Low-temperature Kinetics of the Charge- and Atom-Transfer Reactions (Br+, HBr+ [2∏i, ν+, DBr+ [2∏i, ν+]) + (HBr, DBr) → (HBr+, DBr+, H2Br +, D2Br+, HDBr+)

Article abstract of DOI:10.1021/jp031254k

The charge- and atom-transfer reactions between Br⁺, HBr ⁺, and DBr⁺ ions and HBr and DBr molecules have been studied in a HBr + DBr + He free jet. The ionic reactants in specific internal states were prepared by resonance multiphoton ionization of either HBr or DBr, and the ionic products were analyzed by mass spectrometry. A set of eight energetically possible reactions was considered in each case, including ions born in near-resonant ionization and photodissociation processes. Kinetic equations were integrated numerically over the appropriate reaction time and an optimization problem was solved to determine rate coefficients fit to final fractions of all ions measured in an experiment. Analytical expressions for the final fractions also were obtained and were used to derive the rate coefficients more accurately. The work is an example of a multireaction study without direct observation of all the reaction products.

Full text of DOI:10.1021/jp031254k

J. Phys. Chem. A 2004, 108, 3447-3456
3447
Low-Temperature Kinetics of the Charge- and Atom-Transfer Reactions (Br+, HBr+
[2Πi, W+], DBr+ [2Πi , W+]) + (HBr, DBr) f (HBr+, DBr+, H2Br+, D2Br+, HDBr+)
Andrey E. Belikov† and Mark A. Smith*
Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721
ReceiVed: NoVember 18, 2003; In Final Form: January 29, 2004
The charge- and atom-transfer reactions between Br+, HBr+, and DBr+ ions and HBr and DBr molecules
have been studied in a HBr + DBr + He free jet. The ionic reactants in specific internal states were prepared
by resonance multiphoton ionization of either HBr or DBr, and the ionic products were analyzed by mass
spectrometry. A set of eight energetically possible reactions was considered in each case, including ions born
in near-resonant ionization and photodissociation processes. Kinetic equations were integrated numerically
over the appropriate reaction time and an optimization problem was solved to determine rate coefficients fit
to final fractions of all ions measured in an experiment. Analytical expressions for the final fractions also
were obtained and were used to derive the rate coefficients more accurately. The work is an example of a
multireaction study without direct observation of all the reaction products.
I. Introduction
mechanism was realized in ∼30% of the reaction events under
thermal conditions.
In our previous studies,1,2 we have investigated the state-
selective hydrogen and deuterium atom-transfer reactions
The state-selective charge-transfer reaction
DBr+ (2Πi, V+) + HBr f HBr+ (2Πi′, V′+) + DBr (3)
was investigated by Xie and Zare,9 under thermal conditions,
HBr+ [2Πi, V+] + H2 f H2Br+ + H
HBr+ [2Πi, V+] + HBr f H2Br+ + Br
(1a)
(2a)
for i ) /2, /2; V+ ) 0, 1. The rate coefficients summed over
all energetically permitted states of products were determined
to be 4.1 × 10-10, 1.4 × 10-10, 3.8 × 10-10, and 2.3 × 10-10
cm3/s for the (3/2, 0), (3/2, 1), (1/2, 0), (1/2, 1) states of the reactant.
A similar tendency toward lower rate coefficients with vibra-
tional excitation was observed2 for reactions 2 with DBr+.
Presently, we report the results of a more-detailed study of
all possible ion-molecule reactions in the HBr + DBr mixture
after state-selective (2+1) resonance-enhanced multiphoton
ionization (REMPI) of either HBr or DBr molecules. When the
(2+1) REMPI of HBr (DBr) is explored in the HBr + DBr
mixture, some fraction of minor ionic species (DBr+ (HBr+)
and Br+) is always present. The first are born in near-resonance
ionization processes (or in resonance if the resolution of the
ionizing laser is low), because of similar internal states; the
second are presumably products of the photodissociation of the
HBr+ and DBr+ ions. These minor ions were included in the
kinetic consideration, because they can have a significant role
in the production of common product ions. In Section II, we
describe the experimental technique for a kinetic study of the
ion-molecule reactions in the free jet flow reactor based on
the REMPI preparation of reactants and mass spectrometry of
the products. The set of kinetic equations for ion-molecule
reactions in a free jet is presented in Section III, both in its
general form and in application to the reactions in the (HBr +
DBr + HBr+ + DBr+ + Br+) mixture. The rate coefficients
have been found using two procedures. The first one, described
in Section IV, is the numerical simulation of the reactions in
the free jet and fitting to the experimental data. This simulation
provides preliminary values of the rate coefficients and, what
may be more important, gives the opportunity to analyze the
role of every reaction in determining the final distribution of
1
3
and
DBr+ [2Πi, V+] + D2 f D2Br+ + (D)
DBr+ [2Πi, V+] + DBr f D2Br+ + Br
(1b)
(2b)
for the (i ) /2, /2; V+ ) 0, 1) internal states of the ions. The
rate coefficients of reactions 1 demonstrated clear threshold
behavior and reached values of ∼2 × 10-11 cm3/s for the highest
studied states of the ions. At the same time, rates of the highly
exothermic reactions 2 were almost 2 orders of magnitude faster
(∼1.3 × 10-9 cm3/s) and had to be taken into account, even at
a very low fraction of bromide molecules in the reacting mixture.
Information about charge- and atom-transfer reactions be-
tween hydrogen (deuterium) bromide ions and parent molecules
(or their isotope equivalents) is rather limited. Green et al.3
studied possible channels of the thermal reaction of the HBr+
ions with HBr and DBr molecules and found the total rate
coefficients to be 6.9 × 10-10 cm3/s and 5.8 × 10-10 cm3/s,
respectively, inclusive for charge-transfer (46% and 50% for
HBr and DBr), proton-transfer (32% and 28%), and atom-
transfer (22% for both) channels. Low-temperature rates of these
reactions seemed to be faster by a factor of ∼2.1,2 The negative
temperature dependence might be easily explained if the reaction
proceeded through the formation of collisional complexes4-8
or simply through the attractive ion-dipole interaction potential.
According to the estimations of Green et al.,3 a complex
1
3
* Author to whom correspondence should be addressed. E-mail: msmith@
u.arizona.edu.
† Present address: Institute of Thermophysics, 1, Lavrentjev Ave.,
Novosibirsk, 630090, Russia.
