The importance of NO+(H2O)4 in the conversion of NO+(H2O)n to H3O +(H2O)n: I. Kinetics measurements and statistical rate modeling

Article abstract of DOI:10.1021/jp2032803

The kinetics for conversion of NO⁺(H₂O)_n to H₃O⁺(H₂O)_n has been investigated as a function of temperature from 150 to 400 K. In contrast to previous studies, which show that the conversion goes completely through a reaction of NO ⁺(H₂O)₃, the present results show that NO ⁺(H₂O)₄ plays an increasing role in the conversion as the temperature is lowered. Rate constants are derived for the clustering of H₂O to NO⁺(H₂O)_1-3 and the reactions of NO⁺(H₂O)_3,4 with H ₂O to form H₃O⁺(H₂O)_2,3, respectively. In addition, thermal dissociation of NO⁺(H ₂O)₄ to lose HNO₂ was also found to be important. The rate constants for the clustering increase substantially with the lowering of the temperature. Flux calculations show that NO⁺(H ₂O)₄ accounts for over 99% of the conversion at 150 K and even 20% at 300 K, although it is too small to be detectable. The experimental data are complimented by modeling of the falloff curves for the clustering reactions. The modeling shows that, for many of the conditions, the data correspond to the falloff regime of third body association.

Full text of DOI:10.1021/jp2032803

ARTICLE
pubs.acs.org/JPCA
The Importance of NOþ(H2O)4 in the Conversion of NOþ(H2O)n to
H3Oþ(H2O)n: I. Kinetics Measurements and Statistical Rate Modeling
Nicole Eyet,†,‡ Nicholas S. Shuman,‡ Albert A. Viggiano,*,‡ J€urgen Troe,§ Rachael A. Relph,^ Ryan P. Steele,^
and Mark A. Johnson^
†Department of Chemistry, St. Anselm College, 100 Saint Anselm Drive, Manchester, New Hampshire 03102, United States
‡Space Vehicles Directorate, Air Force Research Laboratory, 29 Randolph Road, Hanscom Air Force Base, Massachusetts 01731-3010,
United States
§Institut f€ur Physikalische Chemie, Universit€at G€ottingen, Tammannstrasse 6, and Max-Planck-Institut f€ur Biophysikalische Chemie,
D-37077 G€ottingen, Germany
^Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520, United States
ABSTRACT: The kinetics for conversion of NOþ(H2O)n to
H3Oþ(H2O)n has been investigated as a function of temperature
from 150 to 400 K. In contrast to previous studies, which show that
the conversion goes completely through a reaction of NOþ(H2O)3,
the present results show that NOþ(H2O)4 plays an increasing role
in the conversion as the temperature is lowered. Rate constants are
derived for the clustering of H2O to NOþ(H2O)1ꢀ3 and the
reactions of NOþ(H2O)3,4 with H2OtoformH3Oþ(H2O)2,3, respectively. In addition, thermal dissociation of NOþ(H2O)4 to lose HNO2
was also found to be important. The rate constants for the clustering increase substantially with the lowering of the temperature. Flux
calculations show that NOþ(H2O)4 accounts for over 99% of the conversion at 150 K and even 20% at 300 K, although it is too small to be
detectable. The experimental data are complimented by modeling of the falloff curves for the clustering reactions. The modeling shows that,
for many of the conditions, the data correspond to the falloff regime of third body association.
’ INTRODUCTION
The rate constant for reaction 4 is small, prompting speculation that
only one of several isomers of NOþ(H2O)3 reacted. These mechan-
isms were confirmed and details added by a number of further stu-
dies.4ꢀ7
One of the great mysteries of lower atmospheric ion chemistry
was discovered on the first successful flight of a mass spectrometer
into the lower ionosphere on October 31, 1963.1 Positive ion profiles
were measured from 64 to 112 km. At the highest altitudes, NOþ and
O2þ were found to be the primary ions, as expected. However, below
about 85 km, proton hydrates (H3Oþ(H2O)n) became important
and then dominated the spectra below ∼80 km. Both O2þ and NOþ
react with H2O only by clustering. Therefore, much effort over the
next several years was expended to explain the presence of the proton
hydrates. Numerous additional rocket flights proved that the observa-
tion of proton hydrates was not due to water vapor outgassing from
the rocket, a common interpretation. The observations were only
explained 6ꢀ7 years later when cluster-assisted routes to the proton
hydrates were discovered by Ferguson and Fehsenfeld.2 For the O2þ
system, they found that O2þ(H2O) reacted with H2O to form both
H3Oþ and H3OþOH. Both product ions react with H2O to form
H3Oþ(H2O) and then higher order proton hydrates. This was con-
firmed by the Kebarle group.3 The situation for NOþ is more com-
plex and is described by reactions 1ꢀ4.
Recently, there have been several studies of the infrared spec-
troscopy,8,9 metastable ion dissociation, and structure and energetics
of the species involved. The theoretical work by Asada et al.10 shows
that NOþ(H2O)4,5 each have 15 isomers. Previous theoretical work is
summarized in that paper. The presence of isomers was also con-
firmed in the work from the Johnson and Okumura groups9,11 which
showed that infrared dissociation of NOþ(H2O)4 produced NOþ-
(H2O)3, NOþ(H2O)2, and H3Oþ(H2O)2, with the first ion being
the major species. For NOþ(H2O)5, infrared dissociation produced
mainly H3Oþ(H2O)3 with lesser amounts of NOþ(H2O)4. Angel
and Stace12 performed studies on both unimolecular dissociation
of metastable cations and collision-induced dissociation which
showed more equal amounts of products for NOþ(H2O)4 and a
dominance of HNO2 loss for NOþ(H2O)5. A common thread in
these studies is the observation that NOþ(H2O)5 may play a role
in the kinetics—at least at low temperatures, since the ions are
formed in supersonic beams.
NOþ þ H2O þ M T NOþðH2OÞ þ M
NOþðH2OÞ þ H2O þ M T NOþðH2OÞ2 þ M
ð1Þ
The theoretical and dynamical work cited above shows a more
complex picture than suggested by past kinetics studies. In part
that stems from the fact that only little work on the kinetics has
ð2Þ
NOþðH2OÞ2 þ H2O þ M T NOþðH2OÞ3 þ M
NOþðH2OÞ3 þ H2O f H3OþðH2OÞ2 þ HNO2
ð3Þ
ð4Þ
Received: April 8, 2011
Revised:
May 12, 2011
Published: May 19, 2011
r
2011 American Chemical Society
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been done since the early days of its discovery and none of the
studies were performed as a function of temperature. Consider-
ing that the region of the atmosphere where these reactions are
the most important is cold (100ꢀ300 K),13 it is worthwhile to
study the kinetics over a wide range of temperatures.
