State-specific reactions HBr+(2IIi, v+) + (H2, HBr) → H2Br+ at low collisional energies

Article abstract of DOI:10.1063/1.1355661

The rate coefficients for hydrogen atom transfer reactions between (H₂,HBr) molecules and the HBr⁺ ions were measured in a state-specific manner under low collisional and rotational energy of reactants in a free jet. Selected spin-orbit and vibrational states of the HBr⁺ ions with narrow rotational distribution were prepared using (2+1) REMPI. All ions (reactants and products) were measured by TOF mass spectrometry. Finally, the resulting data was analyzed in detail.

Full text of DOI:10.1063/1.1355661

State-specific reactions HBr + ( 2 Π i ,v + )+( H 2 ,HBr )→ H 2 Br + at low collisional
energies
Andrey E. Belikov, Christopher Mullen, and Mark A. Smith
Citation: The Journal of Chemical Physics 114, 6625 (2001); doi: 10.1063/1.1355661
View online: http://dx.doi.org/10.1063/1.1355661
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/114/15?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 114, NUMBER 15
15 APRIL 2001
¿
2
¿
¿
State-specific reactions HBr „ ⌸ ,v …¿„H ,HBr…\H Br
i
2
2
at low collisional energies
Andrey E. Belikov,a) Christopher Mullen, and Mark A. Smithb)
Department of Chemistry, University of Arizona, Tucson, Arizona 85721
͑
Received 20 November 2000; accepted 24 January 2001͒
State-specific ion-molecule reactions of H-atom transfer between the HBr and H molecules with
2
ϩ 2
ϩ
HBr ( ⌸ ,v ) were studied in a free jet flow reactor. The selected spin-orbit and vibrational states
of the HBr ion were prepared by resonance-enhanced multiphoton ionization. All of the reactant
i
ϩ
and product ions were monitored using a time-of-flight mass spectrometer. Rate coefficients of the
ϩ
Ϫ12
3
HBr /H reaction vary from Ͻ2ϫ10
cm /s for the lowest spin-orbit-vibrational state to 2.1
2
Ϫ11
3
ϩ
Ϫ9
3
ϫ10
cm /s for the highest. Rates for the HBr /HBr reaction are ϳ1.5ϫ10 cm /s independent
of the internal state of the ion. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1355661͔
I. INTRODUCTION
The atom transfer reaction ͑2͒ was recently studied by
Green et al.28 for the ground vibrational of the lowest spin-
The study of ion–molecule reactions, initially carried out
under high collisional energies in crossed beam, drift tube,
and flowing afterglow experiments, presently moves toward
ϩ 2
ϩ
orbit state, HBr ( ⌸3 ,v ϭ0). Under thermal (T
/2
ϳ300 K) conditions of the experiment a rate coefficient of
1
Ϫ10
3
(
6.7Ϯ1.6)ϫ10
combining resonance-enhanced multiphoton ionization
REMPI͒ and laser-induced fluorescence was previously ex-
cm /s was found. The same technique
low collisional energies in an attempt to provide more de-
tailed information about the mechanism and dynamics of
ion–molecule interactions, potential energy surfaces, and re-
activity of molecules and ions in different internal states.2
A number of experimental techniques, including cryocooled
͑
5
plored by Xie and Zare to measure rate coefficients for the
state-specific charge transfer reaction
–5
ϩ 2
ϩ
ϩ 2
6
2,7
DBr ͑ ⌸ ,v ͒ϩHBr→HBr ͑ ⌸ ,vЈ͒ϩDBr.
͑3͒
drift tubes and traps, and supersonic flow reactors relying
i
iЈ
upon Laval or sonic nozzles in continuous8 or pulsed re-
gimes, have been developed to study low-energy ion–
molecule interactions.