10.1021/jp031254k CCC: $27.50 © 2004 American Chemical Society
Published on Web 03/18/2004

3448 J. Phys. Chem. A, Vol. 108, No. 16, 2004
Belikov and Smith
TABLE 1: Reactions in the (HBr + DBr) Mixture after Photo-ionization of the Bromide Ions HBr+, DBr+, and Br+, and Their
Rate Coefficients
Rate Coefficient (10-9 cm3/s)b
reaction
∆fHa (kcal/mol)
f 3∆2 (v ) 0)
f 3∆2 (v ) 1)
F 1∆2 (v ) 0)
F 1∆2 (v ) 1)
accuracy (%)b
R1c
R2
R3
R4e
R5
R6f
R7
R8
HBr+ + HBr f H2Br+ + Br
HBr+ + DBr f HDBr+ + Br
HBr+ + DBr f DBr+ + HBr
DBr+ + DBr f D2Br+ + Br
DBr+ + HBr f HDBr+ + Br
DBr+ + HBr f HBr+ + DBr
Br+ + HBr f HBr+ + Br
Br+ + DBr f DBr+ + Br
-8.8 ( 0.5
-8.8 ( 1
1.3 [1.5]
1.7 [1.6]
1.0 [1.0]
1.7 [1.6]
1.3 [1.4]
1.6 [1.6]
1.1 [1.0]
1.6 [1.6]
20 [30]
20 [35]
[100]
17 [30]
20 [35]
50 [100]
14 [30]
18 [35]
+0.5 ( 0.5
-8.7 ( 1
0.6d [0.6] for all ionization schemes
1.4 [1.5]
1.6 [1.6]
1.1 [1.1]
1.7 [1.6]
1.4 [1.4]
1.5 [1.6]
1.1 [0.9]
1.5 [1.6]
-9.7 ( 1
-0.5 ( 0.5
-3.4 ( 0.5
-2.4 ( 0.5
0.6 [0.6] for all ionization schemes
2.7 [2.5]
1.6 [1.8]
2.7 [2.5]
1.6 [2.5]
2.8 [2.5]
1.7 [2.5]
2.6 [2.5]
1.6 [2.5]
a Based on Lias et al.12 (see text in Section III). b Results of numerical simulation given in square brackets. c Data for thermal conditions from
Green et al.: k1 ) 0.7 ( 0.2;3 low-temperature data from Belikov et al.: k1 ) 1.4 ( 0.2.1,2 d Assumed to be equal to k6. e Low-temperature data
from Belikov et al.: k4 ) 1.3 ( 0.3.1,2 f Data for thermal conditions from Xie and Zare: k6 ) 0.4 ( 0.08.9
products. Analytical expressions for the final ionic distribution,
as a function of experimental parameters, are obtained in Section
V and applied to the derivation of the rate coefficients in Section
VI that have been discussed in Section VII.
HBr and DBr. This is probably caused by near-resonance
ionization through some other intermediate states. Despite the
low percentage (<5%) of those secondary ions, they cannot be
excluded from kinetic consideration until their reactivity is
studied. In addition, some fraction of Br+ ions have been
observed in all ionization schemes. Their source is most
probably a photodissociation of the HBr+ and DBr+ ions that
requires only one additional photon.11 This is confirmed by a
nonlinear dependence of the Br+ fraction on the laser power.
On the other hand, the H+ ions, which could be created in a
two-photon dissociation process,11 have never been detected in
our experiments. According to this, we included in our
consideration reactions with Br+ ions and excluded those with
H+ cations.
II. Experiment
Kinetics of the ion-molecule reactions were studied in a free
jet flow reactor, using (2+1) REMPI for preparation of the ionic
reactants and time-of-flight (TOF) mass spectrometry for
analysis of the ionic products. The experimental equipment and
techniques have been described in detail elsewhere;10 thus, here
we discuss only the salient features. A pulsed axisymmetric
nozzle (General Valve) with an orifice diameter of 0.4 mm was
used as a gas source (with a typical pulse length of 600 µs and
a frequency of repetition of 10 Hz). The stagnation temperature
was kept constant in all experiments: T0 ) 295 K. The
stagnation pressure was varied from 50 Torr to 400 Torr. The
diffusion pump (Edwards, 12 in.) provided a low background
pressure (Pbkg < 10-5 Torr) under all flow rates, thus excluding
significant penetration of the background molecules into the free
jet core. The REMPI laser beam was focused by a lens with a
focal length of 15 cm onto the center streamline of the jet at
some distance zi from the exit of the nozzle. The laser radiation
in the range of interest, λ ) 250-270 nm (∆λ ≈ 0.01 nm),
was produced from the frequency-doubled (BBO) output of a
Nd:YAG pumped dye laser (Coumarin model 503). Ions
continue in the flow, interacting with neutrals in the jet core
until at some distance zf , they were extracted into the TOF mass
spectrometer, using a rapidly applied transverse electric field.
Typical experimental values were zi ) 10 mm and zf ) 29 mm.
State-selective ions of HBr+ (2Πi , V+) and DBr+ (2Πi , V+)
III. Kinetics of Ion-Molecule Reactions in the HBr +
DBr Free Jet
The general form of an ion-molecule reaction can be
expressed as
+
l
Ii+ + Ml f Ij + Mm{kij }
(4)
where I+ and Mj are the ionic and neutral species, and kl is the
i
ij
rate coefficient of transformation of the ion I+i to the ion Ij+ in
collision with the molecule Ml. Inputting an absolute number
density of specific ions n+ and neutrals ni, an absolute number
i
density of all ions n+) ∑ini+ and neutrals n ) ∑ini , a relative
density of ions N+ ) n+/n and neutrals Ni ) ni /n; ∑iN+ ) ∑iNi
i
i
i
) 1, we can transform the initial set of kinetic equations for
absolute densities of different species in a free jet
3
were prepared by (2+1) REMPI through the f ∆2 (V ) 0), f
dn+i
1
1
3∆2 (V ) 1), F ∆2 (V ) 0), and F ∆2 (V ) 1) Rydberg
intermediates. According to the REMPI-LIF and REMPI-PES
studies of Xie and Zare,9 REMPI through these states produces
the HBr+/DBr+ (2Πi , V+) ions almost exclusively (>98%) in
one spin-orbit and vibrational state, namely (i ) 3/2, V+ ) 0),
)
(kl n+n - kl n+n ) - n+f(t)
(5)
∑
jl
j
l
ij
i
l
i
dt
j,l
(where the last term describes temporal expansion in the free
jet) to the set for relative values
3
1
1
(i ) /2, V+ ) 1), (i ) /2, V+ ) 0), and (i ) /2, V+ ) 1),
respectively. Rotational transitions for the resonance multiphoton
ionization of the HBr (DBr) molecules were chosen as a
compromise between intensity of a line and its isolation from
lines of other isotopic analogues. In most cases, we used R(1)
lines and in some experiments S(1). REMPI spectra of the HBr
and DBr molecules through the same f 3∆2 (V ) 0) or F 1∆2 (V
) 0) intermediate states lie in the same spectral regions and
we always observed some fraction of ions of the other hydrogen
isotope. Moreover, low-level isotopic contamination was ob-
dN+i
) n (kl N+N - kl N+N )
(6)
∑
ji
j
l
ij
i
l
dt
j,l
Under REMPI ionization of HBr+ (or DBr+) ions in the (HBr
+ DBr) mixture, a small but finite quantity of minor ionic
species (Br+ and DBr+, or Br+ and HBr+) can be observed.
According to this fact, we include in our further analysis all
possible reactions with all ionic species. The possible reactions
are listed in Table 1, along with the 0 K reaction enthalpies.
