Hot water from cold. the dissociative recombination of water cluster ions

Article abstract of DOI:10.1021/jp9095979

Dissociative recombination of the Zundel cation D₅O2⁺ almost exclusively produces D + 2 D₂O with a maximum kinetic energy release of 5.1 eV. An imaging technique is used to investigate the distribution of the available reaction energy among these products. Analysis shows that as much as 4 eV can be stored internally by the molecular fragments, with a preference for producing highly excited molecular fragments, and that the deuteron shows a nonrandom distribution of kinetic energies. A possible mechanism and the implications for these observations are addressed.

Full text of DOI:10.1021/jp9095979

J. Phys. Chem. A 2010, 114, 4843–4846
4843
Hot Water from Cold. The Dissociative Recombination of Water Cluster Ions†
R. D. Thomas,*,‡ V. Zhaunerchyk,‡,∇ F. Hellberg,‡ A. Ehlerding,‡ W. D. Geppert,‡ E. Bahati,§
§
§
§
|
⊥
⊥
¨
M. E. Bannister, M. R. Fogle, C. R. Vane, A. Petrignani, P. U. Andersson, J. Ojekull,
J. B. C. Pettersson,⊥ W. J. van der Zande,# and M. Larsson§
Department of Physics, Stockholm UniVersity, SE-106 91 Stockholm, Sweden, Physics DiVision, Oak Ridge
National Laboratory, Oak Ridge, Tennessee 37831-6377, USA, FOM Instituut AMOLF, Kruislaan 407, 1098 SJ
Amsterdam, The Netherlands, Department of Chemistry, Atmospheric Science, UniVersity of Gothenburg,
SE-412 96 Gothenburg, Sweden, and Institute for Molecules and Materials, Radboud UniVersity Nijmegen, P.O.
Box 9010, NL-6500 GL Nijmegen, The Netherlands
ReceiVed: October 7, 2009; ReVised Manuscript ReceiVed: January 15, 2010
Dissociative recombination of the Zundel cation D5O+2 almost exclusively produces D + 2 D2O with a maximum
kinetic energy release of 5.1 eV. An imaging technique is used to investigate the distribution of the available
reaction energy among these products. Analysis shows that as much as 4 eV can be stored internally by the
molecular fragments, with a preference for producing highly excited molecular fragments, and that the deuteron
shows a nonrandom distribution of kinetic energies. A possible mechanism and the implications for these
observations are addressed.
Introduction
would terminate clustering, preventing further growth.14 Indeed,
the DR of n ) 2-6 clusters efficiently leads to the predominant
Gas-phase molecular clusters represent a way of studying
phenomena of interest in bulk but with the precision of gas-
phase methods. Water cluster ions, that is, H+ (H2O)n, are one
of the most important examples of such species, as n increases
they span the range between gas and condensed phase systems.
The high mobility and structure of the hydrated proton in water
have long puzzled researchers. The large proton affinity of H2O
means the proton cannot exist in isolation, and the smallest water
clusters vary between proton-bridge structures, for example, the
“Zundel” cation (H+ (H2O)2, n ) 2), and oxonium ion (H3O+,
n ) 1) centered, for example, the “Eigen” cation (H3O+ (H2O)3,
n ) 4). Liquid-phase experiments show the transition time scale
between the Zundel and Eigen forms is fast, with proton transfer
occurring in less than 100 fs, and that the delocalized proton’s
zero-point energy is important; for example, in the Zundel cation
the proton essentially rattles around in-between the two oxygen
atoms without any effective potential barrier,1,2,4–8 highlighting
the complicated nature of these systems.1–3 Proton motion is
then significant in any dynamics4,6–8 and the Zundel cation
represents the ideal system for investigating these dynamics.
Water cluster ions occur naturally in the D region of the
earth’s atmosphere (60-90 km)9 and nominally reach a cluster
size of n ) 6 though in the cold polar regions clusters up to n
) 21 have been observed.10 In the top few kilometers of the D
region the electron density decreases by almost an order of
magnitude. The dominant mechanism behind this decrease is
dissociative recombination (DR).11 In DR, a molecular ion
recombines with a free electron and dissociates into neutral
products (see e.g., refs 12–13). DR with water cluster ions
(>80%) production of nH2O + H.3,15,16 Extensive mid-infrared
lasing by water molecules has been reported in a supersonic
plasma expansion where it was suggested that the necessary
population inversion could be produced through the DR of water
cluster ions17 since DR is known to lead to population inversions
and strong mid-IR to far-IR laser action in H atoms.18 The DR
of the fully deuterated Zundel cation, chosen for experimen-
tal reasons,3,12 produces almost exclusively (>95%) two D2O
molecules and a D atom, with a maximum kinetic energy release
of 5.1 eV. By revealing the dynamics occurring in this reaction
we report here on the distribution of the available energy in
this channel and furthermore suggest a mechanism capable of
explaining the observation of the lasing lines in a water plasma
as well as shine light on the elusive nature of the solvated proton.
Experimental Section
Studies at ion storage rings on the DR of XH+2 type ions,
where X is a heavy atom, for example C, covalently bonded to
two H atoms, show that the H atoms are extremely mobile; X
+ H2 is often observed to be populated at 10% of the reaction
flux.12,13 Several such ions have a linear ionic ground-state
geometry, indicating that extreme bending or tunnelling must
be occurring during the reaction to explain the observation of
this channel. Importantly, similar motion in heavier systems,
for example, CO+2 to form C-O2, has never been observed12
pointing to the mobile and quantum nature of the H atom.
Extreme motion is also observed in the dominant product
channel of these ions (X + 2H)12,19 and so investigating the
dynamics in the dominant channel in the DR of the Zundel
cation should prove enlightening.
Investigating the internal energy of molecular fragments in
the DR process is difficult and nontrivial from experimental
and theoretical perspectives. Experimental studies into the DR
of H+3 , H3O+ and CH+5 have shown that vibrationally excited
fragments are produced.21,26,27 A theoretical treatment of the DR
of NH+4 has been reported, both supporting the experimental
† Part of the special section “30th Free Radical Symposium”.
* To whom correspondence should be addressed. E-mail: rdt@fysik.su.se.
‡ Stockholm University.
§ Oak Ridge National Laboratory.
| FOM Instituut AMOLF.
⊥ University of Gothenburg.
# Radboud University.
∇ Current Address: Institute for Molecules and Materials, Radboud
University Nijmegen.
10.1021/jp9095979  2010 American Chemical Society
Published on Web 02/11/2010