In the present work the rate constants for H2O clustering to
NOþ(H2O)1ꢀ3 and the conversion of NOþ(H2O)3ꢀ4 to proton
hydrates from 150 to 400 K have been measured. Indeed the
mechanism is more complex than previously thought; NOþ(H2O)4
plays a prominent role and the temperature dependences are steep.
Here kinetics studies for the pertinent reactions in a helium buffer
and complementary statistical rate modeling of the rate constants
are presented so that the results can be transferred to a nitrogen
buffer, as well as to broader ranges of temperature and pressure than
assessed in laboratory work. Part II of this series will address the
infrared spectroscopy of NOþ(H2O)4 and thermodynamics calcu-
lations of the various species involved.
not deliver the larger concentrations of H2O necessary at higher
temperatures.
H2O was observed to be condensing on the flow tube walls at a
low temperature. Normally, when kinetics are studied in our
laboratory, flows are increased in equal steps and then decreased.
This handles potential signal drift exceptionally well. However,
we found that at low temperatures the time for signals to become
stable after a H2O concentration decrease was many minutes,
indicating that the H2O which had been sticking to the cold walls
was outgassing. Therefore, the low temperature data presented were
taken only by increasing H2O concentrations and allowing for
several minute wait time between each data point. In addition, we
found that at some point enough water adhered to the flow tube
walls so that all ion signals decayed dramatically. Then the instru-
ment had to be shut down and warmed up before data could again
be taken. The time before shutdown could be as short as 2 h.
To derive rate constants, an Eulerian equation solver was used
to fit the data. Time steps were on the order of 1ꢀ10 μs (total
reaction time ∼ ms). Rate constants were derived from a Monte
Carlo procedure described in depth previously.15 For each reaction,
rate constants were assumed for the forward rate constants. Physical
constraints on the trial values were imposed; for example, no rate
could occur above the collisional value or below the detection limit.
Equilibrium constants were fixed using experimentally or theoreti-
cally determined thermodynamics. The ion concentrations were
then predicted as a function of the H2O concentration; a weighted
least-squares parameter, which we refer to as the goodness-of-fit, was
calculated by comparing the predicted ion concentrations to the
experimental data. Approximately 100 000 trial values were done for
each data set. Plots of the individual rate constants versus the
goodness-of-fit parameter were then used to derive the forward
rates. The rate constants were fixed at the minima of such plots,
when they existed. By eye, it was determined when the goodness-of-
fit parameter was large enough (GOF(max)) to clearly lead to bad
fits. The width of the rate constant versus goodness-of-fit curves at
GOF(max) then determined the error limits. The system is complex
enough that for many conditions only a few rate constants
could be derived with certainty, with others having poorly defined
minima. Varying the equilibrium constants (by varying the thermo-
chemistry) of the reactions, while also varying the rate constants, did
not provide better defined rate constants and/or little thermochemi-
cal information.
’ EXPERIMENTAL SECTION
The measurements were performed in the Air Force Research
Laboratory's selected ion flow tube (SIFT). The instrument has
been described in detail previously,14 and only a brief discussion
is given here. Ions are created in a moderate pressure ion source,
mass selected, and injected into a reaction flow tube through a
Venturi injector. The ions are thermalized by a helium bath gas.
Water vapor is added downstream, and a small amount of the gas
is sampled into a quadrupole mass spectrometer through a
pinhole in a nose cone. The ions are then mass analyzed by a
second quadrupole mass filter and detected by a discrete dynode
multiplier. The flow tube is heated or cooled in four zones by
resistance heaters or pulsed liquid nitrogen, respectively.
NOþ(H2O)n ions are created in the source from a mixture of
NO and H2O. Our goal was to make and inject individual clusters
into the flow tube so that individual reactions could be studied in
isolation, particularly reaction 4. However, due to the fragile
nature of the reactants, H2O ligands are lost during the injection
process. Therefore, the kinetics had to be analyzed as a complete
set. Details are described later.
A heated neutral injector is used to introduce water vapor at
low temperatures. A thin (1/8 in.) stainless steel tube is silver
soldered to a thick 1/4 in. tube, both coaxial tubes otherwise
being electrically insulated from each other and the flow tube.
Passing a current through the inlet preferentially heats the thin
inner tube. A thermocouple is placed near the tip to monitor the
temperature. In this manner, H2O is prevented from freezing in
the inlet while minimizing the amount of heat transferred to the
buffer gas. Nevertheless, the actual temperature of the reaction
zone is likely to be higher than the reported temperatures (which
are measured at the wall) by an unknown but small (∼10 K)
amount. This is taken into account in our error analysis, such as
described in the analysis section.
Normally, we report errors as 25% for absolute rate constants
and 15% for differences from one temperature to another. However,
several conditions discussed above indicate that our errors here are
probably much larger, even when the rate constants are well-defined
by the goodness-of-fit plots: (1) the temperature is subject to error
due to the heated inlet; (2) the results are very sensitive to the back
reactions, which are in turn very sensitive to the thermochemistry
and the uncertain temperature; (3) the freezing water vapor may
have altered the sampling efficiency—certainly at 150 K after tens of
minutes of H2O exposure. Estimating the effects of each potential
problem is difficult. Individual errors are discussed in detail as all of
the data are reported. The statistical modeling of the rate constants
given below also suggests that individual errors must have been
considerably larger than 25%.
Water vapor is introduced by two methods. At 250 K and
above, where the reaction is relatively slow, helium is bubbled
through H2O to create large concentrations in the flow tube
(∼1013 molecules cmꢀ3). The pressure over the reservoir is
monitored, and the flow rate is derived by assuming that the
helium becomes saturated with water vapor. At low tempera-
tures, a different method is used since less H2O is needed as the
reaction becomes faster. Mixtures of 5ꢀ10% H2O in He are
made, and the mixture flows directly into the flow tube through
an MKS flow controller. The latter method is simpler but does
’ RESULTS
Determination of Rate Constants. Reactions 1ꢀ4 were
previously considered as being the complete set important in the
atmospheric conversion of NOþ(H2O)n to H3Oþ(H2O)n. In the
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Figure 1. Modeled (lines) and measured (points) ion concentrations at
150 K (assuming k4 = 1.0 ꢁ 10ꢀ10 cm3 moleculeꢀ1 sꢀ1).
present study, NOþ(H2O)4 is observed but not predicted by the
mechanism given above. Therefore, the additional clustering reaction
NOþðH2OÞ3 þ H2O þ M T NOþðH2OÞ4 þ M ð5Þ
is assumed to compete with reaction 4 at low temperature. Once
formed, NOþ(H2O)4 may undergo three competing reactions. It
could collisionally dissociate, that is, undergo the reverse of reaction
5; it would form proton hydrates in a reaction similar to reaction 4,
NOþðH2OÞ4 þ H2O f H3OþðH2OÞ3 þ HNO2 ð6Þ
or release nitrous acid via thermal dissociation.
