Kinetics of sulfur oxide, sulfur fluoride, and sulfur oxyfluoride anions with atomic species at 298 and 500 K

Article abstract of DOI:10.1021/jp066198c

The rate constants and product-ion branching ratios for the reactions of sulfur dioxide (SO₂^-), sulfur fluoride (SF _n^-), and sulfur oxyfluoride anions (SO_xF _y^-) with H, H₂, N, N₂, NO, and O have been measured in a selected-ion flow tube (SIFT). H atoms were generated through a microwave discharge on a H₂/He mixture, whereas O atoms were created via N atoms titrated with NO, where the N had been created by a microwave discharge on N₂. None of the ions reacted with H ₂, N₂ or NO; thus, the rate constants are <1 × 10^-12 cm³ s^-1. SO_xF_y ^- ions react with H by only fluorine-atom abstraction to form HF at 298 and 500 K. Successive F-atom removal does not occur at either temperature, and the rate constants show no temperature dependence over this limited range. SO₂^- and F^- undergo associative detachment with H to form a neutral molecule and an electron. Theoretical calculations of the structures and energetics of HSO₂^- isomers were performed and showed that structural differences between the ionic and neutral HSO ₂ species can account for at least part of the reactivity limitations in the SO₂^- + H reaction. All of the SO_xF _y^- ions react with O; however, only SO₂ ^- reacts with both N and O. SO_xF_y^- reactions with N (SO₂^- excluded) have a rate constant limit of <1 × 10^-11 cm³ s^-1. The rate constants for the SO_xF_y^- reactions with H and O are ≤25% of the collision rate constant, as seen previously in the reactions of these ions with O₃, consistent with a kinetic bottleneck limiting the reactivity. The only exceptions are the reactions of SO₂ ^- with N and O, which are much more efficient. Three pathways were observed with O atoms: F-atom exchange in the reactant ion, F^- exchange in the reactant ion, and charge transfer to the O atom. No associative detachment was observed in the N- and O-atom reactions.

Full text of DOI:10.1021/jp066198c

1852
J. Phys. Chem. A 2007, 111, 1852-1859
Kinetics of Sulfur Oxide, Sulfur Fluoride, and Sulfur Oxyfluoride Anions with Atomic
Species at 298 and 500 K
Anthony J. Midey*,† and A. A. Viggiano
Air Force Research Laboratory, Space Vehicles Directorate, 29 Randolph Road, Hanscom Air Force Base,
Massachusetts 01731-3010
ReceiVed: September 21, 2006; In Final Form: January 4, 2007
-
The rate constants and product-ion branching ratios for the reactions of sulfur dioxide (SO2 ), sulfur fluoride
-
(SFn ), and sulfur oxyfluoride anions (SOxFy-) with H, H2, N, N2, NO, and O have been measured in a
selected-ion flow tube (SIFT). H atoms were generated through a microwave discharge on a H2/He mixture,
whereas O atoms were created via N atoms titrated with NO, where the N had been created by a microwave
discharge on N2. None of the ions reacted with H2, N2 or NO; thus, the rate constants are <1 × 10-12 cm3
s-1. SOxFy- ions react with H by only fluorine-atom abstraction to form HF at 298 and 500 K. Successive
F-atom removal does not occur at either temperature, and the rate constants show no temperature dependence
over this limited range. SO2- and F- undergo associative detachment with H to form a neutral molecule and
-
an electron. Theoretical calculations of the structures and energetics of HSO2 isomers were performed and
showed that structural differences between the ionic and neutral HSO2 species can account for at least part
-
of the reactivity limitations in the SO2 + H reaction. All of the SOxFy- ions react with O; however, only
-
-
SO2 reacts with both N and O. SOxFy- reactions with N (SO2 excluded) have a rate constant limit of <1
× 10-11 cm3 s-1. The rate constants for the SOxFy- reactions with H and O are e25% of the collision rate
constant, as seen previously in the reactions of these ions with O3, consistent with a kinetic bottleneck limiting
-
the reactivity. The only exceptions are the reactions of SO2 with N and O, which are much more efficient.
Three pathways were observed with O atoms: F-atom exchange in the reactant ion, F- exchange in the
reactant ion, and charge transfer to the O atom. No associative detachment was observed in the N- and O-atom
reactions.
