
3
LIFBASE to first simulate in the thermal spectrum the inten-
8
(circles); O( P) þ C
6
D
12 ! OD n ¼ 0 (squares) and OD n ¼ 1 (triangles).
sity of a particular line excited from a specific L-doublet, fine-
2
structure, rovibrational level of the X P state. The intensity of
0
CD
cyclo-C
4
. Both OD n ¼ 0 and 1 are significantly populated for
the equivalent line in the reactive spectrum was then simulated
by re-optimising the relevant population. The fractional thermal
population is known straightforwardly from the Boltzmann
distribution at room temperature. It may therefore be used with
the ratio of populations in the two simulations to calculate a
correctly calibrated relative population in the reactive spectrum.
By repeating the process for different lines the relative reactive
populations of the levels are built up. Statistics on the relative
populations were obtained from at least four independent
experimental runs and generally from several branches within
each spectrum, depending on the chance blending of lines.
This comparative method happens to be particularly well-
0
6
D
12 . We did not search for OD n ¼ 2. For CD
4
, only
0
OD n ¼ 0 is detectable at a level where rotational populations
0
could be derived. However, there was a very weak OD n ¼ 1
signal that just exceeded the noise level, from which we esti-
mate on the same assumption as above that the branching into
0
OD n ¼ 1 for CD
4
is ꢀ 0.06.
0
1
Fig. 3 illustrates the distributions over N for the F com-
ponent of OD in the significantly populated product levels.
The features of the OD rotational distributions mirror those
5
seen previously for CH
0
4
and cyclo-C
6
H
12 . The OD n ¼ 0
distribution is significantly hotter for CD4 than for cyclo-
C D . For cyclo-C D itself, the rotational distribution is
substantially colder in n ¼ 1 than in n ¼ 0.
3
6
12
6
12
0
suited to the O( P) þ hydrocarbon reactions because of the
0
characteristically cold rotational distributions. Our confidence
in it is reinforced by the fact that the relative intensities of the
lines in a single spectroscopic branch in the simulation generally
agreed within ꢀ 20% with those in the experiment. Never-
The average characteristics of the various OH and OD dis-
tributions are collected in Table 1, reflecting the qualitative
comments above. The uncertainties quoted only include the
statistical estimate of the precision and not the accuracy as it
might be influenced by systematic factors in the method of
extracting populations. For the sake of later discussion, in
each case we have equated the average energy in rotation to
that of a Boltzmann distribution. This allows the assignment
of a corresponding apparent temperature. We do not, of
course, expect a Boltzmann distribution to be a perfect
description of a dynamically produced population. If Boltz-
mann plots are constructed they are indeed moderately non-
0
theless, there was a practical limitation for the highest N levels.
Their fractional populations in the thermal spectra were too
small to allow the intensities of the lines to be assessed reliably.
0
0
For levels with N > 8 and 12 in n ¼ 0 of OH and OD, respec-
tively, we instead extrapolated the effective linestrengths
established for the lower lines. The observed variation with N
0
depended on whether the monochromator or interference filter
had been used to isolate the fluorescence, but was typically no
more than 20% of the last thermally calibrated line. The
0
interference filter data were more reliable for the higher N lines
because of the wider range of wavelengths detected in emission.
The distributions we have reported here are therefore a
Table 1 Average energies in rotation, hErot i, and equivalent Boltz-
mann temperatures, Trot , for observed OH and OD product vibra-
tional levels
0
synthesis of monochromator and filter data for lower N lines,
but exclusively filter data for the higher lines (which in any case
represent a very small fraction of the total product yield).
hEroti=cmÀ1a
a
Reaction
Product level
Trot=K
3
0
b
b
b
Rotational distributions
O( P) þ CH
4
OH n ¼ 0
322 ꢁ 32
464 ꢁ 48
563 ꢁ 68
376 ꢁ 18
197 ꢁ 18
347 ꢁ 12
200 ꢁ 8
3
0
b
O( P) þ CD
4
OD n ¼ 0
391 ꢁ 46
3
0
The OH rotational distributions were found to be similar to
9
those measured previously for CH
O( P) þ cyclo-C
6
H
D
12
12
OH n ¼ 0
260 ꢁ 12
137 ꢁ 12
241 ꢁ 8
139 ꢁ 6
0
OH n ¼ 1
4
initiated by 248 nm
photolysis of NO , and for cyclo-C H with either longer or
3
0
O( P) þ cyclo-C
6
OD n ¼ 0
2
6
12
0
3
shorter photolysis wavelengths (or other methods of O( P)
OD n ¼ 1
6
,7
0
production ). Both OH n ¼ 0 and 1 were readily observed
a
Quoted uncertainties represent 2s error limits (95% confidence in-
tervals) of the mean evaluated purely from the statistical variation in
at least four independent measurements. They do not include any esti-
mate of systematic uncertainties, which may exceed the statistical scat-
0
from cyclo-C
6
H
12 . Only OH n ¼ 0 could be detected for CH
4
.