Figure 2. Goodness-of-fit plots at 150 K. (a) Variation of k4, leading to a
poorly defined value; (b) variation of k6, leading to a well-defined
optimum value (see text).
NOþðH2OÞ4 þ M f H3OþðH2OÞ2 þ HNO2 þ M ð7Þ
The complete mechanism only became visible when an extended
temperature range was addressed. Normally in a SIFT experiment,
one reaction is studied at a time. The complexity of the chemistry
under study here made that impossible. In addition to reactions
1ꢀ7, clustering to form higher-order proton hydrates also occurs,
The solid lines in Figure 1 represent the modeling results
described below. The modeling includes reaction 4 to produce
H3Oþ(H2O)2. The orange line on the plot shows that this ion
should be produced in quantities below our detection limit, con-
sistent with our observations. Several facts lead to a switchover from
reaction 4 to reaction 6 as the dominant conversion reaction. The
clustering rates at 150 K are all fast, approaching gas kinetic limits,
and leading to a fast chain of reactions required to produce
H3OþðH2OÞn þ H2O þ He T H3OþðH2OÞnþ1 þ He ð8Þ
While NOþ(H2O)4 was observed at 150, 200, and 250 K, its
importance being most clearly observed at 150 K, it probably still
plays a role at 300 K although its concentration was below our
detection limit. Data analysis at 150 K is simplified because
thermal dissociation reactions (reactions 7 and the reverse of
reactions 2, 3, 5, and 8) do not occur on the time scale of our
experiment. In turn this eliminates uncertainties in the thermo-
chemistry from impacting the modeling and also leads to a
reduced set of reactions. The points in Figure 1 show ion
concentrations as a function of H2O concentration at 150 K.
At low [H2O], mainly NOþ and NOþ(H2O) are observed.
NOþ(H2O)4 was the largest NOþ hydrate observed. The
smallest H3Oþ-containing hydrate observed was H3Oþ(H2O)3.
If reaction 4 was occurring, the observation of H3Oþ(H2O)2
would be expected, unless reaction 8 for n = 2 was much more
rapid than reaction 7. However, the modeling shows that at
150 K, reaction 4 is significantly slower than reaction 6.
NOþ(H2O)4.. Reaction 4 is endothermic by ∼6 kcal molꢀ1
;
therefore it would be expected to become slower with decreasing
temperature (as presented later, it is difficult to derive a true tem-
perature dependence) and at 150 K should be unable to compete
with reaction 5. Finally, reaction 6 is slightly exothermic and fast,
providing a facile route to proton hydrates. The result is that, for
NOþ(H2O)3, the clustering reaction 5 to produce NOþ(H2O)4 is
significantly faster than conversion to proton hydrates (reaction 4).
NOþ(H2O)4 then almost exclusively reacts by reaction 6 to
produce H3Oþ(H2O)3. Flux calculations for the various reactions
involving NOþ(H2O)3,4 are presented below.
Figure 2 shows the goodness-of-fit parameter versus rate
constants for the two reactions with H2O that lead to proton
hydrates, reactions 4 and 6. Reaction 4 is poorly defined by this
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procedure. This is confirmed by photodissociation branching
data presented in part II and by Okumura et al.16 The data were
also modeled without these constraints; the resulting rate con-
stants were less defined, and temperature trends were erratic, that
is, they did not follow simple monotonic trends.
The derived rate constants are listed in Table 1 for 150, 200,
250, and 300 K data; they are either represented as second-order
or as third-order rate constants. For falloff effects see the
statistical rate modeling given below. For each reaction, a best
fit value is listed in bold, and upper and lower limits are listed in
standard text, if they could be determined from the data. For
equilibrium reactions, the thermodynamic values used to fix the
equilibrium constant, and hence the back reactions are listed.
Previous data taken at 300 K data are listed in the last column. No
rate data are shown for reaction 2, the initial H2O clustering to
NOþ, since the rate is slow and was only poorly measured for the
amount of H2O added in the present experiments.
Data were also taken at 400 K, but minimal clustering and no
proton hydrates were observed. These data were not useful
except to emphasize the steep temperature dependences of the
clustering rates. Presumably at higher H2O concentrations,
proton hydrates would be observed.
The only rate constants that are well-defined at all tempera-
tures are those for addition of a subsequent water to NOþ-
(H2O)1,2. The clustering reactions get much faster with
decreasing temperature and roughly increase with n. There is
good agreement between our value for NOþ(H2O) clustering
and previous data at 300 K but poor agreement for n = 2
clustering. However, that disagreement is the result of the added
complexity of the current model. If all rate constants are allowed
to be variable over larger ranges, the value for that third-order
Figure 3. As for Figure 1 but for T = 200 K. The solid lines represent the
model with the lowest goodness-of-fit parameters, see text. Removing
the thermal decomposition of NOþ(H2O)4 (reaction 7) and redeter-
mining the rate constants provides the fits given by the dashed lines.
modeling since so little H3Oþ(H2O)2 is observed. The rate constant
was allowed to vary from 1 ꢁ 10ꢀ9 (approximately the collisional
rate constant) to 1 ꢁ 10ꢀ15 cm3 moleculeꢀ1 sꢀ1 (the detection limit
of the experiment). Reaction 6 is well-defined by the modeling, and
the rate constant must be close to that of the collisional rate constant.
The difference between the very shallow minimum in 2a and the
more pronounced one in 2b is significant. Similar plots were used to
derive all rate constants and their error limits.
