State-specific low temperature reactions (HBr+, DBr +) [2 Πi,v ] + (H2, D 2): Channels and rates

Article abstract of DOI:10.1016/j.cplett.2003.12.129

The channels of the HBr⁺(Π_i,v)+D₂ and DBr⁺(Π_i,v)+H₂ ion-molecule reactions were investigated in a state-selective manner at low temperatures in a free jet. The selected spin-orbit and vibrational states of the ions were prepared by resonance-enhanced multiphoton ionisation. All three energetically accessible channels of the reactions were under consideration using time-of-flight mass spectrometry. The dependence of the rate coefficient of the atom transfer channel versus reaction energy appears to be common to all ion-molecule pairs studied here and previously: HBr⁺+H₂, HBr ⁺+D₂, DBr⁺+H₂, DBr ⁺+D₂.

Full text of DOI:10.1016/j.cplett.2003.12.129

Chemical Physics Letters 387 (2004) 7–11
www.elsevier.com/locate/cplett
State-specific low temperature reactions
(HBrþ, DBrþ) [2Pi; v] + (H2, D2): channels and rates
a
Andrey E. Belikov , Mark A. Smith
b,
*
a
Institute of Thermophysics, 1 Lavrentjev Ave., Novosibirsk 630090, Russia
b
Department of Chemistry, University of Arizona, 1306 E. University Dr., Tucson, AZ 85721, USA
Received 11 November 2003
Published online: 18 February 2004
Abstract
The channels of the HBrþ(Pi; v) + D2 and DBrþ(Pi; v) + H2 ion–molecule reactions were investigated in a state-selective manner
at low temperatures in a free jet. The selected spin–orbit and vibrational states of the ions were prepared by resonance-enhanced
multiphoton ionisation. All three energetically accessible channels of the reactions were under consideration using time-of-flight
mass spectrometry. The dependence of the rate coefficient of the atom transfer channel versus reaction energy appears to be common
to all ion–molecule pairs studied here and previously: HBrþ + H2, HBrþ + D2, DBrþ + H2, DBrþ + D2.
Ó 2004 Elsevier B.V. All rights reserved.
2
DBrþð Pi; vþÞ þ H2 ! HDBrþ þ H
ð4Þ
1. Introduction
As the reaction energy, Dei;v, is different for the re-
actions (1)–(4) even for the same spin–orbit (i) and vi-
brational state (v) of the ions, the combined data can
provide the rate coefficient k ¼ f ðDei;vÞ with greater
detail. In addition, investigation of the reactions be-
tween crossed-isotope reactants gives us a possibility to
study all possible different channels:
In our previous work [1,2] we studied the ion–mole-
cule reactions
2
HBrþð Pi; vþÞ þ H2 ! H2Brþ þ H
ð1Þ
ð2Þ
2
DBrþð Pi; vþÞ þ D2 ! D2Brþ þ D
under low collisional energies in a free jet and found that
their reactivity displays a threshold behaviour depend-
ing on total energy independent of the internal states of
the ions. Rate coefficients of the reactions (1) and (2)
appear to obey a unique function of excess energy in
each reaction that takes into account collisional and
internal energy of both reactants as well as the heat of
formation of the reactants and products. In an at-
tempt to confirm and extend that result, in the present
communication we report the analogous data for the
reactions
2
HBrþð Pi; vþÞ þ D2 ! DBrþ þ HD
and
ð3aÞ
2
HBrþð Pi; vþÞ þ D2 ! D2Brþ þ H
ð3bÞ
ð4aÞ
ð4bÞ
2
DBrþð Pi; vþÞ þ H2 ! HBrþ þ HD
2
DBrþð Pi; vþÞ þ H2 ! H2Brþ þ D
The methodology and technique of the study was
similar to that previously reported [1,2] for the investi-
gation of the reactions (1) and (2). Briefly, the reactions
were studied in a pulsed free jet (nozzle diameter D ¼ 0:4
mm) of the HBr(<1%) + D2 or DBr(<1%) + H2 mix-
tures. The HBrþ(2Pi; vþ) or DBrþ(2Pi; vþ) ions were
produced in a state-selective manner [3] by resonance-
enhanced multiphoton ionisation, (2 + 1) REMPI, at
2
HBrþð Pi; vþÞ þ D2 ! HDBrþ þ D
ð3Þ
* Corresponding author. Fax: +1-520-621-8407.