The heats of formation at T ) 0 K for H, HBr, HBr+, H2Br+,
3
served even under ionization through the f ∆2 (V ) 1) and F
1∆2 (V ) 1) states, the spectra of which are well-separated for

Low-Temperature Kinetics of Transfer Reactions
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3449
D, DBr, Br, and Br+ ions/species were 51.6 ( 0.1, -7 ( 0.2,
262 ( 0.5, 218 ( 0.5, 52.5 ( 0.1, -8 ( 0.2, 28.2 ( 0.1, and
300.6 ( 0.1 kcal/mol, respectively (values taken from Lias et
al.12). The heat of formation for the DBr+ cation was estimated
as 261.9 ( 0.5 kcal/mol by comparison of the lowest internal
levels of the HBr+ and DBr+ ions and the heats of formation
for pairs (D, Br+) and (H, Br+). The heat of formation for the
D2Br+ cation was estimated based on the assumption that a
substitution of isotopes leads to the same effect for the (H2Br+,
D2Br+) and (H2O+, D2O+) pairs:
these measurements were repeated for each path of ionization,
3
using the Rydberg intermediate states f ∆2[2Π3/2, V ) 0]; f
1
1
3∆2[2Π3/2, V ) 1]; F ∆2[2Π1/2, V ) 0]; F ∆2[2Π1/2, V ) 1].
Because of the small difference between ion masses (compared
to their absolute values), an equal collection/detection efficiency
was assumed. Ratios between measured signals then represent
ratios between fractions of corresponding ions. Thus, the signals
from masses of 79, 80, ..., 85, normalized by the sum of all
signals, represent the fractions of the 79Br+, H79Br+, (81Br+
+
D79Br+ + H279Br+), (H81Br+ + HD79Br+), (H281Br+ + D81Br+
+ D279Br+), HD81Br+, D281Br+ ions in the extraction point of
∆fH{D2Br+} ≈ ∆fH{H2Br+} + ∆fH{D2O+} -
∆fH{H2O+} ) 217 ( 1 kcal/mol (7)
the flow. In the notation of eq 8, they are N+3 /2, N1+/2, (N3+
+
N+2 + N+4 )/2, (N1+ + N6+)/2, (N4+ + N+2 + N+5 )/2, N6+/2, and
N5+/2, assuming equal concentration of X79Br+ and X81Br+
ions that are dependent on the initial ratios [H79Br]/[H81Br] and
[D79Br]/[D81Br], as well as on ionization wavelength, and will
be verified for our conditions below.
Presently available values for some rate coefficients are shown
in the notes to Table 1.
The kinetics of ionic species along a free jet axis (z) is
described by the following set of equations:
IV. Numerical Simulation
dN+1
Almost all differential equations of the system (eqs 8),
excluding eq 8c, contain interference with each other and cannot
be integrated analytically in their original form. To derive
relations between the rate coefficients and experimental data,
we need to simplify some of eqs 8. As a first step of analysis,
a numerical integration of eqs 8 was conducted. All eight
reactions listed in Table 1 were simulated numerically. The flow
was considered as a uniform gas mixture with a constant fraction
of all original molecules (He, HBr, DBr) from the nozzle to an
extraction point. Gas parameters were considered to obey the
"spherical expansion” model.13 The entire reaction region
(between zi ) 10 mm and zf ) 29 mm, i.e., zi/D ) 25 and zf/D
) 72) belongs to the so-called “hypersonic” component of the
flow; therefore, the flow velocity u is approximately constant
and the number density n is well-described by the formula n )
n0z20/z2, where n0 is the stagnation gas density and z0 ) aD (D
is the nozzle diameter and a ) 0.401 and 0.298 for monatomic
and diatomic gases, respectively).
n
u
)
)
(-k1N+1 N1 - k2N+1 N2 - k3N+1 N2 + k6N2+N1 +
( )
dz
k7N+3 N1) (8a)
dN+2
dz
n
(-k4N+2 N2 - k5N+2 N1 - k6N+2 N1 + k3N1+N2 +
( )
u
k8N+3 N2) (8b)
dN+3
dz
n
u
)
(-k7N+3 N1 - k8N3+N2)
(8c)
(8d)
(8e)
(8f)
( )
dN+4
dz
n
u
)
)
k1N+1 N1
( )
dN+5
dz
n
k4N+2 N2
( )
u
Equations 8 were integrated numerically, beginning from the
point of ionization, zi, where a fraction of each ion was
dN+6
dz
+
considered to be a parameter: N+(zi) ) aHBr , N (zi) ) aDBr
+
+
,
n
)
(k2N+1 N2 + k5N2+N1)
1
2
and N+(zi) ) aBr and N (zi) ) 0, N (zi) ) 0, and N (zi) ) 0.
+
+
+
( )
+
u
3
4
5
6
The fraction of the minor ionic species (Br+, DBr+ in SET I
and Br+, HBr+ in SET II) was not large (usually <5%) and
they were not able to affect product distributions of the primary
reactions dramatically. However, their role in secondary reac-
tions was significant. For example, under resonant ionization
of the HBr+ ions, there is a low probability that the presence
of some portion of the DBr+ and Br+ ions is important in
determining the kinetics of the HBr+ and H2Br+ ions. However,
even their low fraction may be dominant in the kinetics of the
D2Br+. The original (at the point of ionization, zi) fraction of
where the fractions of the HBr and DBr molecules, N1 ) [HBr]/
n and N2 ) [DBr]/n, as well as the unique flow velocity (u) are
considered to be constants over the entire reaction region from
the point of ionization, zi, to the point of detection, zf. The gas
density and the relative densities of the ions N+1 ) [HBr+]/n+,
N+2 ) [DBr+]/n+, N3+ ) [Br+]/n+, N4+ ) [H2Br+]/n+, N+
)
5
[D2Br+]/n+, and N6+ ) [HDBr+]/n+ are functions of the
distance from the nozzle (z).
The rate coefficients k1,..., k8 were studied based on the kinetic
equations (eqs 8) and experimental data on the relative fraction
of ions (N+, ..., N+) produced in the reaction region between zi
+
+
+
the ions aHBr , aDBr , and aBr (which is considered to be
independent of the stagnation pressure, P0, but dependent on
ionization wavelength) and the rate coefficients k1,..., k8 (which
are considered to be independent of temperature, but again,
dependent on the internal state of the ions created) were taken
as parameters of numerical integration and were determined by
a best fit to the experimental data.
1
6
and zf. Seven signals, corresponding to the masses 79, 80, ...,
85 amu, were measured as functions of the total stagnation
pressure, P0, at every particular fraction of bromide molecules,
(N1 + N2) ) ([HBr] + [DBr])/n. Two sets of experiments were
performed. In the first set, referenced below as (SET I), the
(2+1) REMPI of HBr+ was used in the He + HBr + DBr
mixtures with the ratio of [HBr]/[DBr] ≈ 3.7 ( 0.2 and total
fraction of bromides from 0.32% ( 0.02% to 2.0% ( 0.1%. In
the second one, referenced hereafter as (SET II), the (2+1)
REMPI of DBr+ was explored under [HBr]/[DBr] ≈ 0.37 (
0.02 and a total fraction of bromides in the same limits. All
The results of this optimization are shown in Table 1 (in
square brackets) and provide an approximate estimation for the
rate coefficients, because the efficiency and accuracy of the
multiparametric fitting decreases sharply with the number of
parameters and places high demands on the accuracy and the
body of experimental data. The second goal of the simulation

3450 J. Phys. Chem. A, Vol. 108, No. 16, 2004
Belikov and Smith
(81)
Br
Table 2 for every ionization path. Because the values of a
+
(79)
and a
cannot be found independently, we have assumed
+
DBr
that a minor species has the same isotopic fractions: in the case
(79)
DBr
of (2+1) REMPI of HBr+ (SET I), the a
value was
+
(81)
assumed to be equal to the a
value and the a(81) value was
+
+
DBr
Br
derived from extrapolation of the S81 signal; whereas in the case
of (2+1) REMPI of DBr+ (SET II) the aB(8r1) was assumed to be
+
equal to the a(79) and the a(79) was found from a(81) + a(79)
.