The most important clue for the importance of reaction 7, the
thermal decomposition of NOþ(H2O)4 to lose HNO2, was
observed at 200 K. The raw data are shown in Figure 3 along with
model fits. Both H3Oþ(H2O)2 and H3Oþ(H2O)3 were observed
as primary proton hydrates. Successive proton hydrates up to and
including n = 7 (not shown for clarity) are formed from subsequent
clustering at all low temperatures. These data were modeled with
the method described above. The result of modeling reactions 1ꢀ8
is illustrated by the solid lines in Figure 3. Modeling of reactions
1ꢀ6 and 8 provides the fits shown by the dashed lines. It was not
possible to obtain a good fit without reaction 7 unless reaction 4
occurred at nearly a collisional rate. The latter is not consistent with
the temperature dependence of this rate constant predicted by the
measured higher temperature rate constants for reaction 4
(discussed shortly.) Therefore, reaction 7 must be included in
the reaction model, even if the rate constants determined become
less defined. This reaction also has an effect on higher temperature
data, even at 300 K where NOþ(H2O)4 is not observed.
rate constant increases to 2.9 ꢁ 10ꢀ28 cm6 moleculeꢀ2
s
ꢀ1, in
good agreement with the published values, but with other rate
constants making little physical sense (odd temperature depend-
ences or unphysical rates). The derived values of the second-
order rate constants for reaction 4 vary from 0.8ꢀ3.6 ꢁ
10ꢀ10 cm3 moleculeꢀ1 sꢀ1. It was not possible to derive a value
at 150 K. The derived values are in agreement with the 300 K
values previously published within error.5,17 The rate constant for
conversion of NOþ(H2O)4 to H3Oþ(H2O)3 could only be
observed at 150 K, see Figure 2b, and as stated previously was
assumed to be similar at all temperatures. The rate constant for
thermal dissociation of NOþ(H2O)4 into H3Oþ(H2O)2 was not
well determined, but it clearly increases with temperature as
expected. The rate constant for production of NOþ(H2O)4
(reaction 5) could only be derived at the two lowest tempera-
tures. The considerable uncertainty in many of the rate constants
stems from potential trade-offs between the various channels.
To determine the relative importance of NOþ(H2O)3 and
NOþ(H2O)4 in the conversion to proton hydrates, flux calcula-
tions were performed. Several species in the reaction system are
either produced or destroyed by two or more competing reactions.
The relative contributions of each reaction are not necessarily
immediately obvious and were deconvoluted from one another by
calculating the total concentrations of each reactant consumed and
each product yielded by each individual forward and reverse
reaction throughout the full reaction time. In effect this calculation
is simply tracking the progress of each reaction while iteratively
solving the coupled differential equations as described above. The
calculations are subject to uncertainty due to the large variations in
rate constants possible, especially at 250 and 300 K. However,
trends are reliable. The percentage of proton hydrates that are
To derive rate data at temperatures above 150 K, the following
simplifying assumptions were made in the data analysis. The
150 K data show that reaction 6 is fast. Exothermic reactions of
this type usually remain rapid at all temperatures. When model-
ing this rate constant, it was constrained to be in the range 1.5ꢀ
3 ꢁ 10ꢀ9 cm3 moleculeꢀ1 sꢀ1, that is, near the collisional value.
In addition, the reverse of reaction 5 should be faster than
reaction 7, and that constraint was added in the Monte Carlo
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Table 1. Rate Constants for Various Reactions of NOþ(H2O)n with H2O (Second-Order Rate Constants** in cm3 moleculeꢀ1 sꢀ1
Third-Order Rate Constants* in cm6 moleculeꢀ2 sꢀ1 a
;
)
k at 150 K,
0.27 Torr
k at 200 K,
0.27 Torr
k at 250 K,
0.34 Torr
k at 300 K,
0.37 Torr
previous value
(300 K)d
upper limit (top), best value
reaction
(middle), lower limit (bottom)
(2)* NOþ(H2O) þ H2O þ He f NOþ(H2O)2 þ He
ΔH = ꢀ65 kJ molꢀ1
4.8 ꢁ 10ꢀ26
4.1 ꢁ 10ꢀ26
2.5 ꢁ 10ꢀ26
2.0 ꢁ 10ꢀ25 (kcoll
1.1 ꢁ 10ꢀ25
7 ꢁ 10ꢀ26
2.0 ꢁ 10ꢀ25 (kcoll
1.3 ꢁ 10ꢀ25
5 ꢁ 10ꢀ26
3.4 ꢁ 10ꢀ9 (kcoll
none
1.2 ꢁ 10ꢀ26
1.8 ꢁ 10ꢀ26
2.4 ꢁ 10ꢀ26
7.5 ꢁ 10ꢀ26
4.3 ꢁ 10ꢀ26
2.8 ꢁ 10ꢀ26
2.3 ꢁ 10ꢀ25 (kcoll
1.1 ꢁ 10ꢀ25
5 ꢁ 10ꢀ26
3.0 ꢁ 10ꢀ9 (kcoll
3.6 ꢁ 10ꢀ10
2 ꢁ 10ꢀ11
9 ꢁ 10ꢀ28
7 ꢁ 10ꢀ28
5 ꢁ 10ꢀ28
1.8 ꢁ 10ꢀ27
1.2 ꢁ 10ꢀ27
8 ꢁ 10ꢀ28
4.8 ꢁ 10ꢀ28
3.0 ꢁ 10ꢀ28
3.7 ꢁ 10ꢀ28
not observed
8.5 ꢁ 10ꢀ11
not observed
not observed
3.3 ꢁ 10ꢀ28
2 ꢁ 10ꢀ28
ΔS = ꢀ85 J molꢀ1 Kꢀ1
(3)* NOþ(H2O)2 þ H2O þ He f NOþ(H2O)3 þ He
)
)
2 ꢁ 10ꢀ28
9 ꢁ 10ꢀ29
4 ꢁ 10ꢀ29
2.5 ꢁ 10ꢀ25 (kcoll
none
ΔH = ꢀ64 kJ molꢀ1
ΔS = ꢀ120 J molꢀ1 Kꢀ1
(5)* NOþ(H2O)3 þ H2O þ He f NOþ(H2O)4 þ He
)
2 ꢁ 10ꢀ26
)
ΔH = ꢀ45 kJ molꢀ1
none
ΔS = ꢀ80 J molꢀ1 Kꢀ1
none
none
(4)** NOþ(H2O)3 þ H2O f H3Oþ(H2O)2 þ HNO2
(6)** NOþ(H2O)4 þ H2O f H3Oþ(H2O)3 þ HNO2
(7)** NOþ(H2O)4 þ He f H3Oþ(H2O)2 þ HNO2
)
)
2.7 ꢁ 10ꢀ9 (kcoll
8 ꢁ 10ꢀ11c
none
)
1.6 ꢁ 10ꢀ10
1.1 ꢁ 10ꢀ10
1.3 ꢁ 10ꢀ12
none
3.4 ꢁ 10ꢀ9 (kcoll
2.8 ꢁ 10ꢀ9
)
fixed to be
fixed to be
fixed to be
1.5ꢀ3 ꢁ 10ꢀ9b
1.5ꢀ3 ꢁ 10ꢀ9b
1.5ꢀ3 ꢁ 10ꢀ9b
9 ꢁ 10ꢀ10
none
none
none
1 ꢁ 10ꢀ13
7.6 ꢁ 10ꢀ14
none
6 ꢁ 10ꢀ12
none
1.2 ꢁ 10ꢀ10
1.5 ꢁ 10ꢀ11
none
none
a Thermochemistry is at 298 K. kcoll is the collisional value. For termolecular kcoll, bimolecular collision rate constants are divided by the number density.
b Set to be small range near 150 K rate, which is relatively well-known. c Shallow minimum. d Average of refs 5 and 17.