,9
10
The rate coefficients were found to vary from
4
Ϫ10
3
3
ϩ
ϫ10
cm /s for the near resonance process (iϭ ,v ϭ0)
2
3
Ϫ11
3
→
(iЈϭ ,vЈϭ0) to 2ϫ10
process (iϭ ,v ϭ0)→(iЈϭ ,vЈϭ1). It should be noted
cm /s for the off resonance
2
Some progress in state-selective ion–molecule reactions
1
2
ϩ
3
2
has been achieved in recent years5
,11–29
and promises to con-
that these reactions were labeled ‘‘charge transfer,’’ but ac-
tually could be ‘‘isotope exchange’’ reactions, which have
similar rates ͓see, for example, Ref. 36 for
tinue owing to advances in state-specific preparation and de-
tection techniques such as high-resolution photoionization
3
0–32
33,34
and photoelectron spectroscopy,
selected-ion flow drift
and photodissociation
Ϫ
Ϫ
Ϫ
Ϫ
OH ͑OD ͒ϩD ͑H ͒→OD ͑OH ͒ϩDH, where rate coeffi-
2
2
2
0
tube, laser-induced fluorescence,
Ϫ10
Ϫ11
3
cients kϭ1.1ϫ10 (5.7ϫ10 ) cm /s were found͔.
In contrast to the thermal and hyperthermal collisional
energies of the investigations mentioned earlier the measure-
ments presented in this work were carried out under the low
temperatures in a free jet flow. A selected internal state of the
ionic reagent was prepared in the same manner by REMPI. A
time-of-flight mass spectrometer was used to register all ions
3
5
spectroscopy. The effects of ion rotational energy on ion–
molecule reactions was less than 10% in most studies,11–16
and, as a rule, the rotational excitation suppressed
1
3,14
reactivity.
Rotational energy of a neutral reactant was
found to be at least as effective as collisional energy in over-
coming an activation barrier for an endoergic reaction17,19
and to be important in competition of different reaction
͑ionized by REMPI and born in collisions͒. Kinetics of the
1
8
channels. In line with the scale of internal energy, vibra-
tional and electronic excitation of reactants led to dramatic
changes of reactivity.5
ions, both initially prepared as well as created in reactions,
provided information about the rate coefficients for the ion–
molecule interactions of interest.
,21–29
In the present article we report results on the low-energy
ion-molecule reactions
II. EXPERIMENT
ϩ 2
ϩ
ϩ
HBr ͑ ⌸ ,v ͒ϩH →H Br ϩH,
͑1͒
͑2͒
i
2
2
A detailed description of the free jet flow reactor, includ-
ing preparation of reagent ions by REMPI and monitoring
products by time-of-flight mass spectrometer, has previously
ϩ 2
ϩ
ϩ
HBr ͑ ⌸ ,v ͒ϩHBr→H Br ϩBr,
i
2
1
3
2
ϩ
10
for iϭ , and v ϭ0,1.
been given elsewhere. Therefore only details appropriate to
2
this experiment are discussed. A pulsed nozzle ͑General
Valve͒ with orifice diameter of 0.4 mm was used as a gas
source. The REMPI laser beam was focused by a 15 cm focal
length lens onto the center streamline of the jet at some dis-
a͒Permanent address: Institute of Thermophysics, Novosibirsk, 630090, Rus-
sia.
Electronic mail: msmith@u.arizona.edu
b͒
0021-9606/2001/114(15)/6625/6/$18.00
6625
© 2001 American Institute of Physics
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1

6626
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
Belikov, Mullen, and Smith
tance, z , from exit of the nozzle. The laser radiation in the
tant in the present work, because we restricted our interests
to spin-orbit and vibrational states of the HBr reagent.
i
ϩ
range of interest, ␭ϭ250–270 nm (⌬␭Շ0.01 nm), was pro-
duced from the frequency-doubled ͑BBO͒ output of a Nd/
YAG pumped dye laser ͑Coumarin 503 and 540A dyes͒.
Ionized particles moved within the free jet core species under
However, this result opens a possibility to study rotationally
selected rate coefficients for the case where rotational relax-
ation is slow or can be correctly accounted for. As the lowest
rotational level of the intermediate states was used, the rota-
tional relaxation under low energy collisions in a free jet
cannot dramatically change the rotational distribution of the
zero-field conditions until at some distance, z , a fast rising
f
repeller pulse extracted them into the entrance aperture of
time-of-flight mass spectrometer. Zero-field conditions of ion
flow inside the reaction region ͑between z and z in space
ϩ
created HBr ions. In the case of fast vibrational and/or spin-
i
f
and between the laser and repeller pulses in time͒ were en-
sured. These conditions could be monitored by measuring
the ion flow velocity and comparing this with the flow ve-
locity of neutral particles, which is well understood for a free
orbit relaxation ͑compared to rate of the studied reactions:
Ϫ11
3
ϩ
Ϫ9
3
ϳ10
cm /s for HBr /H2 and ϳ10 cm /s for
ϩ
HBr /HBr), the measured rate coefficients for higher vibra-
tional and/or spin-orbit states should be considered only as
lower limit of the absolute reaction rates.