+
Br
+
DBr
+
Br
+
DBr
As shown in Table 2, all isotope-substituted ions have similar
fractions in all cases with a small predominance of light species
that, however, is inside the error limits.
Now we can express the experimentally measured ion signals
through the rate coefficients and flow parameters by integration
of eqs 8.
Kinetics of the Br+ Ions. Equation 8c can be simply
integrated in the region between zi and zf, giving
k7N1 + k8N2
Figure 1. Comparison of measured (symbols) and simulated (lines)
fractions of ions at the point of their extraction for (2+1) REMPI of
1
1
N+3 (zf ) ) aBr+ exp -n z2
-
(9a)
(
)
)
]
0 0
(
[
zi zf
u
3
HBr+ through the f ∆2(v ) 0) intermediate state in the He + HBr-
(1.6%) + DBr(0.4%) mixture. The rate coefficients used are presented
in Table 1.
or
ln(N+3 ) ) ln(aBr+) - k ú
(9b)
78
where k78 ) k7η + k8δ and ú is the reaction-time-integrated
number density (ú ) (N1 + N2){n0z2[(1/zi) - (1/zf )]/u}),
0
which is related to the number of collisions experienced between
the ionization point and the detection point in the jet; η ) N1/
(N1 + N2) and δ ) N2/(N1 + N2). Using the variable ú gives an
opportunity for joint analysis of all experimental data obtained
under various total fractions of bromides, (N1 + N2), if the ratio
N1/N2 is kept constant.
Kinetics of the HBr+ and DBr+ Ions. Integration of other
equations from the set of equations (eqs 8) requires some
simplification of them. Note that the set of reactions listed in
Table 1, as well as the set of equations (eqs 8) are symmetric,
relative to isotope-substituted species, and can be transformed
by substitution H S D in every ionic and neutral particle with
consequent substitution of the rates: (k1, k2, k3, k7) S (k4, k5,
k6, k8). Thus, we consider in detail only the kinetic equations
for the case of (2+1) REMPI of HBr+ in the [HBr]/[DBr] )
3.7 mixtures (SET I). Corresponding expressions for the ion
kinetics under (2+1) REMPI of DBr+ in the [HBr]/[DBr] )
0.37 mixtures (SET II) can be obtained by consequent substitu-
tions.
Figure 2. Comparison of measured (symbols) and simulated (lines)
fractions of ions at the point of their extraction for (2+1) REMPI of
1
DBr+ through the F ∆2(v ) 0) intermediate state in the He + HBr-
(0.6%) + DBr(1.7%) mixture.
was to investigate the importance of individual reactions in the
kinetics of ions and to justify a procedure of simplification of
eqs 8 for more-accurate derivation of the rate coefficients. An
example of the comparison between the simulation results and
the experimental data is shown in Figures 1 and 2 for the data
of SET I and SET II, respectively.
As a first approximation, eq 8a was integrated, neglecting
the fourth and fifth terms, which describes an additional portion
of the HBr+ ions produced in charge-transfer reactions R6 and
R7 (refer to Table 1). In this case, the kinetics of the HBr+
ions is presented:
N+1 (ú ) ) aHBr+ exp(-k123ú )
(10)
V. Analytical Solution
Fractions of Ions in the Ionization Region. First, we define
where the effective rate coefficient k123 ) k1η + k2δ + k3δ.
the initial fractions of the HBr+, DBr+, and Br+ ions (aHBr
,
+
This seems to be a correct approximation for data analysis of
+
+
aDBr , and aBr , respectively) in the point of ionization zi
separately for the 79Br and 81Br isotopic species. They were
derived from extrapolation of the corresponding mass-spectro-
metric signals to P0 ) 0. Extrapolation of the signals S79, S80,
+
+
+
the SET I experiments, where aHBr . (aDBr , aBr ) and δ is
significantly higher than η. A corresponding expression for the
kinetics of the DBr+ ions in the SET II experiments is
S81, S82, and S83 gives the values of a(79+), a(79)+, a(81) + a(79)
,
N+2 (ú ) ) aDBr+ exp(-k456ú )
(11)
+
Br
+
Br
HBr
DBr
(81)
HBr
a
+, a(81)+, respectively, where the superscripts indicate the
DBr
isotopic mass of Br in an ion. These variables can be observed
as a limiting case (n f 0) of the data shown in Figures 1-6.
The initial ionic fractions found from these data are listed in
with the effective rate coefficient k456 ) k4δ + k5η + k6η.
Considering the kinetics of the minor isotopic ions (DBr+ in
SET I or HBr+ in the SET II experiments), we must take into

Low-Temperature Kinetics of Transfer Reactions
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3451
TABLE 2: Initial Fraction of the HBr+, DBr+, and Br+ Ions at the Point of Ionization, zi, under Different Ionization Schemes
Fraction of Ions
f 3∆[3/2, V ) 0]
f 3∆[3/2, V ) 1]
F 1∆[1/2, V ) 0]
F 1∆[1/2, V ) 1]
Ionization of HBr+
0.374 ( 0.022
0.348 ( 0.023
0.018 ( 0.005
0.018
0.134 ( 0.012
0.115 ( 0.011
(79)
HBr
(81)
HBr
(79)
DBr
(81)
0.383 ( 0.020
0.383 ( 0.021
0.032 ( 0.007
0.032
0.084 ( 0.008
0.074 ( 0.007
0.402 ( 0.030
0.396 ( 0.032
0.036 ( 0.008
0.036
0.289 ( 0.019
0.246 ( 0.018
0.053 ( 0.011
0.053
a
a
a
a
a
a
+
+
+
+a
DBr
(79)
0.085 ( 0.012
0.060 ( 0.010
0.182 ( 0.016
0.178 ( 0.016
+
Br
(81)
+
Br
Sum(79)
0.499 ( 0.024
0.489 ( 0.025
0.526 ( 0.026
0.481 ( 0.027
0.523 ( 0.032
0.492 ( 0.034
0.524 ( 0.025
0.477 ( 0.026
Sum(81)
Ionization of DBr+
0.104 ( 0.012
0.101 ( 0.013
0.330 ( 0.021
0.305 ( 0.021
0.080 ( 0.014
0.080
(79)
HBr
(81)
HBr
(79)
DBr
(81)
0.069 ( 0.010
0.065 ( 0.010
0.399 ( 0.026
0.407 ( 0.025
0.017 ( 0.006
0.017
0.122 ( 0.014
0.119 ( 0.013
0.325 ( 0.022
0.336 ( 0.023
0.042 ( 0.011
0.042
0.108 ( 0.011
0.107 ( 0.011
0.320 ( 0.020
0.335 ( 0.020
0.058 ( 0.011
0.058
a
a
a
a
+
+
+
+
DBr
(79)
a
+
Br
(81)
+b
Sum(79)
a
Br
0.485 ( 0.030
0.489 ( 0.029
0.514 ( 0.028
0.486 ( 0.026
0.489 ( 0.027
0.497 ( 0.026
0.486 ( 0.025
0.500 ( 0.025
Sum(81)
a a(D8B1)r was assumed to be equal to a(79)
.
