The dynamics of the Cl+n-C4H10→HCl( v′, j′) + C4H9 reaction at 0.32 eV

Article abstract of DOI:10.1063/1.1792593

Rotational state resolved center-of-mass angular scattering and kinetic energy release distributions were analyzed from experimental velocity-map ion images of the HCl (v′=0, j′=0-6) products of the reaction of chlorine with n-butane. It was shown that th

Full text of DOI:10.1063/1.1792593

The dynamics of the Cl +n- C 4 H 10 → HCl (v ′ ,j ′ )+ C 4 H 9 reaction at 0.32 eV
M. J. Bass, M. Brouard, C. Vallance, T. N. Kitsopoulos, P. C. Samartzis, and R. L. Toomes
Citation: The Journal of Chemical Physics 121, 7175 (2004); doi: 10.1063/1.1792593
View online: http://dx.doi.org/10.1063/1.1792593
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/121/15?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 15
15 OCTOBER 2004
The dynamics of the Cl¿n-C H \HCl„v ,j …¿C H
Ј Ј
4
10
4
9
reaction at 0.32 eV
M. J. Bass, M. Brouard, and C. Vallance
The Physical and Theoretical Chemistry Laboratory, The Department of Chemistry, University of Oxford,
South Parks Road, Oxford, OX1 3QZ, United Kingdom
T. N. Kitsopoulos, P. C. Samartzis, and R. L. Toomes
Department of Chemistry, University of Crete, 714 09 Heraklion, Greece and Institute of Electronic
Structure and Laser, Foundation for Research and Technology-Hellas, 711 10, Greece
͑Received 1 June 2004; accepted 22 July 2004͒
Rotational state resolved center-of-mass angular scattering and kinetic energy release distributions
have been determined for the HCl ( ϭ0, j ϭ0–6) products of the reaction of chlorine with
v
Ј
Ј
n-butane using the photon-initiated reaction technique, coupled with velocity-map ion imaging. The
angular and kinetic energy release distributions derived from the ion images are very similar to those
obtained previously for the Cl plus ethane reaction. The angular distributions are found to shift from
forward scattering to more isotropic scattering with increasing HCl rotational excitation. The kinetic
energy release distributions indicate that around 30% of the available energy is channeled into
internal excitation of the butyl radical products. The data analysis also suggests that H-atom
abstraction takes place from both primary and secondary carbon atom sites, with the primary site
producing rotationally cold, forward scattered HCl ( ϭ0) products, and the secondary site
v
Ј
yielding more isotropically scattered HCl ( ϭ0) possessing higher rotational excitation. The
v
Ј
mechanisms leading to these two product channels are discussed in the light of the present findings,
and in comparison with studies of other Cl plus alkane reactions. © 2004 American Institute of
Physics. ͓DOI: 10.1063/1.1792593͔
I. INTRODUCTION
straction from a secondary carbon atom over the temperature
range of 295–470 K.17 The different behavior was proposed
to arise from the formation of a weakly bound complex dur-
ing abstraction of a secondary H atom. A preference for ab-
straction of an H atom from secondary carbon atoms over
primary carbon atoms was observed in the relative rate ex-
periments carried out by Tyndall et al.14 and Sarzynski and
Sztuba.17 In both experiments, 29% of the butyl products
were found to result from abstraction of a primary H atom,
and 71% from abstraction of a secondary H atom.
A key feature of the reactions of chlorine atoms with
alkanes containing more than two carbon atoms is the avail-
ability of several reaction pathways, namely, abstraction of a
hydrogen atom from a primary, secondary, or tertiary carbon
atom. It is therefore of interest to investigate the reactivities
of these sites, and the reaction dynamics associated with the
different chemical channels. The reaction of atomic chlorine
with n-butane (n-C4H10) can proceed via two pathways:
Clϩn-C4H10→HClϩCH2CH2CH2CH3
In contrast to the kinetic work, to date the dynamics of
the two reactive pathways have not been examined. Ab initio
calculations on the transition state geometries of the Cl plus
propane and Br plus propane and n-butane reactions at both
primary and secondary carbon sites show a near collinear
X-H-C arrangement ͑where X is Br or Cl͒,19,20 suggesting
that the Cl plus n-butane reaction is likely also to be charac-
terized by a near-linear transition state. By virtue of this, the
dynamics of abstraction of a primary ͑and possibly second-
ary͒ H-atom from n-butane are anticipated to be similar to
those for H-atom abstraction from ethane.21
At collision energies Շ0.5 eV, the HCl products of the
abstraction reactions of Cl with a variety of alkanes are
found predominantly in the ground vibrational state and are
rotationally cold.22–26 The products of abstraction from a
secondary or tertiary carbon atom are generally more rota-
tionally excited than those formed by abstraction from a pri-
mary carbon site.23–26 Abstraction from secondary and ter-
tiary carbon atoms is found to be favored by a factor of 2–3
␪
⌬rH0ϭϪ8.4Ϯ2.1 kJ molϪ1
,
͑1͒
→HClϩCH3CHCH2CH3
␪
⌬rH0ϭϪ23.1Ϯ2.1 kJ molϪ1
.
͑2͒
The different exothermicities1–4 of reactions ͑1͒ and ͑2͒ sug-
gest that the dynamics of the competing pathways may be
investigated by quantum state selective measurements of the
scattering of the HCl ( , j ) products.
v
Ј Ј
There have been numerous kinetic studies of the reaction
of chlorine atoms with n-butane.5–17 The recommended
value of the absolute rate coefficient is (2.05Ϯ0.07)
ϫ10Ϫ10 cm3 moleculeϪ1 sϪ1, independent of temperature
over the range 290–600 K.18 In recent relative rate experi-
ments using gas chromatographic product analysis, Sarzyn-
ski and Sztuba found a weak negative temperature depen-
dence for abstraction of H atoms from a primary carbon
atom, and a weak positive temperature dependence for ab-
0021-9606/2004/121(15)/7175/12/$22.00
7175
© 2004 American Institute of Physics
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7176
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
Bass et al.
over the statistical ratio of primary to secondary or tertiary
atoms.23–26
allows determination of both the c.m. angular scattering and
kinetic energy release distributions of the products. The simi-
lar analytical procedures employed here, described briefly in
Sec. II B, allow determination of the HCl rotational quantum
state resolved differential cross-sections, the internal excita-
tion in the butyl coproducts, and the relative reactivity of the
n-butane to primary and secondary H atom abstraction.
These results are presented in Sec. III, while in Sec. IV and
V we discuss our findings in the context of previous work on
the Cl plus alkane reactions, and present our final conclu-
sions.
Photon initiated ͑photoloc͒ experiments24–26 on a variety
of Cl plus alkane reactions have tended to assume that the
systems may be approximated to three-body reactions, im-
plying that internal modes of the alkyl fragments are not
excited. Within this approximation, the products of abstrac-
tion from primary carbon sites are seen to be more forward
scattered than the products of abstraction from secondary or
tertiary sites. Suits and co-workers have studied the reactions
of chlorine with propane27 and n-pentane28 at a series of
collision energies using a crossed molecular beam apparatus.