Introduction
To both further the previous flow-tube studies of the oxidation
- 14,15
chemistry of SOxFy
and better understand the reactivity
Sulfur dioxide (SO2-), sulfur fluoride (SFn-), and sulfur
oxyfluoride anions (SOxFy-) have been observed in plasma
environments where SF6, O2, and H2O are present in the
discharge.1-5 These ions have also been seen in atmospheric-
pressure methane-oxygen flames doped with SF6 and SO2.6,7
Thus, the ion chemistry of these species has been studied to
examine their reactivities.5,8-13 Recently, kinetics experiments
have been conducted to determine the formation pathways for
these ions, particularly through oxidation by O3 and O2.14,15
Extensive theoretical calculations of the structures and energetics
of these ions have augmented these measurements and have
helped to explain the observed chemistry.14,16-21
of these anions, the rate constants and product-ion branching
ratios for the reactions of SOxFy- ions with H, H2, N, N2, NO,
and O have been studied in a selected-ion flow tube (SIFT) at
298 K. The H-atom reactions were also studied at temperatures
up to 500 K. In addition, a series of theoretical calculations of
-
the structures and energetics of the possible HSO2 isomeric
-
species involved in the associative detachment reaction of SO2
with H were performed to better understand the observed
chemistry. These results can be compared with the extensive
previous calculations of the neutral HSO2 isomers created
through the H + SO2 neutral reaction.37-49
Atomic species can also be present in discharge environments,
including hydrogen, nitrogen, and oxygen atoms. The kinetics
of the reactions of H and H2 with a variety of cations and anions
have been previously studied,22-27 including a recent study from
our laboratory of the reactions of POxCly- ions with H and H2.28
Analogous surveys of N- and O-atom ion-molecule chemistry
have also been done.8,26,27,29-36 However, the only previous
Experimental Section
The SIFT has been described in detail elsewhere;50 however,
a brief description follows for the current experiments. SOxFy
-
ions were generated by electron impact on appropriate reagent
gases in a remote source chamber. The desired reactant ion was
selected with a quadrupole mass filter and then injected into a
fast flow of helium buffer gas (AGA, 99.995%) in the
temperature-controlled flow tube. After thermal equilibration,
the neutral reactant was introduced into the reaction region. After
reaction over a known distance for a previously measured
reaction time, the remaining reactant ions and all of the product
ions were sampled through a blunt-nose cone containing a small
aperture, then analyzed with a second quadrupole mass filter,
and detected with a conversion dynode electron multiplier.
-
-
-
studies of SOxFy reactions with atoms are for SF6 and SF5
reacting with H and O,8,9,13 and only one qualitative measure-
-
ment of the reaction of SO2 with N and O atoms has been
made.10
* To whom correspondence should be addressed. E-mail:
Anthony.Midey@hanscom.af.mil.
† Under contract to the Institute for Scientific Research, Boston College,
Chestnut Hill, MA 02467.
10.1021/jp066198c CCC: $37.00 © 2007 American Chemical Society
Published on Web 02/17/2007

-
Kinetics of SO2-, SFn-, and SOxFy with Atomic Species
J. Phys. Chem. A, Vol. 111, No. 10, 2007 1853
TABLE 1: Rate Constants and Products for the Reaction of
SOxFy- Ions with H Atoms Measured in a Selected-Ion Flow
Tube (SIFT) from 298 to 500 K
The H-atom reactions were also studied at 500 K in a previous
flow tube with decades of use. However, the O-atom reactions
required very clean surfaces to minimize charging effects.
Measuring the O-atom reactions in the old flow tube was
problematic in that ion signals slowly disappeared, presumably
because of surface oxidation creating insulating surfaces.
Therefore, the measurements were conducted in a newly
constructed stainless steel flow tube that used improved vacuum
seals to allow future temperature-dependent studies to be made
up to 900 K when heating upgrades are completed. Also, a solid-
graphite nose cone was used for the N- and O-atom experi-
ments to further decrease charging effects caused by O-atom
reactions on the sampling surface. This nose cone replaced the
graphite-coated stainless steel version used in previous experi-
ments.
rate constant
(×10-9 cm3 s-1) [kcol
]
298K
rxn
(kJ mol-1
∆H
reactants
products
)
298 K
500 K
F- + H
HF + e-
-242
1.6a [2.0]
1.4 [2.0]
SF5- + H
SF6- + H
no reaction
<0.005 [1.9] <0.005 [1.9]
0.31 [1.9] 0.25 [1.9]
<0.005 [1.9] <0.005 [1.9]
0.18 [1.9]
0.23 [1.9]
SF5- + HF
-431
SOF3- + H no reaction
SOF4- + H SOF3- + HF
-470
38b
0.12 [1.9]
0.26 [1.9]
SO2- + H
HSO2 + e-
cis-HOSO + e-
-62b
SO2F- + H no reaction
SO2F2- + H SO2F- + HF
<0.005 [1.9] <0.005 [1.9]
0.32 [1.9] 0.26 [1.9]
-388
a Fehsenfeld et al.13 b ∆H0f for the neutral product from G2
Various combinations of source gases were required to
generate the different sulfur oxide, sulfur fluoride, and sulfur
oxyfluoride anions,14 and they are briefly described as follows:
SF6 (Matheson, 99.99%) was used to generate F-, SF5-, and
SF6-, whereas neat SO2 (Matheson, 99.98%) was used to
generate SO2-. Gas mixtures of 1-5% SF6 in He were used
whenever possible to prolong the lifetime of the rhenium and
filaments used in the electron-impact ion source with this gas.
Thoriated iridium filaments were alternatively used when
oxygen-containing reagents were present. However, pure SF6
was also used to increase the ion production as needed. SO2F-
corrected values of Laakso et al.42
trap that minimized the contribution of trace impurities in the
NO to the observed reactivity. Rate constants for the N2 and
NO reactions had relative uncertainties of (15% and absolute
uncertainties of (25%, whereas the N- and O-atom reac-
tions had relative uncertainties of (25% and absolute uncertain-
ties of (40%.52,53 A larger uncertainty in the rate constant for
SF5- + O was observed because the value approached the lower
limit of measurements possible with O atoms using this
technique.
