Vibrational excitation of H2O and HOD molecules produced by reactions of OH and OD with cyclo-C6H12, n-C4H10, neo-C5H12, HCI, DCI and NH3 as studied by infrared chemiluminescence

Article abstract of DOI:10.1063/1.475626

The room-temperature reactions of OH(OD) radicals with cyclo-C₆H₁₂,n-C₄H₁₀, and neo-C₅H₁₂ have been investigated by observing the infrared chemiluminescence from the H₂O(HOD) molecules generated in a fast-flow reactor. These hydrocarbon molecules are representative for abstraction from secondary and primary C-H bonds. The total vibrational energy released to H₂O(HOD) was in the range of (f_v)=0.55-0.65. The majority (80%-85%) of the vibrational energy is in the stretching modes and the main energy release is to the local mode associated with the new OH bond. The dynamics associated with the energy disposal to H₂O(HOD) resemble the H+L-H dynamics for the analogous reactions of F atoms. The data from H₂O and HOD are complementary because of the different collisional coupling between the energy levels of the v₁. v₂. and v modes: however, no specific isotope effect was found for the energy disposal to H₂O versus HOD for reactions with the hydrocarbon molecules. In contrast, a very unusual isotope effect was found between the OH+HCl and OD+ HCl pairs The latter reaction gave the expected stretching mode excitation of HOD: however, the OH reaction gave H₂O molecules with virtually no vibraitonal energy. This anomalous situation is partly associated with an inverse secondary kinetic-isotope effect, but the main isotope effect is on the dynamics of the energy disposal process itetf.

Full text of DOI:10.1063/1.475626

Vibrational excitation of H 2 O and HOD molecules produced by reactions of OH and
OD with cyclo- C 6 H 12 , n- C 4 H 10 , neo- C 5 H 12 , HCl, DCl and NH 3 as studied by
infrared chemiluminescence
N. I. Butkovskaya and D. W. Setser
Citation: The Journal of Chemical Physics 108, 2434 (1998); doi: 10.1063/1.475626
View online: http://dx.doi.org/10.1063/1.475626
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 108, NUMBER 6
8 FEBRUARY 1998
Vibrational excitation of H2O and HOD molecules produced by reactions
of OH and OD with cyclo-C6H12, n-C4H10, neo-C5H12, HCl, DCl
and NH3 as studied by infrared chemiluminescence
N. I. Butkovskayaa) and D. W. Setserb)
Department of Chemistry, Kansas State University, Manhattan, Kansas 66506
͑Received 30 July 1997; accepted 30 October 1997͒
The room-temperature reactions of OH͑OD͒ radicals with cyclo-C6H12, n-C4H10, and neo-C5H12
have been investigated by observing the infrared chemiluminescence from the H2O͑HOD͒
molecules generated in a fast-flow reactor. These hydrocarbon molecules are representative for
abstraction from secondary and primary C–H bonds. The total vibrational energy released to
H2O͑HOD͒ was in the range of
f ϭ0.55–0.65. The majority ͑80%–85%͒ of the vibrational
͘
v
͗
energy is in the stretching modes and the main energy release is to the local mode associated with
the new OH bond. The dynamics associated with the energy disposal to H2O͑HOD͒ resemble the
HϩLϪH dynamics for the analogous reactions of F atoms. The data from H2O and HOD are
complementary because of the different collisional coupling between the energy levels of the ␯1 ,
␯2 , and ␯ modes; however, no specific isotope effect was found for the energy disposal to H2O
3
versus HOD for reactions with the hydrocarbon molecules. In contrast, a very unusual isotope effect
was found between the OHϩHCl and ODϩHCl pairs. The latter reaction gave the expected
stretching mode excitation of HOD; however, the OH reaction gave H2O molecules with virtually
no vibrational energy. This anomalous situation is partly associated with an inverse secondary
kinetic-isotope effect, but the main isotope effect is on the dynamics of the energy disposal process
itself. © 1998 American Institute of Physics. ͓S0021-9606͑98͒00406-1͔
GeH4.7 This paper reports the vibrational state distributions
I. INTRODUCTION
of H2O and HOD formed from H-atom abstraction reactions
from cyclo-C6H12, n-C4H10, neo-C5H12, HCl, DCl, and NH3
by hydroxyl radicals. Infrared emission in the 2400–
3900 cmϪ1 range, corresponding to ⌬␯1ϭϪ1, ⌬␯2ϭϪ2,
and ⌬␯3ϭϪ1 transitions of H2O and HOD was observed
from a fast-flow reactor. Analysis of these spectra gives the
nascent vibrational distributions from the reactions, except
for the collisionally coupled ␯ and ␯ modes of H2O and ␯
The H-atom abstraction reactions by hydroxyl radicals
are attractive targets for studies of state-to-state reaction ki-
netics, because these reactions are of widespread importance
to atmospheric and combustion chemistry, and because their
reaction dynamics are intrinsically interesting. Although the
activation energies of these reactions are small
(0–2 kcal molϪ1), so are the preexponential factors in the
Arrhenius equation, because of the restricted geometry of the
early transition states.1 The latter is a consequence of the
nearly linear orientation requirement of the half-filled p or-
bital of OH(X2⌸) and the H–R bond. The vibrational en-
ergy states of H2O ͑or HOD͒ are sufficiently sparse that the
vibrational energy distributions from H-atom abstraction re-
actions can be measured and compared to the HF and HCl
vibrational distributions from the analogous H-atom abstrac-
tion reactions by F or Cl atoms.2,3 In addition to providing
data for a new set of reactions of the HϩLϪH class,4 the
H-atom abstraction reactions by OH radicals present the op-
portunity to study systematically the bending mode excita-
tion for reactions giving triatomic products. The dynamics
associated with formation of new bonds that generate bend-
ing modes in the product is an active theoretical question.5 In
recent work we have analyzed the vibrational excitation of
isotopic water molecules formed in the reactions of OH and
OD radicals with HBr and DBr ͑Ref. 6͒ and with HI and
1
3
1
and ␯ modes of HOD.
2
The HBr, GeH4, and HI reactions are highly exoergic
and the H2O and HDO vibrational populations extend to the
available energy limit, which is three ͑HBr, GeH4͒ and four
͑HI͒ quanta in stretching vibrations. In the HBr reaction, the
mean fraction of the available energy released as vibrational
energy,
f , was 0.65, with about 30% of the vibrational
͘
v
͗
energy released to the bending mode of H2O. Inverted dis-
tributions in the stretching modes are expected for HϩL
ϪH reaction dynamics.3,4 This expectation was confirmed
by the data and by quasiclassical trajectory calculations for a
realistic repulsive potential-energy surface8,9 for the
OHϩHBr reaction. The mechanism for excitation of the
bending mode is more complicated and seems to depend on
both specific features of the potential surface and stretch-
bend coupling in the exit channel.5,8 In direct abstraction
͑i.e., reaction on a repulsive potential surface͒ the old OH
bond is nearly a spectator, although small differences in the
OH stretch distribution for HOD versus H2O, vide infra, sug-
gest that the old bond may receive some energy. The GeH4
and HI reactions gave less stretching excitation and more
a͒
Permanent address: Institute of Chemical Physics, Russian Academy of
Sciences, 117334 Moscow, Russian Federation.
b͒
Author to whom correspondence should be addressed.
0021-9606/98/108(6)/2434/14/$15.00
2434
© 1998 American Institute of Physics
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J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
TABLE I. Kinetic and thermodynamic data for the OH͑OD͒ϩHR reactions.a
N. I. Butkovskaya and D. W. Setser
2435
b
Reaction
k298
Ea
Ref.
D0(R–H)
94.2Ϯ2
Ref.
16
E
͗ ͘
av
73Ϯ12
73Ϯ5
25Ϯ2
28Ϯ2
8.5Ϯ0.4
0.78Ϯ0.16
1
17
13,18
19
27.1Ϯ2.2
27.4
24.7Ϯ0.7
25.0
OHϩC6H12→H2OϩC6H11
ODϩC6H12→HDOϩC6H11
OHϩC4H10→H2OϩC4H9
ODϩC4H10→HDOϩC4H9
OHϩC5H12→H2OϩC5H11
0.88Ϯ0.20
-
1.54Ϯ0.20
96.7Ϯ0.5c
20
1
99.6Ϯ1.4
97.9Ϯ1.0
13
21
22.4Ϯ2.2
ODϩC5H12→HDOϩC5H11
OHϩHCl→H2OϩCl
͑1.2͒
0.7Ϯ0.2
22.4d
7.9Ϯ0.3
6.8Ϯ0.3
4.4Ϯ0.6
3.5Ϯ0.5
1.1Ϯ0.1
1.3Ϯ0.2
1.6Ϯ0.3
24
22
22
23,25
22
22
102.2Ϯ0.1
20
18.6Ϯ0.4
-
-
ODϩHCl→HODϩCl
OHϩDCl→HODϩCl
18.9Ϯ0.4
18.3Ϯ0.4
1.5Ϯ0.1
-
-
ODϩDCl→D2OϩCl
18.6Ϯ0.4
15.6Ϯ0.7
OHϩNH3→H2OϩNH2
1.8Ϯ0.4
24
106.7Ϯ0.3
20
aRate constants are in units of 10Ϫ13 cm3 moleculeϪ1 sϪ1; activation energies, bond energies, and available
reaction energies are in kcal molϪ1
.
bAvailable energies for deutero-isotopic reactions were calculated accounting for the change in zero vibration
energies of reactants and products.
cSecondary C–H bond.
dThe 0.3 kcal molϪ1 decrease of Ea due to the change in zero-point energies at the transition state was estimated
from kOH /kODϷ0.5 ͑see text͒.
bending excitation with f Ϸ0.5 and 0.4, respectively. The
for reactions ͑1͒–͑3͒ and ͑6͒ and nϭ3.5 for reactions ͑4͒ and
͑5͒. The reaction enthalpies were calculated from Dؠ0͑H–R͒
͗
͘
v
involvement of an intermediate complex in the HI reaction
mechanism is likely,7 but the dynamical interpretation for the
GeH4 reaction is less certain. In order to better understand
the mechanism of energy disposal to H2O ͑and HOD͒, we
have determined the stretching and bending vibrational dis-
tributions for several less exoergic reactions than HBr. These
reactions differ from the previous three examples in that
small barriers exist, and conventional transition-state theory
seems to explain the thermal rate constants.10–13 Although
these reaction rates are slower than for HBr, the infrared
emission from a fast-flow reactor still was a viable experi-
mental technique. The H2O and HOD vibrational distribu-
tions may help to understand the role of the polyatomic R
fragment in reaction dynamics.3,5,14 Cyclohexane is of spe-
cial interest in this regard, because it was one of the few
ؠ
20
and D0͑HO–H͒ϭ118.08Ϯ0.03 kcal molϪ1
.