In the former case the scattered propyl radical products were
detected using 9.5 eV vacuum ultraviolet synchrotron radia-
tion coupled with quadrupole TOF mass spectrometry of the
resulting ions. The center-of-mass ͑c.m.͒ angular scattering
distribution was seen to be nearly isotropic, with a peak in
the forwards direction and a smaller peak in the backwards
direction. The propyl products were found to be more for-
ward and sideways scattered with increasing collision en-
ergy. Interestingly, these studies also suggest that, at the low-
est collision energy, 40%–50% of the available energy is
partitioned into the internal degrees of freedom of the
products.27,28 Based on the low rovibrational excitation ob-
served by Varley and Dagdigian in the HCl products of the
Cl plus propane reaction at a similar collision energy,25 it
was concluded that most of the available energy must be
channeled into internal modes of the propyl radical products,
and therefore that these fragments cannot be considered as
spectators in the reaction.27,28
II. METHOD
A. Experimental procedures
The experiments were performed using the ion imaging
apparatus at the Institute for Electronic Structure and Laser
in Crete, which has been described in detail elsewhere.30,31 A
1:1 mixture of Cl2 and n-butane stored in a glass bulb at a
backing pressure of ϳ600 Torr was coexpanded in a pulsed
molecular beam using a homemade piezoelectric nozzle with
a 1 mm orifice operating at 10 Hz. Standard velocity-
mapping ion optics32 were mounted directly in front of the
nozzle, with the nozzle and the repeller plate maintained at
the same voltage to avoid electrical discharging during the
gas pulse.
Midway between the repeller and extractor plates the
molecular beam was intersected at right angles by the
counter-propagating radiation from two lasers. Photolysis of
Cl2 at 355 nm using the third harmonic output of a Nd:
͑YAG͒ laser ͑ϳ20 mJ per pulse͒ afforded nearly monoener-
The Cl plus n-butane reaction has recently been studied
at 0.32 eV by Toomes and Kitsopoulos using an unskimmed
crossed beam technique.29 Angular scattering distributions
were extracted from the returned images by direct integration
of the raw data over velocity. Unlike forward convolution
methods, this approach does not take into account the differ-
ing sensitivities to forward and backward scattered products
or the speed distribution of the Cl atoms. Differentiation be-
tween the two available reaction pathways was thus not pos-
getic ground state Cl (2P3/2) atoms traveling at 1675 msϪ1
.
Assuming that the relative motion between the molecular
chlorine precursor and butane is small, due to efficient trans-
lational cooling in the jet expansion, the photolysis defines
the relative motion of the chlorine atom and the butane mol-
ecule, yielding a mean collision energy of 0.32 eV with a full
width at half maximum of 0.06 eV. The spread is due to
residual thermal motion of the precursor and reagent, and
was calculated using an estimated translational temperature
of 50 K, based on probe-only images of background HCl
͑Ref. 33͒ ͑see below͒.
sible. The HCl ( ϭ0, j ϭ1–4) products were found to be
v
Ј
Ј
predominantly forward scattered, while the HCl ( ϭ0, j
v
Ј
Ј
ϭ5) products were more isotropically scattered. The scatter-
ing dynamics observed for the Cl plus butane reaction were
found to be very similar to that for Cl plus ethane. Given this
fact, coupled with the results of earlier work by Varley and
Dagdigian,24–26 which indicated that both primary and sec-
ondary or tertiary hydrogen abstraction processes contribute
to most of the product HCl/DCl rotational states, it was con-
cluded that the primary or secondary nature of the H atom
abstracted exerts little influence over the scattering dynamics
in the Cl plus n-butane reaction.29
In the following paper, we describe the results of a pho-
toloc study of the title reaction in which the HCl products
have been probed by velocity map ion imaging. The experi-
mental work, performed in Crete and described in Sec. II A,
uses the same apparatus as that employed in our earlier study
of the Cl plus ethane reaction.21 In that work, velocity-map
ion images of the HCl products of the photon-initiated reac-
tion were analyzed using a moment expansion method which
The HCl ( ϭ0) products were detected with rotational
v
Ј
state-resolution via ͑2ϩ1͒ resonantly enhanced multi photon
ionization ͑REMPI͒, either through the Q branch of the
E(1⌺ϩ) state34–36 for j ϭ0–5, or through the R branch of
Ј
the F(1⌬2) state34–36 for j ϭ1, 3 and 6. The probe radiation
Ј
was generated using the frequency-doubled output of a
Nd:YAG pumped optical parametric oscillator ͑Spectra-
Physics Pro 250, MOPO͒ with a typical pulse energy of ϳ1
mJ. For each transition the probe laser was scanned over the
Doppler profile of the HCl product. Both photolysis and
probe laser beams were linearly polarized in the plane of the
detector and were focused using 25 cm focal length lenses.
The timing of the experiment was controlled using digital
delay pulse generators ͑SRS DG535͒. A short delay of be-
tween 120 and 150 ns between the photolysis and probe laser
pulses allowed sufficient HCl product density to build up
prior to detection. Due to the narrow focus of both laser
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J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
The Clϩn-C4H10→HCl (vЈ,jЈ)ϩC4H9 reaction
7177
beams, care was taken to ensure that fly-out was avoided ͑see
Sec. III͒. Suitable electrostatic potentials applied to the re-
peller and extractor plates of the ion optics effected velocity
mapping32 of the ionized reaction products onto the detector
͓a pair of matched MCPs ͑Hamamatsu͒ coupled to a P46
phosphor anode ͑Proxitronic͔͒. H35Clϩ ions were detected
mass selectively by pulsing the voltage applied to the MCPs
from Ϫ1100 V to Ϫ1600 V at the appropriate time of flight.
The resulting images were captured using a charge coupled
device camera ͑Cohu 4910͒ and sent to a PC for signal av-
eraging ͑EYESPY Software by k-Space Associates͒.
As discussed previously,21 velocity calibration of the ion
images was achieved by direct detection of the Cl (2P3/2
)
photofragments from Cl2 photolysis at 355 nm via the
4p 4P3/2 2P3/2 transition at 240.46 nm.37 Cl images were
obtained under similar time-delay and molecular beam inten-
sity conditions to those used for the studies of the Cl plus
ethane and Cl plus butane bimolecular reactions. The radial
coordinate of the resulting images could be transformed di-
rectly into velocity using the known single velocity of the Cl
photofragment.38,39 Direct Abel inversion of the Cl images
allowed determination of the speed resolution of the appara-
tus, which was found to be ϳ6%.21 The Abel-inverted image
yielded a translational anisotropy parameter, ␤0 , close to
Ϫ1.0 for the photodissociation process, suggesting that col-
lisional scrambling of the Cl velocity distribution prior to
reaction is unlikely to be a serious problem in the present
experiments.21
FIG. 1. ͑a͒ Background subtracted images and ͑b͒ Legendre moments of
order 0 ͑
͒, 2 ͑
͒, and 4 ͑¯͒ for HCl
ϭ0, j ϭ1 ͑top͒, 3
͓vЈ
Ј
͑middle͒, and 6 ͑bottom͔͒. The error limits on the experimental Legendre
Acquisition of ion images of reactively scattered HCl
was complicated by the presence of a cold background HCl
signal arising from unwanted side reactions in the gas lines.