Table 2. Modeled Yield of Proton Hydrates Formed from
Statistical Modeling of Rate Constants. The 300 K mea-
surements of the rate constants for the formation of the hydrates
NOþ(H2O)n with n = 1ꢀ35,6,17 have been extended toward
lower temperatures for n = 2 and 3 and rate constants for n = 4
were added in the present experiments. It was assumed
previously5,6,17 that at pressures near 1 Torr the reactions were
at their limiting low-pressure third-order limit. By analogy, the
rate data in Table 1 were represented as third-order rate
constants. However, one cannot expect that third-order behavior
prevails for all n at all temperatures studied and all pressures of
interest for ionospheric applications. For this reason, modeling of
the rate constants in terms of statistical unimolecular rate theory
appears obligatory (see, e.g., the previously presented modeling of
the hydration reaction of hydronium18 and ammonium cations19 as
well as more recent work on hydration reactions in general).20
We consider a limiting low pressure range where the
second-order rate constant k, here denoted by k0, is propor-
tional to the bath gas concentration [M], that is, where the
reaction is third order. At high pressure, there is a limiting
range where the second-order rate constant k is independent
of the bath gas concentration and reaches a value k¥ which
possibly is given by ionꢀmolecule capture theory.20ꢀ23 Earlier
in the paper this was termed “collisional” or “gas kinetic”. In
the falloff range in between, the rate constant k gradually
changes from k0 to k¥.
NOþ(H2O)3
a
H3Oþ(H2O)n yield
T/K
[H2O]/molecules cmꢀ3
(in %) from NOþ(H2O)3
150
200
250
300
3 ꢁ 1011
6 ꢁ 1011
1 ꢁ 1013
3 ꢁ 1013
0.3
4
60
80
a Errors are difficult to estimate given the uncertainties in the derived rate
constants, particularly at 250 and 300 K.
produced by conversion of NOþ(H2O)3 (reaction 4) rather than
NOþ(H2O)4 increases from essentially zero (0.3%) at 150 K to
80% at 300 K; see Table 2. The increase follows roughly an
exponential dependence on 1/T. The 150 K flux is the most
accurate since it is based on the fact that no H3Oþ(H2O)2 is
observed. At 200 K, conversion of NOþ(H2O)4 (reaction 6)
dominates protonhydrate production; at250 K, NOþ(H2O)3 and
NOþ(H2O)4 are equally important in producing proton hydrates
within uncertainty (tens of percent), and at 300 K, the conversion
to proton hydrates is dominated (80%) by conversion of
NOþ(H2O)3 (reaction 4). This shows that the old mechanism
is probably not exclusively responsible for proton hydrate produc-
tion (due to the large errors in this calculation, a value nearer 100%
is possible but less likely) but that roughly 20% of the conversion
to proton hydrates occurs through NOþ(H2O)4 even though it is
not observed. The flux calculations also show that, at 150 K,
NOþ(H2O)4 is formed by reaction 6 almost exclusively (99.9%).
This pathway's branchingfractiondrops to 20%at200 K and 1%at
300 K. At the higher temperatures, the branching fraction for the
reverse of reaction 5 increases.
k0 and k¥ generally have quite different temperature depend-
ences such that the bath gas concentration at which the center of
the falloff range is located moves with temperature. The limita-
tions of the described experiments did not allow us to study
details of the pressure dependences of the rate constants and to
locate them along the respective falloff curves. In addition, the
temperature dependences of k could only be specified to a limited
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Table 3. Modeled Low Pressure Strong Collision Rate Coefficients k0sc from eq 9 for NOþ(H2O)nꢀ1 þ H2O þ He f
NOþ(H2O)n þ He (see text)
T/K
n
150
200
250
300
350
400
1
1.5 ꢁ 10ꢀ28
5.0 ꢁ 10ꢀ26
1.3 ꢁ 10ꢀ27
6.5 ꢁ 10ꢀ27
1.5 ꢁ 10ꢀ24
3.6 ꢁ 10ꢀ27
3.1 ꢁ 10ꢀ26
6.6 ꢁ 10ꢀ29
1.2 ꢁ 10ꢀ26
1.4 ꢁ 10ꢀ28
6.6 ꢁ 10ꢀ28
1.5 ꢁ 10ꢀ25
2.1 ꢁ 10ꢀ28
3.3 ꢁ 10ꢀ27
3.5 ꢁ 10ꢀ29
3.9 ꢁ 10ꢀ27
2.0 ꢁ 10ꢀ29
9.5 ꢁ 10ꢀ29
2.3 ꢁ 10ꢀ26
2.1 ꢁ 10ꢀ23
5.4 ꢁ 10ꢀ28
2.1 ꢁ 10ꢀ29
1.5 ꢁ 10ꢀ27
3.6 ꢁ 10ꢀ30
1.8 ꢁ 10ꢀ29
4.3 ꢁ 10ꢀ27
2.8 ꢁ 10ꢀ30
1.1 ꢁ 10ꢀ28
1.3 ꢁ 10ꢀ29
6.1 ꢁ 10ꢀ28
8.2 ꢁ 10ꢀ31
4.1 ꢁ 10ꢀ30
1.0 ꢁ 10ꢀ27
4.7 ꢁ 10ꢀ31
2.7 ꢁ 10ꢀ29
9.2 ꢁ 10ꢀ28
2.8 ꢁ 10ꢀ28
2.2 ꢁ 10ꢀ31
1.1 ꢁ 10ꢀ30
2.3 ꢁ 10ꢀ28
1.0 ꢁ 10ꢀ31
7.7 ꢁ 10ꢀ30
2a
2b
2c
2d
3e
3f
a Low frequency oscillator model of NOþ(H2O)2. b Low frequency oscillator model of NOþ(H2O)2 and ring structure of NOþ(H2O)3. c Low frequency
oscillator model of NOþ(H2O)2 and trigonal structure of NOþ(H2O)3; d Low frequency oscillator model of NOþ(H2O)2 and Cs structure of
NOþ(H2O)3. e Cs structure of NOþ(H2O)3 and ring þ 1 front down structure of NOþ(H2O)4. f Ring structure of NOþ(H2O)3 and ring þ 1 front
down structure of NOþ(H2O)4.