We estimate from the level of baseline noise, and on the basis
that previous measurements of the branching for cyclo-C H
12
are correct, that the upper limit on the branching ratio into
6
b
0
6
–8
ter as discussed in the text. Values for OH and OD n ¼ 0 from CH
4
0
and CD , respectively, may have been slightly reduced by an inability
4
OH n ¼ 1 from CH
4
is 4 0.03.
More original are the OD distributions, which have not been
0
to observe populations in the next N level above the last observed level
due to spectroscopic blending.
investigated systematically for cyclo-C D12 and not at all for
6
4
76
Phys. Chem. Chem. Phys., 2002, 4, 473–481

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linear. Nevertheless, the temperature provides a single con-
venient measure of the extent of rotational energy release.
Although the qualitative trends with reactant and product
vibrational level are the same, we systematically find somewhat
lower absolute average energies in rotation for the OH products
9
than in our previous work. We doubt that any differences are
necessarily connected with changes in the photolysis wavelength
to 266 nm. It is more likely that they are related to different
procedures used to extract populations from the raw data.
More significant are the comparisons between OH and OD
within this study, where a common photolysis wavelength and
method of analysis were used. A very clear result is that the
rotational energy release is very similar for the OH and OD
products in a given vibrational level for a particular reactant.
This is reflected in the average values in Table 1. The agree-
ment is particularly convincing for cyclohexane, but we note
that there is a slight additional uncertainty in the averages for
CH and CD because of spectroscopic blending of lines for
4
4
0
the next N above the last observed level. Probably more
striking is the similarity of the distributions themselves. The
effect is illustrated in Fig. 4, where the various F
tributions are plotted as a function of rotational energy.
Fig. 5 Collected OH and OD fine-structure state ratios for both
isotopes and all observed product vibrational levels of reactions (1)
and (2). Identifying symbols as in Fig. 4.
0
1
(N ) dis-
towards Hund’s case (b), which would eventually lead to the
Fine-structure distributions
association of F
rotation interaction.
We have re-measured for confirmation purposes the F =F
1 2
and F labels with levels split by the spin-
As is very well known and has been widely discussed in this
2
and many other contexts, the open-shell nature of the X P
ground state of OH gives rise to two manifolds of rotational
1
2
6
–9
0
ratio reported several times previously
0
for OH n ¼ 0 from
0
cyclo-C
0
6
H
12 . Importantly, the N -dependence of this ratio for
levels, labelled F and F . At low values of N the angular
momentum coupling most closely approximates to Hund’s
case (a). In this limit the F and F manifolds correspond to
1
2
OH n ¼ 1 was further examined, expanding on the limited
6
previous data. Similarly, the single previously undeveloped
1
2
6
0
result for OD n ¼ 0 from cyclo-C D was extended, and the
6
12
the O ¼ 3=2 and 1=2 spin-orbit components, respectively. The
0
first data for OD n ¼ 1 obtained for this reactant. The mea-
surements are more challenging for the methane substrates
because of the poorer signal-to-noise. Nevertheless, we have
F state lies lower in energy. The splitting for the lowest level,
1
0
À1
39
N ¼ 1, is around 125 cm for OH, and only slightly higher
À1
40
131 cm ) for OD. With increasing N there is a progression
0
(
9
obtained confirmation of our single previous measurement of
0
the ratio for OH n ¼ 0 from CH
4
, and the first results of this
0
kind for OD n ¼ 0 from CD .
4
The results of this fairly extensive survey of the F
=F ratios
1 2
are collected in Fig. 5. The most striking feature is that, within
the statistical scatter, there is a general commonality of
behaviour. In all cases there is preference for the lower-lying F
1
0
component that declines steadily with N . A similar trend had
0
been seen previously for the OH n ¼ 0 products from various
5
hydrocarbons, but is now confirmed to extend to the higher
product vibrational level and to be essentially independent of
hydrogen isotope.