If only
Dؠ298͑H–R͒ values were available, they were converted to
zero using Kirchoff’s equation, which gives Dؠ0͑H–R͒
ϭDؠ298͑H–R͒Ϫ1.4 kcal molϪ1 from the assumption that the
heat capacities of the alkyl radicals are identical with those
of their parent hydrocarbons. Zero-point energy consider-
ations lead to slightly different energetics for the OD reac-
tions, which is reflected in the E values of Table I.
͗
͘
av
The large isotope effect found for the energy disposal
from ͑4͒ and ͑4D͒ encouraged us to try experiments with
DCl and NH3.
OH͑OD͒ϩDCl→HDO͑D2O͒ϩCl,
OH͑OD͒ϩNH3→H2O͑HOD͒ϩNH2.
͑5,5D͒
͑6,6D͒
reactions with F atoms that did not provide HF( ,J) excita-
v
tion to the thermochemical limit.3,14,15
The E from ͑6͒ is smaller than for ͑4͒, but one quantum
͗
͘
av
The rate constants and the associated thermochemistry
for the reactions studied in this paper are given in Table I.
Because the bond energies for secondary C–H bonds are
significantly weaker than those of primary bonds, the sec-
ondary abstraction rate dominates over primary abstraction at
298 K for n-C4H10.13 The maximum excitation for reactions
͑1–3͒ is two O–H stretching vibrational quanta.
of stretching vibration still can be excited. These reaction
rates are slower than for reactions ͑1–4͒ and the Einstein
coefficients for emission from HOD (⌬␯1ϭϪ1) and from
D2O (⌬␯3ϭϪ1) are smaller than from HOD (⌬␯3ϭϪ1)
and from H2O (⌬␯3ϭϪ1). The emission intensity from ͑6͒
was extremely weak, and this rate is near the limit that can
be studied at 298 K by infrared emission from our flow re-
actor.
The reaction with HCl is of special interest, because it
completes the HBr and HI series and because the reverse
reaction is an example of state-selective chemistry in which
excitation of stretching modes promote reaction more than
excitation of the bending states.26–30 The product vibrational
excitation from ͑4͒ and ͑4D͒ should provide interesting data
for interpretation using the principle of microscopic revers-
ibility. A population inversion has been observed for ͑000͒
and ͑010͒ states of H2O from the reactions of OH with cyclo-
C6H12 using time-resolved laser infrared absorption/gain
OH͑OD͒ϩc-C6H12→H2O͑HOD͒ϩC6H11,
OH͑OD͒ϩn-C4H10→H2O͑HOD͒ϩC4H9,
OH͑OD͒ϩneo-C5H12→H2O͑HOD͒ϩC5H11.
͑1,1D͒
͑2,2D͒
͑3,3D͒
The available energy is even less for reaction ͑4͒ and only
one quantum of stretch excitation is possible.
OH͑OD͒ϩHCl→H2O͑HOD͒ϩCl.
The energy available to the products was obtained from the
enthalpy changes,
ϭϪ⌬Hؠ ϩnRTϩE , where nϭ4
͑4,4D͒
E
͗
͘
av
a
0
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2436
J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
spectroscopy.31 However, no information was obtained for
the distribution in the stretching mode. Quantum dynamical
models for the OHϩHCl, CH4, and NH3 reactions favor the
ground vibrational state for the H2O product.9,32,33 All of the
short reaction time. Numerical calculations for the typical
reaction conditions ͑see the figure captions͒ showed that,
even
(10Ϫ10 molecule cmϪ3 sϪ1
OHϩR→H O ϩM
for
the
highest
possible
for
rate
constant
secondary
)
the
above reactions can be compared with the HF( ) vibrational
reaction and ⌬tϭ0.25 ms, the
v
Ј
Ј
2
energy disposal from F-atom reactions,2,3,14,15 which is domi-
͓H O ͔/͓H O͔ ratio does not exceed 0.1. Furthermore, the
Ј
2
2
nated by the HϩLϪH dynamics, no isotope effect has been
combination product, ROH, would be collisionally stabilized
at 0.5 Torr and the radical concentration will be reduced by
reaction with the excess NO2.
found for f (HF) versus f (DF) .
͗
͘
͗
͘
v
v
II. EXPERIMENTAL METHODS
A. Experimental apparatus and techniques
B. Vibrational relaxation of H2O and HOD
The experimental apparatus and procedures have been
described in our preceding papers.6,7 The infrared chemilu-
minescence spectra from vibrationally excited H2O and HDO
molecules from the reactions of OH and OD radicals with
reagent molecules were recorded by a Fourier transform in-
frared spectrometer ͑BIORAD͒, which viewed the emission
from the fast-flow reactor through a NaCl window. Each
measured spectrum represents the average of 1024 scans of
the spectrometer with a spectral resolution of 1 cmϪ1. The
experimental spectra were adjusted for the response function
of the FT spectrometer, which was measured from a cali-
brated black-body source. The OH or OD radicals ͑and NO͒
were produced via the reaction of H or D with excess NO2 in
the prereactor (⌬tϭ1.5 ms) section of the flow reactor.6,7
The H or D atoms were generated by flowing a H2͑D2͒/Ar
mixture through a microwave discharge. The H and D atom
concentrations were monitored by the HCl infrared emission
from the addition of Cl2 as a reagent. The reactants were
introduced into the reactor through a ring injector located 20
cm downstream of the hydrogen and nitrogen dioxide inlets
and 3.5 cm upstream of the observation window. The total
pressure could be varied from 0.5 to 2.0 Torr by changing
the Ar flow rate or by reducing the pumping speed. At a
pressure of 0.5 Torr, the maximum flow velocity was about
140 m sϪ1, corresponding to a reaction time of ϳ0.25 ms.
The concentration of H or D atoms was in the range of
(2–4)ϫ1013 molecule cmϪ3; the NO2 concentration was
maintained between 8 and 20ϫ1013 molecule cmϪ3. The re-
The question of vibrational relaxation must be explicitly
considered because of the higher reagent concentrations than
in our previous work.6,7 The H2O spectra from the HBr and
GeH4 experiments were not affected by overall vibrational
relaxation at Ͻ0.7 Torr and ⌬tр0.5 ms; although, the popu-
lations in the ␯ and ␯ modes are equilibrated and only the
1
3
total population in the ␯ reservoir could be observed.34–36
1,3
A similar equilibration takes place between the ␯ and 2␯
1
2
modes of HOD. Although higher reagent and OH ͑and OD͒
concentrations were required to obtain satisfactory spectra
than for the HBr reaction, the Ar pressure and the reaction
times were the same as before.6,7 Therefore we just need to
evaluate the effects of the higher reagent, OH, NO, and NO2
concentrations. The 300 K rate constants, k1,3(M), for
34
quenching of 1,3ϭ1 states by partner M are k1,3(Ar͒
v
34,36
ϭ6.2ϫ10Ϫ14
ϭ͑2–3͒ϫ10Ϫ11, k1,3(HCl)36ϭ8.4ϫ10Ϫ12 cm3 moleculeϪ1
Ϫ1. Typical conditions for the hydrocarbon experiments at
0.5 Torr were Ar ϭ1.8ϫ1016, H ϭ1.5ϫ1013, OH ϭ3
, , and k1,3(H2O͒
k1,3(H2)35ϭ8ϫ10Ϫ13
s
͓
͔
͓
͔
͓
͔
2
ϫ1013,
NO ϭ1ϫ1014, and ͓HR͔ϭ2ϫ1013molecule
͔
2
͓
cmϪ3, giving characteristic times for H2O(␯1,3) relaxation
of t͑Ar͒Ϸ1 ms, t͑H2͒Ϸ90 ms, t͑OH͒Ϸ1.6 ms, and
t͑HR͒Ϸ4.3 ms ͑it was assumed that the relaxation rates by
OH are the same as relaxation by H2O, and relaxation by HR
is 16 times faster than relaxation by H2͒. These estimates
show that only Ar and OH could be important relaxation
partners. The effect of Ar was tested during the OHϩGeH4
study, and the onset of noticeable vibrational relaxation of
H2O occurred at у0.7 Torr. To test the quenching efficiency
of hydroxyl radicals, spectra were measured in this work for
OH ϭ0.7 to 2.9ϫ1013 from the OHϩHBr reaction at 0.7
agent
concentrations
were
in
the
1–10ϫ1013
molecule cmϪ3 range for reactions ͑1–4͒. The DCl and NH3
reactions, which were studied less extensively, required re-
agent concentrations of about 1ϫ1014 molecule cmϪ3. The
vibrationally excited OH radicals from the HϩNO2 reaction
relaxed during passage through the prereactor. Before intro-
ducing the DCl flow, the reactor and the inlet tubing were
treated by D2O to prevent D/H isotopic exchange on the
walls.