extent. In this situation, theoretical modeling of k(T,[M]) is
helpful and extends the representation of the rate constants. In
view of the uncertainty of the rate data we simplify the
calculations to some extent by focusing attention on the limit-
ing low and high pressure rate constants k0 and k¥. We then
represent the falloff transition between the limiting ranges in
analogy to the results for the H3Oþ(H2O) and NH4þ(NH3)
systems.18,19
Table 4. Modeled High Pressure Rate Coefficients k¥/cm3
moleculeꢀ1 sꢀ1 from eq 10 for NOþ(H2O)nꢀ1 þ H2O f
NOþ(H2O)n (see text)
T/K
n
150
200
250
300
350
400
1
2
3
4
3.80 ꢁ 10ꢀ9 3.3 ꢁ 10ꢀ9 3.0 ꢁ 10ꢀ9 2.8 ꢁ 10ꢀ9 2.6 ꢁ 10ꢀ9 2.5 ꢁ 10ꢀ9
3.5 ꢁ 10ꢀ9 3.1 ꢁ 10ꢀ9 2.8 ꢁ 10ꢀ9 2.6 ꢁ 10ꢀ9 2.5 ꢁ 10ꢀ9 2.3 ꢁ 10ꢀ9
3.4 ꢁ 10ꢀ9 3.01 ꢁ 10ꢀ9 2.7 ꢁ 10ꢀ9 2.5 ꢁ 10ꢀ9 2.4 ꢁ 10ꢀ9 2.2 ꢁ 10ꢀ9
3.2 ꢁ 10ꢀ9 2.9 ꢁ 10ꢀ9 2.6 ꢁ 10ꢀ9 2.4 ꢁ 10ꢀ9 2.3 ꢁ 10ꢀ9 2.2 ꢁ 10ꢀ9
We express k0 in the form24
Fvib, hðE0ÞFEkTFanhFrot
k0 ꢂ ½MꢃβcZ
QvibðH2OÞQvibðNOþðH2OÞnÞ
Table 5. Strong Collision Broadening Factors F(y) Used in
This Work (y = k0/k¥ and Modeling Results for H3Oþ þ
H2O þ He f H3Oþ(H2O) þ He (from Hamon et al.18)
!
3=2
Qel, rotðNOþðH2OÞnþ1Þ
h2
ð9Þ
Qel, rotðH2OÞQel, rotðNOþðH2OÞnÞ 2πμkT
y
10ꢀ4 10ꢀ3 10ꢀ2 10ꢀ1
F(y) 0.90 0.75 0.53 0.31
1
101
102
103
104
where βc is a collision efficiency related to the average energy
transferred per collision <ΔE> through βc/(1 ꢀ βc1/2) ≈ ꢀ<ΔE>/
FEkT. Z is represented by the Langevin collision frequency Z = kL =
2πe(R/μ)1/2 with the polarizability R of M and the reduced mass μ
of the collision pair M-NOþ(H2O)n; Qvib,rot,el are vibrational,
rotational, and electronic partition functions, respectively; Fvib,h(E0)
is the harmonic vibrational density of states of the adduct NOþ-
(H2O)n at its dissociation energy E0, FE accounts for the energy
dependence of Fvib,h, Fanh accounts for anharmonicity,25,26 and Frot is
0.20 0.27 0.40 0.53 0.65
fied for the asymmetric top character of H2O, in the form
k¥=kL ꢂ 0:4767x þ 0:6200 for x g 2
2
ꢂ ðx þ 0:5090Þ =10:526 þ 0:9754 for x e 2
ð10Þ
with x = μ0,eff/(2RkT)1/2. Here, R is the polarizability of H2O (with
R = 1.45 ꢁ 10ꢀ24 cm3) and μD,b = 1.07 μD,b is an effective dipole
moment20 of water (with μD,b = 1.857 D). Table4summarizesvalues
for k¥ calculated with eq 10.
a rotational factor (here represented by its maximum value Frot,max
,
i.e., the value determined in absence of centrifugal barriers). The
molecular parameters required for the calculation of k0 are given in
the Appendix. Large additional anharmonicity effects may put the
frequencies of the low frequency modes in question. For this reason,
we put the lowest frequencies (below 25 cmꢀ1) arbitrarily at
25 cmꢀ1. In addition, there is the problem of the partication of
several isomers of the hydrates, that is, three stable isomers (trigonal,
ring, and Cs) for NOþ(H2O)3 and 15 stable isomers10 for NOþ-
(H2O)4. At this stage it remains uncertain how to account for the
isomer formation in a proper way. We nevertheless show in Table 3 a
series of calculations of strong collision rate constants k0sc (i.e., values
for k0 putting βc = 1 and for M = He) for the formation of specific
isomers. One should also note that the isomers after their formation
may interchange by thermal isomerization processes and establish
isomer equilibria.
Because of the uncertainties in the modeling of the limiting
rate constants and in the experimental data, we refrain from
doing a complete rate calculation in the intermediate falloff
range. Instead, we employ the same strong collision “broadening
factors” F(y) in the falloff representation24
k=k¥ ¼ ½y=ð1 þ yÞꢃFðyÞ
ð11Þ
þ
þ
(where y = k0/k¥) as for the formation of H2O5 and N2H7
treated previously,18,19 see Table 5. For example, one has F(y = 1)
= Fcenter ≈ 0.2, F(y = 10ꢀ2) ≈ 0.6, and F(y = 102) ≈ 0.4
In the following we compare the measured rate constants with
modeled falloff curves. This is problematic for reaction 1, which
was experimentally not accessible in the present work but for
which previous data5,17 are available near 300 K and 1 Torr; see
Figure 4. One observes that reaction 1 near 300 K and 1 Torr
We assume that k¥ is represented sufficiently well by ionꢀdipole
capture theory in the form of the SuꢀChesnavich equation,21 modi-
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Figure 5. Modeled strong collision falloff curves for (2) NOþ(H2O) þ
H2O þ He f NOþ(H2O)2 þ He at T = 150, 200, 250, and 300 K (from
top to bottom; measurements from the present work at 150 (Y),200 (y),
250 (O), and 300 K (b); measurements at 300 K from ref 5 (3) and16
(2); for the meaning of the modeled curves, see Figure 4 and text).