L-doublet populations
Each of the OH rotational levels within each spin-orbit
manifold is further split by L-doubling. The two components
0
00
have respective A and A reflection symmetries. In the limit of
high rotation, they correspond to the unpaired p-electron
density being in, or perpendicular to, the plane of rotation.
We have investigated the L-doublet ratios for different pro-
duct levels of the various reactants. This is illustrated in Fig. 6
0
for the F
1
(N ) components. The F
2
results are similar but more
scattered. This is partly because of the poorer signal-to-noise
associated with the lower F populations, but also because both
the OH and OD (1,0) Q branches happen to be extensively
2
2
blended. In no case was a systematic deviation from unity
5
identified, also agreeing with the previously available results.
Fig. 4 Product state distributions as a function of rotational energy
in the F manifold. Distributions have been normalised to have the
same area. Lower panel: OH and OD n ¼ 0. O( P) reaction with CH
open circles), CD (filled circles), cyclo-C 12 (open squares) and
cyclo-C
Discussion
1
0
3
4
(
4
6
H
Rotational energy distributions
0
3
6
D
12 (filled squares). Upper panel: OH and OD n ¼ 1. O( P)
6 6
reaction with cyclo-C H12 (open triangles) and cyclo-C D12 (filled
triangles).
The aim of confirming the trends in the OH mechanical
rotational distributions through isotopic substitution has been
Phys. Chem. Chem. Phys., 2002, 4, 473–481
477

View Article Online
parameter, the geometry at the classical turning point, angular
scattering, and OH rotational motion.
2
4
What Gonza
be divided roughly into two categories of ‘‘rebound’’ and
‘non-rebound’’. The rebound trajectories, as the name sug-
´
lez and coworkers find is that trajectories may
‘
gests, are predominantly back-scattered. This can be traced to
a tendency towards low impact parameters. As a consequence,
a high proportion of the initial translational energy may be
used to penetrate into repulsive regions of the potential. This
allows closer approach of the reactants and, more crucially,
reaction through energetically less favoured bent geometries.
The bending angle creates a torque during the impulsive
separation of the products that ultimately causes OH rotation.
In contrast, the non-rebound trajectories have character-
istically higher impact parameters, which makes them less
efficient in converting translational to potential energy. They
reach less repulsive regions of the potential, producing less
rotationally excited OH that is more forward scattered.
0
24
Fig. 6 Collected OH and OD L-doublet ratios in the F
both isotopes and all observed product vibrational levels of reactions
1) and (2). Identifying symbols as in Figs. 4 and 5.
1
manifold for
Gonzalez and coworkers calculations suggest that the
´
non-rebound trajectories only contribute significantly at rela-
tively high collision energies. At our typical experimental
energies, they predict that rebound trajectories would be
strongly dominant. On this basis, we now present a simplified
analysis of the effects of isotopic substitution on the assump-
tion that OH rotation derives entirely from impulsive energy
release via a modestly bent geometry, to see if it is consistent
with the experimental observations.
(
successfully achieved. The OD distributions reproduce the
qualitative features of those for OH which have been more
5
widely measured for the higher hydrocarbons, but, as we have
9
stressed, only once previously for the parent compound CH
4
.
The distributions are all characteristically cold, but with
H
In this limit, the initial recoil velocity, n , imparted to the
0
noticeably more rotational energy release into OD n ¼ 0 for
hydrogen atom as it is repelled by the radical fragment, R, is
simply derived from energy and linear momentum conserva-
tion:
4 6
CD than for cyclo-C D12 . This is despite the converse trend
in the exothermicity, as shown in Fig. 1. The same effect for
OH products has been interpreted previously as a stereo-
ꢀ
ꢁ
9
dynamical effect, related to a wider cone of acceptance for
1=2
2mRE
vH ¼
ð3Þ
abstraction of a hydrogen atom from the sterically less-crow-
ded methane molecule. The trend towards lower rotational
m m
H
HR
6
–9
i
E is the energy being released repulsively and m are the masses
energy release in the higher vibrational level seen previously
for normal cyclo-C H is also reproduced in the results for
of the various fragments. Since m
R
=mHR ꢂ 1, it can be seen that
6
12
the hydrogen atom velocity is approximately inversely propor-
tional to the square root of the mass of the isotope involved.
The rotational angular momentum that this generates as the
H atom attaches to the O atom is
6 12
cyclo-C D .