-
and SO2F2 were created using a mixture of 1% SF6 in He
The product-ion distributions were obtained by extrapolating
the measured branching ratios to zero atom concentration to
minimize the effects of any secondary chemistry. As discussed
below, most of the ions did not react with N atoms. Therefore,
the O-atom concentration was varied simply by changing the
NO concentration over the course of the titration. For the
reaction of SO2- with N, the N-atom concentration was scanned
by varying the microwave discharge power at a fixed N2 flow
and by varying the N2 flow at a fixed microwave discharge
power to obtain the N-atom branching ratios. To help differenti-
ate between the products from the N- and O-atom reactions with
-
combined with a small amount of SO2 in the source. SOF4
-
and SOF3 were generated through the association reaction of
SF6- and H2O. This chemistry required introduction of the room-
temperature vapor pressure from a distilled-water sample along
with a mixture of 1% SF6 in He into a source block cooled to
262 K. Dissolved gases were removed from the water through
several freeze-pump-thaw cycles.
Hydrogen atoms were generated via microwave discharge on
a mixture of H2 (Liquid Carbonics, 99.999%) and He in a Pyrex
tube, giving typical H-atom dissociation fractions of around
5-10%.28 The H2 flow was scanned while the helium flow and
microwave power were kept fixed in order to vary the H-atom
concentration. Given the relatively small amount of dissociation,
most of the H2 remained and was introduced into the flow tube.
Consequently, the reactions of SOxFy- with H2 were measured
first. The concentration of H atoms at 298 K was calibrated
using the known rate constant for F- + H at 298 K.13 This
value had not been determined at 500 K. Therefore, a mixture
of CF2Br2 (Matheson, >99%) and SF6 was added to the source
to simultaneously generate Cl- and F- in order to establish a
value for the F- + H rate constant relative to the known Cl- +
H rate constant at 500 K.51 The F- rate constant at 500 K could
then be used to calibrate the H-atom concentration for determin-
ing the other rate constants at this temperature. Rate constants
for the H2 reactions had relative uncertainties of (15% and
absolute uncertainties of (25%, and the H-atom reactions had
relative uncertainties of (20% and absolute uncertainties of
(30%.28
-
SO2 where both atoms reacted, O atoms were also generated
by a microwave discharge on a mixture of 1% O2 in He while
the flow of the mixture was scanned at fixed microwave power
to vary the O-atom concentration. This method was utilized
previously in the O2- and PO2Cl- reactions.52,53 The branching
ratios for the major product ions have uncertainties of (5%.54
Results
-
(a) SOxFy + H and H2. Table 1 summarizes the kinetics
-
results for the reactions of SOxFy ions with H atoms at 298
and 500 K. The heats of reaction at 298 K given in Table 1
were determined from the experimental55,56 and G2 corrected
theoretical14,42 standard heats of formation at 298 K for the
relevant species. None of the ions listed in Table 1 react with
H2. Consequently, an upper limit for the rate constant of <1 ×
10-12 cm3 s-1 can be deduced for the H2 reactions. SF5 does
-
not react with H atoms, as seen in previous flowing afterglow
experiments.8 A rate constant of 3.1 × 10-10 cm3 s-1 for the
SF6- reaction with H was found in the SIFT, which agrees with
the flowing afterglow value of 2.7 × 10-10 cm3 s-1 of
Fehsenfeld et al.13 within the experimental uncertainties. All of
the rate constants for the H-atom reactions are e25% of the
Langevin collision rate constant, kcol, similar to the reactions
of SOxFy- with O3.14,15 No temperature dependence of the rate
constants was observed over the limited temperature range from
298 to 500 K, within the uncertainty of the measurements.