4844 J. Phys. Chem. A, Vol. 114, No. 14, 2010
Thomas et al.
Although this assignment procedure generally is not valid,
for example, it is incorrect for linear or close-to-linear
D2O-D-D2O geometries, we motivate its validity in the present
case by demonstrating from analysis of the break-up dynamics
that such geometries are not important in this reaction. One
method often used to visualize break-up dynamics is the Dalitz
plot.12,20–22 The coordinates of the Dalitz plot are defined as
m
m
1
3
η1 )
3(c - b)
(2a)
(2b)
Figure 1. (a) Experimentally measured TTD distribution. (b) TD
distributions for experimental data (solid squares) and data sets
generated from a Monte Carlo simulation which have a contribution
larger than 2% are shown by dashed curves. The quoted energy
corresponds to the kinetic energy given to the fragments in these
contributing data sets. The best-fit is shown by the solid curve.
ꢀ
1
m1
m2
1
3
η2 )
2 +
a - 1
(
[
)
]
where m3 is the D5O2 mass, and a, b, and c are the fraction of
the available kinetic energy, ER, received by the D and two D2O
molecules, respectively, such that a + b + c ) 1. To help with
the analysis, if we define b < c, then conservation of kinetic
energy and momentum dictate that a and b are given by:
result that NH3 + H is the dominant channel and predicting the
reaction-energy partitioning among the products; the dominant
share of the available energy (4.7 eV) is given to vibrational
excitation of the NH3 fragment with an average value of Ev )
4.0 ( 0.2 eV, and little to rotation or translation.28 However,
for H+3 the channel H2 + H does not dominate in zero eV
collisions and for the other ions the amount of energy available
for internal excitation of the molecular product in the dominant
channel is low since multiple covalent bonds are broken. It is
certainly not clear or predictable how the available energy would
be distributed in a cluster ion, in which the structure is deter-
mined by the weakest bonds and the dominant channel involves
breaking two such bonds while still leaving over 5 eV of energy
available for use.
The current experiment has been performed at CRYRING,
Stockholm University, and the facility and experimental pro-
cedures are described in detail elsewhere and are not discussed
here.12 The data were obtained with an imaging detector which
measured only the positions of the neutral products produced
in the reaction, so-called 2D data.12,13
2m2
0 e a e
m3
am (2m - am )
√
1
2
1
2
3
1
2
(1 - a) -
e b e (1 - a)
[
]
m2
(3)
Each point on the Dalitz plot corresponds to a particular
dissociation geometry, illustrated in Figure 2a.
The experimental data are the transverse projections of the
fragment’s com momenta randomly oriented in space with
respect to the detector plane, so to extract the actual dissociation
geometries a Monte Carlo (MC) simulation is used to account
for all possible orientations of the molecular frame as well as
other experimental considerations, that is, it allows us to model
the response of our detector.22,21,22 This approach was first used
by Mu¨ller and Cosby to investigate dynamics in the fragmenta-
Results and Analysis
Defining the total displacement, TD, as
23
0.5
tion of H3 and subsequently has also proven valuable in
m2
TD ) d2D +
(d2(D O) + d2(D O)
)
2
(1)
DR.12,19 The deconvolution procedure described in refs 21 and
24 implies that the experimentally measured Dalitz plot must
be divided by that generated by the MC simulation in which
the break-up molecular geometries were fully randomized. Those
geometries which would be mischaracterised due to the assign-
ment procedure are shown by the blank regions in Figure 2b.
Figure 2c shows simulated data in which the break-up geometry
is completely randomized. Figure 2d plots the ratio of the
experimental data shown in 2b to the simulated data shown in
Figure 2c and so reflects the real fragmentation dynamics.
Analysis indicates that the fragmentation is not random but that
the distribution of deuteron kinetic energies shows definite
structure.
(
)
2
1
2
m1
where m1 and m2 are the D and D2O masses, respectively, and
dx is the distance of fragment x from the center-of-mass (com),
the kinetic energy available to the fragments can be found, that
is, small TD means less kinetic energy is released and higher
internal excitation of the water molecules. To establish a com
position the fragments must be identified, and since this is not
explicitly possible the following approach is employed. The
three fragments define the break-up triangle and the length of
each side is histogrammed, TTD. The TTD distribution for all
accepted events is plotted in Figure 1(a). Analysis of this
distribution shows two peaks; one at very small and one at very
large distances, and these are expected to correspond to the
D2O-D2O and D-D2O intrafragment separations, respectively.
Based on this, the fragments were assigned in the following
way: the fragment which is further away from the other two
than they are from each other should be D atom. Indeed, if
the fragments receive the same momenta upon break-up, the
displacement of the D will be 10 times larger than those of the
D2O fragments. Having defined the com, the solid squares in
Figure 1b show the experimentally determined TD distribution.
Information about the break-up dynamics can also be obtained
from the distributions of the parameters a and b, which are
independently retrieved in a fashion similar to that utilized for
the Dalitz plot. Figure 3a plots the experimental data while
Figure 3b shows simulated data where one of the investigated
parameters, either a or b, was fully randomized. Normalizing
the experimental data set to the simulated random data set gives
the true distributions and these are shown in Figure 3c. The
kinetic energy of the D atom is not random, showing a broad
peak with a maximum at a ≈ 0.8. These results are consistent