This background signal was observed as a bright spot in the
center of the HCl images, which could be minimized by
using fresh gas mixtures every Ϸ3 h. Probe-only images of
the background HCl were obtained after collection of each
signal image and were subtracted from the signal images.
However, since the background subtraction is imperfect ͑see
Fig. 1͒, this central portion of the image was not used in the
data analysis. It should be stressed that the region of the
image obscured by the cold background signal corresponds
to backward scattering of the HCl products with about half
of the energy appearing as c.m. kinetic energy, and we do not
believe this missing region of data significantly impairs the
analysis.
moments of the images lie in the range 6%–14% for j ϭ0 to j ϭ6, as
discussed in the Sec. II B.
Ј
Ј
tional kinetic energy release ft can be written as a Legendre
polynomial expansion
dft
P ␪,w͒ϵP ␪, f ͒
͑
͑
ͯ ͯ
t
dw
dftЈ
1
ϭ
a
nmPn cos ␪͒P fЈ͒
,
͑3͒
͑
͑
ͯ ͯ
͚
m
t
4 n,m
dw
where w is the c.m. speed of the HCl,
fЈϭ 2f Ϫ1͒,
͑
t
t
and
dftЈ
mHCl
mC H
w
ϭ2M
.
ͯ ͯ
B. Data analysis
dw
EtЈ,max
10
4
The analysis method followed that developed to fit the
Doppler-resolved laser induced fluorescence ͑LIF͒ profiles of
the products generated in photon-initiated reactions.33,40–44
This procedure allows for the distribution of product c.m.
velocities that arises from population of different internal
quantum states in the butyl coproduct. The method relies on
fitting Legendre moments of the image with a set of suitably
chosen basis functions, and has been described in detail
previously.21 We have also recently demonstrated the general
approach by applying a similar analysis to photofragment ion
images.45
The maximum possible kinetic energy release EЈt,max is given
by
␪
EtЈ,maxϭϪ⌬rH0ϩEtϩEC H ϪEHCl
.
4
10
In these equations M is the total mass, Et is the collision
energy, and EC H and EHCl , appearing in the final expres-
4
10
sion, are the average internal energy of the C4H10 precursor
͑taken to be zero͒ and the fixed internal energy of the probed
HCl quantum state, respectively. The moments of the c.m.
distribution were assumed to be independent of the compara-
The joint distribution in c.m. scattering angle ␪ and frac-
tively narrow spread of reactant relative speeds,
.
vr
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7178
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
Bass et al.
For a reaction initiated by linearly polarized photolysis
basis functions also allowed for the instrument resolution,
which was estimated from Cl-atom photofragment images
͑see Sec. II A͒.
radiation, the corresponding lab frame velocity distribution
takes a particularly simple form. We define the lab frame
with the z axis parallel to the photolysis polarization vector ⑀,
and the x axis along the photolysis propagation vector. ͑Note
that for the pump-probe geometry employed in this work, the
photolysis propagation and electric vectors lie in the image
plane, i.e., the xz plane.͒ In the absence of rotational align-
ment effects, which tend to be small for HCl due to efficient
hyperfine depolarization,46,47 it has been shown33,43,48,49 that
integration of the joint c.m. scattering distribution of Eq. ͑3͒
over the reagent and precursor velocities leads to the lab
velocity distribution
Low order experimental image moments M ( p) were
v
L
obtained by integration of the image over angular coordinate
␾:
1
1
ML
͒ϭ
I
,
͑vp
͑vx vz ͑
͒ 2Lϩ1͒
͵
2
Ϫ1
ϫPL cos ␾͒ pd cos ␾,
͑8͒
͑
v
where I( ,␾)ϵI(
vp
,
)
, and
and are the appro-
vz
vx vz vp
vx
priate projections of the lab velocity in the image plane ͑pro-
portional to the pixel coordinates of the image͒. Recall that
in the present experiments the only nonzero moments of the
image are those with Lϭ0 and 2. The experimental image
P
,⌰ ͒ϭ
B
͒P cos ⌰ ͒
͑4͒
͑v
͑v
͑
͚
v
L
L
v
L
moments M ( p) for Lϭ0 and 2 were then fit simulta-
v
L
with Lϭ0 and 2, and where ⌰v is the angle between the
photolysis ⑀ vector and the HCl lab velocity vector v. PL(...)
are the Legendre polynomials. Explicit expressions for the
neously using the simulated moments M ( p) generated
v
L
from a linear combination of the basis functions bL(...)
B ( ), which are proportional to the bipolar moments
v
ML
͒ϭ
a
nmbL n,m; ͒.
vp
͑9͒
͑vp
͑
L
͚
bL(L0; ) averaged over all reagent velocities, have been
nm
v
0
presented previously in the context of Doppler profile
The fitting coefficients anm were determined by minimizing
␹ for the fit using a genetic algorithm subroutine, in which
analysis.33,43 B ( )ϵP( ) is the lab speed distribution of
2
v
v
0
the products, and the lab frame translational anisotropy is
the fitting coefficients were constrained to lie within their
physical limits. The choice of basis function ensures that the
coefficients returned by the fit, anm , correspond to the mo-
ments of the joint c.m. distribution given in Eq. ͑3͒. Satis-
factory fits to the data could be obtained by assuming a joint
c.m. distribution of separable form, for which the anm coef-
ficients may be set equal to anϫdm , where an and dm are the
coefficients for the Legendre expansion of the angular and
kinetic energy release distributions, respectively. Converged
fits to the data were obtained with four moments in cos ␪ and
four moments in ft ͑also see Sec. III͒.
␤( )ϭB ( )/B ( ).
v
v
v
0
2
The expression for a simulated ion image I( p ,␾) may
v
be obtained by integrating Eq. ͑4͒ over y . This yields
v
I
,␾͒ϭ
M
͒PL cos ␾͒,
͑5͒
͑vp
͑vp
͑
͚
L
L
where
and ␾ are the radial and angular polar coordinates
vp
of the image, and the nonzero moments M ( p) are given by
v
L
v2p
ϱ
The error limits on P(cos ␪) and P(ft) were determined
M0
͒ϭ
2B0 ͒ϩ
͑v
Ϫ1 B2
͑vp
͑v
͒
͵
ͫ
ͩ ͪ
ͬ
v2
using
a Monte Carlo technique, described in detail
0
elsewhere.50 The error limits on the fitted experimental mo-
ments were determined to range from 6% to 14% of the
1/2
v2
ϫ
d
͑6͒
͑7͒
v
ͩ
ͪ
2
v2 vp
zeroth order moment for j ϭ0 to j ϭ6, based on the varia-
Ј
Ј
Ϫ
tion in the moments obtained from individual ion images.
2
These error limits were used to determine the threshold ␹
and
values employed in the Monte Carlo error analysis ͑see Ref.
50 for details of this procedure͒.