Oxygen atoms were generated by titrating N atoms with NO
(Matheson, 99.5%), where the N atoms had been created via
microwave discharge on pure N2 (AGA, 99.999%).36,52,53 The
-
separate reactions of SOxFy ions with N2 and NO were
measured first because only about 1% dissociation of N2
occurred in the discharge. This method also required studying
the N-atom reactions first. To minimize secondary-ion chemistry
at higher NO concentrations, the titration was performed using
a 10% mixture of NO in He passed through a molecular sieve

1854 J. Phys. Chem. A, Vol. 111, No. 10, 2007
Midey and Viggiano
s-1 based on the Fehsenfeld value for SF6-. Using the present
value, one finds that the Hunton et al. value for SF5- increases
to 2.2 × 10-11 cm3 s-1, reducing the discrepancy to a factor of
2.4. As mentioned previously, this rate constant is approaching
the lower limit that can be determined with O atoms, and a
factor of 2 difference might be all that is possible.52,53
Examining Table 2, three major reaction pathways arise in
the reactions of SOxFy- with O atoms. These channels are given
by the equations
TABLE 2: Rate Constants and Product Branching Ratios
for the Reactions of SOxFy- Ions with N and O Atoms
Measured in a Selected-Ion Flow Tube (SIFT) at 298 Ka
rate constant
298K
rxn
(kJ mol-1
branching ∆H
ratio
(×10-10 cm3 s-1
)
reactants
products
F- + SOF4
)
[kcol]
SF5- + O
SF6- + O
1.00
1.00
0.60
0.40
1.00
>0.90
<0.10
1.00
1.00
1.00
-150
-41
-120
-4
-382
-83
41
-34
-11
-60
0.54 [5.6]
1.1 [5.5]
1.5 [5.7]
O- + SF6
SO2F- + O F- + SO3
SO3- + F
SO2F2- + O SO3F- + F
SO2- + N SO- + NO
S- + NO2
0.91 [5.6]
1.8 [7.2]
SOxFy- + O f SOx+1Fy-1- + F
SOxFy- + O f F- + SOx+1Fy-1
SOxFy- + O f O- + SOxFy
(2a)
(2b)
(2c)
SO2- + O O- + SO2
SOF3- + O SO2F2- + F
SOF4- + O F- + (SO2F2 + F)
4.0 [5.9]
0.77 [5.6]
0.79 [5.6]
a None of the ions listed above, excluding SO2-, react with N atoms;
therefore, k < 1 × 10-11 cm3 s-1
.
Exchange of a F atom for an O atom in the reactant ion as
shown in eq 2a is one major pathway and is observed in the
The major reaction pathway with H atoms is F-atom
abstraction to form HF as given by
SO2F-, SO2F2-, and SOF3 reactions. Another major reaction
-
channel involves loss of F- from the reactant ion with
concomitant incorporation of the O atom into the corresponding
neutral fragment as given in eq 2b. This pathway was seen with
SF5-, SO2F-, and SOF4-. Reactions 2a and 2b differ only in
which fragment has the negative charge. Charge transfer to form
O- is the third reaction pathway, and it is the only product
channel seen with SF6- and SO2-. This observation is consistent
with the electron affinities (EAs) of the corresponding neutral
SOxFy species.14,16 Only SF6 and SO2 have EA values (∼1.1
eV) that are below the oxygen atom EA of 1.46 eV.55 Grabowksi
et al. observed only O- products in analogous experiments on
SO2- + O in a flowing afterglow, performed using both N-atom
titration and O2/He discharge generation to make O atoms.
However, those experiments were performed to bracket the EA
of SO2, and rate constant measurements were not made.10 In
addition, the neutral products for the SOF4- reaction are given
in parentheses in Table 2 because calculations of the SO2F3
structure and energetics showed that it is metastable with respect
to dissociation into SO2F2 and F as shown.14,17
SOxFy- + H f SOxFy-1- + HF
(1)
However, successive halogen-atom abstraction from the product
ions was not observed as previously seen in the reactions of
POxCly- with H to form HCl,28 despite the fact that the primary
SOxFy product ions in Table 1 have spin-allowed exothermic
channels to form HF.
-
Associative detachment of H to the reactant ion to form a
neutral product and an electron is the other reaction pathway
seen. This channel can be monitored by measuring the total
ion current at the nose-cone aperture and the total reactant and
product-ion counts at the detector as a function of H-atom
concentration. If electrons and neutral molecules are produced
rather than ions, both the total ion counts detected and the nose-
cone current observed will decrease as the H-atom concentration
increases because electrons rapidly diffuse to the flow-tube walls
-
and are not be collected at the nose cone. Only F- and SO2
react with H atoms in this manner. The details of the SO2
-
reaction to form HSO2 products will be addressed in detail later.
No associative detachment was observed with any of the ions
during the titration experiments. Associative detachment with
O atoms is >34 kJ mol-1 endothermic for all of the ions except
SO2-, for which the process to generate SO3 is 241 kJ mol-1
exothermic. However, although sampling issues from O-atom
interactions with the nose-cone surface were minimized, small
effects cannot be completely eliminated. These effects can create
difficulties in accurately measuring small changes in the nose-
cone current that would indicate the production of rapidly
diffusing electrons in the flow tube from associative detachment.
Therefore, a minor contribution from associative detachment
-
(b) SOxFy + N, N2, NO, and O. Table 2 summarizes the
-
kinetics results for the reactions of SOxFy ions with N and O
atoms at 298 K. The heats of reaction at 298 K given in Table
2 were similarly determined from the experimental55,56 and
corrected G2 method theoretical14,42 standard heats of formation
at 298 K for the relevant species. None of the ions react with
N2 and NO. Thus, the upper limit for both the N2 and NO rate
-
constants could be given as <1 × 10-12 cm3 s-1. Only SO2
-
reacts with both N and O. The remaining SOxFy ions do not
react with N atoms, the rate constant being <1 × 10-11 cm3
s-1. This limiting value is higher than that for H atoms because
only ca. 1% dissociation of N2 occurs, leading to lower absolute
total N- and O-atom concentrations,52,53 which are 5-10 times
lower than those achievable with H atoms.
-
cannot be ruled out in the SO2 and O reaction.