Another advantage of using the f ⌬2 and F ⌬2 states as
intermediates in the (2ϩ1) REMPI scheme for HBr is the
3
7
jet flow. In our HBr(Ͻ5%)ϩH mixture we always ob-
2
ϩ
3
1
served a slightly smaller flow velocity for the HBr ions
compared to the velocity derived from energetic consider-
ation for equilibrium flow. This difference decreased at
lower HBr fractions and at higher stagnation pressures, and
was interpreted as the well-known ‘‘velocity slip’’ effect for
a free jet flow mixture of heavy and light molecular
ϩ
ϩ
small quantity of ionic atomic fragments (H , Br )
produced.39 These ions can play a role in HBr and H Br
ϩ
ϩ
2
kinetics and, hence, introduce uncertainty in the results. For
ϩ
all experiments, the H signal was always less than 1%,
ϩ
3
7
while the Br signal varied, and at times could be compa-
species. The value of the velocity slip effect as well as an
estimation of collisional energy of the reagents will be pre-
sented in Sec. III B.
ϩ
ϩ
rable to the HBr and H Br signals at the highest laser
2
ϩ
powers. Fortunately, the efficiency of the Br production
depends nonlinearly on laser power and their relative con-
centration was decreased to a few percent or lower by main-
taining low laser powers for all studies where rate coeffi-
cients were determined.
The distances z and z , as well as the stagnation pres-
i
f
sure p , define a number of collisions between ions and
0
neutral reagents in the time interval between ionization and
extraction. This in turn determines the range of rate coeffi-
cients that can be measured in our experimental scheme.
Typical experimental values were z ϭ1 cm, z ϭ3 cm, p
i
f
0
ϭ80–300 Torr, and %HBrϭ0.4–2.8. The low HBr frac-
tions were used to achieve greater accuracy in the study of
reaction ͑1͒, which was much slower than reaction ͑2͒. An
additional reason to use the low-density/low-HBr-
concentration flows was to avoid clustering that may effect
both gas-dynamic properties and chemistry. Appearance of
clustered ions was monitored and thereby controlled through
mass spectrometry. A low limit for rate coefficients, which
are still measurable under these conditions, can be easily
estimated using the density distribution in a free jet. For
III. RESULTS AND DISCUSSION
A. Kinetics in a free jet reactor
ϩ
Loss of the HBr ions along free jet axis, initially pre-
pared by REMPI at point z , are caused by the reactions ͑1͒
i
and ͑2͒, as well as by geometric expansion of the flow
ϩ
ϩ
ϩ
Ϫd͓HBr ͔/dtϭk ͓H ͔͓HBr ͔ϩk ͓HBr͔͓HBr ͔
1
2
2
ϩ
ϩ͓HBr ͔f͑t͒.
͑4͒
ϩ
Ϫ12
3
Here ͓X͔ is a concentration of particles X; k and k are the
rate coefficients of reaction ͑1͒ and ͑2͒; and function f(t)
describes the geometric expansion of the flow. Inputting ␣ as
reaction of HBr with H , this limit is ϳ5ϫ10
cm /s and
1
2
2
Ϫ10
3
ϩ
ϳ10
easily decreased to ϳ2ϫ10
cm /s for HBrϩHBr . However, the latter can be
Ϫ12
3
cm /s by using higher HBr
a fraction of HBr molecules in the H ϩHBr mixture, ␣
2
concentrations in the mixture, which effectively increase
both the collisional frequency and reaction time through de-
creasing flow velocity.
ϭ͓HBr͔/(͓HBr͔ϩ͓H ͔), an effective rate coefficient
2
k ϭk ͑1Ϫ␣͒ϩk ␣,
͑5͒
1
2
1
2
ϩ 2
ϩ
State-selective ions of HBr ( ⌸ ,v ) were prepared by
i
3
3
and total gas density nϭ HBr ϩ H , Eq. ͑4͒ can be ex-
͓
͔
͓
͔
(
2ϩ1) REMPI through the f ⌬ (vϭ0), f ⌬ (vϭ1),
2
2
2
1
1
pressed as
F ⌬ (vϭ0), and F ⌬ (vϭ1) Rydberg intermediates, using
2
2
the R͑1͒ line in all cases. The laser radiation wavelengths
ϩ
ϩ
ϩ
Ϫd͓HBr ͔/dtϭk n͓HBr ͔ϩ͓HBr ͔f͑t͒.