Our principal new quantitative result on the rotational
branching is that the absolute rotational energy release is
almost independent of isotope for a given reactant and
hydroxyl product vibrational level. The average values in
Table 1 and especially the distributions in Fig. 4 illustrate this
point. To a reasonable approximation it will also be true that
the fraction of the available energy being converted to
hydroxyl rotation is similarly independent of isotope. Isotopic
substitution has only a modest kinematic effect on the centre-
of-mass collision energy. Its effects on the reaction exother-
micity are also quite small relative to the average energy of
reactants crossing the barrier, as shown in Fig. 1. This shift
ꢀ
ꢁ1=2
mHmO
mOH
2mRE
jOH ¼ mOHvHbeff
¼
beff
ð4Þ
mHmHR
where beff is an effective impact parameter or lever arm that
depends only on the O–H–R angle. Given that m =m is also
1, the OH angular momentum is approximately directly
proportional to the square root of the mass of the hydrogen
isotope.
Finally, the OH rotational energy is
O
OH
ꢀ
0
is largest for n ¼ 1 products (only characterised from cyclo-
ꢀ
ꢁ
2
Eb 2e ff
hexane), but this appears not to perturb significantly the
rotational energy release.
rot
OH
jOH
mOmR
E
À
¼
ð5Þ
2
OH
2
OH
2mOH
r
mOHmHR
r
It is interesting to consider how this new information on
isotope effects reflects on the accepted mechanism for the
where rOH is the OH bond length. The approximately linear
3
2
O( P) þ hydrocarbon reactions. As noted in the Introduction,
dependence of both jOH and mOH on m
energy that is approximately independent of the mass of the
hydrogen atom. Taking the specific case of O þ CH versus
(and noting that the mass of the R fragment also
H
leads to a rotational
the characteristically cold rotational distributions have been
interpreted as strong evidence for an abstraction mechanism
through predominantly collinear geometries. Among other
things, the observed lack of an experimental OH L-doublet
preference is also consistent with this conclusion. All levels of
ab initio calculation support such a preferred geometry. The
most recent theoretical examination of the nuclear dynamics is
4
O þ CD
4
changes slightly because of the substitution of the non-reactive
hydrogen atoms), eqn. (5) predicts that the OH rotational
energy should be only 10% higher than for OD. This figure is
even smaller at 7% for the O þ cyclo-C
6 6
H12 and C D12 pair.
2
4
that of Gonza
´
previous discussions.
lez and coworkers, who have expanded on
5
We conclude therefore that an impulsive abstraction
mechanism does appear at least qualitatively consistent with
our experimental observation of a lack of a significant
dependence of the hydroxy rotational energy on hydrogen
isotope. Admittedly we have used a rather crude model and
it would be desirable to test this conclusion more rigorously
through scattering calculations on the available potential
,10,17
They used a QCT approach on a
model O–H–(CH ) pseudo-triatomic surface deduced from
3
their full-dimensional ab initio electronic structure calcula-
tions. From the point of view of predicting the likely effects of
isotopic substitution on rotational energy release, the most
critical feature of their analysis is the interplay between impact
4
78
Phys. Chem. Chem. Phys., 2002, 4, 473–481

View Article Online
2
2
surfaces. Although Palma and Clary
3
have included
O( P) þ CD in their latest reduced dimensional quantum
4
scattering calculations, their treatment did not include a pre-
diction of product rotational partitioning. There are also
currently no classical trajectory results available for CD
would be an interesting test to see if the relatively successful
4
. It
1
7
prediction of the OH rotational distribution for normal CH
could be repeated for CD on the Gonzalez and coworkers
4
´
4
surface.
Clearly, identifying that the OH and OD rotational dis-
tributions are equivalent in terms of energy amounts to saying
that they are not the same in terms of angular momentum.
There are therefore other conceivable mechanisms in which the
OH rotation would not be independent of isotope, but which
are excluded by the observations. For example, a stripping
mechanism in which the OH rotation derived primarily from
conversion of a fixed proportion of reactant orbital angular
momentum, l, to product rotation, j’, would fall into this
category.
3
It has been noted previously that the O( P) þ hydrocarbon
reactions share a close resemblance with some aspects of the
2
9,10
corresponding Cl( P) þ hydrocarbon reactions.
Sub-
stantially more dynamical insight has been gained into the
2
41
Cl( P) reactions, as detailed in a recent review by Valentini.