Figure 4. Modeled strong collision falloff curves for (1) NOþ þ H2O þ
He f NOþ(H2O) þ He at T = 150 and 300 K [experimental results for
T = 300 K from refs 5 (3) and 16 (2)]; the straight lines indicate the
low- and high-pressure limits; the curved lines are modeled falloff curves,
see text).
indeed is close to the low-pressure limit, and it remains near to
this limit when the temperature is lowered to 150 K. The
modeling corresponds to a temperature coefficient in k0 ꢀTꢀm
of the order of m ≈ 2.8. By increasing the pressure one observes
gradual deviations from third-order behavior. However, in this
system this effect is not very pronounced; for example, k/k0 only
changes from 0.9 to 0.5 when the pressure increases from 1 to
100 Torr. The measured rate constants do not deviate far from
the modeled limiting low pressure strong collision values before
any fine-tuning of the modeling is performed.
Considering next reaction 2 (for which optimum experimental
results were obtained in the present work), falloff deviations from
third-order behavior are more pronounced than for reaction 1.
Figure 5 compares the experimental data from the present work
and from refs 5 and 17 with modeled falloff curves. One realizes
that pressures of 1 Torr at 150 K nearly correspond to the center
of the falloff curve, whereas they are closer to the low-pressure
limit at 300 K, k nevertheless being about a factor of 2ꢀ3 below
the extrapolated low pressure value of k0. The presently mea-
sured values at 150 and 200 K are about a factor of 4 above, at 250
and 300 K a factor of 2ꢀ3 below the modeled values. In view of
the above-described uncertainties (in particular the mode with
the lowest frequency), the results should be considered as
satisfactory. In any case, deviations from third-order behavior
at pressures near 1 Torr are considerable, and Figure 5 should be
used for extending the pressure and temperature ranges.
One expects even larger deviations from third-order behavior
for reactions 3 and 5. At this stage, the problem of the contribu-
tion of isomer formation to k0 needs to be addressed. As the
formation of NOþ(H2O)3 in Cs-symmetry dominates because of
the larger number of low frequency modes, only this pathway
needs to be considered. Figure 6 shows the results. One
concludes that the reaction is near to its high pressure limit at
1 Torr for temperatures below 200 K and falls below the high
Figure 6. As for Figure 5, for (3) NOþ(H2O)2 þ H2O þ He f
NOþ(H2O)3 þ He.
pressure limit at higher temperatures. As we have arbitrarily put
the lowest frequencies (calculated values below 25 cmꢀ1) to a
value of 25 cmꢀ1, the discrepancy with the measurements at 250
and 300 K may be an artifact of the modeling.
At this stage it appeared meaningless to model k0sc for all 15
individual isomers of NOþ(H2O)4 forming from the 3 isomers of
NOþ(H2O)3 in reaction 3. Instead we only considered one
representative example, the formation of a “ring þ 1 front down”
structure for n = 4 (see Appendix for its properties) from the ring
structure for n = 3. The result is included in Table 3. As the
reaction can lead to 15 isomers of n = 4, the overall rate constant
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comparison with the experimental results in Table 1 indicates
that reaction 6 indeed is capture-controlled, as the measured and
modeled rate constants agree. On the other hand, reaction 4 is
about 1 order of magnitude slower than the capture-controlled
process, which has to be attributed to its endothermicity of
6 kcal molꢀ1. However, that value would suggest much lower
values of k4 than fitted. Therefore, one cannot rule out that the
observed concentrations of H3Oþ(H2O)2 could also stem from
the thermal dissociation of H3Oþ(H2O)3 such as formed by the
fast reaction 6.
’ CONCLUSIONS
Previous work at 300 K on the conversion of NOþ(H2O)n to
H3Oþ(H2O)m found that all of the conversion occurred for n = 3.
Temperature dependence measurements of the complicated
kinetics system where NOþ sequentially clusters to H2O and then
forms proton hydrates were presented here. Several competing
reactions are identified as the temperature is lowered. At 150 K,
NOþ(H2O)3 rarely reacts with H2O to form H3Oþ(H2O)3 but
over 99% of the time forms NOþ(H2O)4; this hydrate reacts rapidly
with H2O to form H3Oþ(H2O)3. The temperature dependences of
the clustering rates were found to be steep, although large errors in
deriving rate constants in the complicated system prevented
definitive values. Interestingly, flux calculations show that NOþ-
(H2O)4 plays a small but nonzero role in conversion to proton
hydrates at 300 K, even though it is not observed. Thermal
dissociation of NOþ(H2O)4 to lose HNO2 is also observed. This
study emphasizes the importance of studying temperature depend-
ences in ionꢀmolecule clustering reactions since such studies often
reveal hidden reactions.27
Figure 7. As for Figure 5, for (5) NOþ(H2O)3 þ H2O þ He f
NOþ(H2O)4 þ He.
is the sum of all 15 rate constants. Therefore, we tentatively
multiplied the single value by 15 and then divided by 2 because it
is probable that a medium value was selected. Figure 7 shows the
corresponding falloff curves. As in Figure 6, the comparison with
the measurements at 150 and 200 K suggests that these experi-
ments again were done close to the high pressure limit.
In principle, the present modeling allows one to estimate the
change of the rate constants when the bath gas changes from He
to the atmospherically pertinent N2. For that the collision
efficiency βc and the Langevin collision frequency Z in the
expression 9 for k0 are modified. As the related changes are
smaller than the general uncertainties of the modeling, however,
they are not specified here.
When NOþ(H2O)4 reacts with H2O to form proton hydrates,
specifically H3Oþ(H2O)3, and nitrous acid, HNO2, the derived
rate constant is found to agree with the results from ionꢀdipole
capture theory. On the other hand, the clustering reactions
NOþ(H2O)n þ H2O þ M f NOþ(H2O)nþ1 þ M require an
analysis in terms of statistical unimolecular rate theory. Modeling
results show that the clustering reactions at pressures around 1
Torr are not in the third-order low pressure limit but in the falloff
transition range toward the second-order high pressures limit.
This influences the temperature coefficients of the rate constants
at constant pressure. The full picture of the temperature and
pressure dependences of these reactions, therefore, requires
modeling of the full falloff curves.
The present results show that in the mesosphere, where the
temperatures are low, conversion of NOþ(H2O)n clusters to
proton hydrates will occur much rapidly than previously thought.
Rate constants become fast enough that conversion through a
sequential mechanism involving N2 and CO2 clusters and ligand
switching may not be needed. Details await modeling calcula-
tions beyond the scope of the present article.