Hot Water from Cold
J. Phys. Chem. A, Vol. 114, No. 14, 2010 4845
Figure 2. Dalitz plots showing: (a) The break-up geometries constructed from the fragment momentum vectors. The momentum of the D atom is
shown in red. (b) The experimental data. (c) The results from the Monte Carlo simulation assuming a random distribution of break-up geometries
in the molecular frame. (d) The real distribution of geometries.
Figure 4. Three internal angles (a) and three distance ratios (b) of the
break-up triangle. Experimental data are given by the solid symbols
and the solid lines show the results from the Monte Carlo simulation.
were extracted: the ratio of the sides in the break-up triangle;
shortest/medium (dSM), shortest/longest (dSL), and medium/
longest (dML), and the three internal angles of this triangle;
largest (AL), medium (AM), smallest (AS). When these parameters
are generated using random distributions of a or b the results
do not fit the experimental observations whereas those obtained
using the normalized distributions shown in Figure 3(c) fit
extremely well, and these results are shown (solid lines) in
Figure 4 together with the experimentally determined distribu-
tions (solid symbols). The method of particle assignment will
always be wrong for linear or close-to-linear D2O-D-D2O
geometries. However, the lack of a peak at large internal angles
(Figure 4a) allowed us to conclude that the molecule hardly
ever dissociates from such geometries. As such, the particle
assignment procedure used in calculating TD is reliable for
Figure 3. The parameters a and b represent the energy sharing between
the three fragments. The top plot (a) shows the experimental data, the
middle plot (b) shows data from the Monte Carlo simulation for which
all allowed values of one of the investigated parameters, a or b, are
equally probable. The bottom plot (c) shows the result obtained when
the experimental data (a) is normalized by the simulated data (b). In
each plot a and b are shown as solid circles and squares, respectively.
with the derived distributions in the Dalitz plot. According to
eq 2a, the range of a values from 0.75 to 0.9 will correspond to
η2 values ranging from 0.19 to 0.3. Furthermore, if additionally
we consider distribution of parameter b in the range of
0.025-0.075 with a being 0.8, the corresponding η1 values are
from 0.08 to 0.23.
2
almost all of the events analyzed. Since TD is directly
It is instructive to verify the validity of the fragment
assignment procedure. The derived a and b distributions were
used as input parameters for the simulation that generated break-
up triangles defined by the three fragments, and the following
sets of parameters, which are independent of particle assignment,
proportional to ER, distribution of the available reaction energy
can now be investigated by analysis of the TD data without
biasing the results. It is important to point out that the Dalitz
plot is probably more accurate when obtaining dynamical
information, since it shows the correlation between the a and b