E-mail addresses: belikov@itp.nsc.ru (A.E. Belikov), msmith@
u.arizona.edu (M.A. Smith).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2003.12.129

8
A.E. Belikov, M.A. Smith / Chemical Physics Letters 387 (2004) 7–11
d½HBrþꢀ=dt ¼ ꢁk1½HBrꢀ½HBrþꢀ ꢁ k2½D2ꢀ½HBrþꢀ
ꢁ k3½D2ꢀ½HBrþꢀ;
some distance from the nozzle (zi ¼ 0:6, 1.0 or 1.4 cm).
Results of ion–molecule reactions were analysed by
mass spectrometry at a downstream point, zf ¼ 3:0 cm.
Relative number densities of the ions were measured as
ratios between corresponding signals of ions with masses
from 79 to 85 amu and their changes under variation of
stagnation pressure, p0, and initial fraction of bromides
in the mixtures, in other words, under variation of ion–
molecule collision number. In Section 2 we consider
kinetics of the ion–molecule reactions in a free jet and
derive expressions between their rate coefficients and
relative densities of ionic species. Then (in Section 3) we
use these expressions to determine the rate coefficients
from the measured final ion composition.
ð5Þ
d½H2Brþꢀ=dt ¼ k1½HBrꢀ½HBrþꢀ;
d½HDBrþꢀ=dt ¼ k2½D2ꢀ½HBrþꢀ;
d½DBrþꢀ=dt ¼ k3½D2ꢀ½HBrþꢀ;
ð6Þ
ð7Þ
ð8Þ
where k1, k2, k3 are the rate coefficients of the reactions
R1, R2, R3 from Table 1; [M] designates the number
density of the particular M molecule; [Mþ] is the frac-
P
tion of the Mþ ions ( [Mþ] ¼ 1). Using the fraction of
ions instead of their absolute number density permits us
to exclude from the equations a term that describes the
change of an ion number density in consequence to the
flow expansion. Let a ¼ [HBr]/([HBr] + [D2]) ¼ [HBr]/n
represent the fraction of the HBr molecules in the
HBr + D2 mixture with the total number density n and u
to be the flow velocity (a and u are considered as a
constant along the reaction region, whereas nðzÞ ¼ n0
2. Kinetics
As reactions in the HBr + D2 and DBr + H2 mixtures
are symmetric relative to H $ D substitution, we con-
sider only one of them as an example, HBr + D2, and
2
final results can be easily transformed to the case of the
2
ðaD=zÞ , according to spherical expansion model of the
DBr + H2 experiment. After the HBrþð Pi¼1=2;3=2; vþ
¼
free jet [7]). After conversion d=dt ¼ uo=oz and inte-
gration from the point of ionisation, zi, to the point of
detection, zf , Eq. (5) gives
0; 1Þ ions are selectively produced at the point of ioni-
sation, they continue in the flow and react with neutral