1/2
v2p
v2
ϱ
M2
͒ϭ
2B2
͒
d .
v
͑vp
͑v
͵
ͩ ͪ
ͩ
ͪ
2
v2
v2 vp
0
Ϫ
III. RESULTS
The present analysis relies on using Eqs. ͑6͒ and ͑7͒ to gen-
erate sets of basis functions, b (n,m; p) which are then fit-
A. Images and Legendre moments
v
L
ted to the experimental data. The basis functions were ob-
tained by replacing the full c.m. frame joint distribution of
Representative velocity-map ion images and the corre-
sponding zeroth, second, and fourth order Legendre mo-
Eq. ͑3͒, used to simulate M ( p), by the product of two
v
ments are shown in Fig. 1 for HCl ( ϭ0, j ϭ1, 3, and 6͒
v
Ј Ј
L
Legendre polynomials, Pn(cos ␪)Pm(ftЈ). The basis functions
͑the images have been background subtracted and quadrant
averaged for clarity͒. It can be seen, particularly in the zeroth
order image moments, that the intensity shifts towards the
center of the images with increasing HCl rotational state.
This change in the intensity distribution could reflect either
more backwards scattering or lower kinetic energy releases
associated with the HCl products formed in higher rotational
states. It should also be noted that, within the experimental
were generated by Monte Carlo integration of the relevant
terms in the c.m. scattering distribution over all reactant and
precursor velocities, in much the same way as previously
performed for Doppler-profile analysis.44 A translational
beam temperature transverse to the beam direction of 50 K
was assumed, which ͑as noted in Sec. II A͒ provides a good
description of the images obtained for background HCl. The
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J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
The Clϩn-C4H10→HCl (vЈ,jЈ)ϩC4H9 reaction
7179
curs exclusively through abstraction from secondary carbon
atoms, although much better than those for abstraction from
primary carbon atoms only, are seen to show the opposite
trends, with the fits increasing in quality for products formed
in higher rotational states, and the returned Lϭ2 moment fits
at low j found to be broader than those determined experi-
Ј
mentally. Qualitatively, these observations suggest that reac-
tion at a primary carbon atom tends to produce HCl in low
rotational states, while reaction at a secondary carbon atom
favors production of higher rotational states of HCl ͑see be-
low͒.
A more plausible analysis, which allows for both reac-
tion pathways and the relative contribution of each to the
total signal, yields the fits shown in Fig. 3. In this case, the
c.m. angular scattering and fractional kinetic energy release
distributions are constrained to be the same for reactions in-
volving abstraction of either a primary or secondary H atom
͑as justified below͒. This approach allows the relative contri-
bution of each reaction channel to be determined. Inclusion
of both reaction pathways is found to improve the quality of
FIG. 2. Zeroth and second order Legendre moments ͑
͒, and fits to those
moments ͑
͑left͒ or only secondary ͑right͒ carbon atoms. From top to bottom, data are
shown for HCl ( ϭ0), products born in j ϭ0, 3, and 6. The fits were
͒, assuming H-atom abstraction from either only primary
the fits for the HCl ( ϭ0) products formed in low rota-
v
Ј
2
tional states, as indicated by significant reductions in ␹
compared with the values obtained assuming only primary or
secondary H-atom abstraction ͑see Fig. 2͒. For the HCl (
vЈ
Ј
performed using basis function sets with four moments each in the c.m.
angular scattering distribution and the kinetic energy release distribution.
v
Ј
2
ϭ0, j ϭ6) products, however, the value of ␹ is unchanged
Ј
by inclusion of the primary H atom abstraction channel, re-
flecting the fact that the vast majority of the HCl products in
this rotational state are formed by abstraction from a second-
ary carbon atom ͑see below͒. The conclusions that both pri-
mary and secondary abstraction channels contribute to reac-
tion is in accordance with the previous photon-initiated
experiments using isotopically substituted alkanes by Varley
and Dagdigian24–26 and Koplitz and co-workers.23
signal-to-noise ratio of the data, the fourth order Legendre
moments are very close to zero. This suggests that any an-
gular momentum polarization of the HCl products has little
influence on the form of the image moments, as consistent
with the analysis described in Sec. II B.
Owing to the arrangement of the experimental apparatus
used, it was not possible to scan the probe laser reliably over
the extended wavelengths required to obtain the full rota-
tional structure of the REMPI spectrum of the nascent HCl
reaction products, and therefore the rotational population dis-
tribution was not determined. However, on the basis of the
observed signal intensities for each transition studied, the
rotational Boltzmann temperature was estimated qualita-
tively to be 180Ϯ50 K. The rotational population distribution
Fits to the experimental Legendre moments were also
carried out allowing different c.m. angular scattering and
fractional kinetic energy release distributions to be associ-
ated with each channel ͑i.e., the channels were treated non-
2
separably͒. The ␹ values returned from these fits were not
found to be significantly lower than those obtained from the
more constrained fits performed above, despite requiring al-
most double the number of fitting parameters. After appro-
priate averaging, the c.m. angular scattering and kinetic en-
ergy release distributions for each reaction pathway returned
from these fits were seen to be in very good agreement with
those obtained when the distributions are constrained to be
the same for each reaction channel. The derived branching
ratios also showed the same trends as those obtained from
the more constrained analysis. For these reasons, it was felt
that constraining the c.m. angular scattering and fractional
kinetic energy release distributions to be the same for reac-
tions involving abstraction of either a primary or secondary
H atom was warranted.
at this temperature peaks quite narrowly at j ϭ2, with a
Ј
short tail extending to j ϭ9. These data are discussed further
Ј
in Sec. IV.
B. Angular and kinetic energy release distributions
Initial fits to the data were attempted assuming the HCl
product signal arose exclusively from H-atom abstraction at
either primary or secondary carbon sites. The resulting fits to
the data are shown in Fig. 2 for HCl products born in
v
Ј
ϭ0, j ϭ0, 3 and 6. In the case of abstraction occurring from
Ј
primary carbon atoms only, the quality of the fits is seen to
decrease drastically with increasing HCl rotational excita-
tion. The high velocity sections of the experimental moments
for the three rotational states are seen to be poorly repro-
duced by the fits. In addition, the fits to the second order
Legendre moments, which are sensitive to the velocity-
dependent translational anisotropy, show structure sharper
than seen in the experimental data. The fits obtained using
basis sets calculated by assuming that product formation oc-
The angular and energy resolutions of the current study
were determined by investigating the dependence of the re-
turned distributions and the primary-to-secondary abstraction
channel weighting on the number of fitted moments em-
ployed, as shown in Fig. 4 for HCl ( ϭ0, j ϭ0, 3, and 6͒.
v
Ј
Ј
The truncation point for the number of basis functions used
2
was determined by observing the dependence of ␹ on the
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7180
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
Bass et al.
FIG. 4. The dependence of the returned c.m. angular scattering ͑left͒ and
kinetic energy release ͑right͒ distributions on the number of moments em-
ployed. From the top, the data are for HCl ( ϭ0, j ϭ0, 3, and 6͒. The
vЈ
Ј
solid lines represent fits to the data using four moments in the CM angular
scattering distribution and four moments in the kinetic energy release dis-
tribution. The three dotted lines are fits with basis sets of dimension
(n,m)ϭ(3,3), ͑4,5͒, and ͑5,5͒. The relative weighting between the two re-
action channels for each rotational state are within the error limits shown in
Fig. 6 ͑see Table I͒.
tering distribution finer than can be described by a four-term
Legendre expansion. The returned distributions and the rela-
tive weighting between the two reaction pathways are, how-
ever, remarkably consistent as the number of moments used
is varied. The relative contributions of the two reaction chan-
nels associated with the distributions shown in Fig. 4 are
given in Table I, and are all seen to lie with the 2␴ error
bounds of the final analysis.