4846 J. Phys. Chem. A, Vol. 114, No. 14, 2010
Thomas et al.
parameters. However, the main reason to retrieve the a and b
parameters independently was to use them in the Monte Carlo
simulation to check the validity of the assignment procedure
and to obtain the TD distributions.
Conclusion
Excited water molecules are efficiently produced in the DR
of the Zundel cation and, furthermore, are created with a
nonthermal vibrational population. We conclude that only the
indirect DR process through excitation of the proton motion is
capable of creating the states necessary to produce the rovibra-
tionally excited water molecules, in a collisional process similar
to that observed by Leone and co-workers,25 and that the
subsequent decay of these states could also explain the observed
mid-infrared lasing reported in a supersonic plasma expansion.17
Although it cannot be ruled out that the deuterons produced in
the reaction excite other water molecules in the plasma, analysis
shows that they would have a broad range of kinetic energies
much less than 1.8 eV and, since it is predicted that the
efficiency of the excitation is sensitive to the translational
energy,25 it is not clear that this would be sufficient to explain
the observed lasing and so plasma modeling is necessary to
determine the effectiveness of this process. In either case, DR
would be the initial reaction mechanism responsible for the
observed lasing.
Due to the experimental conditions and the small difference
between ro-vibrational energy levels, TD distributions are
generated by the simulation for values of ER from 0 to 5.1 eV
in steps of 0.3 eV. The individual distributions are then scaled
and the sum is compared with the experimental data. The relative
contribution of each channel to the best-fit summed distribution
can then be extracted. The results are shown in Figure 1b, where
the dashed lines plot individual distributions, the solid line are
the best-fit sum, and the relative contribution of each channel
is also given. Analysis shows that as much as 4 eV is partitioned
into internal excitation of the water molecules and that low
excited states are not significantly populated.
Discussion
In the Zundel cation the proton oscillates back and forth
between the two water molecules over an almost barrier-less
potential surface.4–8 In direct DR, the neutral system is created
directly on a repulsive surface which promptly dissociates.12,13
Here, this will map each D2O with their Zundel ion-geometry
onto the ground state D2O surface. However, since the differ-
ences in the bond-lengths and internal angles between these two
states are significantly less than 10%,5 this mechanism would
induce very little excitation in the fragments and so is unlikely
to be the relevant mechanism here. In indirect DR, the electron
excites nuclear motion and is captured into a vibrationally
Acknowledgment. The authors thank the CRYRING staff
at the Manne Siegbahn Laboratory for their tireless work and
excellent support. This work was supported by the Swedish
Research Council and STINT. RDT is funded under the IHP
Programme of the EC under contract HPRN-CT-2000-00142.
The work of WJvdZ is part of the research of the “Stichting
voor Fundamenteel Onderzoek der Materie”. EB, MEB, MRF,
and CRV are supported by the U.S. DOE, Office of Basic
Energy Sciences under contract DE-AC05-00OR22725 with UT-
Battelle, LLC.
+
excited Rydberg state.12,13 For a Rydberg state with D5O2 as
the ion core, if it is the proton’s motion which is vibrationally
excited, the weak potential surface would allow the proton to
undergo multiple high-energy collisions with the water mol-
ecules before the system dissociates. Leone and co-workers
reported that translational-to-vibrational energy transfer in
collisions of 2.2 eV H atoms with H2O molecules was extremely
effective, and multiple emitting states with high vibrational and
rotation quantum numbers were observed to be created in these
collisions.25 Here, this would create the highly rovibrationally
excited water molecules which are observed experimentally.
Since these states are created in a similar collision mechanism
to that investigated by Leone and co-workers, the subsequent
decay of these states could also be responsible for the lasing
observed in the experiments of Saykally and co-workers and
confirm DR as the responsible reaction mechanism.17,25 It cannot
be ruled out that the deuteron leaves without interacting and
excites other water molecules. However, (Figure 3c) the fraction
of the kinetic energy taken by the deuteron is very broad and
although it peaks at ≈ 0.85, the actual kinetic energy available
to the fragments (Figure 1b) is predominantly less than 1.8 eV,
implying that the majority of deuterons are produced with kinetic
energies much less than 1.5 eV, and the efficiency of impulse-
excitation is predicted to be sensitive to the translational
energy.25
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JP9095979