+
b a(B8r1) was assumed to be equal to a(79)
.
+
Br
+
+
DBr
tion of the H2Br+ ions, N4+, is described by eq 8d, using N+1 (ú)
from eq 10 for SET I and from eq 15 for SET II. Integration of
eq 8d gives
account all terms of eqs 8a and 8b, because the importance of
the fourth and/or fifth terms is quite possible here. Integration
of eq 8a using eq 9a for a fraction of the Br+ ions, N3+(z), and
eq 11 for a fraction of the DBr+ ions, N2+(z), gives
aHBr+ηk1[1 - exp(-k123ú)]
N+4 (ú) )
≈ aHBr+ηk1ú (16)
aDBr+k6η
k123
N+1 (ú) ) exp(-k123ú) aHBr
+
[1 - exp(k123 -
+
{
k456 - k123
for SET I and
aBr+k7η
k456)ú] +
[1 - exp(k456 - k78)ú] (12)
}
aHBr+ + aDBr+ηk3ú aBr+ηk7ú
k78 - k123
N+(ú) ) ηk ú
+
(17)
(
)
4
1
2
2
The corresponding expression for the DBr+ ions in the experi-
ments of SET I is
for SET II. Analogously, the kinetics of the D2Br+ ions is
described by
aDBr+k3δ
N+2 (ú) ) exp(-k456ú) aDBr
+
[1 - exp(k456 -
+
aDBr+δk4[1 - exp(-k456ú)]
{
(k123 - k456
)
N+5 (ú) )
≈ aDBr+δk4ú (18)
k456
aBr+k8δ
k123)ú] +
[1 - exp(k456 - k78)ú] (13)
}
k78 - k456
and
Certainly, eqs 12 and 13 describe the kinetics of the HBr+ and
DBr+ ions in both experimental sets rather well; however, they
are absolutely inappropriate for analysis of experimental data,
especially for the kinetics of the H2Br+, D2Br+, and HDBr+
ions, because integration of eqs 8d-f leads to multiterm
expressions that include all eight rate coefficients. Instead of
them, considering results of SET I, we will use eq 10 for the
HBr+ ions, that answer to the first term in eq 12, and a linearized
approximation of eq 13 for the DBr+ ions
aDBr+ + aHBr+δk6ú aBr+δk8ú
N+(ú) ) δk ú
+
(19)
(
)
5
4
2
2
respectively. At last, the kinetics of the HDBr+ ions (N6+) is
described by eq 8f, which, after integration by the same manner
and simplification to linear terms only, leads to the expression
+
N6 (ú) ) (aHBr+δk2 + aDBr+ηk5)ú ) k25ú
(20)
Thus, a fraction of the ionic species Br+, HBr+, DBr+, H2Br+,
D2Br+, and HDBr+, at the point of extraction zf, is described
by eq 9, eq 10 or 15, eq 11 or 14, eqs 16 and 17, eqs 18 and
19, and eq 20, respectively.
N+2 (ú) ≈ aDBr+ + a +k δú + a +k δú
(14)
HBr
3
Br
8
+
that is based on the following experimental conditions: aHBr
+
+
. (aDBr , aBr ), δ/η ) 3.7, and kiú , 1 for all rate coefficients
ki. The kinetics of the DBr+ and HBr+ ions in the SET II
experiments is considered, based on eqs 11 and 15, respectively:
VI. Rate Coefficients
Charge-Transfer Reaction: Br+ + HBr (DBr) f Br +
HBr+ (DBr+) and Rate Coefficients k7 and k8. Br+ ions
disappear in reactions 7 and 8 (see Table 1), according to eq 9.
The experimental data of SET I and SET II are shown in Figure
3. Here, and below, we present only results for REMPI of the
HBr and DBr molecules through the F 1∆2[2Π1/2, V ) 1] states,
N+1 (ú) ≈ aHBr+ + a +k ηú + a +k ηú
(15)
DBr
6
Br
7
Kinetics of the H2Br+, HDBr+, and D2Br+ Ions. Now we
consider the kinetics of other minor ionic species. In both
experimental sets, they are H2Br+, HDBr+, and D2Br+. Evolu-

3452 J. Phys. Chem. A, Vol. 108, No. 16, 2004
Belikov and Smith
Figure 3. Kinetics of the Br+ ions, observed by the signal of mass 79
(S79), as a function of the number of collisions with the bromide
molecules. Open symbols represent (2+1) REMPI of HBr+ through
the F 1∆2 (V ) 1) Rydberg state in the He + HBr + DBr mixture with
the constant ratio [HBr]/[DBr] ) 3.7 and various total fractions of
bromides ((]) 3.2%, (0) 2.0%, (4) 1.0%, (+) 0.6%, and (O) 0.4%).
Closed symbols represent (2+1) REMPI of DBr+ through the F 1∆2 (V
) 1) state in the mixture with the ratio [HBr]/[DBr] ) 0.37 and various
total fractions of bromides ((9) 2.4%, (2) 1.1%, and (b) 0.5%). Lines
are the best linear approximations of the data.
Figure 4. Kinetics of the HDBr+ ions (S84) in experiments of SET I
(open symbols) and SET II (closed symbols). Experimental conditions
and symbols are the same as those given in Figure 3.
because other data are qualitatively the same. The ratio [HBr]/
[DBr] ) 3.7 (SET I) and 0.37 (SET II) was kept constant inside
one set and the total fraction of bromides in the He + HBr +
DBr mixture was varied from 0.4% to 3.2%. The S79 signal,
corresponding only to the 79Br+ ion, was used here, because,
as shown previously, the fractions of the 79Br+ and 81Br+ ions
are almost the same and the 81Br+ signals are interfered by the
H279Br+ and D79Br+ signals. The effective rate coefficient (k78
) k7η + k8δ), as well as the initial fraction of Br+ ions (aBr ),
+
were derived from the slope and intersection with the axis ú )
0 in Figure 3, according to eq 9b. The actual rate coefficients
for reactions 7 and 8 (see Table 1) then were obtained by
comparison of k78(SET I) and k78(SET II). The results seem to
be independent of the ionization path: k7 (in units of 10-9 cm3/
s) ) 2.7 ( 0.4, 2.7 ( 0.4, 2.8 ( 0.4, and 2.6 ( 0.4 and k8 (also
in units of 10-9 cm3/s) ) 1.6 ( 0.3, 1.6 ( 0.3, 1.7 ( 0.3, and
Figure 5. Kinetics of the D2Br+ ions (S85) in experiments of SET I
(open symbols) and SET II (closed symbols). Experimental conditions
and symbols are the same as those given in Figure 3.
3
3
1.6 ( 0.3 for ionization through the f ∆2 (V ) 0), f ∆2 (V )
1
1
1), F ∆2 (V ) 0), and F ∆2 (V ) 1) states.