For reaction with the vibrational ground state of methane, the
mechanism has been concluded
relatively low-impact parameter collisions with near-collinear
4
1,42
to be direct abstraction via
geometries. This is clearly reminiscent of the mechanism pro-
3
Fig. 7 Degeneracy-weighted OH and OD fine-structure state dis-
3
posed above for O( P) þ CH
4
. The effects of isotopic sub-
stitution on the rotational distributions of the HCl and DCl
tributions from O( P) þ cyclohexane, reaction (2). Lower panel: OH
0
and OD n ¼ 0; cyclo-C
6
H
12 (open squares) and cyclo-C
6
D12 (filled
0
2
42
squares). Upper panel: OH and OD n ¼ 1; cyclo-C H (open trian-
6
12
products of Cl( P) þ CH
4 4
and CD have also been measured.
6
gles) and cyclo-C D12 (filled triangles). In both panels, the experi-
Reassuringly, the HCl and DCl absolute rotational energies are
also very similar, further consistent with similar abstraction
mental results (with error bars) are joined by solid lines. Predictions on
the basis of equivalent Boltzmann rotational temperatures, as dis-
cussed in the text, are joined by dotted lines.
2
mechanisms operating for Cl( P) and O( P) with methane. We
3
2
note also that the Cl( P) studies
30,43
have uncovered a con-
tribution to reaction from thermally excited bending and tor-
sion vibrational states. This cannot be excluded as a possibility
Fig. 7 how different the observed F =F ratios are from those
1
2
3
in the current studies on O( P) reactions, particularly since
that would have been observed if they had been simply a facet
of the overall mechanical rotational energy release. As dis-
cussed above, each of the experimental product rotational
distributions is reasonably well characterised by an equivalent
1
9–23
reduced dimensional quantum scattering calculations
3
predict strong vibrational enhancements for O( P) þ CH
4
.
1 2
Boltzmann temperature (Table 1). The F =F ratios that would
Fine-structure state partitioning
be expected on the basis of these temperatures have been
0
As in previous work on hydrocarbons containing normal
5
hydrogen, we see a clear preference for the F fine-structure
state of the OH product. This is confirmed systematically for
the first time to apply to OD products from deuterated
hydrocarbons. The quality of the data for cyclohexane is also
included in Fig. 7. For OH and OD n ¼ 0 products, the pre-
1
dicted F =F ratios moderately exceed the observed values. In
1
2
0
contrast, for n ¼ 1 the predicted ratio is much too high, lying
well beyond any experimental uncertainty.
We conclude therefore that the product spin–orbit branch-
ing is clearly decoupled from the factors that determine the
deposition of mechanical rotational energy. This lends support
to the proposition that this branching is a truly electronic
effect, with a potential explanation lying in the coupling of
adiabatic electronic surfaces. This idea was first proposed in
significantly improved. This allows a confident identification of
0
a systematic decline with N in the F
1
=F
2
ratio, for both OH
and OD, even after the correction for the different spatial
0
degeneracies of F
1
and F
2
levels sharing the same N has been
applied. The data are presented in this form in Fig. 7.
A principal question we are attempting to address is whether
the fine-structure state partitioning is a reflection of the same
factors as those that govern the product nuclear framework
rotation. If these were the same factors, a particular product
level should receive its share of the population only on the
basis of its energy and degeneracy, independent of spin–orbit
manifold. Because, as discussed above, the OH and OD
rotational energy release are almost identical for a given
vibrational manifold, the observed similarity of the OH and
OD fine-structure state partitioning does not happen to help
resolve this question.
6
the original work of Andresen and Luntz, but has subse-
2
5
quently been refined and developed.
2
5
The essence of the later models is summarised in Fig. 8. A
collinear geometry is assumed, justified by the low levels of
rotational energy release as discussed above. The entrance
3
channel surfaces correlate with the distinct O( P ) fine-struc-
j
3
ture states. Only the degenerate P surface is reactive, with the
3
À
S
filled p-orbital towards the hydrocarbon. The OH product
surface corresponding to an unfavourable orientation of a
3
fine-structure surfaces similarly correlate with the reactive P
1
surface and an unreactive P surface. The product state par-
titioning is predicted by projecting the flow of population from
Much more incisive is a careful comparison of the fine-
structure state partitioning in the different product vibrational
3
the initial O( P ) states through intermediate surfaces to the
j
0
levels. The rotational distributions in OH and OD n ¼ 1 are
OH products.
As we have shown previously, the prediction on the
0
25
much colder than those in n ¼ 0 (see Fig. 4 and Table 1).