species HBr and D2. The energetically accessible reac-
tions are listed in Table 1 along with the excess of energy
for zero Kelvin formation of reactants and products
[4,5] and the masses of the initial and final ions. As we
never detected ions of mass 85 amu in REMPI of HBrþ
experiments (more correctly speaking, the correspond-
ing signals were undetected against the noise level, which
means their fraction was less than 2%), we conclude the
reaction (R4) from Table 1 is not efficient enough to be
considered here. Then, kinetics of the HBrþ, DBrþ,
H2Brþ and HDBrþ ions is described as
½HBrþꢀf ¼ ½HBrþꢀi expðꢁkꢂfÞ;
ð9Þ
where kꢂ ¼ k1a þ k2ð1 ꢁ aÞ þ k3ð1 ꢁ aÞ is the effective
rate coefficient and f ¼ ðn0a2D2=uÞð1=zi ꢁ 1=zf Þ is the
reaction time integrated number density which is related
to the number of collisions experienced between ioni-
sation and detection point in the jet. As a signal of
80 amu, S80, corresponds exclusively to the H79Brþ ions,
its fraction as function of f, permits us to derive the rate
coefficient kꢂ as well as the initial fraction [H79Brþ]i
under REMPI production
Table 1
Energetically accessed reactions in the HBr + D2 (DBr + H2) mixtures
Rate coefficient
Reaction
DHf (kcal/mol)a
Ion mass (amu)
Reactants
Products
(2 + 1)REMPI of HBrþ in the HBr + D2 mixture
b
R1
R2
R3
R4
k1
k2
k3
k4
HBrþ + HBr!H2Brþ + Br
HBrþ + D2 ! HDBrþ + D
HBrþ + D2 ! DBrþ + HD
HBrþ + D2 ! D2Brþ + H
)9 ꢃ 1
80, 82
80, 82
80, 82
80, 82
81, 83
82, 84
81, 83
83, 85
+7.5 ꢃ 1
)1 ꢃ 0.5
+7.5 ꢃ 1
(2 + 1)REMPI of DBrþ in the DBr + H2 mixture
c
R5
R6
R7
R8
k5
k6
k7
k8
DBrþ + DBr ! D2Brþ + Br
DBrþ + H2 ! HDBrþ + H
DBrþ + H2 ! HBrþ + HD
DBrþ + H2 ! H2Brþ + D
)7 ꢃ 1
81, 83
81, 83
81, 83
81, 83
83, 85
82, 84
80, 82
81, 83
+7.6 ꢃ 1
+1 ꢃ 0.5
+9.5 ꢃ 1
a Based on [4,5] and estimation of relative zero point energies of the product ions.
b Measured as (6.7 ꢃ 1.6) ꢄ 10ꢁ10 cm3/s at T ꢅ 300 K [6] and as (1.4 ꢃ 2) ꢄ 10ꢁ9 cm3/s in a free jet [1].
c Measured as (1.3 ꢃ 2) ꢄ 10ꢁ9 cm3/s in a free jet [2].

A.E. Belikov, M.A. Smith / Chemical Physics Letters 387 (2004) 7–11
9
states produces the HBrþ/DBrþ(2Pi; vþ) ions almost
exclusively (more than 98%) in a single spin–orbit and
vibrational state, namely, (i ¼ 3=2; vþ ¼ 0), (i ¼ 3=2;
vþ ¼ 1), (i ¼ 1=2; vþ ¼ 0), and (i ¼ 1=2; vþ ¼ 1), re-
spectively. Thus, the reactions R1–R8 were studied for
each of these four internal states of the ions. Corre-
sponding rate coefficients are presented in Table 2.