͑6͒
1
2
were ␭ϭ269.3, 261.2, 259.6, and 252.1 nm, respectively. As
5
Since the duration of the gas pulse ͑ϳ600 ␮s͒ is much longer
than all other times associated with any of the processes
studied, the jet can be considered as a continuous flow that
allows Eq. ͑6͒ to be rewritten as
was shown by Xie and Zare, REMPI through these states
ϩ 2
ϩ
produces the HBr ( ⌸ ,v ) ion almost exclusively ͑more
i
than 98%͒ in one spin-orbit and vibrational state, namely,
3
2
ϩ
3
2
ϩ
1
2
ϩ
1
2
ϩ
(
iϭ ,v ϭ0), (iϭ ,v ϭ1), (iϭ ,v ϭ0), and (iϭ ,v
3
4
ϭ1), respectively. Moreover, according to REMPI-LIF,
REMPI-PES and zero kinetic energy–pulsed field ionization
ϩ
ϩ
ϩ
Ϫd͓HBr ͔/dzϭk ͑n/u͓͒HBr ͔ϩ͓HBr ͔f ͑z͒, ͑7͒
1
2
1
3
8
͑
ZEKE-PFI͒ studies, only a few rotational levels of the
for a flow along the free jet axis z.
All measurements were carried out in the hypersonic re-
gion, where the model of spherical expansion works very
ϩ
HBr ion are populated about the J value of the intermediate
state selected. The rotational distribution was not so impor-
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ϩ
2
ϩ
ϩ
6627
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
The reaction HBr ( ⌸ ,v )ϩ(H , HBr)→H Br
i
2
2
well.40 Under this model, the gas flow velocity, u, is a con-
stant of independent of z and the gas density is found to drop
spherically as
Flow velocity of hydrogen in the HBrϩH mixture can
be found from simple energy balance
2
2
H
2
m u
␥
H
2
mHBru
HBr
2
R
nϭn ͑z/z ͒Ϫ2.
͑8͒
kBT0
ϭ͑1Ϫ␣͒
ϩ␣
ϩ͑1Ϫ␣͒EH
2
0
0
␥
Ϫ1
2
2
Here n is the stagnation density, z ϭaD, D is the nozzle
0
0
R
t
t
ϩ␣E ϩ͑1Ϫ␣͒E ϩ␣E
,
͑10͒
HBr
H
HBr
diameter, and a is a constant which is dependent on the heat
capacity ratio ␥ϭC /C and is equal to 0.401 and 0.298 for
2
7
5
p
v
where k is the Boltzmann’s constant, ␥ϭ , T is the stag-
B
0
5
7
␥
ϭ and , respectively.
3 5
nation temperature, m
and mH2 are the molecular masses,
HBr
t
H
Integration of Eq. ͑7͒ from the point of ion production,
R
R
H
t
E
, E and E ,E are the frozen rotational and trans-
HBr
HBr
2
2
z , to the point of ion extraction, z , gives
i
f
lational energies ͑per molecule͒. The terminal rotational
population of H2 in a free jet was measured by Latimer as
N :N :N :N ϭ0.22:(0.74–0.75):0.03: ͑Ͻ0.01—inside er-
ror limits͒ for p ϭ500 Torr, Dϭ0.5 mm and T ϭ298 K.
Assuming that the population ratios ͑separately and indepen-
dently for ortho- and para-hydrogen͒, N /N0 and N /N ,
freeze in a point of the flow with the same gas density, an
estimation of the terminal rotational distributions for another
stagnation pressure can be made using the isentropic relation
between gas-dynamics parameters in the free jet: Tn1
ϭconst. For our typical stagnation pressure of 150 Torr (D
ϩ
2
24
͓
ϩ
HBr ͔
n0z0
1
1
zf
ln
ͩ
ͪ
ϭk12
ͩ
Ϫ
ͪ
.
͑9͒
ϩ
HBr ͔ ϩ͓H Br ͔
zf
u
zf zi
0
1
2
3
͓
zf
2
0
0
ϩ
ϩ
The ratio between the HBr and H Br ion concentrations
2
was measured as a ratio between their corresponding time-
2
3
1
of-flight signals while varying the stagnation gas density, n0 ,
for a number of HBr concentrations in the mixture, ␣. The
effective rate coefficient k12 was derived by the best fit to Eq.