The c.m. angular scattering and kinetic energy release
distributions for HCl ( ϭ0, j ϭ0–6) returned from the
v
Ј
Ј
fits are shown in Fig. 5. A steady trend is seen in the c.m.
angular scattering distributions, with the predominantly for-
ward scattering of HCl products formed in low rotational
states shifting to more isotropic scattering for the HCl prod-
ucts formed in the highest rotational states. The kinetic en-
ergy release distributions are insensitive to HCl rotational
state, with only a modest trend towards higher kinetic energy
release with higher HCl rotational excitation. Note that the ft
values shown on the x axes in Fig. 5 refer to the fractional
energy release for the specific HCl quantum state in question.
The relative contributions from pathways ͑1͒ and ͑2͒ are
plotted against rotational state in Fig. 6. In general, primary
H-atom abstraction is seen to be largely associated with low
FIG. 3. Zeroth and second order Legendre moments ͑
͒, and fits to those
moments ͑ ͒ for HCl ( ϭ0, j ϭ0) ͑top͒ through to HCl ( ϭ0,
vЈ vЈ
Ј
j ϭ6) ͑bottom͒. The fits were performed using basis function sets with four
Ј
moments each in the c.m. angular scattering distribution and the kinetic
energy release distribution. The very low speed section of the moments
(
pϽ255 msϪ1) was not included in the fits, as discussed in Sec. II B. The
v
error limits on the experimental Legendre moments of the images lie in the
range 6%–14% for j ϭ0 to j ϭ6 as discussed in the Sec. II B.
Ј
Ј
rotational excitation of the HCl ( ϭ0) products, while ab-
v
Ј
straction of a secondary H atom dominates for HCl (
v
Ј
number of fitting coefficients employed. In the present case,
␹ did not decrease by a significant amount with inclusion of
more than four moments in either the c.m. angular scattering
distribution or the kinetic energy release distribution, indicat-
ing that the experiment is insensitive to features of the scat-
ϭ0) products produced with higher rotational energies; this
is in good agreement with the qualitative conclusion drawn
from the single channel fits. The nascent HCl product rota-
tional population distributions for the two pathways may be
calculated using the Boltzmann rotational temperature of 180
2
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J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
The Clϩn-C4H10→HCl (vЈ,jЈ)ϩC4H9 reaction
7181
TABLE I. Relative contributions of the reaction pathways involving abstraction of a H atom from primary ͑1°͒
and secondary ͑2°͒ carbons sites determined from fits using basis sets generated with n Legendre moments in
the c.m. angular scattering distribution and m Legendre moments in the kinetic energy release distribution. The
c.m. distributions returned from these fits are shown in Fig. 4. Error limits for the optimum ͑4,4͒ fit represent
2␴ errors resulting from statistical errors in the fit; these data are shown in Fig. 6.
HCl ( ϭ0,j )
vЈ
Ј
0
3
6
(n,m)
1°
2°
1°
2°
1°
2°
͑3,3͒
͑4,5͒
͑5,5͒
͑4,4͒
0.70
0.61
0.61
0.30
0.39
0.39
0.42
0.44
0.43
0.58
0.56
0.57
0.00
0.03
0.03
1.00
0.97
0.97
0.73 ͑Ϯ0.16͒
0.27 ͑Ϯ0.16͒
0.47 ͑Ϯ0.15͒
0.53 ͑Ϯ0.15͒
0.00 ͑Ϯ0.23͒
1.00 ͑Ϯ0.23͒
secondary H-atom abstraction to be significantly rotationally
hotter than those of primary H-atom abstraction. The overall
branching ratios determined from these population distribu-
tions show that 52%Ϯ6% of products are formed by abstrac-
tion of hydrogen from primary carbon atoms, while
48%Ϯ6% are the products of secondary H-atom abstraction.
Allowing for the 3:2 statistical abundance of primary to sec-
ondary H atoms, this corresponds to abstraction of an atom
in the secondary position being favored by a factor of 1.4
Ϯ0.4 over that of abstraction of an atom in the primary po-
sition. It should be borne in mind that the value determined
for this ratio is sensitive to the estimate made of the HCl
rotational temperature, and is thus subject to relatively large
errors.
K estimated in the preceding section for the total HCl (
v
Ј
ϭ0) signal, in conjunction with the relative contributions of
each reaction pathway ͑see Fig. 7͒. The rotational population
distributions obtained in this way show the HCl products of
The mean values obtained from the fractional kinetic
energy release distributions shown in Fig. 5, f , corrected
͗ ͘
t
for the HCl ( ϭ0,j ) rotational energy, are given in Table
v
Ј
Ј
II. The mean internal energies in the butyl fragments are seen
to remain fairly constant with HCl rotational state for both
reaction pathways. A weighted average over the HCl rota-
tional quantum states investigated for each reaction channel
gives the overall fraction of available energy deposited into
the internal degrees of freedom of the n- and s-butyl radicals,
FIG. 5. Returned c.m. angular scattering ͑left͒ and kinetic energy release
͑right͒ distributions for HCl ( ϭ0, j ϭ0) ͑top͒ through to HCl ( ϭ0,
vЈ vЈ
Ј
j ϭ6) ͑bottom͒. Optimum fits to the data were obtained with four moments
Ј
in both the c.m. angular scattering distribution and the kinetic energy release
distribution. Error bars represent 2␴ errors resulting from statistical errors in
the fits, which include estimates of the error limits on the experimental
image moments, as discussed in Sec. II B. Note that in the right-hand panels,
the ft scale refers to the state-specific fractional kinetic energy release,
which does not include the rotational energy in the HCl product ͑see Table
II͒.
FIG. 6. The relative contributions to the HCl ( ϭ0,j ) products by ab-
vЈ
Ј
straction of H-atoms from primary carbon atoms ͑--᭿--͒ and secondary
carbon atoms ͑--᭺--͒. Error bars represent 2␴ errors resulting from statisti-
cal errors in the fits, which include estimates of the error limits on the
experimental image moments, as discussed in Sec. II B.
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7182
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
Bass et al.
FIG. 7. The rotational population distributions for the HCl ( ϭ0,j ) prod-
vЈ
Ј
ucts formed by abstraction of H atoms from primary carbon atoms ͑--᭿--͒
and secondary carbon atoms ͑--᭺--͒, calculated using the relative contribu-
tions of each channel determined from the fits ͑see Fig. 6͒ and assuming a
Boltzmann distribution for the total rotational population characterized by a
rotational temperature of 180 K ͑--ࡗ--͒. Error bars represent 2␴ errors
resulting from errors in the fits, which include estimates of the error limits
on the experimental image moments, as discussed in Sec. II B.
f
(n-C H ) and f (s-C H ) , as ϳ0.3 in both cases.