As it was observed previously [1,2,6], the atom
transfer reactions between the (HBrþ, DBrþ) ions and
parent molecules are very efficient. Their rate coefficients
are close to those estimated by the simple Average
Dipole Orientation (ADO) model for an ion-dipole
capture [8]
ln S80 ¼ ln½H79Brþꢀi ꢁ kꢂf:
ð10Þ
As Eq. (9) presents a fraction of the HBrþ ions re-
maining at an arbitrary point, z, below zi, we could use it
to integrate Eqs. (6)–(8), deriving expressions for the
H2Brþ, HDBrþ and DBrþ ions. However, looking
at Eqs. (6)–(8) and taking into account that
[H2Brþ]i ¼ [HDBrþ]i ¼ [DBrþ]i ¼ 0, we can immediately
write
½H2Brþꢀf =½HDBrþꢀf =½DBrþꢀf
¼ k1a=k2ð1 ꢁ aÞ=k3ð1 ꢁ aÞ:
ð11Þ
Eq. (11) cannot be used directly to find the rate co-
efficients, since both the H2Brþ and DBrþ ions have the
same masses (81 or 83) and are indistinguishable in our
experiments. The sum of Eqs. (6) and (8) gives
"
#
ꢀ
ꢁ
ꢀ
ꢁ
1=2
1=2
ap
l
2
k ¼ 2pq
1 þ clD
;
ð14Þ
p kTap
dð½H2Brþꢀ þ ½DBrþꢀÞ=dt ¼ ½HBrþꢀnðk1a þ k3ð1 ꢁ aÞÞ
where q is the charge on the ion, ap is the polarizability
of the molecule, l is the reduced mass, lD is the dipole
moment of the molecule, k is BoltzmannÕs constant, T is
the absolute temperature and c is the degree of orien-
tation of the dipole in the ion field. The limiting case,
c ¼ 0, represents the ion-induced dipole interaction, that
(providing a lower limit of the ion-dipole capture) is
independent of temperature and for the (HBrþ, DBrþ)–
(HBr, DBr) pairs leads to the rate coefficient equal to
0.7 ꢄ 10ꢁ9 cm3/s. A higher limit is provided by a Locked
Dipole Approximation (LD, c ¼ 1) that gives kLDfT ¼
300 Kg ¼ 2 ꢄ 10ꢁ9 cm3/s and kLDfT ¼ 10 Kg ¼ 7 ꢄ
10ꢁ9 cm3/s. The intermediate ADO model (0 < c < 1) is
more realistic, providing good agreement with numer-
ous experiments [8]. For the (HBrþ, DBrþ)–(HBr, DBr)
ion–molecule interaction the rate coefficients are
kADO ¼ 0:9 ꢄ 10ꢁ9 and 3 ꢄ 10ꢁ9 cm3/s for T ¼ 300 and
10 K, respectively (here we took cf300 Kg ¼ 0:18 and
cf10 Kg ¼ 0:3, calculated according to [8]). Any more
accurate estimates meet with difficulties caused by the
non-equilibrium flow properties in a free jet.
¼ ½HBrþꢀnkꢂꢂ:
Comparison of Eqs. (7) and (12) leads to the ratio
ð12Þ
ð½H2Brþꢀf þ ½DBrþꢀf Þ=½HDBrþꢀf ¼ kꢂꢂ=k2ð1 ꢁ aÞ ð13Þ
that along with Eq. (10) and the definition kꢂ ¼ kꢂꢂ
þ
k2ð1 ꢁ aÞ was used to measure all rate coefficients of
interest. The rate coefficient kꢂꢂ and k2 were found from
experimental data on S80 ¼ f ðfÞ and S83=S84 (or S81=S84)
according to Eqs. (10) and (13). After the effective rate
coefficient kꢂꢂ was measured at a number of various a,
the true rate coefficients k1 and k3 were derived from
kꢂꢂ ¼ k1a þ k3ð1 ꢁ aÞ ¼ f ðaÞ.