Ϫ␥
͑9͒ for every particular value of ␣. Finally, dependence of
k
1
2
o
n
␣
a
l
l
o
w
e
d
f
o
r
d
e
t
e
r
m
i
n
a
t
i
o
n
t
h
e
r
a
t
e
c
o
e
f
fi
c
i
e
n
t
s
k
1
and k , according to Eq. ͑5͒.
2
ϭ0.4 mm; T ϭ298 K) the terminal rotational distribution of
0
H2 derived by this manner should be close to
N :N :N :N ϭ0.16:(0.68–0.75):0.09:(Ͻ0.07) that corre-
0
1
2
3
R
sponds to frozen rotational energy of EH /k from 180 K to
B. Flow properties of the HBr¿H free jet
B
2
2
2
50 K. Since the last three terms of Eq. ͑10͒ are much
In this section we specify and discuss the gas-dynamic
parameters used in kinetic equations ͑6͒–͑9͒ as applied to the
smaller than that value, they can be neglected under estima-
tion of the flow velocity for H . The value of u , estimated
2
H
2
HBrϩH free jet. Both of these gases are diatomic, and their
2
from Eq. ͑10͒ for p ϭ150 Torr, ␣ϭ0.02, is (2230
Ϯ50) m/s, increasing to (2620Ϯ50) m/s in the ␣ϭ0 limit
0
equilibrium flow is described by the heat capacity ratio ␥
7
5
ϭC /C ϭ . However, these molecules, H especially, have
p
v
2
͑the error limits are mostly caused by uncertainty in the ter-
a very small rotational moment of inertia, and consequently,
minal rotational distribution of H ).
2
a very large spacing between rotational energy levels (B
e
Ϫ1
41
If this significant difference between the measured
ϭ60.85 and 8.46 cm for H and HBr, respectively͒. As a
2
(
uHBr) and estimated (u ) flow velocities is really caused
H
2
result, the rotational energy of the molecules is frozen very
by ‘‘velocity slip’’ between heavy HBr and light H mol-
ecules in the free jet, it poses an interesting point regarding
the HBr/H collisional energy. Dispersion of velocity ͑tem-
perature in the equilibrium case͒ is very low in a free jet for
every gas species, but relative velocity between molecules of
different types is not small. The difference of 870 m/s cor-
responds to a center mass collisional energy of about 5.2
ϫ10 eV. This value is much higher than the dispersion of
velocity, so, more accurately speaking, in the case of reaction
close to the exit of a nozzle in a free jet, and the gas expands
2
5
3
as monatomic (␥ϭC /C ϭ ) below this point, since the
p
v
rotational energy does not participate in further energy trans-
fer processes. According to the measurements of Latimer,
2
4
2
the rotational energy of H freezes at z/DϽ0.7 under a stag-
2
nation pressure of p ϭ500 Torr and a nozzle diameter D
0
ϭ0.5 mm. Thus, to determine the constant z in Eq. ͑8͒ for a
0
Ϫ3
HBr/H free jet with a small fraction of HBr, a linear inter-
2
5
3
7
polation of a between its values for ␥ ϭ and ␥ ϭ 5 was
1
2
ϩ
between HBr and H we measure a cross section corre-
used.
2
sponding to the collisional energy estimated above, and not
strictly a rate coefficient in its phenomenological sense ͑i.e.,
as a cross section averaged over Maxwellian velocity distri-
The flow velocity, u, from Eqs. ͑7͒ and ͑9͒ defines the
ϩ
time for reaction, t ϭu(z Ϫz ), of the HBr ions in the
R
f
i
space between ionization and detection points, and is thus
the velocity of interest, rather than that of all other particles.
To derive the rate coefficients from Eq. ͑9͒, an experimen-
ϩ
bution͒. For the HBr /HBr reaction, the velocity dispersion
is small, as is the average relative velocity of these particles.