͓
͔
Torr with HBr ϭ1.5ϫ1013 and NO ϭ1.8ϫ1014 and ⌬t
͓
͔
͓
͔
2
ϭ0.35 ms. The H2O(␯1,3 ,␯2) distributions from these spec-
tra were unchanged. The vibrational relaxation of H2O by
NO2 apparently has not been studied, but we did not notice
any change in the spectra when varying the NO2 concentra-
tion from 2 to 15ϫ1013 molecule cmϪ3 for the OHϩHBr
reaction.
Commercial tank grade Ar was passed through two mo-
lecular sieve traps cooled by a acetone/dry ice mixture and
one cooled by liquid N2. The latter was on the low-pressure
side of the metering value. Tank grade H2, D2, and NO2
were used without purification. Hydrogen chloride ͑Mathe-
son͒, DCl ͑Cambridge Isotope Laboratories͒ and commercial
grade NH3, n-C4H10, neo-C5H12, and c-C6H12 were purified
by several freeze-pump-thaw cycles.
The dominant loss process from the ␯ stretching res-
1,3
ervoir is transfer of population to the bending manifold of
levels37
H O ␯ ͒ϩM→H O 2␯ ͒ϩMϩ506 or 605 cmϪ1
,
͑7͒
͑
͑
2
1,3
2
2
Secondary processes for reactions ͑1͒–͑3͒ were not im-
followed by sequential loss of bending quanta. The analo-
gous process with HOD
portant as sources of water (H O ) molecules, because of the
Ј
2
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J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
2437
HOD ␯ ͒ϩM→HOD 1,2␯ ͒ϩMϩ983 or 925 cmϪ1
͑
͑v
3
2
͑8͒
should be less effective due to the larger energy defect, and
the pressure for onset for HOD (␯3) relaxation is expected to
be substantially higher than for H2O (␯1,3). Relaxation of the
2␯ bending mode by Ar is approximately three times
2
faster,34 k2v2ϭ2ϫ10Ϫ13, than for ␯
and the measured
1,3
bending distributions from experiments with long ⌬t or high
pressure of Ar must be regarded with some caution.
The relaxation of H O( 1,3ϭ1) by HCl must be dis-
v
2
cussed separately, because the H2O emission intensity from
reaction ͑4͒ was very weak. Since only H O( 1,3ϭ1) or
v
2
HOD( 3ϭ1) can be products from ͑4, 4D͒, vibrational re-
v
laxation cannot be experimentally identified from the change
in the emission spectra with variation of HCl concentration.
Fortunately, rate constants and product states have been ex-
plicitly identified for HCl as the collision partner.35,36 Our
experiments for the HCl reaction were run at 0.7 Torr with a
reaction time of 0.35 ms and ͓HCl͔ up to
8
ϫ1013 molecule cmϪ3. Process ͑7͒ is the major (у0.7) re-
laxation pathway for H2O(␯1,3) molecules colliding with
HCl, rather than V-V transfer, but the relaxation time of
H O( 1,3ϭ1)
is
about
1.5
ms
for
͓HCl͔
v
2
ϭ8ϫ1013 molecule cmϪ3, and this relaxation route can be
neglected. The number of collisions with Ar is two times
larger than in experiments at 0.5 Torr, but the vibrational
relaxation time ͑0.72 ms͒ is still longer than the reaction
FIG. 1. Infrared chemiluminescent spectra of H2O and HOD. Raw infrared
chemiluminescent spectra from reactions of OH ͑a͒ and OD ͑b͒ with cyclo-
hexane at 0.5 Torr (⌬tϭ0.25 ms), NO ϭ3ϫ1013, ͓OH͔ϭ͓OD͔ϭ6ϫ1012
͓
͔
2
time. We conclude that quenching of H O( 1,3ϭ1) by HCl
v
2
and ͓C6H12͔ϭ1.6ϫ1013 molecule cmϪ3. The response corrected spectra in
the 3300–3900 cmϪ1 region are shown for H2O ͑c͒ and HOD ͑d͒ together
with the simulated best-fit spectra ͑upper spectrum with dashed lines͒ for the
distributions given in Tables II and III. The scale of the spectrum from the
OH reaction has been expanded by a factor or 2.7 in ͑c͒.
for Ar should not be of major concern in the experiments for
reaction ͑4͒. The question of V-V exchange for H O(2 2) or
v
2
HOD( 1,2ϭ1) states will be discussed when the data for
v
reaction ͑4,4D͒ are presented.
C. Assignment of vibrational distributions
equilibrated (
,
,
)/( ϩi, Ϫ2i, 3), iϭ0,1,..., levels
v1 v2 v3 v1 v2
v
The raw emission spectra ͓Figs. 1͑a͒ and 1͑b͔͒ from the
cyclohexane reactions consist of ⌬␯1ϭϪ1 and ⌬␯3ϭϪ1
transitions in the 3300–3900 cmϪ1 range from H2O and
⌬␯3ϭϪ1 transitions in the 3300–3900 cmϪ1 range and
⌬␯1ϭϪ1 and ⌬␯2ϭϪ2 transitions in the 2400–3000 cmϪ1
range from HOD. Vibrational populations were obtained by
computer simulation of the H2O and HOD spectra after they
were corrected for the response function of the detector. The
method is based on calculation of H2O and HOD fundamen-
of HOD and the cited quantum number refers to the maxi-
mum
number (iϭ0) in the set. The utilization of the
v2
2400–3000 cmϪ1 spectra enables the total population in the
3ϭ0 stretching state to be assigned after populations in the
v
dark ͑000͒ and ͑010͒ states are estimated from the population
in the (020)/(100) equilibrated pair, assuming that they fol-
low the statistically calculated relations. The calculated spec-
tra, which are shown by the dashed lines, were fitted to the
experimental spectrum by a least-squares method that gave
equal weight to the entire spectrum.6,7
tal emission bands from the known ␯1 , 2␯2 , and ␯ absorp-
3
tion bands,38 taking into account the cubic dependence of the
emission intensity upon the transition frequency and the
Boltzmann rotational population.6,7 The H2O spectra in the
3300–3900 cmϪ1 range were modeled as a superposition of
bands corresponding to ⌬␯1ϭϪ1 and ⌬␯3ϭϪ1 transitions
The H O(
ϭ0) and HOD( 3ϭ0) populations were
v1,3
v
2
also assigned using information-theoretical analysis. Linear
vibrational surprisal plots have been found for reactions of
OH and OD radicals with HBr, HI, and GeH4, which gave
excitation up to three or four stretching quanta. The hydro-
carbon reactions have only two points for each surprisal plot,
and the linearity of the plots was assumed. The prior distri-
butions, Pؠ, which are given in Tables II and III, were cal-
culated as described in Refs. 6 and 7 using two statistical
reference models: model I, which treats the products as
H2O͑HOD͒ϩan atom for computation of the density of
states, and model II, which includes the three rotational de-
grees of freedom of the alkyl radical in the calculation of the
from (
,
) vibrational states with
ϭ
ϩ 3ϭ1 and
v1,3 v2
v1,3 v1 v
2, and 2р3. The HOD spectra consist of two parts: a
v
3300–3900 cmϪ1 range, which can be simulated by funda-
mental and combination bands from ⌬␯3ϭϪ1 transitions
from the levels with 3ϭ1 and 2, 1,2р4 and a
v
v
2400–3000 cmϪ1 range composed of emission bands from
⌬␯1ϭϪ1 and ⌬␯2ϭϪ2 transitions ͓see Figs. 1͑a͒ and
1͑b͔͒. The notation
is used to denote the reservoir of
v1,2
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2438
J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
TABLE II. Vibrational distribution of H2O from the reactions of OH with cyclohexane, n-butane, and neopen-
tane.
P01,3
P01,3
b
c
c
\
0
1
2
у3
P1,3
P1,3
Model II
P1,3
Model I
v2
a
v1,3
cyclo-C6H12
0
1
2
P2
P20
-
-
-
8.3
-
-
8.8
42.6
48.6
64.1
31.8
4.1
5.0
44.4
50.6
74.4
24.2
1.3
23.0
39.5
61.5
47.2
15.4
13.8
29.5
27.4
46.7
53.3
9.1
14.6
-
10.8
n-C4H10
0
1
2
P2
P20
-
-
-
9.6
-
5.8
-
12.0
53.6
34.4
68.5
29.5
2.0
5.1
57.8
37.1
78.7
20.9
0.4
25.4
28.9
53.5
50.0
20.1
10.2
30.5
27.8
60.9
39.1
10.0
13.6
6.0
8.6
neo-C5H12
0
1
2
P2
P20
-
-
-
8.2
-
17.5
70.5
12.0
73.1
26.4
0.5
4.9
81.3
13.8
83.0
17.0
0.05
50.0
14.5
63.1
53.3
27.3
85.5
14.5
28.3
27.1
8.5
12.9
Ͻ2.5d
6.8
a
ϭ
ϩ
.
v1,3 v1 v3
bP1,3(0) is neglected.
cP1,3(0) from linear surprisal plots.
dEstimated upper limit of P (Ͼ3) for 1,3ϭ0.
v
2
density of states. The differences between Pؠ1,3(fv)H O and
III. EXPERIMENTAL RESULTS
2
Pؠ3(fv)HOD should be remembered. The prior for H2O in-
A. Reactions of OH and OD with cyclohexane
cludes the statistical distributions for both
and
states,
v3
v1
whereas the prior for HOD is just the statistical distribution
for states.