However, the fine-structure state partitioning in all of these
levels is essentially the same (Fig. 5). We attempt to illustrate in
assumption of purely adiabatic behaviour is in poor agreement
with experiment. Consequently, we examined the probability
Phys. Chem. Chem. Phys., 2002, 4, 473–481
479

View Article Online
is also invalid if the products are significantly aligned and
therefore don’t span all mJ levels equally. On dynamical
grounds this is more probable as product rotation increases,
although it is also true that the degeneracy correction then
becomes less significant.
Caution should clearly be exercised not to over-interpret the
apparent success of the model because it has still only been
possible to compare it against what is essentially a single
experimental observation. The question of whether this really
reflects a residual memory of the entrance channel populations
would be more incisively tested if these could be varied inde-
pendently. That has not yet been achieved experimentally. As
4
8
has been discussed recently by Brouard and coworkers, there
are other reactions, such as H þ N O, H O and CO , for
2
2
2
which there are no fine-structure splittings in the entrance
channel but which nevertheless produce a similar F preference
in the OH product. These must, by definition, be controlled by
1
4
exit-channel effects. Brouard et al. deduce that the results
8
imply partially non-adiabatic behaviour, lying between fully
4
9
adiabatic and fully scrambled (suddenly recoupled ) limits.
We therefore thoroughly agree that a single observation of
product fine-structure state partitioning is not a very incisive
indicator of entrance channel mixing. Nevertheless, if partially
non-adiabatic behaviour is observed in the exit channel of
reactions for which it is excluded in the entrance channel, it is
reasonable to expect that it may take place in both entrance
and exit channels for reactions where both possibilities exist.
3
This is just the case for the O( P) þ hydrocarbon reactions,
2
5
as has been included in our model. A theoretical resolution
3
of this question for systems such as O( P) þ CH
4
may well
3
Fig. 8 Fine-structure correlations in the reaction of O( P) with a
have to wait for future developments of the rigorous ab initio
methods just beginning to be applied to model three atom
hydrocarbon (assumed cylindrically symmetric) via a collinear geo-
metry. Upper panel: fully adiabatic correlations. Lower panel: partially
non-adiabatic correlations, with mixing of surfaces (indicated by
broken lines) which have the same parity and projection of total
electronic angular momentum, O.
2
6,27
systems such as Cl and F þ H2 .
Conclusions
of kinetically induced coupling of the surfaces. There was
independent information available on the coupling strengths of
entrance-channel surfaces from magnetically selected mole-
cular beam scattering measurements of total elastic cross-sec-
New dynamical experimental results have been obtained for
3
the reaction of O( P) þ deuterium-substituted hydrocarbons
CD and cyclo-C D12 . These have successfully confirmed the
4 6
main features of hydroxyl radical rotational energy release
observed here, and previously, for normal hydrogen com-
pounds.
4
4
tions. There was also evidence of consistent propensity rules
4
5
in j-changing inelastic collisions. On this basis we proposed
25
that there should be effectively complete non-adiabatic mixing
of populations on surfaces sharing the same parity and value
of O, the projection of the total electronic angular momentum
onto the collinear axis.
The rotational energy release is found to be essentially
independent of the hydrogen isotope for all observed OH and
OD product levels of both reactions. This fits in with the
accepted mechanism for the reaction involving a direct, near-
collinear abstraction, with the product rotation determined
primarily by the geometry at the point of repulsive energy
release.
The fine-structure state partitioning is found to be inde-
pendent of isotope and, significantly, of OH or OD product
vibrational level. This implies that the determination of fine-
structure populations is decoupled from the factors controlling
mechanical rotational energy release. It appears consistent
with a previously derived model that includes selected non-
adiabatic couplings between adiabatic fine-structure surfaces.
4
6,47
Adopting the available experimental values
of the initial
photolysis in the relevant elec-
tronic band (which, if anything, should apply better at 266 nm
3
j 2
O( P ) populations from NO
4
6
25
where they were measured ), we predicted an OH F
ratio of 1.72. This is encouragingly comparable to, although
1
=F
2
0
exceedingly slightly on average, the limiting low N degen-
eracy-corrected values for different product vibrational levels
and isotopomers of cyclohexane in the new results in Fig. 7.
The similar values for different product vibrational levels, as
observed experimentally, is also compatible with the model
because it does not distinguish between them. Furthermore,
none of the assumptions in the model would suggest that OH
and OD should differ, at least in the limit of rotationless
2
5
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