Product identification in the SO2- reactions proved difficult.
Only O- was observed as a product when the O2/He discharge
method was used, and this ion was assigned as the only product
in the O-atom reaction. In the N2 discharge, both m/z ) 32 and
48 ions were observed from N-atom reaction, where the latter
product can be assigned to SO-. The former product is S-, at
least partially generated as a secondary ion from the reaction
of SO- with N, especially given that it increases with increasing
N-atom concentrations. Extrapolating to zero N-atom concentra-
tion, the 32 amu product ion still appears to account for roughly
10% of the total primary products from SO2-. Producing S-
from SO2- + N is 41 kJ mol-1 endothermic, which is roughly
energetically possible given the average thermal kinetic and
-
-
-
Neither SF6 nor SF5 reacts with N atoms. SF6 is found
to charge transfer to O atoms with a rate constant of 1.1 ×
10-10 cm3 s-1. This value is about a factor of 2 higher than that
for the SF5 reaction of 5.4 × 10-11 cm3 s-1, which produces
-
F- and SF4O. A previous measurement of the SF6- rate constant
by Fehsenfeld8 in a flowing afterglow (5 × 10-11 cm3 s-1) is a
factor of 2 lower than the present value. Considering that the
previous measurement reported a factor of 2 uncertainty, these
values are in agreement. Hunton et al.9 measured the ratio of
the SF6- and SF5- rate constants to be 5:1. In those experiments,
an SF5 rate constant was determined to be 1.1 × 10-11 cm3
rovibrational energy57-59 available in the SO2 + N reaction
-
-

-
Kinetics of SO2-, SFn-, and SOxFy with Atomic Species
J. Phys. Chem. A, Vol. 111, No. 10, 2007 1855
-
system at 298 K. The reaction of SO2- with N to generate O2
and HOSO isomers at the CCSD(T) level with several basis
sets. However, analogous calculations at these levels of theory
for the HSO2 anion structures are beyond the scope of the
and NS is 151 kJ mol-1 endothermic, eliminating that possibility.
These observations most likely indicate that the secondary
-
-
reaction of SO- with N is quite a bit faster than the SO2
current study. Consequently, a series of less computationally
reaction, but direct production of S- cannot be ruled out.
-
expensive calculations were made for the isomers of HSO2
Therefore, only limits for the branching ratios are given in Table
2.
ion at the same levels of theory previously utilized for probing
the corresponding neutral HSO2 isomers.37,43,44,46 Using the same
levels of theory affords meaningful comparisons of the results
for the anion and neutral species.
Discussion
The energetics were calculated at the G2 level for direct
comparison with the G2 calculations of the neutral structures
on the H + SO2 potential energy surface,42,43 as well as the
(a) POxCly- vs SOxFy- Reactivity with H, N, and O Atoms.
No temperature dependence of the rate constants and product
-
branching ratios was observed for the reactions of both SOxFy
-
thermochemistry of the SOxFy ions and neutrals calculated
and POxCly- ions28 with H atoms from 298 to 500 K. In addition,
using G2 theory.14,17 Optimized geometries and harmonic
-
-
the rate constants for both the SOxFy and POxCly reactions
with H were all e25% of the Langevin collision rate constant
from 298 to 500 K. These observations are similar to the
reactivity trends observed in the reactions of SOxFy- ions with
O3,14,15 where a kinetic bottleneck hinders the reactivity, despite
the availability of highly exothermic spin-allowed reaction
pathways. Although ion-molecule reactions that seem to violate
spin conservation have been observed that still have large rate
constants,60 a similar kinetic bottleneck as in the O3 reactions
also appears to limit the rate constants for these systems reacting
with H atoms. The current observations might indicate that the
intermediate lifetime is short and that the reactants cannot
sample the whole reactive surface. The small polarizabilities
of these neutrals would be consistent with this possibility.
The primary SOxFy-1- product ions shown in Table 1 formed
via eq 1 do not undergo an additional removal of F atom, in
-
vibrational frequencies for the anionic HSO2 isomers were
calculated at the HF/6-31G(d) level, with further geometry
optimization of these structures at the MP2(Full)/6-31G(d) level
as part of the G2 calculation. In addition, density functional
theory (DFT) computations of the structures and vibrational
frequencies were performed at the B3LYP/6-311G(d,p) level,
which follows a series of HF and MP2 computations by Qi et
al. for the neutral H + SO2 potential surface using this basis
set.44
To also examine the effects of electron correlation that have
been observed in neutral HSO2 isomer calculations even at high
levels of theory,42,46,47,49 computationally inexpensive MP2
geometry optimizations and vibrational frequency calculations
for the singlet HSO2- isomers were also performed at the MP2/
6-311++G(2d,2p) level. These results can be directly compared
to the corresponding MP2 neutral structure results of Isoniemi
et al.37 that employed this larger basis set. The optimized
structural parameters are reported in Table 3 for several different
methods as defined by the diagram in Figure 1. The G2 0 K
energies and 298 K enthalpies are listed in Table 4, along with
the corresponding G2(MP2) values. The G2 energies in Table
4 of the structures given in Table 3 at the MP2(Full)/6-31G(d)
level in the G2 method are plotted in Figure 2 relative to the
lowest-energy HSO2- ion. Wavefunction stability was verified
at the HF, B3LYP, and MP2/6-311++G(2d,2p) levels of theory
for all of the ions listed in Table 3.