The emission spectra of H2O and HOD from reactions
͑1͒ and ͑1D͒, corrected for response function, are shown in
v3
TABLE III. Vibrational distribution of HDO from the reactions of OD with cyclohexane, n-butane, and
neopentane.
P30
Model I
P30
Model II
a
b
c
c
\
0
1
2
3
у4
P3
P3
P3
v1,2
v3
cyclo-C6H12
2.9
0
1
2
P1,2
P01,2
5.7
33.2
28.1
67.0
28.0
3.2
3.4
5.0
11.6
18.4
5.3
8.2
1.7
3.2
18.8
48.0
33.1
14.2
48.1
37.7
82.2
16.5
1.3
9.4
50.8
39.8
86.6
11.9
0.4
13.5
23.4
4.9
13.5
2.9
16.8
n-C4H10
0
1
2
P1,2
P01,2
7.1
27.1
19.5
53.7
30.9
4.8
7.8
7.6
20.2
19.6
6.8
11.1
2.4
4.1
1.7
22.8
50.1
27.1
17.5
49.8
32.8
84.7
14.7
0.6
10.2
54.1
35.6
89.9
9.9
0.2
17.9
23.7
6.5
12.7
1.7
13.0
neo-C5H12
0
1
2
-
-
-
-
28.3
61.9
9.8
87.9
12.0
0.13
11.6
76.3
12.1
92.5
7.5
0.01
52.2
13.3
57.7
34.3
15.2
19.3
86.7
13.3
d
P1,2
16.5
21.1
20.7
23.8
3.1
11.7
1.9
9.1
P01,2
aSee Sec. II C for definition of
.
v1,2
bP3(0) from computer simulation.
cP3(0) from linear surprisal plots.
dEstimated using statistical P1,2 distribution for 3ϭ0.
v
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J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
2439
Figs. 1͑c͒ and 1͑d͒. Tables II and III give the vibrational
distributions that were used to obtain the simulated spectra.
The H2O distribution shows a high degree of stretching ex-
citation with P1,3(1:2)ϭ47:53. This stretching excitation for
H2O is confirmed by the distribution obtained for HOD by
simultaneous simulation of the 3300–3900 cmϪ1 and
2400–3000 cmϪ1 ranges, which gives P3(0:1:2)
ϭ19:48:33. The P3 distribution is inverted, with the maxi-
mum population in ϭ1. The
v3
distribution for H2O and
v2
distribution for HOD are narrow and the excitation
the
v1,2
of the bending mode is very modest. In fact, the thermo-
chemical limits are H O( 2)ϭH2O(1,3) and ͑2,1͒ and
,
v1,3
v
2
the P ( 1,3ϭ1) distribution does not extend to the thermo-
v
2
chemical limit. The limits for HOD are (
, 1,2)ϭ(1,4) and
v
v3
͑2,2͒ and this distribution also does not reach the limit.
The best vibrational distributions for H2O and HOD, se-
lected with the help of surprisal analysis, are P1,3(0:1:2)
ϭ9:43:49 and P3(0:1:2)ϭ14:48:38, respectively. Better
agreement between the measured P ( 3) distribution of
v
3
HOD and that obtained from a linear surprisal plot was ob-
tained using the model I prior. The satisfactory agreement
between the measured P3(0) and the surprisal extrapolation
for HOD supports the use of linear surprisals for P1,3
H2O. The mean fractions of the available energy released as
( 1,3) of
v
FIG. 2. Response corrected chemiluminescent spectra of H2O and HOD.
Reactions of OH ͑a͒ and OD ͑b͒ with n-butane at 0.5 Torr (⌬t
ϭ0.25 ms),
NO ϭ1.6ϫ1014, ͓OH͔ϭ͓OD͔ϭ2ϫ1013 and ͓C4H10͔
͔
2
vibrational energy are f (H O) ϭ0.62 and f (HDO)
͘
͓
͗
͘
͗
v
2
v
ϭ2ϫ1013 molecule cmϪ3. The upper spectra shown by the dashed lines are
the simulated best-fit spectra for the distributions given in Tables II and III.
The scale of the spectrum for the OH reaction has been expanded by a factor
of 2.
ϭ0.57. The fraction of the vibrational energy in bending for
H2O is / f ϭ0.14, and in the O–H stretch mode of
f
͗
͘ ͗ ͘
v
v2
HOD is f / f ϭ0.84. The bending distribution, P ( 2),
v
͗
͘ ͗ ͘
v3
v
2
for H2O was calculated and renormalized assuming that the
P ( ϭ0) component is similar to that for P ( 1,3ϭ1).
v1,3
v
2
2
The bending excitation is below the statistical prediction and
best-fit calculated spectra shown by the dotted curves were
obtained with the vibrational distributions given in Tables II
and III. The experimental H2O and HOD vibrational distri-
butions are P1,3(1:2)ϭ61:39, and P3(0:1:2)ϭ23:50:27.
The P3 distribution is strongly inverted, as for cyclo-C6H12,
the P distribution has a inverse correlation with
,
v1,3
2
The emission from H2O molecules produced in reaction
͑1͒ can be weaker than the HOD emission from reaction ͑1D͒
for three reasons. First, the nearly isoenergetic ␯ and ␯
3
1
stretching vibrational levels of H2O are equilibrated in Ar
with the maximum population in 3ϭ1. However, the rela-
v
carrier gas,6,34 giving ␯3 :␯1ϭ0.36:0.64 relative populations
tive populations in
ϭ2 and 3ϭ2 are slightly less than
v1,3
v
at 300 K. Since the sum band intensity for the ␯ fundamen-
1
for the reaction with cyclo-C6H12. The bending distributions,
P2(H2O) and P1,2(HOD), from reactions ͑1,1D͒ and ͑2,2D͒
are similar, but the distributions from butane are slightly
more extended.
The H2O and HOD distributions, with P1,3(0) and
P3(0) estimated via the surprisal plots, are P1,3(0:1:2)
ϭ12:54:34 and P3(0:1:2)ϭ18:50:33 after the renormaliza-
tion. The agreement between the measured HOD distribution
from analysis of the ⌬␯1ϭϪ1 plus ⌬␯2ϭϪ2 spectra and
that obtained from the linear surprisal plot is not as good as
for reaction ͑1͒; this is explained by the difficulty of fitting
the lower quality spectrum in the 2400–3000 cmϪ1 range
tal, Sؠv(␯1 ,H2O), is only about 0.07 of that for
Sؠ (␯3 ,H2O),38 the ␯ excitation of H2O gives an effective
1,3
v
intensity of 0.427Sؠv(␯3 ,H2O). Second, the O–H oscillator
strength in HOD, Svؠ (␯3 ,HOD), is higher than S0v(␯3 ,H2O)
by a factor of ϳ1.3;38 this ratio of band intensities was ob-
tained from the HITRAN absorption band sum intensities
1.42ϫ10Ϫ21 cmϪ1/molecule cmϪ2 for HOD and 7.20
ϫ10Ϫ18 for H2O, and the natural H to D isotope abundance
99.985:0.015. Third, the rate constant for a reaction with OD
can be smaller ͑normal secondary kinetic-isotope effect͒ or
larger ͑inverse secondary kinetic-isotope effect͒. Based upon
two sets of spectra, the integrated intensity ratio, IHOD /IH O
,
from ͑2D͒. The mean fractions are f (H O) ϭ0.65 and
͗
͘
2
v
2
f (HOD) ϭ0.60. The Pc and the Pb3 distributions give
was 2.9Ϯ0.6. Including the ϭ0–2 and 1,3ϭ0–2 relative
v3
v
͗
͗
͘
v
1,3
populations from Tables II and III in the analysis gives
͓HOD͔/͓H2O͔ϭ1.1Ϯ0.3. Thus the secondary kinetic-isotope
effect is effectively unity.
f
/ f ϭ0.19 as the fraction of energy in the bending
͘ ͗
͘
v2
v
vibration of H O, and f / f ϭ0.81 as the fraction of the
͗
͘ ͗
͘
v
2
v3
energy in the O–H stretch of HOD. As would be expected
for secondary C–H bonds, the energy disposal for reactions
͑1,1D͒ and ͑2,2D͒ are very similar.
B. Reactions of OH and OD with n-butane
The ratio of integrated emission intensities, IHOD /IH O
,
2
The H2O and HOD spectra in the 3300–3900 cmϪ1
range from reactions ͑2͒ and ͑2D͒ are shown in Fig. 2. The
was 2.7Ϯ0.6 from comparison of two pairs of spectra at 0.5
Torr. Conversion to the ͓HOD͔/͓H2O͔ ratio gives 1.0Ϯ0.2,
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2440
J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
f (HOD) ϭ0.51; the fraction of bending energy for H O is
͗
͘
v
2
0.19, and the fraction for O–H stretching in HOD is 0.76.
We used reactions ͑3͒ and ͑3D͒, which mainly give mol-
ecules with one excited stretching quantum, to check for the
relative relaxation rates of H2O (␯1,3) and HOD (␯3). The
relative H2O and HOD emission intensities measured at 0.5
Torr (⌬tϭ0.25 ms) was compared with that measured at 0.7
Torr (⌬tϭ0.35 ms) and 1.25 Torr (⌬tϭ0.6 ms). The ratios
of the integrated intensities, IH O /IHOD , were 0.15, 0.17, and
2
0.05, respectively. Assuming that the relaxation rates are not
identical, the data prove that the relaxation of H O(
v1,3
2
ϭ1,2) and HOD( 3ϭ1,2) for Ͻ0.7 Torr may be neglected.
v
For higher pressure and longer time, conversion of
H O(
2
ϭ1) to H O(2 2) occurs. This rate is expected to
v1,3
v
2
be faster than for the similar process with HOD( 3ϭ1).
v
The spectra in Fig. 3 clearly show that IH O is much
2
weaker than IHOD for the same C H
and ͓OH͔ϭ͓OD͔.