͘ ͗ ͘
4 9 int 4 9
͗
int
The weights for each quantum state for each channel used in
calculating this average were taken from the HCl (
v
Ј
ϭ0,j ) rotational populations shown in Fig. 7.
Ј
FIG. 8. Contour map and wireframe plots of the product velocity-angle flux
averaged over HCl rotational state for abstraction of H atoms from ͑a͒
primary and ͑b͒ secondary carbon sites. Plots ͑c͒ correspond to the total flux
for the reaction, where both primary and secondary H atoms are abstracted.
The plots were obtained using the results shown in Figs. 5 and 7.
The data shown in Figs. 5 and 7 may be used to create
two-dimensional ͑2D͒ contour maps and the corresponding
3D ‘‘wireframe’’ plots of the product flux as a function of
HCl speed and c.m. scattering angle P(w,␪t). Plots are
shown for the products of H-atom abstraction from primary
only, secondary only, and both carbon sites in Fig. 8. In
generating these plots, the c.m. angular scattering and kinetic
energy release distributions for the individual HCl rotational
states have been averaged using the same weighting factors
as above. The contour map for primary H-atom abstraction is
seen to have a smaller radius than that for secondary H-atom
abstraction, reflecting the lower exothermicity of this reac-
tion pathway. The broader angular scattering distribution
seen for secondary H-atom abstraction results from the
greater contribution to rotationally excited HCl ( ϭ0)
v
Ј
products by this reaction pathway. The contour map calcu-
lated for the overall reaction including both pathways mim-
ics the results that would be obtained from a crossed molecu-
TABLE II. HCl ( ϭ0,j ) state-resolved, and state-averaged energy disposal data for the two pathways in the
vЈ
Ј
Cl plus n-butane reaction. The data have been obtained assuming mean available energies of 3280 cmϪ1 for
primary H-atom abstraction and 4510 cmϪ1 for secondary H-atom abstraction. The errors on the state-resolved
f
values are typically Ϯ0.05. The averaging over rotational state was performed using a Boltzmann rotational
͘
͗
t
population distribution calculated at 180 K for the HCl ( ϭ0) products, weighted by the contribution of each
vЈ
pathway for the rotational state in question. HCl ( ϭ1) has been shown to be produced in negligible quantities
vЈ
in the reactions of Cl with both propane and i-butane at similar collision energies,25,26 and is thus neglected,
despite being energetically accessible in both reaction pathways.
Clϩn-butane→HClϩn-C4H9
Clϩn-butane→HClϩs-C4H9
f
(n-C H )
f (s-C H )
͗ ͘
int 4 9
HCl ( ϭ0,j )
vЈ
frot͑HCl)
f
͗
͘
frot͑HCl)
f
͗ ͘
t
Ј
͗
͘
int
4
9
t
0
1
2
3
4
5
6
0.00
0.01
0.02
0.04
0.06
0.10
0.14
0.02
0.72
0.75
0.67
0.62
0.66
0.68
0.59
0.69
0.28
0.00
0.00
0.01
0.03
0.05
0.07
0.10
0.04
0.73
0.76
0.68
0.64
0.68
0.70
0.62
0.68
0.27
0.24
0.31
0.34
0.28
0.23
0.27
0.29
0.24
0.31
0.33
0.28
0.22
0.28
0.28
Average
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J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
The Clϩn-C4H10→HCl (v ,j )ϩC H reaction
Ј Ј
7183
4
9
lar beam experiment without product quantum state
resolution.
studies provide a mean collision energy of only ϳ0.04 eV,
with the result that the barrierless abstraction of H atoms
from secondary carbon sites is favored over abstraction of H
atoms from primary carbon sites. The much higher collision
energies of around 0.32 eV afforded by Cl2 photolysis, how-
ever, are sufficient to surmount the barrier to primary H-atom
abstraction, resulting in more equal reactivities of the two
carbon atom sites observed in the current study.
IV. DISCUSSION
A. Rotational population distribution
The HCl rotational temperature estimated here ͑180Ϯ50
K͒ is in reasonable agreement with that obtained for the Cl
plus propane reaction by Varley and Dagdigian,25 but is
slightly hotter than that estimated for the ClϩCH3CD2CH3
reaction ͑70–100 K͒ studied by Koplitz and coworkers,23
and that determined for the Cl plus i-butane reaction ͑120 K͒
by Varley and Dagdigian.26 The differences are thought to
reflect ͑a͒ the number of primary and secondary or tertiary
H-atoms available in the alkane reactants ͑there are six pri-
mary and four secondary H atoms in n-butane, while there
are nine primary H atoms and only one tertiary H atom in
i-butane͒, and ͑b͒ the higher exothermicity associated with
abstraction of H-atoms from secondary and tertiary carbon
sites compared with primary carbon sites. It is noteworthy
that the product HCl rotational population distribution esti-
mated here for the HCl products of the reaction of chlorine
atoms with n-butane is very similar to that determined by
Varley and Dagdigian for the reaction of atomic chlorine
with propane.25 This similarity reflects the comparable ratios
of primary to secondary H-atoms in propane and n-butane,
and the similar exothermicities of the respective channels in
the two reactions.
According to the distributions shown in Fig. 7, the HCl
products of primary H-atom abstraction are formed with an
average rotational energy of around 60 cmϪ1, while second-
ary hydrogen abstraction yields an average HCl rotational
energy of ϳ170 cmϪ1. This degree of rotational excitation in
the products of the two reaction pathways is again in reason-
able agreement with the results of Varley and Dagdigian for
the ClϩCD3CH2CD3 and Clϩ(CH3)3CD reactions, where
in the former the average rotational energies were found to
be 84 and 110 cmϪ1 for the DCl and HCl products,
respectively,25 while in the latter the HCl and DCl products
were found to have average rotational energies of 50 and 100
cmϪ1, respectively.26 Each of these studies suggest that the
HCl products of the reaction at a primary site are born colder
than those from secondary attack, in qualitative agreement
with the present findings.
The reactivity enhancement for secondary H-atom ab-
straction obtained here is also somewhat lower than observed
in the photoloc studies of the Cl plus propane reaction.23,25,26
Koplitz and co-workers found abstraction of hydrogen or
deuterium atoms from the secondary carbon site to be fa-
vored by a factor of 2–3 over abstraction from a primary
carbon site in the ClϩCH3CD2CH3 and ClϩCD3CH2CD3
reactions,23 while Varley and Dagdigian found abstraction
from the secondary carbon site to be favored by a factor of
2.7Ϯ0.5 over that from the primary site in the Cl
ϩCD3CH2CD3 reaction.25 The latter authors also found ab-
straction of the deuterium atom from the tertiary carbon site
in (CH3)3CD to be a factor of 2.7Ϯ0.3 more reactive than
the primary carbon sites.26 The comparison between the
present work and the previous photoloc studies is compli-
cated by kinetic isotope factors, which will also affect the
H/D-atom abstraction reactivity, together with differences in
collision energy distribution. The study of the Cl
ϩCD3CH2CD3 reaction by Varley and Dagdigian25 is prob-
ably the most directly comparable with the present work
͑both in terms of system and the collision energy conditions
employed͒. The difference in enhancement obtained by Var-
ley and Dagdigian,25 compared with that found here, could
well be due to isotope effects, which will raise the effective
barrier for abstraction of a deuterium atom from a ͑primary͒
C-D bond over that of an H atom from a ͑secondary͒ C-H
bond.