-
contrast to the successive Cl atom removal with the POxCly
ions.28 The reactivity pattern observed here follows the bond
order of the central S atom in the reactant ion (defined as the
sum of twice the number of S-O bonds plus the number of
S-F bonds) as also seen in reactions with O3.14,15 In that work,
-
the SOxFy ions with an even number of total bonds react,
whereas the ions with an odd number of bonds do not. The
secondary reactions of the main product ions to form another
HF molecule are both exothermic and spin-allowed. However,
the primary product ions with odd numbers of bonds are closed-
shell stable species, limiting their reactivity.
-
In contrast to the H-atom reactions, all of the SOxFy ions
Two stable minimum-energy structures exist for singlet-
-
react with O atoms. Interestingly, the rate constants for the
O-atom reactions with all of the anions are again e25% of the
Langevin collision rate constant, the exception being SO2- and
maybe SO-. The similar trends in reaction efficiency as seen
with H and O3 indicate that an analogous kinetic bottleneck
exists in this system, possibly indicative of common features
of the respective potential energy surfaces.
electronic-state HSO2 anions. The global minimum-energy
-
structure has an HSO2 form with the H bound to the S atom
out of the plane. The other lowest-energy structure has an
HOSO- arrangement with the H atom out of the plane. Both
the cis- and trans-HOSO- planar structures were found to be
transition states. The neutral trans-HOSO structure has been
shown to be a transition state to rotation of the H atom around
the S-O bond.37,42,44-47,49 Both the cis and trans ionic transition-
state structures have an O-H wag as the imaginary frequency,
indicating that these structures play similar roles. In addition,
all four methods agree that HOSO- is nonplanar. All of the
methods also showed that the neutral HOSO arrangement of
atoms is the global minimum for all of the neutral structures.
With the neutral HOSO arrangement, whether the actual
structure of the global minimum is a nonplanar HOSO or a cis
planar HOSO geometry depends on the theoretical method and
the basis set used.37,42,44-47,49 Despite the unresolved issue of
whether the neutral HOSO global minimum-energy structure
is planar or not, the energy difference between the planar and
nonplanar HOSO structures at the CCSD(T) level of theory is
-
(b) SO2 Ion Chemistry. As seen in Table 1, associative
-
detachment of H atoms to SO2 produces neutral HSO2
products. The structures and energetics of the various neutral
HSO2 isomers have been extensively studied both experi-
mentally37-41 and theoretically.37-49 However, the anion that
could be temporarily created during the associative detachment
involving H atoms has not been characterized. Consequently,
structure and energetic calculations for the potential isomers of
the HSO2 ions were performed using Gaussian 03.61
-
Recently, high-level calculations of the H + SO2 ground-
electronic-state potential energy surface were made by Ballester
and Varandas using double many-body expansion (DMBE)
methods fit to ab initio full-valence complete-active-space
calculations at the FVCAS/aug-cc-pVDZ and aug-cc-pVTZ
levels.45 Napolion and Watts also recently performed coupled-
cluster calculations of the structures and energetics for the HSO2
<1 kJ mol-1 49 The HOSO- ions are 15-47 kJ mol-1 higher
.
in energy than the HSO2- ions, depending on the level of theory
used. A third transition-state structure having a planar C2V HSO2

1856 J. Phys. Chem. A, Vol. 111, No. 10, 2007
Midey and Viggiano
-
TABLE 3: Bond Lengths and Bond Angles Calculated for the HSO2 Isomers at Different Levels of Theory Grouped by
Methoda
r(H-S)
(Å)
r(H-O)
r1(O-S)
r2(O-S)
-HOS
-OSO
-HOSO
ion
(Å)
(Å)
(Å)
(deg)
(deg)
(deg)
method/ref
HF/6-31G(d)
1HOSO-
3HOSO-
2HOSO
1HOSO-
3HOSO-
2HOSO
0.949
0.951
0.969
1.726
2.160
1.655
1.538
1.537
1.468
105.3
101.8
111.5
107.3
146.1
108
64.2
-44.9
59.5
Binns and Marshallb
MP2(Full)/6-31G(d)
0.975
0.975
0.983
1.807
2.112
1.661
1.563
1.580
1.482
102.0
101.6
106.9
110.2
169.2
109.8
71.0
0.0
0.0
Laakso et al.c
1HOSO-
0.962
0.969
1.809
1.655
1.556
1.475
101.3
106.3
108.2
109.0
76.1
0.1
MP2/6-311++G(2d,2p)
2HOSO
Isoniemi et al.d
1HOSO-
0.964
1.834
1.567
101.8
109.7
71.2
B3LYP/6-311G(d,p)
-
1HSO2
1.379
1.339
1.492
1.439
1.492
1.439
101.3
106.6
114.8
123.6
HF/6-31G(d)
2HSO2
Binns and Marshallb
1HSO2
1.432
1.521
1.521
101.1
115.7
MP2(Full)/6-31G(d)
-
-
1HSO2
1.401
1.366
1.519
1.461
1.519
1.461
100.1
106
114.2
124.6
MP2/6-311++G(2d,2p)
2HSO2
Isoniemi et al.d
1HSO2
1.469
1.523
1.523
101.0
114.6
B3LYP/6-311G(d,p)
-
ion transition states
cis-1HOSO-
0.951
0.979
0.968
0.968
1.739
1.821
1.821
1.847
1.549
1.573
1.566
1.577
100.2
102.7
103.5
102.2
104.2
0
0
0
0
HF/6-31G(d)
95.0
95.3
96.3
MP2(Full)/6-31G(d)
MP2/6-311++G(2d,2p)
B3LYP/6-31G(d,p)
trans-1HOSO-
trans-2HOSO
0.950
0.952
1.758
1.632
1.532
1.456
105.8
105.3
104.1
110.1
180.0
180.0
HF/6-31G(d)
Binns and Marshalla
0.977
0.966
0.966
1.852
1.858
1.884
1.558
1.547
1.561
99.6
100.2
99.3
107.4
104.5
107.2
180.0
180.0
180.0
MP2(Full)/6-31G(d)
MP2/6-311++G(2d,2p)
B3LYP/6-31G(d,p)
a Structural parameters from the literature for the corresponding neutral HSO2 isomer calculated at the same level of theory are shown in italics.