͔
͓
5
12
The actual IHOD /IH O ratio is 6.2Ϯ1.2, which is twofold
2
larger than for reactions ͑1͒ and ͑2͒. Conversion of the inten-
sity ratio to a concentration ratio gives ͓HOD͔/͓H2O]ϭ1.9
Ϯ0.4, and an inverse secondary kinetic-isotope effect ap-
pears to exist for abstraction from primary C–H bonds. As a
point of contrast with the HCl reaction, vide infra, it should
be noted that reactions ͑3͒ and ͑3D͒ do give the same energy
disposal pattern, even though kOH /kODХ0.5.
FIG. 3. Response corrected chemiluminescent spectra of H2O and HOD.
Reactions of OH ͑a͒ and OD ͑b͒ with neopentane at 0.5 Torr (⌬t
Ϸ0.25 ms),
NO ϭ7ϫ1013, ͓OH͔ϭ͓OD͔ϭ2ϫ1013 and ͓C5H12͔
͔
2
͓
ϭ8ϫ1013 molecule cmϪ3. Reactions of OH ͑c͒ and OD ͑d͒ at 0.7 Torr
(⌬tϷ0.35 ms),
NO ϭ9ϫ1013,
͓OH͔ϭ͓OD͔ϭ3ϫ1013
and
͓
͔
2
͓C5H12͔ϭ1.1ϫ1014 molecule cmϪ3. The scales for the spectra in ͑a͒ and ͑c͒
have been expanded relative to those of ͑b͒ and ͑d͒ by a factor of 4. The
upper spectra shown by the dashed lines in ͑a͒ and ͑b͒ are the simulated
best-fit spectrum for the distributions given in Tables II and III.
D. Reactions of OH and OD with HCl
The rate constants for reactions ͑4͒ and ͑4D͒ are about
50% smaller than for the neo-C5H12 reactions, but the same
range of concentrations and ⌬t still could be used for the ͑4,
4D͒ experiments. The raw spectra in the 2500–3900 cmϪ1
range from reactions ͑4͒ and ͑4D͒ taken at 0.7 Torr and
͓HCl͔ϭ6ϫ1013 molecule cmϪ3 are shown in Fig. 4. The
most striking result is the absence of H2O chemilumines-
cence from reaction ͑4͒, whereas the HOD emission intensity
from ͑4D͒ is comparable with those from the OD reactions
with hydrocarbons. The emission in the 2600–3000 cmϪ1
range observed from both reactions is the fundamental band
of HCl. The V–V energy transfer from H2O and HOD to
HCl will be analyzed in Sec. III E. The 3200–3900 cmϪ1
and the secondary kinetic-isotope effect for ͑2,2D͒ is negli-
gible and in agreement with the cyclohexane result.
C. Reactions of OH and OD with neopentane
The rate for abstraction from primary C–H is slower
than for reactions ͑1͒ or ͑2͒, and the C5H12 concentration was
increased by a factor of 4, relative to the cyclo-C6H12 and
C4H10 reactions, to obtain the 3300–3900 cmϪ1 spectra
shown in Fig. 3. Comparison of Figs. 3͑a͒ and 3͑b͒ shows
that the H2O emission is nearly five times weaker than from
the HOD. The same difference is shown in the spectra ac-
quired at 0.7 Torr and ⌬tϭ0.35 ms. The spectra measured at
0.5 Torr with a reaction time of 0.25 ms ͓Figs. 3͑a͒ and 3͑b͔͒
were used for simulations and the best-fit vibrational distri-
butions are given in Tables II and III. Since the HOD chemi-
luminescence in the 2400–3000 cmϪ1 range did not exceed
the noise level, the P3(0) population could not be estimated
from the experimental data. The available energy for reaction
͑3͒ is 22.4Ϯ2.2 kcal molϪ1, which is 2–3 kcal molϪ1 less
chemiluminescence from ͑4D͒ is the ␯ fundamental band of
3
HOD with a distribution of ͑001͒ and (011)ϭ73:27. The
emission from the ␯ and 2␯ modes of HOD with the band
1
2
centers at 2724 and 2782 cmϪ1, respectively, could not be
observed, because, even at the lowest HCl concentration and
reaction time, this region was always overlapped by the rela-
tively strong HCl emission. This intrinsic overlap is illus-
trated in Fig. 5͑c͒, which shows the ␯1 , 2␯2 , and ␯ funda-
3
mental bands of HOD.
If the secondary kinetic-isotope effect is kOH /kODϭ1.0
and if the same fraction of H2O and HOD molecules are
produced with one quantum of stretching excitation, the
than for ͑2͒, and E is just sufficient for excitation of the
͗
͘
v
second O–H stretching level. The 1,3ϭ2 or 3ϭ2 state
v
v1,3
v
IH O /IHOD ratio should be 0.33. The maximum inverse
populations are about 14% of the
or 3ϭ1ϩ2 distribu-
v
2
tions. The P3(0) and P1,3(0) were estimated from the sur-
prisal analysis for model I ͑see Tables II and III͒; the renor-
malized P1,3 and P3 distributions are inverted with
kinetic-isotope effect22 would be 0.5 and the smallest ex-
pected intensity ratio would be Ϸ0.17, if both ͑4͒ and ͑4D͒
have the same energy disposal. The experimental emission
intensity ratio from reaction ͑4͒ and ͑4D͒ was difficult to
P1,3(0:1:2)ϭ20:69:12 and P3(0:1:2)ϭ28:62:10. The mean
fraction of vibrational energy is f (H O) ϭ0.54 and
assign because IH O was so weak. In fact, no H2O emission
͗
͘
v
2
2
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J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
2441
FIG. 4. Raw infrared emission spectra from the reactions of OH and OD
FIG. 5. Comparison of the HOD emission spectra from the reactionsof OD
with HCl: ͑a͒ OHϩHCl reaction, 2 Torr (⌬tϭ1.1 ms) with OH ϭ8
͓
͔
with HCl and HBr at 1 Torr and ͓OD͔ϭ4ϫ1013 molecule cmϪ3
: ͑a͒
ϫ1013 and ͓HCl͔ϭ2.8ϫ1014 molecule cmϪ3; ͑b͒ ODϩHCl reaction, 1.2
ODϩHCl reaction with ͓HCl͔ϭ6ϫ1013 molecule cmϪ3; ͑b͒ ODϩHBr reac-
Torr
(⌬tϭ0.6 ms)
with
OD ϭ4ϫ1013
and
͓HCl͔
͓
͔
tion with ͓HBr͔ϭ1.6ϫ1013 molecule cmϪ3; ͑d͒ calculated ␯3 , ␯1 , and 2␯
2
ϭ6ϫ1013 molecule cmϪ3; ͑c͒ OHϩHCl reaction, 0.7 Torr (⌬tϭ0.35 ms)
with OH ϭ4ϫ1013 and ͓HCl͔ϭ6ϫ1013 molecule cmϪ3; ͑d͒ ODϩHCl re-
fundamental emission bands of HOD. The spectrum used for simulation was
essentially identical to that shown in ͑a͒,but the pressure was 0.7 Torr.
͓
͔
action,
0.7
Torr
(⌬tϭ0.35 ms)
with
OD ϭ4ϫ1013
and
͓
͔
͓HCl͔ϭ6ϫ1013 molecule cmϪ3. The intensity scale for ͑b͒ has been reduced
by a factor of 8.5.
0.7 Torr for the following concentrations ͑in mole-
cule cmϪ3͒:
HCl ϭ1.9ϫ1013,
HBr ϭ1.5ϫ1013,
͓ ͔
͓
͔
was observed from ͑4͒ using typical reagent concentration
for ⌬tϭ0.3 to 1.2 ms and no emission was observed even for
OH ϭ8ϫ1013 and ͓HCl͔ϭ3ϫ1014 molecule cmϪ3. Our es-
͓H2͔ϭ͓D2͔ϭ1.7ϫ1013, and NO ϭ4.5ϫ1013. The HOD
͓
͔
2
and H2O intensities were linearly dependent on the HCl and
HBr concentrations in this range, which shows that vibra-
tionally excited HOD and H2O molecules were not quenched
by the reactants. The relative integrated intensities were ͑in
arbitrary units͒ 1.03 (ODϩHCl), 7.02 (OHϩHBr) and 11.43
(ODϩHBr). The H2O emission from OHϩHBr corresponds
to P1,3(0:1:2:3)ϭ20:42:28:6;6 Boltzmann weights for the
͓
͔
timate for an upper limit to the IH O /IHOD ratio from ͑4͒ and
2
͑4D͒ is 0.07Ϯ0.07. Clearly, the inverse kinetic-isotope effect
alone cannot explain such a low yield of H O( 1,3ϭ1).