C. Angular scattering distributions
The c.m. angular scattering distributions shown in Fig. 5
are in good agreement with those recently obtained by
Toomes and Kitsopoulos from images recorded using the un-
skimmed crossed molecular beam technique.29 Note also that
they are very similar to those obtained previously for the Cl
plus ethane reaction.21,29 Comparison of the total c.m.
velocity-angle flux map generated for the Cl plus n-butane
reaction shown in Fig. 8 with that obtained by Suits and
co-workers for the Cl plus propane reaction27 reveals that
more forward scattering is seen in the current photoloc study
than in the crossed molecular beam experiment. Also con-
trary to that work, here we find that abstraction of an H atom
from a primary carbon site is associated predominantly with
forward scattering, while more isotropic and less forward
peaked scattering is seen for the products of secondary
H-atom abstraction ͑see further discussion in Sec. IV D͒.
The differing propensities in the c.m. angular scattering
of the products formed in the two abstraction pathways, and
the different HCl product rotational excitation associated
with each, suggests that somewhat different mechanisms are
needed to explain the dynamics of the Cl plus n-butane sys-
tem. Consider first the mildly exothermic primary H-atom
B. Branching fraction
The relative reactivity of the primary and secondary car-
bon sites is in broad agreement with that obtained from the
kinetics experiments performed by Tyndall et al.14 and
Sarzynski and Sztuba.17 The kinetic studies show a more
pronounced reactivity of the secondary site than observed
here, possibly reflecting the different collision energy distri-
butions in the thermal measurements, together with the dif-
ferent activation energies for the two reaction pathways. The
positive activation energy for abstraction of hydrogen from
primary carbon sites indicates a barrier in this reaction path-
way, while no such barrier is present for secondary H-atom
abstraction, where the activation energy is found to be
negative.17 The thermalized Cl atoms used in the kinetic
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7184
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
Bass et al.
abstraction channel, producing forward scattered products
and HCl formed in low rotational states. The dynamical char-
acteristics of this abstraction pathway closely match those of
a peripheral chemical reaction, in which forward scattering
from a direct exoergic atom transfer reaction is proposed to
be an indication of abstraction of an atom at the periphery of
a reagent.51 As was mentioned in Sec. I, transition state cal-
culations on the Cl plus propane and Br plus n-butane sys-
tems suggest that the optimum geometry for both abstraction
channels in the Cl plus n-butane reaction is likely to be that
in which the Cl-H-C atoms are arranged collinearly. In this
arrangement, the impact parameter b for the abstraction of an
H atom from a primary carbon site is necessarily nonzero
and relatively large. This corresponds to an opacity function
P(b) for this reaction pathway which is zero ͑or very small͒
at low b and peaks at impact parameters on the order of the
distance from the center of mass of the n-butane molecule to
the chlorine atom in the transition state, ϳ4 Å ͑i.e., the pe-
riphery of the n-butane molecule͒.
The more exothermic abstraction of an H atom from a
secondary carbon site produces a broader, forward peaking,
scattering distribution, with greater HCl rotational excitation.
As for abstraction of an H atom from a primary carbon site,
this reaction pathway is expected to be direct and to have a
collinear transition state. From similar considerations to
those used in the primary reaction channel, the estimated
range of impact parameters over which the opacity function
for this reaction pathway is nonzero extends from bϭ0 to
Ϸ2.5 Å. For a direct reaction occurring primarily at low
impact parameters, products are expected to be predomi-
nantly backward scattered. While the observed scattering is
not as extreme as this, greater backwards and sideways scat-
tering is seen for this reaction pathway than for abstraction of
an H atom from a primary carbon site, and a more rebound-
type mechanism is thus suggested for this reaction channel.
This is consistent with the higher rotational excitation found
for the HCl products formed in this reaction pathway. For-
ward scattering of the products of collisions taking place at
lower impact parameters may be taken to be an indication of
a wide cone of acceptance, where the approach of the chlo-
rine atom is not tightly constrained to be collinear with the
breaking C-H bond. Release of energy along the axis of the
C-H bond for these slightly bent transition states yields rota-
tional excitation of the HCl products, as observed for this
reaction pathway. The observed scattering dynamics can thus
be qualitatively accounted for through this interplay between
the impact parameter and the angle of approach of the reac-
tants.
similar level of excitation of the internal modes in the butyl
coproducts, despite differentiation between the two reaction
pathways not being possible in their study.29 The mean frac-
tions of the total available energy found in internal excitation
of the n-butyl and s-butyl cofragments in the present inves-
tigation are slightly higher than the 22% found for the ethyl
radical products of the Cl plus ethane reaction,21 probably
reflecting the higher collision energy employed in the Cl plus
n-butane reaction, and the greater number of low energy in-
ternal modes in the butyl radical compared with the ethyl
radical. The level of rotational excitation of the HCl products
is very similar in the two reaction systems.
In their crossed molecular beam study on the reaction of
chlorine with propane, Suits and co-workers found 40%–
50% of the available energy was deposited into the internal
modes of the HCl and propyl products, and concluded that
most of this energy resides in the propyl radicals.27 This is a
significantly greater internal excitation of the alkyl cofrag-
ment than found here for the Cl plus n-butane reaction, or
previously for the Cl plus ethane reaction.21 Also note that
more backward scattering was seen in the Cl plus propane
crossed molecular beam study than in our photoloc investi-
gations of Cl plus butane and ethane.21 These two observa-
tions are likely to be linked, and may be symptomatic of a
systematic error, either in the photoloc experiments, or in the
crossed molecular beam experiments of Suits and
co-workers.27,28 In the latter case, the alkyl fragments were
detected using vacuum ultraviolet synchrotron radiation
͑with a photon energy of 9.5 eV͒ to effect photoionization of
the alkyl radicals, with the resulting ions detected mass spec-
trometrically. If alkyl radical products born with excited in-
ternal modes were preferentially ionized in that study, then
the data obtained would be biased towards greater internal
excitation of the alkyl products. Furthermore, Suits and co-
workers have subsequently suggested that photoionization of
alkyl radicals at 7.9 eV is relatively insensitive to primary
alkyl radical products.52 If photoionization at 9.5 eV also
showed a similar, though presumably more modest, bias
against detection of ͑forward scattered͒ primary products,
this would explain why the molecular beam experiments dis-
play more backward scattering, and more internal excitation,
than the present study. A similar difference between the re-
sults of crossed molecular beam experiments using photoion-
ization of alkyl products by Suits and co-workers and those
from photoloc studies of the cofragments has been seen in
the reactions of O(3P) with saturated hydrocarbons.53–55
Bulb experiments carried out by Kajimoto and co-workers
with Doppler-resolved LIF detection of the OH fragments
find the products of the reactions of O(3P) with i-butane and
cyclohexane to be almost isotropically scattered.56,57 In the
case of the O(3P) plus c-hexane reaction, around 60% of the
available energy was seen to be deposited into the cyclo-
hexyl products. At similar collision energies, however, Suits
and co-workers found the i-butyl and c-hexyl fragments to be
strongly backward scattered, with a slightly greater fraction
of the available energy found as internal excitation of the
alkyl products.54
D. Energy partitioning
On average, just under 30% of the available energy is
seen to be channeled into the internal modes of both the n-
and s-butyl radical coproducts. Owing to the different exo-
thermicities for the two reaction pathways, this corresponds
to energies of around 950 and 1260 cmϪ1 being partitioned
into internal excitation of the n-butyl and s-butyl cofrag-
ments, respectively. The HCl rotational state resolved prod-
uct speed distributions obtained from the unskimmed crossed
beam experiments by Toomes and Kitsopoulos suggest a
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J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
The Clϩn-C4H10→HCl (v ,j )ϩC H reaction
Ј Ј
7185
4
9
E. Internal excitation of the butyl
Rotational angular momenta of ϳ28ប are calculated to be
generated for rotation about the a axis. The main rotational
excitation of the s-butyl products is thus likely to be around
the a axis. As in the case of the n-butyl radical, in practice
rotation will be about all three axes, with lower values for J
and K than predicted from the extremes presented here.