b Reference 46. c Reference 42. d Reference 37.
is 2.112 Å, suggesting that this species is more like an [OH-
SO]- complex. The OSO bond angles in singlet HOSO- and
neutral HOSO are within ca. 1° of each other, but the triplet
anion has an almost-linear OSO arrangement. In addition, the
HOS bond angle is 3-5° lower in both the singlet- and triplet-
state ions.
Figure 1. Structural parameters defined for the HOSO- and HSO2
ions as given in Table 3.
-
arrangement was also found using all of the methods listed in
Table 3. However, a wavefunction instability arises with all of
the methods; thus, it is not discussed further.
-
As seen in Table 1, the reaction of SO2 with H to from
HSO2 is 38 kJ mol-1 endothermic, which is barely energetically
accessible at 298 K given the translational and rovibrational
energy available to the reactants,57-59 whereas formation of
planar cis-HOSO would be 63 kJ mol-1 exothermic. These
reaction enthalpies were determined using the heats of formation
at 298 K of Laakso et al. based on G2 theory for HSO2 and
HOSO with a (10 kJ mol-1 uncertainty as derived from the
reaction thermochemistry of several neutral reactions.42 How-
ever, the DFT heat of formation value at 298 K of Denis and
Ventura for HSO2 was evaluated to be 36.8 kJ mol-1 lower
according to a series of calculations at the B3LYP and B3P91W
levels using various-size basis sets for several reaction se-
-
A search for stable triplet-electronic-state HSO2 isomers
shows that two stable geometries can be found using the HF
and MP2 optimizations from the G2 calculations. The lower-
energy triplet structure has an HOSO- arrangement, lying 155
-
kJ mol-1 above the singlet HSO2 global minimum and 104.5
kJ mol-1 above the singlet HOSO- isomer. The other geometry
found is essentially a very weakly bound planar complex with
an HSO2--type arrangement having an SO2- moiety with a H-S
distance of 3.191 Å. This complex is comparable in energy to
the reactants, which is consistent with having the H atom
positioned at such a great distance. The wavefunctions are stable
at the HF/6-31G(d) level for both species.
quences. This value has an uncertainty of (8 kJ mol-1 48
. Using
the DFT value indicates that H + SO2- would be only around
1 kJ mol-1 endothermic to form HSO2, compared to 4 kJ mol-1
exothermic for HSO2 using an experimental estimation of
∆Hf298K gleaned from S-H bond energies measured through
chemiluminescence studies of SO2/H2/N2/O2 flames.62-64 In spite
of this range of values, associative detachment to form the
neutral HSO2 isomeric form is energetically feasible at 298 K.
-
Examining the structures in Table 3, all of the singlet HSO2
bond lengths at the different levels of theory are around 0.04-
0.06 Å longer than those in neutral HSO2. The S-O bonds in
both the neutral species and the anion are consistent with S-O
-
double bonds. The SO2 moiety in HSO2 is also structurally
similar to neutral SO2.57,58 The singlet- and triplet-state HOSO-
ions have a slightly shorter O-H bond than the neutral species.