3. Results and discussion
The procedure of measurements described above was
applied in eight experimental sets (four REMPI
schemes, exploiting the f 3D2ðv ¼ 0Þ, f 3D2ðv ¼ 1Þ,
F 1 D2ðv ¼ 0Þ and F 1D2ðv ¼ 1Þ Rydberg intermediates of
HBr in the HBr + D2 and DBr in the DBr + H2 mix-
tures). According to REMPI-LIF and REMPI-PES
studies of Xie and Zare [3], (2 + 1) REMPI through these
Efficiencies of the HBrþ + D2 and DBrþ + H2 reac-
tions are much lower. An upper limit of the experi-
mental rate coefficient k4 (H ! D2 substitution channel)
was estimated from the fact that the signal of the D2Brþ
Table 2
State-specific rate coefficients of the HBrþ + (HBr, D2) and DBrþ + (DBr, H2) ion–molecule reactions
Reaction
Internal state of ion (i; v)
(3/2, 0)
(3/2, 1)
(1/2, 0)
(1/2, 1)
Rate coefficient (10ꢁ10 cm3/s)
R1
R2
R3
R4
R5
R6
R7
R8
HBrþ + HBr ! H2Brþ + Br
HBrþ + D2 ! HDBrþ + D
HBrþ + D2 ! DBrþ + HD
HBrþ + D2 ! D2Brþ + H
DBrþ + DBr ! D2Brþ + Br
DBrþ + H2 ! HDBrþ + H
DBrþ + H2 ! HBrþ + HD
DBrþ + H2 ! H2Brþ + D
(k1)
(k2)
(k3)
(k4)
(k5)
(k6)
(k7)
(k8)
13.2 ꢃ 1.6
0.01 ꢃ 0.01
0.08 ꢃ 0.03
11.1 ꢃ 1.5
13.8 ꢃ 1.8
0.04 ꢃ 0.02
0.06 ꢃ 0.03
11.8 ꢃ 1.6
0.18 ꢃ 0.04
0.05 ꢃ 0.03
0.02 ꢃ 0.01
0.03 ꢃ 0.02
<0.005
14.8 ꢃ 2.2
0.01 ꢃ 0.01
0.05 ꢃ 0.03
11.3 ꢃ 2.3
0.04 ꢃ 0.02
0.06 ꢃ 0.03
13.2 ꢃ 1.9
0.06 ꢃ 0.02
0.12 ꢃ 0.04
12.1 ꢃ 2.1
0.17 ꢃ 0.04
0.16 ꢃ 0.05
Unobserved

10
A.E. Belikov, M.A. Smith / Chemical Physics Letters 387 (2004) 7–11
0.25
0.2
ions was undetectable in the HBr + D2 experiments. The
corresponding rate coefficient k8 (D ! H2 substitution)
in the DBr + H2 mixture was principally unmeasured
since a low concentration of the H2Brþ ions could not
be seen at all on a background of the major ion, DBrþ,
having the same mass. The rate coefficients k3 and k7
(H ! D and D ! H isotopic substitution channels) ap-
peared to be rather small and almost independent of the
internal states of the ions. The exception was observa-
tion of a higher rate coefficient for the excited spin–orbit
state of the DBrþ ions in reaction (R7). As for D- and
H-atom transfer channels (reactions R2 and R6), the
rate coefficients increase with internal energy of the ions,
and may be understood considering an energy diagram
in Fig. 1 (the diagram for the DBrþ + H2 reaction looks
similar to those for HBrþ + D2, presented in the figure).
The lowest spin–orbit and vibrational state lies under
the endothermicity level (even taking into account its
uncertainty) for all conceivable populated rotational
levels of D2 and HBrþ. Thus, this state should not be
reactive. Indeed, the measured rate coefficient was zero
within error (see Table 2). The highest of the considered
states (i ¼ 1=2, v ¼ 1) leads to a potential reaction which
is completely exothermic and demonstrates the largest
rate coefficient. Other states studied, (i ¼ 3=2, v ¼ 1)
and (i ¼ 1=2, v ¼ 0), are partially exothermic dependent
on rotational levels of HBrþ and especially D2. Their net
rate coefficients should have intermediate values, as was
observed in our experiments.
HBr+ +H2
DBr+ + D2
HBr+ + D2
DBr+ +H2
0.15
0.1
0.05
0
-0.4
-0.2
0
0.2
0.4
Excess of energy [eV]
Fig. 2. Rate coefficients for reactions (1)–(4) as a function of excess of
energy.
where Ekin is the collisional energy; ꢀi;vðJ; JþÞ is the sum
of the internal energy of an ion and molecule pair; NJ
0
þ
and NJ , are the rotational level populations; DHf is the
enthalpy of reaction at 0 K. The terminal rotational
þ
distributions, NJ and NJ , were estimated based on ex-
perimental results [9,10] in the manner of [1,2]. It should
be noted, that the overwhelming part of the horizontal
error bars in Fig. 2 arises from uncertainty of the DHf0
values shown in Table 1.