Reaction of HDBr+ Production: HBr+(DBr+) + DBr-
(HBr) f HDBr+ + Br and Rate Coefficients k2 and k5. The
rate coefficients k2 and k5 were determined by comparison of
k25 measured in two experimental sets, and k25 was derived,
according to eq 20, from S84(ú), which represents the fraction
of HD81Br+ isotope. In the case of DBr+ REMPI (SET II), when
the fraction of HBr+ ions is small, additional information about
the kinetics of N+6 was received from a combination of other
signals:
states, the k2 and k5 values (× 10-9 cm3/s, (20%) were 1.7,
1.7, 1.6, and 1.6 for the HBr+ ions, and 1.6, 1.7, 1.5, and 1.5
for the DBr+ ions, respectively. Actually, the determined rate
coefficients k2 represent an average rate of the H79Br+/D81Br
H+-transfer and the H81Br+/D79Br D-transfer processes, which
are inseparable in our experiments, and the rate coefficient k5
represents the D79Br+/H81Br D+-transfer and the D81Br+/
H79Br H-transfer reactions.
Reaction of D-atom and/or D+-ion Transfer: DBr+ + DBr
f D2Br+ + Br and Rate Coefficient k4. One more rate
coefficient can be derived directly from the experimental data.
It is k4 that representsreaction R4 from Table 1. Figure 5 presents
data on evolution of the S85 signal that corresponds to the
D281Br+ ions. These data are linear in all investigated ranges
of ú for both experimental sets, which justifies use the linear
approximation in eq 18 or the first term of eq 19 for
interpretation of the data of both experimental sets. Taking into
+
[H81Br+] + [HD79Br+] - [H79Br+]
N6
S82 - S80
)
≈
(21)
Σ(I+)
2
where Σ(I+) is the sum of all ions. The dependencies of the S84
ion signals on the integrated number density of hydrogen
bromides, ú, are shown in Figure 4 for SET I and SET II. In
the (Π3/2, V ) 0), (Π3/2, V ) 1), (Π1/2, V ) 0), and (Π1/2, V ) 1)

Low-Temperature Kinetics of Transfer Reactions
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3453
transfer (R1) can be found from k123: k1(× 10-9 cm3/s) ) 1.3,
1.0, 1.3, 1.1 for the (Π3/2, V ) 0), (Π3/2, V ) 1), (Π1/2, V ) 0)
and (Π1/2, V ) 1) ionic states. Accuracy of this derivation was
estimated as 25%, because of low and very low weights of the
terms that contain the rate coefficients k2 and k3, respectively.
VII. Analysis and Discussion
The rate coefficients of reactions R1-R8, listed in Table 1,
have been determined to be the best fits of eqs 9b, 10, 11, 14-
18, and 20 to the final fraction of ions measured in the
experiment. As expected, both procedures (simulation and direct
kinetics) have led to similar results. Wider error limits for the
rates found by the simulation procedure are explained by some
uncertainty in the statistical weights that have been chosen for
ionic species in the fitting procedure. Accuracy of the rates found
from Figures 3-6 is defined by applicability of the assumed
kinetic model to our experimental conditions, as well as by
accuracy of the measurements of the final ion fractions and the
2
value of ú ) (N1 + N2 )[n0z0 (1/zi - 1/zf)/u]. Processes such as
Figure 6. Kinetics of the HBr+ ions in SET I (open symbols) and of
the (DBr+ + H2Br+) ions in SET II (closed symbols). Experimental
conditions and symbols are the same as those given in Figure 3.
clustering or quenching of the excited states were excluded from
our consideration, based on the fact that the kinetics of the ions
was dependent only on the parameter ú under a variety of
particular experimental conditions, such as the position of
ionization and detection points or the number density of
individual gas species. The parametrization of the data indicates
that (i) they are the result of binary collisions of bromides, which
are not subject to quench by or charge transfer to the He atoms;
and (ii) the gas density in the flow obeys the spherical expansion
model without an observable effect of flow heating by conden-
sation. In addition, the appearance of cluster ions was easily
determined and controlled by mass spectrometry. In regard to
quenching of the excited spin-orbit and vibrational states of
the ions, it is difficult to imagine a channel that involves
anything other than vibrational excitation of neutral hydrogen
bromides. The rates of these energy transfer channels are
unknown but are expected to be slow; that hypothesis is
supported by the lack of evidence for any of measured rates,
depending upon the mole fraction of hydrogen bromide.
However, we cannot exclude energy transfer to HBr/DBr and,
in this case, the measured rate coefficients for the excited ions
must be considered only as their upper limits. Most of the
expressions are derived from exact equations in the “low-
density” approximation, which is justified for our experimental
conditions if values of the rates are not too high (k ≈ 10-9 cm3/s
or less). A contribution of every neglected term to the final
fraction of ions was verified by a numerical simulation
procedure. Thus, it has been established that the simplified
equations work rather well. Uncertainty in the rate coefficients
caused by scattering of the ion fraction data can be estimated
as 3%-15% (see Figures 3-6).
+
+
account values of aDBr (SET I), aDBr (SET II), δ(SET I), and
δ(SET II), we receive k4(× 109 cm3/s) ) 1.5, 1.3, 1.4, and 1.1
((24%) from SET I and 1.4, 1.1, 1.4, and 1.1 ((17%) from
SET II for the DBr+ (Π3/2, V ) 0), (Π3/2, V ) 1), (Π1/2, V ) 0),
and (Π1/2, V ) 1) states, respectively.
Effective Rate Coefficients for Kinetics of HBr+ and DBr+
Ions and Rate Coefficients k1, k3, and k6. The rate coefficients
k1, k3, and k6 cannot be found from our experiments directly.
Their estimation is based on the kinetics of HBr+ and DBr+
ions and the rate coefficients found previously. Loss of the HBr+
ions in experiments of SET I is shown in Figure 6. The data
were analyzed using eq 10, with an effective rate coefficient
(I)
123
k
) (k1η(I) + k2δ(I) + k3δ(I)), which was found as k(1I2)3(×
10-9 cm3/s) ) 1.5, 1.3, 1.5, and 1.3 ((15%) for the H79Br (Π3/2
,
V ) 0), (Π3/2, V ) 1), (Π1/2, V ) 0), and (Π1/2, V ) 1) ions. The
intersection of the data with the ordinate axis also gives the
(I)
(II)
values of a
presented in Table 2. The rate coefficient k
456
+
HBr
) k4δ(II) + k5η(II) + k6η(II) that describes loss of DBr+ ions has
been found from the corresponding data of SET II. Because
both signals of the D79Br+ and D81Br+ ions were intervened
with other ions of the same masses, we used a combination
S(8I1I) - S(7I9I) ) [81Br+] + [D79Br+] + [H279Br+] -
N+2 N+4 N+2
[79Br+] ≈
+
≈
(22)
2
2
2
and neglected the contribution of the H279Br+ ions, which was
<5% as it was estimated by comparison of D2Br+ and HBr+
signals (S85 and S80) in the SET I experiments. The second set
of data in Figure 6 presents the data for definition of the rate
coefficient k(4I5I6) and value of aD(IIB)r+ from eq 11. For the (Π3/2, V
Actual accuracy of the ú value is defined by applicability of
the gas-dynamic model assumed rather than by the accuracy of
values measured. The latter errors were estimated as follows:
5%-7% for the bromide fractions N1 and N2; < 3% for the
stagnation density n0; and 5% for the distances zi and zf. The
“spherical expansion” model works very well to describe gas
density in a free jet. Accuracy of this description was checked
in many experimental studies,13,14 and errors can be estimated
as <3%. The situation with gas temperature and flow velocity
is more complicated; however, they are also very important in
defining the reaction time (as TOF between the ionization and
extraction points) and the temperature, to which the measured
rate coefficients should be attached. They are still very predict-
able in the initial equilibrium portion of the flow. Far from the
) 0), (Π3/2, V ) 1), (Π1/2, V ) 0), and (Π1/2, V ) 1) states of
(II)
the D79Br+ ions, the effective rate coefficients k (× 10-9
456
cm3/s, (15%) were 1.6, 1.5, 1.4, and 1.4, respectively.