Energy release into the vibrational modes of the butyl
radical products may be associated with relaxation of the
CH2 or ϾC-H moieties from the pyramidal geometries ex-
pected to be adopted in the transition state, to the near planar
arrangement in the products. This change in geometry could
give rise to excitation of the out-of-plane CH2 or ϾC-H
rocking modes; the frequency of the out-of-plane CH2 mode
in n-butyl has been measured to be 520 cmϪ1, and its motion
is thought to be almost independent of the nonradical portion
of the hydrocarbon chain.58–61 For the Cl plus ethane reac-
tion it has been shown that a Franck-Condon model of the
vibrational excitation of the CH2 rocking mode predicts un-
realistic levels of vibrational excitation.21 From the similari-
ties in the vibrational frequencies of the radical rocking
modes and the associated transition state geometries, one
would expect similar ͑i.e., unrealistic͒ levels of excitation to
be predicted in the Cl plus n-butane reaction. However,
lower levels of excitation could be generated if there was a
more gradual relaxation of the geometry of the CH2 moiety
from the transition state to the products.
The internal excitation of the n-butyl and s-butyl radical
products may reside in rotational and/or vibrational degrees
of freedom. Consider first the abstraction of an H atom from
a primary carbon site in n-butane. Assuming the product
n-butyl radical is well approximated as a near-prolate sym-
metric top with a rigid carbon frame, its rotational levels are
given approximately by
2
¯
¯
F J,K͒ӍBJ Jϩ1͒ϩ AϪB͒K ,
͑10͒
͑
͑
͑
where, assuming the n-butyl radical adopts the lowest energy
conformation, the average rotational constant about the b or
Ϫ1
¯
c axes, Bϭ0.5(BϩC), is calculated to be ϳ0.123 cm
,
with AӍ0.827 cmϪ1. If all the energy observed to be chan-
neled into internal excitation of the n-butyl radicals was ro-
tational in origin, in the two extreme cases this would corre-
spond to end-over-end rotational excitation of n-butyl to J
Ӎ88, Kϭ0, or rotational excitation about the a axis to J
ϭKӍ34. Similar considerations to those used in the discus-
sion of the internal excitation of the ethyl product of the Cl
plus ethane reaction,21 where an impulsive release of the
reaction exothermicity along the breaking C-H bond in the
transition state geometry was assumed to impart a torque on
the ethyl fragment, leads to the prediction of n-butyl rota-
tional angular momenta of ϳ40ប for end-over-end rotation,
or of ϳ25ប about the a axis. This estimate is a lower limit,
since the energy found to be partitioned into the n-butyl radi-
cal is greater than the reaction exothermicity. In a peripheral
mechanism, higher torques may be expected to be imparted
on the n-butyl radical from abstraction of the H atom by a
fast moving chlorine atom. Note that the actual rotation is
likely to be about all three axes with intermediate values of J
and K, since the breaking C-H bond is not necessarily in the
plane of the carbon backbone. End-over-end rotation is ex-
pected to dominate, however, due to the larger torque exerted
for this motion.
V. CONCLUSIONS
Rotational state resolved c.m. angular scattering and ki-
netic energy release distributions have been determined from
experimental velocity-map ion images of the HCl ( ϭ0, j
v
Ј
ϭ0–6) products of the reaction of chlorine with n-butane.
Analysis of the images suggests that abstraction of both pri-
mary and secondary H atoms occurs, and has allowed esti-
mates to be made of the relative contributions of these two
abstraction pathways for each HCl ( ϭ0) rotational quan-
v
Ј
tum state investigated. Abstraction of an H atom from a pri-
mary carbon site is found to produce rotationally very cold
For the secondary H-atom abstraction channel, the rota-
tional constants for the s-butyl radical product can be esti-
HCl ( ϭ0) products which are forward scattered, whereas
v
Ј
Ϫ1
¯
mated to be Bϭ0.5(BϩC)Ӎ0.118 cm
,
and
A
abstraction of an H atom from a secondary carbon site yields
more isotropically scattered HCl products formed with
higher rotational excitation. It is suggested that a peripheral
reaction mechanism is responsible for the primary H atom
abstraction channel, whilst a more rebound-type mechanism
is seen to account for the dynamics of the secondary abstrac-
tion channel. The returned kinetic energy release distribu-
tions show that around 30% of the available energy is found
as internal excitation of the n-butyl and s-butyl products.
Possible sources of this excitation have been discussed.
Ӎ0.891 cmϪ1. The maximum rotational state accessible if
all the observed available energy deposited into internal
modes of the s-butyl is found as end-over-end rotation is J
Ӎ104, Kϭ0, while for rotational excitation about the a axis,
JϭKӍ38. Impulsive release of the reaction exothermicity
along the breaking C-H bond in the transition state is not
expected to yield such high levels of end-over-end rotation,
but is more likely to excite rotation about the a axis. The axis
of the breaking bond passes very close to the c.m. of the
s-butyl, thus an impulse will exert only a very small torque
on the newly forming radical, and, owing to the high mo-
ments of inertia about the b and c axes, will yield only mod-
est levels of end-over-end rotational excitation. Using a tran-
sition state geometry based on the structure of n-butane, this
is indeed seen to be the case, with end-over-end rotational
angular momenta of only ϳ34ប found to be generated. The
moment of inertia about the a axis is much lower, however,
and the component of the impulse about this axis is thus
expected to induce higher levels of excitation about this axis.
ACKNOWLEDGMENTS
The Oxford group thanks the Royal Society and the
EPSRC for research grants. We also gratefully acknowledge
the EU ͑through Project No. HPRN-CT-1999-00007͒ for
their support of the Research Training Network, Reaction
dynamics. T.N.K. and R.L.T. also thank the EU for the Net-
work Reactives HPRN-CT-2000-0006, and the joint EU and
Hellenic Ministry of Education program Applied Molecular
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7186
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
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