However, the middle S-O single bonds in both the singlet and
triplet isomers are substantially longer (>0.07 Å) than those in
neutral HOSO. The terminal S-O bond is closer in length to a
S-O double bond, but it is also over 0.07 Å longer than in the
neutral species. In fact, the central S-O bond in triplet HOSO-
-
Using the G2 heats of formation for the singlet HSO2 and
HOSO- isomers given in Table 4 calculated from the atomi-
zation method based on the G2 0 K energies and 298 K
enthalpies of Laakso et al.,42 the reactions of H with SO2 to
-
produce HSO2 and HOSO- ions are 219 and 270 kJ mol-1
-

-
Kinetics of SO2-, SFn-, and SOxFy with Atomic Species
J. Phys. Chem. A, Vol. 111, No. 10, 2007 1857
-
TABLE 4: Energetics for the HSO2 Isomers Calculated Using G2 and G2(MP2) Theory, Including the Vertical Detachment
Energy (VDE) of the Anion and the Electron Affinity (EA) for the Adiabatic Neutral Transition
G2 (0 K)
energy
(hartrees)
G2 (298 K)
enthalpy
(hartrees)
∆E (0 K)
G2(MP2) (0 K)
energy
G2(MP2) (298 K)
enthalpy
∆E (0 K)
G2
G2(MP2)
ion
(kJ mol-1
0
)
(hartrees)
(hartrees)
(kJ mol-1
0
)
1HSO2
-548.639 560
-548.531 208a
-548.621 823
-548.516 703b
-548.618 691
-548.612 592
-548.582 037
-548.635 400
-548.617 035
-548.629 573
-548.521 787a
-548.609 731
-548.506 891b
-548.606 765
-548.600 356
-548.570 411
-548.625 412
-548.604 943
-
vertical 2HSO2
1HOSO-
46.6
52.1
vertical 2HOSO
cis-1HOSO -
trans-1HO SO-
3HOSO-
-548.614 278
-548.608 174
-548.576 281
54.8
70.8
151.0
-548.602 352
-548.595 939
-548.564 655
59.9
76.7
155.3
∆H2f 98K
VDE
G2
∆H2f 98K
VDE
G2
G2(MP2)
G2(MP2)
(kJ mol-1
)
(kJ mol-1
)
(kJ mol-1
)
(kJ mol-1
)
-
1HSO2
-389.1
-340.9
258.5
284.5
-413.8
-360.0
256.9
283.0
1HOSO-
G2 EAc
G2(MP2) EAd
(kJ mol-1
)
(kJ mol-1
)
2HSO2
276.0
109.6
270.0
103.2
2HOSO
a Geometry of the HSO2 anion. b Geometry of the HOSO- anion. c G2 (0 K) neutral energies from Laakso et al.42 d G2(MP2) (0 K) neutral
energies from Frank et al.40
-
-
Figure 3. Cycle of SO2 ion-molecule chemistry combining the
current results with previous measurements from refs 14, 15, 53, and
65-68. The numbers in parentheses are the products of the branching
-
Figure 2. Energies of the isomers of HSO2 and HSO2 species in kJ
ratio for the product channel with the reaction efficiency, where the
mol-1 plotted relative to the minimum-energy HSO2 ion structure.
-
efficiency is defined as the ratio of the observed rate constant, k, to the
The energies were calculated at the G2 level of theory as shown in
Table 4 and the references therein for the structures given in Table 3
optimized at the MP2(Full)/6-31G(d) level in the G2 method.
collision rate constant, kcol
.
the reaction. The G2(MP2) EA and vertical detachment energy
(VDE) values given in Table 4 derived from the neutral energies
of Frank et al.40 are <7 kJ mol-1 different from the G2 values
for both systems, so the qualitative arguments still hold. Detailed
scans of the potential energy surface for the anions are beyond
the scope of the current work.
exothermic, respectively. However, as seen in Table 4, if neutral
-
HSO2 is produced via vertical electron detachment from HSO2
,
the reaction would require 26 kJ mol-1 more energy than the
adiabatic process. An even greater difference of over 100 kJ
mol-1 (>1 eV) in energy is found for the vertical vs adiabatic
processes with HOSO-. Thus, given the differences in the
anionic and neutral structures, the detachment process might
access parts of the neutral potential energy surface where the
Franck-Condon factors are not favorable under the current
reaction conditions. This possibility would be even greater for
the triplet HOSO- isomer that has a substantially different
structure than any of the local minima on the HSO2 surface.
These observations are consistent with the observed H-atom rate
constant being <25% of the collision rate constant, creating a
kinetic bottleneck. Furthermore, large barriers to both formation
of HOSO from H + SO2 and to isomerization from HSO2 to
cis-HOSO have been found.37,40,43-45 Similar barriers might arise
on the anionic singlet potential surface that would also hinder
Combining the current experimental results with previous ion
chemistry measurements at 298 K,14,15,53,65-68 an overview of
-
the interrelated pathways for the SO2 oxidation products can
be derived as shown in Figure 3. The numbers in parentheses
are reaction efficiencies determined using the equation
k
kcol
reaction efficiency ) f
(3)
where f is the branching ratio for a given product channel
generated by a reaction with total rate constant k and kcol is the
Langevin collision rate constant. As seen in Figure 3, a
complicated series of reactions generating a wide variety of ionic

1858 J. Phys. Chem. A, Vol. 111, No. 10, 2007
Midey and Viggiano
-
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-
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-
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O atom. Associative detachment was observed only in the
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Acknowledgment. We thank Thomas Miller for helpful
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Scientific Research under Program EP2303A. A.J.M. was
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