Electron Diffraction Self-Imaging of Molecular Fragmentation in
Two-Step Double Ionization of Water
H. Sann,1T. Jahnke,1T. Havermeier,1K. Kreidi,1C. Stuck,1M. Meckel,1M.S. Scho ¨ffler,1N. Neumann,1
R. Wallauer,1S. Voss,1A. Czasch,1O. Jagutzki,1Th. Weber,1H. Schmidt-Bo ¨cking,1S. Miyabe,2
D.J. Haxton,2A.E. Orel,3T.N. Rescigno,2and R. Do ¨rner1,*
1Institut fu ¨r Kernphysik, J.W. Goethe Universita ¨t, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany
2Lawrence Berkeley National Laboratory, Chemical Sciences and Ultrafast X-ray Science Laboratory,
Berkeley, California 94720, USA
3Department of Applied Science, University of California, Davis, California 95616, USA
(Received 10 December 2010; published 29 March 2011)
We doubly ionize H2O by single photon absorption at 43 eV leading to Hþþ OHþ. A direct double
ionization and a sequential process in which single ionization is followed by rapid dissociation into a
proton and an autoionizing OH?are identified. The angular distribution of this delayed autoionization
electron shows a preferred emission in the direction of the emitted proton. From this diffraction feature we
obtain internuclear distances of 700 to 1100 a.u. at which the autoionization of the OH?occurs. The
experimental findings are in line with calculations of the excited potential energy surfaces and their
DOI: 10.1103/PhysRevLett.106.133001PACS numbers: 33.80.Eh, 33.15.Dj
emission of an autoionization electron, once the excitation
energy is above the ionization potential. If the excited
system however is positively charged, autoionization can
be energetically blocked by the coulomb attraction.
This coulomb blockade is lifted if the excited system
neutralizes by emission of a cation. After the cation has
taken the positive charge far enough away, the blocked
autoionization channel of the now neutral system can open
leading to a time delayed emission of a low energy auto-
ionization electron. Experimental evidence for this very
general scenario has been reported in pioneering experi-
ments on photo double ionization of water  and has been
confirmed for other small molecules [2,3]. For O2such
time delayed autoionization has recently been followed in
real time .
In the present letter we show that the time delayed auto-
this autoionization electron. It shows a pronounced peak in
the direction to which the positive charge has left the
system. If the cation is far (> 200 a:u:) from the excited
neutral fragmentwhenthelatter autoionizes,theslowauto-
ionization electron takes a characteristic diffraction image
of the expelled cation.
To this end we doubly photoionize H2O at a photon
energy of h? ¼ 43 eV. Above the vertical double ioniza-
tion threshold of approximately 39 eV [1,5] the ejection of
the two electrons can either be simultaneous [Eq. (1)],
moderated by electron correlation, or via the two-step
process introduced above [Eq. (2)].
h? þ H2O ! Hþþ OHþþ 2e?;
h? þ H2O ! Hþþ OH?þ e?! Hþþ OHþþ 2e?:
The latter process has a threshold at 34.4 eV [1,2,5].
By detecting the directions and energies of all particles
in coincidence we distinguish pathways (1) and (2). We
select events where the double ionization occurs in two
steps and measure the energy and angular distribution of
the autoionization electron with respect to the direction in
which the proton is expelled.
The experiment was performed at the BESSY synchro-
tron radiation source U125/2 SGM in single bunch
Linearly polarized photons are focussed into a supersonic
H2O gasjet,prepared byexpandingwater vapourthrougha
60 ?m nozzle at a temperature of 110?C. Electrons and
ions created in the interaction region are guided by homo-
genous electric (E ¼ 10 V=cm) and magnetic fields
(B ¼ 7 Gauss)ontotwoRoentdekpositionsensitivemulti-
hit micro channel plate detectors . The electron arm of
the analyzer employed McLaren-time focussing  and a
hexagonal delayline anode  was used in order to reduce
the dead time of the electron detector.
In Fig. 1 we show the energy correlation between the
electrons and ions. We exploit this information to identify
the final states and distinguish channel (1) from (2). By
energy conservation, the final energy (electronic þ
vibrational þ rotational) of the OHþis given by
EOH¼ h? ? Eb? IPH? IPOH? KER ? E1? E2; (3)
where Eb¼ 5:1 eV is the dissociation energy needed to
split H2O to H and OH, IPH¼ 13:6 eV and IPOH¼
13:0 eV are the ionization potentials of ground-state
PRL 106, 133001 (2011)
PHYSICAL REVIEW LETTERS
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? 2011 American Physical Society
H and OH, KER is the measured kinetic energy release of
energies of the two electrons. Figure 1(a) shows that the
1?). As one can see the KER distribution is very different
for the two final states of OHþ. To unravel the correspond-
of the two electrons versus the KER. For events leading to
the X3??groundstate this is shown in Fig. 1(b). Byenergy
conservation the region of valid events is constrained by
the diagonal indicated in the figure (h? ? Eb? IPH?