The rate coefficient k6 can be derived from k(4I5I6) , taking into
account values of k5 and k4 previously given in Section VI: k6
) (6 ( 3) × 10-10 cm3/s for all states of the DBr+ ions. If we
assume a similar value for the reverse reaction (that is confirmed
by the results of Green et al.3 and Xie and Zare9), the rate
coefficient k1 of the reaction of the H-atom and/or H+-ion

3454 J. Phys. Chem. A, Vol. 108, No. 16, 2004
Belikov and Smith
nozzle, however, the equilibrium between different energy
modes is disturbed and the concept of temperature is lost.
Moreover, aerodynamic separation of gases in seeded free
jets15,16 leads to velocity and temperature slip between light and
heavy fractions. In speaking about a translational temperature,
we can introduce parallel and perpendicular temperatures (T|
and T , respectively) as a measure of velocity dispersion along
and across a free jet axis. These temperatures, as well as the
flow velocity, can be estimated in the He + HBr(2%) free jet,
using the results of Tanaka et al.17 for the He + Kr(2%) mixture
(because the masses of HBr and Kr are very similar). For the
same stagnation temperature (T0 ) 295 K) and variation of P0D
(20-80 Torr mm, which is the range of our experiments), they
observed T|He (from 14 to 3 K), T|Kr (from 38 to 9 K), and
∆u/uis (from 0.12 to 0.09), where uis is the isentropic terminal
velocity and ∆u is the difference between velocity of the light
and that of the heavy species (velocity slip). The isentropic
terminal flow velocity in the helium free jet seeded by HBr
with the molar fraction R can be determined from a simple
energy balance. Neglecting the small portion of energy that
remains in the rotational degrees of freedom, we can write
molecule, the LD approximation provides only an upper limit
to the ion-dipole capture rate coefficient that overestimates
(sometimes, seriously) the dipole effect.20 The average dipole
orientation (ADO) model is more realistic, providing a good
agreement with many experiments.4 For the (Br+, HBr+,
DBr+)-(HBr, DBr) ion-molecule interaction, the rate coef-
ficients are kADO(T ) 300 K) ) 9 × 10-10 cm3/s to kADO(T )
10 K) ) 3 × 10-9 cm3/s (here, we used c(300 K) ) 0.18 and
c(10 K) ) 0.3, according to ref 4).
A theory of ion-dipolar molecule interaction was also
developed and the ion-molecule capture rates were calculated
by Su and Chesnavich,21 Su,22,23 Clary,24 Clary et al.,25 Rebrion
et al.,26 and Troe.27,28 Tests on the same ion-molecule pairs
demonstrate good agreement between these approaches at
temperatures of 100 K and higher, where they describe the
experiment very well,24,26,27 whereas the ADO rates are ∼30%
lower. At lower temperatures, the classical trajectory23 and
statistical adiabatic channel models27 give similar results up to
5 K, whereas the rates calculated by adiabatic capture-
centrifugal sudden approximation25 demonstrate a stronger
temperature dependence. However, any more-extensive com-
parison of our experimental rate coefficients does not seem to
be justified, because of a lack of equilibrium between rotational
and translational degrees of freedom in the free jet reactor. Under
the conditions of our experiments, the rotational temperature
of the bromides is ∼80 K, whereas the translational temperature
is ∼10 K. However, both of these temperatures clearly are
essential and have to be taken into account: the rotational
angular momentum of the molecules is important for average
orientation, and their relative velocity defines the collisional
time and energy. Su22 considered the efficiency of ion-dipolar
molecule capture under various collisional energies (from
thermal energy to energies of a few electron volts) and constant
rotational temperature of the neutrals (300 K), but those
conditions are quite different from ours. However, even based
only on comparison with the ADO model, we can conclude
that the measured rate coefficients have reasonable values.
kBT0γ (1 - R)mHeu2is RmHBru2is
)
+
(23)
γ - 1
2
2
where kB is the Boltzmann constant, γ is the heat-capacity ratio
for the mixture (γ ) (2R + 5)/(2R + 3)), T0 is the stagnation
temperature, and mHBr and mHe are the molecular masses. For
the fraction of HBr, R ) 0.01 and 0.02, the isentropic flow
velocities are uis ) 1.60 × 105 and 1.49 × 105 cm/s, respectively.
The velocity of the HBr+/DBr+ ions between the point of
ionization zi and the point of extraction zf was measured by the
delay between pulses of the ionization laser and the sweeping
field. Typical values of the velocity were uHBr ) 1.2 × 105
+
and 1.1 × 105 cm/s for R ) 0.01 and 0.02, respectively, which
demonstrates slightly higher velocity slip effects, compared to
the data of Tanaka et al.17
Looking at the measured rate coefficients, listed in Table 1,
we first notice the relatively high rate (∼10-9 cm3/s) of all the
reactions studied. This is entirely consistent with the fact that
all the reactions are exothermic and occur on potential surfaces
that contain strong ion-dipole interactions. Considering the rate
coefficients for the ion-dipole capture, Su and Bowers4 gave
the following expression:
The rate coefficients k1 and k4 for the atom-transfer reactions
of the HBr+ and DBr+ ions with the parent molecules were
observed to be very similar to those measured in our previous
work, whereas the rate coefficients k2 and k5 for atom transfer
between different isotopic species seemed to be slightly higher
(∼20%). A remarkable (∼70%) isotope effect was observed
only for the charge-transfer reactions between the Br+ ions and
the HBr and DBr molecules; this effect remains unexplained.
The enthalpy of reaction, which is defined as the difference of
the heats of formation at T ) 0 K (see Table 1), is unlikely to
be responsible for the effect, which was equally observed for
all REMPI schemes. If the Br+ ions were produced in photo-
dissociation of the HBr+ and DBr+ ions, the variation of the
photon energies for different REMPI schemes was much more
than the enthalpy of reaction. The excess of energy could be
converted to internal energy of the Br+ ions (exciting the
different 3PJ ground fine structure states or even the 1D excited
state, lying 11 409 cm-1 higher) and/or their kinetic energy,
that ultimately may change the enthalpy of reaction dramatically.