Modeling of the thermal dissociation of NOþ(H2O)4 through
reaction 7 was done by considering the reverse reaction first. As
HNO2 has nearly the same dipole moment as H2O, this reaction
behaves very similarly to reaction 8 with n = 0, and its modeling
follows that elaborated previously.18 It turns out that reaction 7
and its reverse under the present conditions are close to the high
pressure limit where eq 10 applies. Conversion of the recombi-
nation to dissociation rate constants by the use of the equilibrium
constants then lead to k7. The result can be represented in the
form k7 ≈ 1017(T/300 K)ꢀ2 exp(ꢀE0/kT) sꢀ1 where E0/k is in
the range 7200ꢀ9100 K (depending on the considered isomer of
NOþ(H2O)4). For 300 K, this gives k7 in the range 104ꢀ106 sꢀ1
in good agreement with our fitted value of about 105 sꢀ1 (after
converting the second order into a first-order rate constant in
Table 1). However, the fitted value of about 103 sꢀ1 at 200 K
(converted in the same way) is orders of magnitude above the
best fit modeled value and, therefore, must be an artifact.
However, as seen in Table 1, the data are not well fit for this
reaction.
’ APPENDIX: MOLECULAR PARAMETERS USED IN THE
MODELING OF RATE CONSTANTS
Molecular frequencies (in cmꢀ1). NOþ: 2377; H2O: 3651,
1595, 3756; NOþ(H2O): 92, 230, 245, 406, 417, 1645, 2126,
3752, 3859; NOþ(H2O)2: [25], 70, 70, 91, 189, 217, 227, 349,
351, 353, 366, 1654, 1655, 2156, 3781, 3783, 3887, 3887 ([25]
corresponds to the “low frequency oscillator model” (a) used in
Table 3); NOþ(H2O)3: 51, 107, 130, 197, 207, 218, 225, 248,
257, 264, 313, 343, 406, 486, 536, 640, 710, 1632, 1636, 1675,
2090, 3603, 3642, 3780, 3853, 3856, 3885 (corresponds to the
One may also compare the measured rate constants for the
HNO2-forming bimolecular reactions 4 and 6 with results from
ion-dipole capture theory, that is, with eq 10, see above. For
reaction 6, for example, one obtains kcap/10ꢀ9 cm3 moleculeꢀ1
sꢀ1 = 3.2, 2.9, 2.6, and 2.4 at T/K = 150, 200, 250, and 300,
respectively; for reaction 4, the results are almost the same. A
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“ring structure model” (b) used in Table 3); NOþ(H2O)3: 33,
55, 62, 77, 108, 195, 208, 256, 290, 320, 365, 374, 407, 524, 811,
919, 1006, 1594, 1647, 1660, 2040, 3154, 3272, 3789, 3800, 3896,
3910 (corresponds to the “trigonal structure model” (c) used in
Table 3); NOþ(H2O)3: 6.4 [25], 16.1 [25], 48, 67, 108, 116, 181,
184, 189, 210, 275, 321, 324, 326, 343, 347, 1648, 1651, 1653,
2150, 3791, 3792, 3793, 3899, 3899, 3900 (corresponds to the
“Cs structure model” (d) used in Table 3); NOþ(H2O)4: 25, 45,
64, 96, 110, 144, 201, 209, 211, 232, 240, 267, 301, 304, 322, 368,
446, 526, 592, 660, 804, 913, 1635, 1637, 1658, 1687, 2070, 3417,
3472, 3552, 3810, 3850, 3852, 3859, 3922 (corresponds to the
“ring þ 1 down front structure model” (e and f) used in Table 3).
Rotational constants (in cmꢀ1). NOþ: 2.00; H2O: 27.9, 14.5,
9.28; NOþ(H2O): 1.98, 0.23, 0.21; NOþ(H2O)2: 0.22, 0.177,
0.107; NOþ(H2O)3 (trigonal): 0.122, 0.067, 0.045; NOþ(H2O)3
(ring): 0.167, 0.076, 0.055; NOþ(H2O)3 (Cs): 0.101, 0.079, 0.050;
NOþ(H2O)4 (ring þ 1 down front): 0.115, 0.034, 0.031.
Frequencies and rotational constants for NOþ and H2O
are from the JANAF tables,28 for NOþ(H2O)n from CCSD
calculations, for details see Relph et al.9 and part II; for NOþ-
(H2O)2, [25] signals nearly free rotation.
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McCoy, A. B.; Steele, R. P.; Schofield, D. P.; Jordan, K. D.; Viggiano,
A. A.; Ferguson, E. E.; Johnson, M. A. Science 2010, 327, 308.
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2011, 13, 1590.
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M. S.; Okumura, M. J. Chem. Phys. 1994, 100, 7153.
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Ed.; National Technical Information Service: Springfield, VA, 1985.
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Smith, D.; Su, T. J. Chem. Phys. 1990, 93, 1149.
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Dissociation energies (at 0 K, in kcal molꢀ1). NOþ(H2O):
19.2; NOþ(H2O)2: 15.1; NOþ(H2O)3 (ring); 14.4, NOþ(H2O)3
(trigonal): 13.3; NOþ(H2O)3 (Cs): 13.6, NOþ(H2O)4 (ringþ1
down front f NOþ(H2O)3 (Cs)): 12.2; NOþ(H2O)4 (ring þ 1
down front f NOþ(H2O)3 (trigonal)): 12.4; from RI-MP2/aug-
cc-pVTZ calculations of this work, for details see Relph et al.9 and
part II; the NOþ(H2O)4 value coincides with that from Asada
et al.10
(24) Troe, J. J. Phys. Chem. 1979, 83, 114.
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(26) Troe, J.; Ushakov, V. G. J. Phys. Chem. A 2009, 113, 3940.
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(28) JANAF Thermochemical Tables, 4th ed.; Chase, M. W., Ed.;
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Anharmonicity factors: Fanh ≈ 1.66, estimated as for H2O2 and
H2CO26 and for HNO3;25 see text.
Langevin collision frequencies Z for M = He (in cm3
moleculeꢀ1 sꢀ1): 5.5 ꢁ 10ꢀ10 for n = 1 and 2; 5.4 ꢁ 10ꢀ10 for
n = 3 and 4.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: afrl.rvb.pa@hanscom.af.mil.
’ ACKNOWLEDGMENT
The AFRL authors are grateful for the support by the Air
Force Office of Scientific Research of this work. N.E. acknowl-
edges funding from the Institute for Scientific Research of Boston
College (FA8718-04-C-0055) and the Air Force Summer Fa-
culty Fellowship Program. Financial support by the European
Office of Aerospace Research and Development (Grant Award
No FA 8655-10-1-3057) is also gratefully acknowledged.
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