IPOH¼ 11:3 eV).ThepeakatKER ¼ 6:5 eVcorresponds
Such continuous energy distribution is characteristic of a
direct double ionization where both electrons are ejected
simultaneously, mediated byelectron correlation. This
is in striking contrast to the energy distribution in the
interval KER ¼ 1–6 eV. In this region a low energy
electron is created which is almost independent of the
KER associated with a fast electron whose energy is
roughly 10.5 eV—KER. Upon variation of the photon
energy the low energy electron remains unchanged while
the fast electron changes in energy (not shown). From this
we can unambiguously conclude that the fast electron is a
direct photoelectron. The photoabsorption launches the
electron into the continuum and leaves the molecule on a
steeply repulsive region of an H2Oþ?potential energy
surface. The vertical ionization potential which determines
the electron energy then depends on the HO-H bond length
at the instant of photo absorption. The energy of the slow
leading to the1? statewe observe only one peak at KER ¼
6:5 eV with all electron pairs sharing their energy continu-
ously (not shown). This implies that the two-step process
direct process also populates the first excited state. In the
remainder of this letter we will concentrate on events
leading to the ground state.
To identify the states involved in the autoionization we
carried out multireference configuration-interaction calcu-
lations for potential energy curves of H2Oþin this region
[Fig. 2(a)]. We held the H-O-H angle and one OH bond
distance frozen at their H2O equilibrium values. We find
three excited H2Oþstates of 2A0symmetry which all have
substantial oxygen 2s hole character. In the Franck-
Condon region they are 35–39 eV above the H2O ground
state, which leads to the observed photoelectron energies
of 4–8 eV [Fig. 1(b)] at the present photon energy. These
three states, which undergo several avoided crossings as
theH-OH distance increases(marked by circles inFig. 2(a)
], can feed four states which dissociate to Hþþ OH?.
The OH?states—which we identify as ð1?Þ3s, ð1?þÞ3p,
ð1?Þ4s and ð3?Þ3p—are autoionizing states of OH with a
Rydberg electron attached to a bound, excited state of
OHþ. Asymptotically they lie above the3??OHþground
state, so they can decay by autoionization. Since the auto-
ionizing OH?states can be characterized as electron—
OHþscattering resonances, we carried out variational
fixed-nuclei scattering calculations using the Complex
FIG. 2 (color online).
vant states of Hþ-OH?. One OH bond distance and the H-O-H
angle are frozen at the H2O equilibrium value. The Franck-
Condon region is indicated by cross-hatched area and circles
denote areas of avoided crossings. Dashed curve is ground-state
H2Oþþ. (b) Electron energy distribution for the region
KER ¼ 2–5 eV.
(a) Potential energy surface of the rele-
FIG. 1 (color online).
OHþand Hþfor photo double ionization of H2O at h? ¼ 43 eV.
(a) Horizontal axis: kinetic energy release, vertical axis: sum
energy of both electrons and both ions. (b) Horizontal axis:
kinetic energy release, vertical axis: energy of one of the two
electrons. In (b) only events leading to the X3??ground state are
Energy correlation of both electrons and
PRL 106, 133001 (2011)
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Kohn method to obtain the energies and widths of the
autoionizating states . The energies of the four auto-
ionizing states involved were consistent with the asymp-
totes shown in Fig. 2(a), while the lifetimes, i.e., the
inverse of the widths, ranged from 50 fs for the ð1?Þ3s
state to several ps for the other states. In the experiment all
of these states will bevibrationally and rotationally excited
(first vibrational excitation in OHþis at 0.37 eV ),
leading to a broad band of initial and final states for an
Auger decay. Our experimental energy resolution is not
sufficient to resolve these final vibrational excitations.
The measured energy distribution of the autoionization
electron is shown in Fig. 2(b). This spectrum only contains
events for which the KER is between 2 and 5 eV. It shows a
steep decrease from zero and an additional feature at about
0.5 eV. According to the Franck-Condon principle ioniza-
tion of the water molecule can take place at internuclear
distances of up to 2 a.u. In ionization processes leading to
the lowest state shown in Fig. 2(a) this corresponds to a
resulting KER of 2 eV. This is in agreement with the
measured minimum KER [Fig. 1(b)].
We get additional information on the decay from the
angular distribution of the low energy autoionization elec-
trons with respect to the momentum vector of the proton
(Fig. 3). It shows an almost isotropic background with a
distinct ‘‘nose’’ in the direction of the proton. We find that
this feature prevails for the whole region of KER ¼
2–5 eV and electron energy from 0.05 to 2 eV. The angular
distribution of the photoelectrons does not have this nose-
like feature (not shown).
Structures intheangular distributionof molecularAuger
electrons are known to originate from several different
effects: (i) the angular part of the wave function of the
decaying state and the hole are imprinted on the Auger
continuum angular distribution , (ii) emission from
indistinguishable centers in the molecule causes interfer-
ence  and (iii) the emerging electron can be multiply
scattered in the molecular potential , as it is also well
known for photoelectron angular distributions . We
now demonstrate that this last effect of electron diffraction
at the distant proton leads to the formation of the noselike
structure. Even for a KER as small as 2 eV, the Hþ-OH
separation is large compared to the extension of the OH?
state which emits the electron. Hence at the distances
where the Auger electron wave experiences the proton,
the potential of the OHþleft behind is to a good approxi-
mation spherically symmetric and the internal structure of
the OHþis less relevant for the scattering. We therefore
compare the data to a simple classical scattering scenario.