The velocity distribution is close to Maxwellian ͑shifted on
the uHBr value along velocity axis͒ and measured rate coef-
ficients therefore are close to the primary definition.
tally measured ion flow velocity was used: uHBr
ϩ
ϭ(zf
Ϫz )/⌬t, where z and z are the distances from the nozzle
i
i
f
to ionization and detection points in flow and ⌬t is the delay
between ionization and detection moments ͑this delay was
varied to find the maximum in the ion arrival distribution at
different HBr concentrations and stagnation pressures͒. The
C. State-specific rate coefficients
value of uHBr
ϩ
measured under typical experimental condi-
Reactions ͑1͒ and ͑2͒ were studied for four internal
ϩ
2
ϩ
1
3
ϩ
tions (p ϭ150 Torr, ␣ϭ0.02) was (1340Ϯ20) m/s, rising
states of the HBr ( ⌸ ,v ) ionic reagent (iϭ , ; v
0
i
2 2
to (1750Ϯ30) m/s in the ␣ϭ0 limit.
ϭ0,1). Reaction ͑2͒ is exothermic for all four cases with
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6628
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
Belikov, Mullen, and Smith
FIG. 1. Internal state-specific thermochemistry of the reaction
ϩ
2
ϩ
ϩ
ϩ
HBr ( ⌸ ,v ,J )ϩH (vϭ0,J)→H Br ϩH. The energy Eϭ0 is refer-
i
2
2
enced to the lowest internal energy level of the reactants. The threshold of
endothermicity based on the data from Ref. 43 is shown by dashed line.
excess energy of Ͼ0.35 eV.43 An energy diagram for reac-
tion ͑1͒ is presented in Fig. 1 for the first five rotational
ϩ
levels of HBr and for the first four rotational levels of H .
2
The dashed line displays the boundary of exothermicity cal-
culated using heats of formation for all the species of reac-
tion ͑1͒ at Tϭ0 K.43 The rotational levels of the HBr ions
were restricted in accordance with the results of Xie and
FIG. 2. Effective rate coefficient, k ͓see Eq. ͑5͔͒, for production of
H2Br ions in the HBr ( ⌸i ,v )ϩ(HBr, H2) collisions as a function of the
12
ϩ
ϩ
2
ϩ
ϩ
HBr fraction in the HBrϩH flow.
2
3
4
38
Zare and Wales et al., who observed a measurable popu-
lation only at the four to five rotational levels surrounding J,
the level pumped in the REMPI resonance states HBr
temperature value for k relative to the 300 K observations is
2
entirely consistent with expectations. Simple models of ion–
dipole capture predict rate increases in excess of that ob-
served even for modest values of the degree of dipole lock-
ing or correlation.
3
1
ϩ
f ⌬ (vϭ0,J) and F ⌬ (vϭ0,J) used to produce the HBr .
2
2
According to Fig. 1, one may expect that the rate coef-
ficient of the reaction ͑1͒ could rise from k ϭ0 for the
1
ϩ
2
ϩ
The magnitudes of the k1 rate coefficients demonstrate
surprising accordance with our preliminary expectations,
based on thermochemical data. The difference between the
HBr ( ⌸ ,v ϭ0) ions to
a
maximal value for
HBr ( ⌸ ,v ϭ1). As for the HBr ( ⌸ ,v ϭ1) and
HBr ( ⌸ ,v ϭ0) states, only the HBr ions and the H2
3
/2
ϩ
2
ϩ
ϩ
2
ϩ
1
/2
3/2
ϩ
2
ϩ
ϩ
1
/2
ϩ
2
ϩ
rate for HBr ( ⌸ ,v ϭ0) ions and zero is statistically
3
/2
molecules, which have higher rotational energy, are possible
candidates for reaction.
Note that neither internal energy of products nor kinetic
energy of products and reactants were included in this sim-
plified consideration. Nothing can be said about the internal
3
ϩ
2
ϩ
insignificant, k ( ,0)Ϸ0. The rate for HBr ( ⌸ ,v ϭ1)
1
2
1/2
1
ions, k ( ,1), is highest, but much less than the rate of reac-
1
2
tion ͑2͒, and is only 1% of the Langevin limit for ion–
3
2
molecule capture. The rate k ͑ , 1͒ has a low value, but is
1
states ͑electronic, vibrational, or rotational͒ in which the
statistically nonzero. The presented error limits reflect only
statistical scattering of the data. A systematic error may arise
in the case of fast vibrational and/or spin-orbit relaxation and
ϩ
newborn particles (H Br and H͒ appear in the reactions,
2
since we do not have techniques to detect their final states.
What can be said is that additional energy of products leads
to an effective rise of the endothermic barrier; and the kinetic
energy of collisions owing to the ‘‘velocity slip’’ effect may
decrease the endothermicity to about 0.004 eV, which is an
insignificant value compared to the uncertainty of the heat
formation data taken from Ref. 43.