It is interesting to note that although the onset to
reactivity demonstrated in Fig. 2 occurs well correlated
to zero excess energy, the rate of increase of k at DE > 0
is slow. Even for the highest energies probed, the ob-
served rate coefficients are still two orders less than the
Langevin collision limit (1.5 ꢄ 10ꢁ9 cm3/s). Similar low
rate coefficients were measured in the study of the
HBrþ + H2 and DBrþ + D2 reactions [1,2]. Such a result
could be explained if there is a dynamic barrier not ac-
counted for in the simple thermodynamic analysis or if
we suggest an unusually and similarly fast spin–orbit
and vibrational relaxation of the HBrþ and DBrþ ions
to the lowest states. Unfortunately, neither explanation
can be further examined in the context of the current
work and will require more sophisticated probes for
resolution.
In summary, the channels of the HBrþ(Pi; v) + D2
and DBrþ(Pi; v) + H2 ion–molecule reactions were in-
vestigated in (HBr + D2) and (DBr + H2) free jets. The
selected spin–orbit and vibrational states of the ions
were prepared by resonance-enhanced multiphoton
ionisation. All of the reactant and product ions were
monitored using time-of-flight mass spectrometry. A
high efficiency of H (or D) atom transfer in the ion/
parent molecule reaction (HBrþ/HBr and DBrþ/DBr)
with the rate coefficient of 1.3 ꢄ 10ꢁ9 cm3 /s was found in
conformity with our previous results and independently
of the ion internal state. All three energetically accessible
channels of the reactions (3), (3a), (3b), and (4), (4a),
The threshold effect of the atom-transfer XBrþ + Y2
reaction (X, Y ¼ H, D) is demonstrated in Fig. 2, where
the rate coefficients are shown versus the excess of en-
ergy in the reaction
X X
DEi;v ¼ Ekin
þ
½ꢀi;vðJ; JþÞNJ NJþꢀ ꢁ DHf0;
ð15Þ
Jþ
J
0.6
HBr+(i=1/2,v+=1)
HBr+(i=3/2,v+=1)
0.4
0.2
HBr+(i=1/2,v+=0)
HBr+(i=3/2,v+=0)
} J+(HBr+)
0
J{D2} =
0
1
2
3
0
1
2
3
Fig. 1. Energy diagram for the reaction HBrþ(Pi; vþ; Jþ) + D2(J)
! HDBrþ + D. The energy E ¼ 0 is referenced to the lowest internal
energy level of the reactants (i ¼ 3=2, vþ ¼ 0, Jþ ¼ 0, J ¼ 0). The
endothermicity level, including error limits, based on the data from
Table 1 is shown by dotted lines.

A.E. Belikov, M.A. Smith / Chemical Physics Letters 387 (2004) 7–11
11
(4b) were under consideration. The rate coefficient of the
atom–molecule substitution HBrþ + D2 ! D2Brþ + H
was immeasurably small. The rate coefficients of the
isotopic substitutions HBrþ + D2 ! DBrþ + HD and
DBrþ + H2 ! HBrþ + HD were measured between 0.3
and 1.6 ꢄ 10ꢁ11 cm3 /s without a single-valued correla-
tion with the internal states of ions. The rate coefficients
of the D-atom transfer (HBrþ + D2 ! HDBrþ + D) and
H-atom transfer (DBrþ + H2 ! HDBrþ + H) were found
to be negligible, within errors, for the lower spin–orbit
and vibrational states and to rise to 2 ꢄ 10ꢁ11 cm3 /s for
the higher states. The rate coefficient versus reaction
energy dependence appears to be unique for the all ion–
molecule pairs studied here and previously: HBrþ + H2,
HBrþ + D2, DBrþ + H2, DBrþ + D2.
Foundation of Basic Research through Grant No. 03-
03-32316.
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Acknowledgements
The authors gratefully acknowledge financial support
of this work by the National Science Foundation
through Grant No. CHE-9984613 and by the Russian