v
2
In order to estimate the fraction of HOD molecules with
3Þ0 from ͑4D͒, comparisons were made between
v
ODϩHCl and ODϩHBr ͑and OHϩHBr͒. The HBr reactions
were chosen rather than reactions ͑1͒–͑3͒, because the
equilibrated ( ϩi,
,
Ϫi)Ϫ(
,
, 3) levels reduce to
v1
v2 v3
v1 v2 v
0.44 Sؠv(␯3 ,H2O) for the normalized spectrum, i.e., ␣
ϭ0.44. This assignment assumes equal intensities for all
P
1,3(0) and P3(0) populations are better defined for the HBr
reaction.7 The ODϩHBr reaction provides the more direct
comparison of the HOD intensity, but its rate constant has
not been reported ͑except for our estimate7͒, and that is why
we used both reference reactions. The fraction of HOD mol-
combination bands with the same 3 . The HOD emission
from the ODϩHCl reaction can be considered as a pure
Sv(␯3 ,HOD) band (␤ϭ1), since equal transition intensities
v
were assumed for the ͑001͒-͑000͒ and ͑011͒-͑010͒ bands. For
ecules from ͑4D͒ with 3Þ0 can be estimated as Eq. ͑9͒
v
22
k
4Dϭ4.4ϫ10Ϫ13 cm3 moleculeϪ1 sϪ1 and kO2H4ϩHBr values
from 0.45 to 1.1ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1
,
we obtain
f
Þ0͒ϭ kHBr /kHCl͒ ͓HBr͔/͓HCl͔͒ IHCl /IHBr
͒
͑ ͑ ͑
͑v3
f( 3Þ0)ϭ0.6 to 1.1. The HOD distribution from ODϩHBr
v
ϫ ␣S0 PR ͒/␤S0 Pr ͒͒,
͑9͒
͑
͑
͑
v3
is P3(0:1:2:3)ϭ30:35:29:3,6 and the normalized spectrum
corresponds to 1.01Svؠ (␯3 ,HOD). Taking kH /kDϭ1.3 for the
secondary kinetic isotope effect of OHϩHBr and ODϩHBr
HBr
HCl
v3
where kHBr /kHCl is the ratio of rate constants for OH radi-
cals, IHCl and IHBr are the measured integrated water emis-
sion intensities, Sؠ (␯3 ,PrHBr) and Sؠ (␯3 ,PrHCl) are the ␯
as measured in Ref. 2, we obtain f( 3Þ0)ϭ0.7–1.3. Since
v
3
v
v
band sum intensities for triatomic products of HBr and HCl
reactions, and ␣ and ␤ are coefficients that depend on the
vibrational distributions. Some typical spectra are shown in
Fig. 5 for OD reactions with ͓HBr͔ϭ0.25͓HCl͔. Spectra used
for the calculation from all three reactions were recorded at
the fraction cannot exceed unity, the result can be expressed
as f( 3Þ0)Ͼ0.6. Although this conclusion is based on sev-
v
eral approximations, the majority of the HOD molecules
from the ODϩHCl reaction must be produced with one
quanta of O–H stretching vibration. According to the above
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2442
J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
For HCl Ͻ3ϫ1013 molecule cmϪ3, IHOD is a linear func-
͓
͔
tion of ͓HCl͔, whereas the IHCl intensity is proportional to
͓HCl͔2. Thus the HCl emission results from a secondary
step. At higher ͓HCl͔, vibrational quenching of HOD leads to
a constant IHOD , and even to a decrease of IHOD at suffi-
ciently high ͓HCl͔. The slope of the IHCl /IHOD plot can be
used to estimate the sum of the rate constant for reactions
͑10D͒ and ͑11͒. This estimate gives
k10Dϩk11ϭ6
ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1 with an uncertainty of about
50%. This rate constant is larger than the value for ͑10͒,
which partly explains the higher ͑by a factor of 3–6͒ IHCl
from reaction ͑4D͒ than from ͑4͒.
The sum band intensity for the ϭ1← ϭ0 band of
v
v
HCl is equal to 4.75ϫ10Ϫ18, while the intensity sum for the
(020)←(000) band of H2O is only 7.57ϫ10Ϫ20 and that for
38
HOD is 5.64ϫ10Ϫ19 cmϪ1/molecule cmϪ2
.
With account
of the cubic dependence on the transition frequency, the ratio
of Einstein coefficients for the three bands are 50.2͑HCl͒:
1(2␯2 ,H2O):5.1(2␯2 ,HOD). Due to its higher Einstein co-
efficient, the HCl transition can serve to identify the presence
of the H2O(2␯2) or HOD(2␯2ϩ␯1) concentrations. Taking
the upper limit for the rate constant of the V–V exchange
reaction obtained by Zittel and Masturzo,33 kϭ7
ϫ10Ϫ12 cm3 moleculeϪ1 sϪ1, we estimate, that Ͻ0.15 of the
H2O(2␯2) molecules would exchange vibrational quanta
FIG. 6. Dependence of the HOD and HCl emission intensities on HCl con-
centration from the ODϩHCl reaction at
1
Torr and ͓OD͔
ϭ4.6ϫ1013 molecule cmϪ3. The integrated emission intensity from 3400 to
3900 cmϪ1 for HOD is shown by the circles and the IHCl /IHOD is shown by
the squares.
with
HCl
at
0.7
Torr
(⌬tϭ0.35 ms)
and
͓HCl͔ϭ6ϫ1013 molecule cmϪ3. Setting an upper experimen-
tal limit of 0.2 for the ratio of the intensities of H2O(2␯2)
estimations for P ͑0͒, f (HOD) is between 0.50 and 0.67.
͗
͘
3
v
and HCl( ϭ1), we obtain an upper limit of about 0.3 for the
v
In conclusion, the infrared emission data indicate that the
energy disposal for reaction ͑4D͒ is as expected for a direct
abstraction reaction and, thus, attention must be focused on
yield of H2O ͑2␯ or 3␯ ͒ from reaction 1. Based upon this
2
2
indirect analysis for the yield of H2O ͑2␯ and 3␯ ͒ and the
2
2
lack of emission from H2O(␯1,3), we conclude that reaction
(4) mainly releases energy to the translational motion of the
products.
the question of why the H O( 1,2ϭ1) product from ͑4͒ has
v
2
such a small apparent yield.
E. Vibrational excitation of HCl in the OH/OD؉HCl
system
The most probable excitation mechanism of HCl(
ϭ1) in the OH͑OD͒ϩHCl system is vibrational energy
v
F. Reactions of OH and OD with DCl and NH3
Reactions ͑5, 5D͒ are, at least, two times slower than ͑4,
4D͒ and the transition probabilities for D2O(␯1,3) and
HOD(␯1,2) are factors of 6 and 10 smaller than for H2O(␯13)
and HOD(␯3). The only distinct emission from
OH͑OD͒ϩDCl was the fundamental band of DCl in the
1900–2200 cmϪ1 range, which for similar conditions, was
an order of magnitude more intense from reaction ͑5D͒ than
from ͑5͒,as may be seen in Figs. 7͑a͒ and 7͑b͒. No other
transitions could be identified from reaction ͑5͒ ͑the structure
near 2350 cmϪ1 in both spectra corresponds to residual CO2
transfer from the bending levels of H2O ͑or HOD͒.
H O or HOD͒ 2␯ ͒ϩHCl ϭ0͒
͑v
͑
͑
2
2
→H O͑HOD͒ϩHCl ϭ1͒ϩ226 Ϫ104͒ cmϪ1
.
͑v
͑
2
͑10,10D͒
The available energy from ͑4, 4D͒ is sufficient to excite
H2O(3␯2) and this state can also participate in the V–V
process. Since the stretching levels of H2O and the ␯ level
3
of HOD are more than 500 cmϪ1 higher, their V–V ex-
change with HCl( ϭ0) is not important.36 But the O–D
v
absorption.͒
A
weak signal was observed in the
stretch mode of HOD can be involved in V–V exchange:
2600–2900 cmϪ1 range ͓Fig. 7͑b͔͒ from ͑5D͒, which can be
assigned to the fundamental ͑001͒ band of D2O ͓see Fig.
HOD ␯ ͒ϩHCl ϭ0͒→HODϩHCl ϭ1͒Ϫ163 cmϪ1
.
͑
͑v
͑v
1
͑11͒
7͑c͔͒. The sum emission intensity from the ‘‘␯ band’’ of
1,3
According to Zittel and Masturzo, the V–V component, for
H2O(2␯2)ϩHCl is a small part (Ͻ0.1) of the overall rate
constant (4.7ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1), and the major
D2O is approximately three times weaker than S0v(␯1) of
HOD, and the weak D2O emission may correspond to sub-
stantial excitation of stretching vibrations of D2O from reac-
tion ͑5D͒. Thus a parallel with ͑4, 4D͒ seems to exist with
more emission from the reaction of OD than from OH with
DCl. Reactions ͑5͒ and ͑5D͒ could be followed by the energy
exchange processes,
product is just H O( 2ϭ1). Since ͑10D͒ is endoergic, the
v
2
branching fraction should be even less. Plots of the inte-
grated emission intensity, IHOD and of the intensity ratio
I
HCl /IHOD versus HCl concentration are presented in Fig. 6.
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J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
2443
FIG. 8. Chemiluminescent spectra produced in the reactions of OH and OD
with ammonia at 1.0 Torr (⌬tϭ0.5 ms), ͓NO2͔ϭ1.2ϫ1014,
͓OH͔ϭ͓OD͔ϭ4.2ϫ1013, and ͓NH3͔ϭ1.7ϫ1014 molecule cmϪ3. Spectra are
presented on the same intensity scale.
FIG. 7. Raw emission spectra from the reactions of OH and OD with DCl at
1
Torr (⌬tϭ0.5 ms) and ͓OH͔ϭ͓OD͔ϭ4ϫ1013 molecule cmϪ3
:
͑a͒
OHϩDCl reaction with ͓DCl͔ϭ2.2ϫ1014 molecule cmϪ3; ͑b͒ ODϩDCl re-
action with ͓DCl͔ϭ1.8ϫ1014 molecule cmϪ3; ͑c͒ the calculated D2O (␯3)
fundamental emission band. Spectra ͑a͒ and ͑b͒ are plotted on the same
scale.
cyclohexyl radical on a slower time scale than transfer of the
H atom, thus, this energy is retained by the cyclohexyl
radical.15,31
HOD 2␯ ͒ϩDCl ϭ0͒→HODϩDCl ϭ1͒ϩ606 cmϪ1
,
͑
͑v
͑v
2
͑12͒
͑2͒ The fraction of HOD( 3ϭ0) molecules from reac-
v
D O 2␯ ͒ϩDCl ϭ0͒→D OϩDCl ϭ1͒ϩ222 cmϪ1
,
͑
͑v
͑v
2
2
2
tions ͑1D͒ and ͑2D͒ determined by spectra simulation of the
͑13͒
␯
emission and estimated from the surprisal analysis for a
1,2
*
and the larger DCl intensity emission from reaction ͑5D͒
compared to reaction ͑5͒ can be explained by the larger rate
constant associated with the smaller energy defect for reac-
tion ͑13͒ and/or a higher yield of vibrationally excited D2O
molecules.
model I ͑HODϩatom limit͒ prior are in satisfactory agree-
ment. This agreement confirms the use of linear surprisal
plots to estimate P1,3(0) for the OH reactions and P3͑0͒ for
reaction ͑3D͒.