We launch electron trajectories radially from a sphere of
1 a.u. centered at the origin. We locate one Coulomb
potential at the origin and a second one simulating the
proton at a distance R. The starting kinetic energy of the
electron is chosen such that the asymptotic energy matches
the observed continuum energy. This classical modelling,
yielding the red line in Fig. 3, reproduces the observed
angular distribution almost exactly. In the simulation we
have used R as a fitting parameter. The experimental
angular resolution is included in the simulation.
Sample trajectories for R ¼ 800 a:u: are shown in
Fig. 4(a). Note that the proton does not act as a lens
focusing the electrons forward  but rather bends the
trajectories with no preference given to the forward direc-
tion. The deflection function, i.e., the asymptotic angle ?f
at which the electron finally escapes as a function of the
angle ?iat which it was originally launched from the
origin, is shown in Fig. 4(b). For the large distance chosen
here the deflection function obtained for this two center
scenarioisveryclose tothe pureRutherfordscattering case
in which the additional Coulomb potential at the origin is
neglected. Isotropic emission of the electron in three di-
mensions means constant flux into all solid angle elements
d? ¼ 4?sinð?Þd?d? ¼ 4?dcos?d?. If this solid angle
effect is taken into account, the bending of an electron
trajectory initially emitted on the cone at a particular value
?iinto the final forward direction (?f¼ 0) leads to the
increase of flux in the forward direction and the formation
of the nose. The fraction of flux in the forward direction,
i.e., the size of the nose, decreases with internuclear dis-
tance and electron energy [Fig. 4(c)]. We use the calculated
dependence of the size of the nose on energy and R to
estimate the distance Rdecay. The experimental values for
the size of the nose, i.e., the fraction of the total electron
flux into 4? which is in the peak as a function of electron
energy is shown by the symbols in Fig. 4(c). As expected
FIG. 3 (color online).
tween the electron and the proton direction for electron energies
between 0.2 and 0.6 eVand KER between 2 and 5 eV. Black dots
experiment, red line classical simulation for electron energy of
0.2–0.6 eV and internuclear distance R ¼ 800 a:u: at the instant
of autoionization. The simulation is convoluted with the experi-
mental angular resolution.
Measured distribution of the angle be-
PRL 106, 133001 (2011)
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for Rutherford scattering and also seen in the simulations,
decreases with increasing electron energy. Comparing
the simulations with the data, we obtain a value of Rdecay¼
700–1100 a:u:. Since the KER is measured, we can convert
this to a time. A KER of 3 eVand a internuclear distance of
800 a.u. correspond to a delay time of approximately 2 ps
between the photo absorption and the autoionization.
In conclusion, we take advantage of an anisotropy in the
electron angular distribution to probe the distance between
a proton and an autoionizing fragment in a dissociating
molecular ion at the time when autoionization takes place.
We emphasize that our experiment observes the proton in
the diffraction pattern, something commonly taken to be a
weak signal because scattering scales with the charge
squared. We believe that the observed forward electron
flux in the direction of the broken bond is rather general.
It should occur whenever a positively charged fragment is
emitted from a molecule or cluster and at a later time
electrons are emitted. In this case the delayed electron
will trace the direction of the positive fragment. This
should hold, for example, for multiple ionization of clus-
ters. This effect will also be important in all time resolved
photoionization and fragmentation experiments as they
will become possiblewith the new FEL or higher harmonic
sources. Here a first pulse can initiate ionization and dis-
sociation and the second, time delayed pulse will emit a
second photoelectron. Based on our observations we pre-
dict that the forward electron flux observed in the present
experiment will be ubiquitous in such time resolved elec-
tron diffraction experiments.
We want to thank the staff of BESSY II for experimental
support. This work was funded by the Deutsche
Forschungsgemeinschaft and by BMBF. R.D. acknowl-
edges the hospitality of the Division of Chemical
Sciences at LBNL during a sabbatical stay. Work at
LBNL performed under the auspices of the U.S. DOE
and supported by the OBES, Division of Chemical
Sciences under contract DE-AC02-05CH11231.
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electron energy (eV)
fraction of flux in nose
Fraction of flux in nose
FIG. 4 (color online).
0.4 eV. Two coulomb charges are located at the origin and at
x ¼ 800 a:u: and y ¼ 0 a:u:. The electron trajectories are
launched at a radius of 1 a.u. around the origin (see text).
(b) Deflection function, i.e., cosine initial emission angle versus
cosine of asymptotic final angle for electron energy of 0.4 eVand
R ¼ 800 a:u:. (c) Ratio of the flux in the noselike structure (after
subtraction of the isotropic background) and the total flux in 4?
as a function of electron energy. Lines: simulation for different
R. Circles: experimental data.
(a) Sample trajectories for an electron of
PRL 106, 133001 (2011)
1 APRIL 2011