TABLE I. Rate coefficients of the state-specific ion-molecule reaction
ϩ
2
ϩ
ϩ
a
͑
H , HBr͒ϩHBr ( ⌸ ,v )→H Br ϩ͑H, Br͒.
2
i
2
Ionic state
2⌸3/2
,v ϭ0
ϩ
2⌸3/2 ,v ϭ1
ϩ
2⌸1/2 ,v ϭ0
ϩ
2⌸1/2 ,v ϭ1
ϩ
The effective rate coefficients, k (␣), for different in-
1
2
ϩ
Neutral
HBr
ternal states of the HBr ions are shown in Fig. 2 as a func-
13.8Ϯ1.6b
(
15.0Ϯ1.3
16.6Ϯ0.9
12.8Ϯ1.6
tion of HBr fraction in the HBrϩH mixture. Table I presents
2
6.7Ϯ1.6)c
the rate coefficients k and k , derived from linear analysis
1
2
H2
0.047Ϯ0.017 0.084Ϯ0.010 0.207Ϯ0.019
0.016Ϯ0.021
of the experimental data on k (␣) and its extrapolation to
1
2
aUnits of 10Ϫ10 cm /s. The Langevin collision limit for the HBr ϩH sys-
3
ϩ
␣
ϭ0 and ␣ϭ1. The rate of reaction ͑2͒ appears to be about
2
Ϫ10
3
tem is 15ϫ10
cm /s.
two times higher compared to that measured under thermal
b
c
2␴ value.
conditions by Green et al.28 The increase observed in the low
Data from Ref. 28 for thermal conditions.
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ϩ
2
ϩ
ϩ
6629
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
The reaction HBr ( ⌸ ,v )ϩ(H , HBr)→H Br
i
2
2
2
8
thermal conditions by Green et al. The rate coefficient of
ϩ
2
1/2
ϩ
the HBr ( ⌸ ,v ϭ1)/H reaction is seven to eight times
2
less compared to HBr reagent, and decreases for lower lying
ϩ
2
ϩ
internal states up to a zero value for HBr ( ⌸ ,v ϭ0).
3
/2
ACKNOWLEDGMENTS
The authors would like to thank Veronica Jaramillo for
help during the experiment. We also gratefully acknowledge
financial support of this work by the National Science Foun-
dation through Grant No. CHE-9984613.
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M. A. Smith, in Unimolecular and Bimolecular Ion-Molecule Reaction
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ϩ
FIG. 3. Rate coefficient for the reaction HBr ( ⌸ ,v )ϩH (vϭ0)
i
2
ϩ
→
H Br ϩH as a function of the average internal energy of the reactants.
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6
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ϩ
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9
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S. E. Barlow, J. A. Luine, and G. H. Dunn, Int. J. Mass Spectrom. Ion
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Figure 3 presents the measured rate coefficient k versus
an average internal energy of the HBr ( ⌸ ,v ,J ) and
H (J) reactants ͑relative to energy of their lowest internal
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ϩ
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ϩ
͗
⌬E͘i,v
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͚ ͚ ␧i,v͑J,J ͒N N
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ions: ⌺ N ϭ⌺JϩNJϩϭ1. The terminal rotational level
populations N were estimated above. The rotational distri-
bution of the HBr ions was taken from the measurement of
under the same ionization scheme:
N1/2 :N3/2 :N5/2 :N7/2ϭ0.49:0.34:0.14:0.03, neglecting rota-
tional relaxation.
At present, it is unclear as to the relative importance of
HBr vibrational versus electronic energy in assisting this
reaction over the endothermic barrier. From the limited data
set all that can be said is for these low energy collisions there
is a significant effect in the ability of internal energy in HBr
to drive the H atom transfer from H in reaction ͑1͒.
In summary, the rate coefficients for hydrogen atom
transfer reactions between (H , HBr) molecules and the
HBr ions were measured in a state-specific manner under
low collisional and rotational energy of reactants in a free jet.
Selected spin-orbit and vibrational states of the BHr ions
with narrow rotational distribution were prepared using (2
ϩ1) REMPI. All ions ͑reactants and products͒ were mea-
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out at low laser power to minimize production of atomic ions
H , Br ), which were able to participate both in decay of
HBr and production of H Br ions. The low temperature
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