͑3͒ The vibrational distributions are strongly inverted
Reaction ͑6͒ is 3 kcal molϪ1 less exothermic than reac-
tion ͑4͒, and only one stretching level can be expected. The
spectra from NH3 shown in Fig. 8 were recorded with the
same concentrations of OH and OD. The emission from re-
action ͑6͒ was hardly above the experimental limit of sensi-
tivity, but the HOD͑001͒ emission from reaction ͑6D͒ obvi-
ously exceeded the noise level. The spectra in Fig. 8 indicate
a trend similar to the behavior of reactions ͑4͒ and ͑4D͒.
with a preferred population for HOD( 3ϭ1) in all the OD
v
reactions and for H O( 1,3ϭ1) in reactions ͑2͒ and ͑3͒ and
v
2
1,3ϭ2 in reaction ͑1͒. In contrast, the bending distributions
v
decrease with increasing quantum number and the experi-
mental P2 distribution has substantially more population in
2ϭ0 than even the model I prior distribution. The large
v
overall f Ϸ0.6 for reactions ͑1͒–͑3͒ is divided into 80%–
͗
͘
v
85% excitation of the stretching modes and 15%–20% exci-
tation of the bending mode. This pattern of energy disposal is
only consistent with a direct abstraction process.
IV. DISCUSSION
͑4͒ The comparison of IH O /IHOD gave kOH /kODϷ1.0
2
A. Reactions with cyclo-C6H12, n-C4H10, and
neo-C5H12
for reactions ͑1, 1D͒ and ͑2, 2D͒, The measured thermal rate
constant ratios for these reactions also are close to unity,17–19
although kOH /kOD for butane is ϳ0.9. The IH O /IHOD ratio
The results from the reactions with primary and second-
ary C–H bonds may be summarized as follows:
͑1͒ The H2O and HOD vibrational distributions extend to
the thermochemical limit, with the exception of cyclohexane
2
from neo-C5H12 suggests an inverse kinetic-isotope effect of
ϳ0.5, Actually, the ͓H2O͔/͓HOD͔ concentration ratio from
neo-C5H12 has considerable uncertainty because P3(0) and
for which the highest accessible levels H O(
ϭ1, 2ϭ2)
v1,3
P1,3(0) had to be assigned by extrapolation of the surprisal
v
2
and D O( ϭ1, 1,2ϭ4) are not populated. Cyclohexane is a
special case because the ring strain energy is released to the
plots. The surprisal plots themselves have a complication,
v3
v
2
because the 1–2 kcal molϪ1 uncertainty in the thermochem-
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2444
J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
istry affects the P01,3(2) and P03(2) values. Nevertheless, re-
actions ͑3, 3D͒ seem to exhibit an inverse secondary kinetic-
isotope effect for abstraction from primary C–H bonds.
Recent measurements of kOH /kOD for CH4 report 0.91.39
The results from ͑1͒–͑4͒ provide an interesting compari-
son with the HBr reaction, which has no activation energy
barrier and a 300 K rate constant22͑b͒ that is approximately
ten times larger than the rate constant for one secondary
II and III. In each case, the P1,2 distribution is broader than
P2 .
Many transition-state models for OH reacting with
alkanes10–13 have been published and the recent work for
10,11
C2H6
should be representative for primary C–H bonds.
The reaction has a small (2.96 kcal molϪ1) barrier located at
rOЈHϭ1.32 and rCЈ–Hϭ1.19 Å with a HOH angle of 97.6°.
Ј
Such an early transition state on a repulsive potential for a
HϩLϪH mass combination is expected to give f Ϸ0.60
͗
͘
C–H bond. The overall
f
from HBr was 0.61
͘
͗
v
v
Ϯ0.06 from numerous quasi-classical calculations for three-
͑H2O͒–0.63͑HOD͒, but 35% of the energy was in bending
and only 65% in the stretching mode. The GeH4 and HI
reactions released even a higher percentage of the vibrational
energy to the bending mode. The quasiclassical trajectory
calculations8 on a model potential for the OHϩHBr reaction
gave results that closely match the energy disposal for reac-
tions with the C–H bonds. The rapid transfer of the H atom
to the oxygen atom mainly deposits energy in the newly
formed bond with little energy released to the bending coor-
dinate. However, as the H2O͑HOD͒ and Br separate in the
exit channel, some energy is transferred from the stretch co-
ordinate to the bending coordinate.8 This coupling mecha-
nism, which may provide the minimum energy for bending
excitation, could be the dominant mechanism for the mini-
mal bending excitation from reactions with C–H bonds. For
body examples.4 The HOH bending frequency in the tran-
Ј
sition states for the HBr and HCl reactions approaches the
value in the water product. This means that the zero point
energy change in the transition state for OD–H R and
Ј
OH–H R is larger than for the reactants and, hence, an in-
Ј
verse secondary isotope effect is predicted by the standard
transition-state theory formulation. According to Clary’s
model,9 the zero-point energy difference for OH͑OD͒ϩH Cl
Ј
is 138 cmϪ1 ͑Ref. 40͒ and this leads to kOH /kODХ0.52. The
model potential9 for OHϩH Cl is unrealistic in a sense be-
Ј
cause ␯(HOH )‡ is actually larger than for H2O itself. We
Ј
calculated the transition-state frequencies for ODϩC2H6
from the ab initio potential10 and found a 123 cmϪ1 zero-
point energy difference relative to OHϩC2H6. Truhlar
et al.41 has evaluated the secondary kinetic-isotope effect for
OH͑OD͒ϩNH3 and they find kOH /kODϭ0.93 for the com-
plete analysis; the vibrational contribution alone gives
kOH /kODϭ0.46. In summary, transition-state theory suggests
than an inverse kinetic-isotope effect could exist for the
larger E
/ E
͘ ͗
bend
cases, a direct release of energy to
͘
stretch
͗
the bending coordinate that depends explicitly on the poten-
tial surface and/or a stretch-bend coupling mechanism may
exist. The variability of the
straction of H atoms from different parent molecules is an
E
/ E
͘ ͗
bend
ratio for ab-
͘
stretch
͗
OH͑OD͒ϩH R reaction, and the magnitude will be between
Ј
intriguing aspect of OH radical reaction dynamics.
0.5 and 1.0.
In principle, the question of how much, if any, energy is
released to the old bond can be investigated from comparison
of the P3(HOD) and P1,3(H2O) distributions, because the
bending excitation is not very important for reactions ͑1͒–
͑3͒. The approximate fraction of the H2O molecules with
zero energy in the old bond can be obtained from the as-
sumption that the vibrational distribution, Pl,n
newly formed bond, is similar to P ( ) of HOD, since
v3
nearly a local (l) mode. Then, the population in the old bond
B. Reactions with HCl
Reactions ͑4, 4D͒ are the most difficult to understand,
but also they are the most interesting. Even if the maximum
inverse kinetic-isotope effect is assumed ͑which is not sup-
( new), in the
v
ported from experimental rate constant data23͒, the IH O is
is
v3
3
2
too weak to be consistent with the experimentally observed
can be described by
a
conditional distribution
v
IHOD . If H O( 1,3ϭ1) is formed, published rate constants
v
2
new
Pl,o͑vold
; (
new)ϭPv
v vold
l,o
) with newϭ0,1,2. If we assume
predict that vibrational relaxation should not give H O(2
)
v2
2
for our experimental conditions.35,36 Furthermore, the low
that the population in oldϭ2 can be neglected, this distribu-
v
tion is P0l,o(0,1,2)ϭPl0,o(0); 1ϪP0l,o͑0͒; 0 ͑for newϭ0͒ and
v
IHCl suggests that the H O(2 2) concentration also is actu-
v
2
P1l,o(0,1,2)ϭPl1,o͑0͒; 1ϪPl1,o͑0͒;
0
͑for
newϭ1͒ and
v
ally low. Based upon extensive experimental tests, we are
P2l,o͑0,1,2͒ϭ1:0:0 ͑for newϭ2͒. The numerical values for
v
forced to conclude that reaction ͑4D͒ yields vibrationally ex-
cited HOD, as expected, but that reaction ͑4͒ yields vibra-
tional cold H2O with most of the energy released as relative
translational energy. That is, a strong isotope effect exists for
the energy disposal. This isotope effect must have its origin
in quantum restrictions arising from the low density of
vibrational–rotational product states for this reaction with
low exoergicity.
Our attempt to use the OH/OD reactions with DCl and
NH3 to provide examples with similar, but still more restric-
tive thermochemistry and activation barriers, to help eluci-
date the results from the HCl reaction were not convincing
because of the weak signals. However, the qualitative results
suggested that the OD reactions did give higher emission
intensities than the OH reactions.
P0l,o͑0͒ and P0l,o͑1͒ can be found from the P1,3
( 1,3) data,
v
thus
P
1,3(0)ϭP0l,o(0)•P3(0),
P1,3(1)ϭP0l,o(1)•P3(0)
ϩP1l,o(0)•P3(1), which gives for reaction ͑1͒ values of
P0l,o͑0͒ϭ0.64; P0l,o͑1͒ϭ0.36 and Pl1,o͑0͒ϭ0.81; P1l,o͑1͒ϭ0.19.