1/2
Rp
µ
1/2
2
k ) 2πq
1 + cµD
(24)
( )
(
)
[
]
πkTRp
where q is the charge on the ion, Rp the polarizability of the
molecule, µ the reduced mass, µD the dipole moment of the
molecule, k the Boltzmann’s constant, T the absolute temper-
ature, and c the degree of orientation of the dipole in the ion
field. For the case of c ) 0, in regard to the ion-induced dipole
interaction, the relationship (providing a lower limit of the ion-
dipole capture) is independent of temperature; for the (Br+,
HBr+, DBr+)-(HBr, DBr) pairs, the relation is equal to 7 ×
10-10 cm3/s. The simplest model that accounts for the ion-
dipole interaction is probably the locked dipole (LD) ap-
proximation that has been treated by Theard and Hamill18 and
Moran and Hamill,19 which is consequent to c ) 1 in eq 24. In
this case, the rate coefficient for our ion-molecule pairs
increases from kLD(T ) 300 K) ) 2 × 10-9 cm3/s to kLD(T )
10 K) ) 7 × 10-9 cm3/s. Because the ion field cannot
completely freeze the rotational angular momentum of the polar
A second surprise is the relatively low value of the rate of
the simple charge-transfer DBr+/HBr reaction (up to a factor
1
of /3 of that of the atom-transfer channel). As verified by
numerical simulation, the final ion fractions measured in the
experiment were least sensitive to the rate coefficients k3 and
k6. That led to lower accuracy of the rate coefficients, which
was probably caused by the initial creation of both types of
ions at the ionization point zi. The room-temperature rate

Low-Temperature Kinetics of Transfer Reactions
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3455
coefficient k6 (in units of 10-10 cm3/s, (20%) was measured
has been observed for reactions R1 and R4 only and is not
observed for the similar reactions R2 and R5.
by Xie and Zare9 as 4.1, 1.4, 3.8, and 2.3 for the DBr+ [Π3/2
,
V ) 0], [Π3/2, V ) 1], [Π1/2, V ) 0], and [Π1/2, V ) 1] ion states,
respectively. These are a factor of 2-3 less than those measured
presently at low temperatures. The difference is the same for
the rate coefficient k1 (see Table 1 and ref 3) and can be
explained in the frame of the model of the ion-dipole
interaction.
Green et al.3 studied different channels of the reactions
between the H79Br+ ions and H79,81Br/D79,81Br molecules and
found that the charge-transfer, proton-transfer, and hydrogen/
deuterium-transfer channels amounted to 46%/50%, 32%/28%,
and 21%/21%, respectively. In the present study, we cannot
distinguish the products of proton and hydrogen (for HBr+/HBr)
or deuterium (for HBr+/DBr) transfer reactions. However, we
can estimate a portion of the charge-transfer channel in the
HBr+/DBr and DBr+/HBr reactions, which is ∼20%-30%. This
percentage is lower than those observed Green et al.3 and is
primarily caused by an increase of the proton/hydrogen/
deuterium transfer rate at lower temperatures.
VIII. Summary
The charge- and atom-transfer reactions between the HBr+,
DBr+, and Br+ ions and the HBr and DBr molecules have been
studied under low-temperature conditions in a helium free jet.
The HBr+ [2Πi , V+] and DBr+ [2Πi , V+] ions were prepared in
selected spin-orbit (i ) /2 or /2) and vibrational (V+ ) 0 or
1
3
1) states by (2+1) REMPI through the f 3∆2 (V ) 0), f 3∆2 (V )
1
1
1), F ∆2 (V ) 0), and F ∆2 (V ) 1) Rydberg intermediates.
Despite the resonance character of the ionization, a small, but
finite, quantity of byproduct ions (Br+ and H(D)Br+) were
created and observed in each ionization path. All ions (reactants
and products) were measured by time-of-flight (TOF) mass
spectrometry at some distance from the ionization point zi. The
kinetics of these ions, under a variety of [HBr] and [DBr]
concentrations, has been used to derive the rate coefficients of
all energetically permitted reactions. All highly exothermic
reactions, including the Br+/(HBr, DBr) charge transfer and
(HBr+, DBr+)/(HBr, DBr) hydrogen/deuterium transfer, are
observed to be fast (1.0 × 10-9-2.7 × 10-9 cm/s, values of
which are similar to the rate coefficients of the ion-polar
molecule capture estimated in the context of the average dipole
orientation (ADO) model. The low-temperature rate coefficient
of the HBr+(2Π3/2, V+ ) 0)]/HBr hydrogen-transfer reaction
exceeds its room-temperature value measured by Green et al.3
by as much as a factor 2, whereas the rates of almost equi-
energetic DBr+/HBr and HBr+/DBr charge-transfer reactions
are more similar to those measured by Xie and Zare9 for T )
300 K. Only atom-transfer reactions between the same isotopic
species demonstrate a weak negative dependence on vibrational
excitation of the ions that can be explained if the reaction
proceeds through a long-lived, complex forming mechanism.
This work also demonstrates that multireaction processes can
be successfully studied by a single spectroscopic technique, even
for cases in which the reaction products are not all directly
observed.
The only reactions that demonstrate dependence on the
internal state of the ionic reactants or, more exactly, on
vibrational excitation were reactions R1 and R4 (refer to Table
1). The difference in the rate coefficients is small (20%-40%),
but it exceeds the experimental uncertainty. This tendency is
observed for both reactions and for both spin-orbit states in
every reaction, as well as in the work of Xie and Zare.9 Thus,
the favorable reactivity of ions in the ground vibrational state
is statistically confirmed. A similar effect of rotational excitation
has not been observed in our experiments. According to
REMPI-LIF,29 REMPI-PES, and zero-kinetic-energy-pulsed-
field ionization (ZEKE-PFI)30 studies, only a few rotational
levels of the HBr+ ion are populated about the J-value of the
intermediate state selected. In most cases, we realized REMPI
through the lowest rotational level of the intermediates, using
the R(1) and S(0) rotational lines, populating a few of the lowest
rotational levels of the ions. However, in several experiments,
the higher linessR(4), R(5), S(3), S(4)swere explored without
any noticeable effect on the rate coefficients of the reactions
studied. In most studies,31-38 the effects of ion rotational
excitation on ion-molecule reactions were either immeasurably
small or <10% toward suppression of reactivity.33,34 Yet,
sometimes the effect of suppression was significantly stron-
ger.38,39 The effects of vibrational excitation of ions on reactivity
has been observed to be ambiguous.9,37,38,40-49 In some cases,
the vibrational energy simply promotes overcoming an activation
barrier for an endoergic reaction; in other cases, it is important
in reaction dynamics and the competition of different reaction
channels. Dependence of the rate coefficients on vibrational
energy of ionic reactants could be explained, if we suppose that
the reaction goes through a collisional complex formation. Green
et al.3 estimated that ∼28% of the HBr+/DBr proceeded through
a long-lived complex under thermal conditions. The fraction of
the complex forming the channel would be expected to increase
at lower temperatures and is possibly dominant under the near-
10-K conditions realized in our experiments. An inverse
vibrational dependence of the rate coefficients can result in a
complex formation mechanism. Roughly, a complex produced
from an ion in the ground vibrational state can decay to new
products or return to original reactants, whereas a complex
produced from a vibrationally excited ion has the additional
channel of vibrational relaxation. Regardless of the mechanism
that is responsible for the lower reactivity of the vibrationally
excited HBr+ and DBr+ ions, this weak (∼20%-40%) effect
Acknowledgment. The authors gratefully acknowledge
financial support of this work by the National Science Founda-
tion, through Grant No. CHE-9984613, and by the Russian
Foundation of Basic Research, through Grant No. 03-03-32316.
We also thank the reviewers for useful comments and sugges-
tions.
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