The total distribution in the old bond is Pl,o͑0:1:2͒
Ϸ0.86:0.14:0, which corresponds to about 5% of the avail-
able energy in the old bond. The preceding analysis applied
to reactions ͑2͒ and ͑3͒ gives the same result as for ͑1͒. The
difference between P3(HOD) and P1,3(H2O) distributions
from the isotopic reactions, including the inequality of
P3(0)ϾP1,3(0) indicate that the old bond receives a small
fraction of the reaction energy, and it is not a ‘‘pure’’
spectator. The same conclusion can be reached by
comparing the P ( 2) and P1,2
( 1,2) distributions in Tables
v
v
2
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J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
2445
C. Comparison with F-atom reactions
If our conclusion regarding a different energy disposal
for ͑4͒ versus ͑4D͒ is correct, then an explanation is needed
The energy disposal to HF from the reactions of F atoms
with cyclohexane and neopentane are directly compared to
the results for OH reactions in Table IV. Since F atoms ab-
stract both primary and secondary H atoms, CD3CH2CD3
gives the best comparison for secondary abstraction. A simi-
for why the HOϩH Cl reaction gives mainly translational
Ј
energy rather than HOH
͑ 1ϭ1 or 3ϭ1͒, whereas
v v
Ј
DOϩHCl favors DOH( 3ϭ1) and much less translational
v
energy. One obvious difference is that
is a local mode of
v3
HOD and the initial release of energy for HϩLϪH dynam-
larity, including
f Ϸ0.6 and linear surprisal plots, cer-
͘
v
͗
ics is directly to this local mode coordinate.8 On the other
tainly exists for both F and OH reactions. Since the bending
excitation is low for OHϩhydrocarbons, the analogy be-
tween F atoms and OH reactions is closer for hydrocarbons
than for HBr. Some individual details relating to polyatomic
product fragments are worth noting. Systematic studies of F
atomϩHR reactions in which the R was a radical with a
large stabilization energy ͑such as allyl radical͒ established
that this stabilization energy generally was not available to
HF. For HϩLϪH(R) dynamics, the light H atom is trans-
ferred before the R can relax to its equilibrium configuration.
The Fϩcyclohexane case exhibits some evidence for a sta-
bilization energy and modified available energies together
with different models of the prior were explored in the sur-
hand, the initial energy release to the OH coordinate of
Ј
H OH subsequently must evolve to the normal modes of the
Ј
isolated H OH molecule. Since the local mode with one
Ј
quantum of excitation is a linear combination, with equal
weights, of the
and
normal modes, we see no reason
v3
v1
why the evolution step should be restricted. Furthermore, the
OHϩDCl reaction did not seem to favor formation of
HOD͑ 1ϭ1). Attention probably should be focused upon
v
the existence of a fortuitous resonance in the ODϩHCl case
that aids formation of HOD( 3ϭ1).
v
The dynamics for HϩLϪH mass combinations is domi-
nated by the potential-energy release to the new bond as the
H atom hops across the ridge ͑plateau͒ separating the en-
trance and exit channels. The acquisition of one quantum of
OH stretch energy requires that 58% of the available energy
of ͑4͒ be released in the hop. This fraction is slightly smaller
͑56%͒ for the OD reaction because of the zero-point energy
effects. In quantum scattering formulations, one searches for
correlations connecting entrance and exit channel diabats.
Clary et al.9,26 actually examined the OD/OHϩHCl reactions
using their rotating-bond approximation. These calculations
predict the same result for both OH and OD, namely that
neither H2O nor HOD will have significant stretch or bend-
ing excitation. Thus, these calculated results are not helpful.
Based upon the similarity of the OHϩHBr and the OHϩHCl
potentials developed by Clary and the need8 to alter the exit
channel properties of their HBr potential ͓which underesti-
prisal plots3,14 and this is why different E
Table IV for Fϩcyclo-C6H12. The OHϩcyclohexane reac-
tion also shows some evidence for the role of a stabilization
energy, because the H2O and HDO excitation are one
level below the thermochemical limit. The role of stabiliza-
tion ͑or strain energy͒for cyclohexane has been summarized
by Hossenlopp,31 and it will not be discussed further.
were used in
͘
av
͗
v2
V. CONCLUSIONS
The H2O͑HOD͒ vibrational distributions from reactions
of OH͑OD͒ with primary and secondary C–H bonds have-
been determined from analysis of the infrared chemilumines-
cence in a fast flow reactor. The vibrational distributions for
H O and HOD are self-consistent. The overall f (H O) is
͗
͘
mates f (H O) ͔, the HCl potential also should be changed.
͗
͘
2
v
2
v
2
0.60Ϯ0.05 with a strong inversion in the stretching distribu-
tion. About 80% of the vibrational energy is released to the
stretching modes and 20% to the bending mode. The overall
energy disposal to H2O͑HOD͒ resembles that from FϩHR
reactions, and most of the energy is released to the new bond
of H2O͑HOD͒. Based upon model calculations for the
OHϩHBr reaction,8 the bending mode from the OHϩHR
reactions probably receives its energy by coupling to the
stretch mode during traversal of the H2O͑HOD͒ϩR exit
channel. The old OH or OD bond receives little energy, but
it is not a pure spectator. A strong correlation exists for an
increasing fraction of bending excitation of H2O ͑or HOD͒
with increasing reaction exoergicity ͑or increasing reaction
rate constant͒ in the HR, HBr, and GeH4 series. The variabil-
ity of the energy released to the bending mode is an impor-
tant dynamical property for bimolecular water forming reac-
tions. The OH/OD reactions with C5H12 seem to display an
The rotating bond model does not explicitly include the H–O
coordinate, so it would be unrealistic to expect these calcu-
lations to identify the difference between the OH and OD
energy disposal.
Two other differences exist between the OH/ODϩHCl
systems. At thermal collision energies, more rotational levels
are populated for OD because of its smaller moment of in-
ertia. However, the reaction cross section declines with in-
creasing rotational energy,8 so this line of reasoning in not
helpful. A second difference is the lower zero-point energy
for OD than for OH throughout the reactive trajectory from
initial conditions ͑2850 versus 3358 cmϪ1͒ to the transition
state given by Clary ͑2782 versus 3428 cmϪ1͒ to products
͑3910 versus 4496 cmϪ1͒. Thus the reactive scattering for
OH versus OD actually samples a different part of the po-
tential and, perhaps, this could affect the correlation between
initial and final quantum states. The slightly greater exoer-
gicity for the OD reaction, together with a slightly lower
inverse secondary kinetic-isotope effect with
OH /kODϷ0.5; the kinetic-isotope effects for C4H10 and
cyclo-C6H2 are negligible.
a ratio
k
barrier, may enhance the coupling to the HOD( 3ϭ1) state.
v
Nevertheless, the experimental finding ͑if, indeed, it is cor-
rect͒ is highly unusual and merits more study.
Based upon the current data, the OH/OD reactions with
HCl seem to display both an inverse kinetic-isotope effect
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2446
J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
TABLE IV. Summary of energy disposal for OH, OD, and FϩHR reactions.
a
b
Ϫ␭
f
E
/ E
͘ ͗
v
͗
͘
͗
͘
v
v
vs
E
͗
͘
av
Reaction
kcal molϪ1
I
II
l
II
I
II
OHϩC6H12→H2OϩC6H11
OHϩC4H10→H2OϩC4H9
OHϩC5H12→H2OϩC5H11
OHϩHCl→H2OϩCl
27.1
24.7
22.4
18.6
27.4
25.0
22.4
18.9
43.9
42.4
40.0
35.6
-
5.7
5.5
8.2
8.4
9.1
0.62
0.65
0.64
0.68
0.60
0.14
0.19
0.20
0.13
0.18
0.15
5.2
0.54
c
c
ODϩC6H12→HDOϩC6H11
ODϩC4H10→HDOϩC4H9
ODϩC5H12→HDOϩC5H11
ODϩHCl→HODϩCl
6.3
6.3
5.9
-
4.8
-
6.1
5.9
5.9
8.6
8.6
9.0
0.57
0.62
0.51
0.59
0.65
0.58
0.84
0.81
0.76
0.86
0.83
0.81
0.5–0.7
0.54
d
FϩC6H12→HFϩC6H11
7.2
-
9.4
0.44͑0.47͒
0.59͑0.54͒
FϩCD3CH2CD3→HFd
Ϫ0.6e
d
FϩC5H12→HFϩC5H11
0.61
0.55
0.54
FϩHCl→HFϩClf
FϩDCl→HFϩClf
asϭ1,3 for OH reactions and sϭ3 for OD reactions.
bThe fraction of the total vibrational H O energy released to the bending mode,
E
/ E , in reactions with
͘ ͗
͗
͘
2
v2
v
OH and the fraction of HOD vibrational energy found in the O–H mode,
cSee text for comparison of OH versus ODϩHCl.
dReferences 14 and 15.
E
/ E , for reactions with OD.
͗
͘ ͗
͘
v3
v
eOur estimation is based on the distribution given in Ref. 15.
fReference 2.
and a strong isotope effect on the energy disposal. The
ODϩHCl reaction exhibits normal H-atom abstraction dy-
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͗
͘
v
tion seems to have a very low f (H O) , but a large
͗
͘
v
2
f (H O) . This unusual result,which needs independent
͗
͘
T
2
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͑1993͒.
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͗
͘
v
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͘
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J. Chem. Phys., Vol. 108, No. 6, 8 February 1998
N. I. Butkovskaya and D. W. Setser
2447
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