applied
sciences
Review
Molecular Dynamics of XFEL-Induced
Photo-Dissociation, Revealed by Ion-Ion
Coincidence Measurements
Edwin Kukk 1, *, Koji Motomura 2 , Hironobu Fukuzawa 2,4 , Kiyonobu Nagaya 3,4 and
Kiyoshi Ueda 2,4
1
2
3
4
*
Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland
Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan;
[email protected] (K.M.); [email protected] (H.F.); [email protected] (K.U.)
Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan;
[email protected]
RIKEN Spring-8 Center, Sayo, Hyogo 679-5148, Japan
Correspondence: [email protected]
Academic Editor: Malte C. Kaluza
Received: 24 March 2017; Accepted: 12 May 2017; Published: 19 May 2017
Abstract: X-ray free electron lasers (XFELs) providing ultrashort intense pulses of X-rays have
proven to be excellent tools to investigate the dynamics of radiation-induced dissociation and
charge redistribution in molecules and nanoparticles. Coincidence techniques, in particular multi-ion
time-of-flight (TOF) coincident experiments, can provide detailed information on the photoabsorption,
charge generation, and Coulomb explosion events. Here we review several such recent experiments
performed at the SPring-8 Angstrom Compact free electron LAser (SACLA) facility in Japan, with
iodomethane, diiodomethane, and 5-iodouracil as targets. We demonstrate how to utilize the
momentum-resolving capabilities of the ion TOF spectrometers to resolve and filter the coincidence
data and extract various information essential in understanding the time evolution of the processes
induced by the XFEL pulses.
Keywords: free electron laser; Coulomb explosion; radiation damage; molecular dynamics; X-ray
absorption; ultrafast dissociation; coincidence; photoion-photoion coincidence (PIPICO); ion mass
spectroscopy; time-of-flight
1. Introduction
Nuclear motion in molecules and clusters takes place in a timescale starting from a few
femtoseconds. Photoinduced nuclear dynamics—isomerization, bond breakage and dissociation,
Coulomb explosion of molecules and clusters, chemical reactions—have long been of particular interest
from both the fundamental and applied points of view [1–3]. In order to accurately observe such
motion and trace its development, a sufficiently short initiating pulse of radiation is needed as not to
obscure the real dynamics. Lasers have provided such an excitation source. The advent of free electron
lasers (FELs) operating in the UV- and X-ray regime, however, opened up completely new avenues,
providing access to tunable atomic inner-shell multiphoton excitation and ionization in femtosecond
timescales [4–11]. In the present paper, we focus on the unimolecular dissociation reactions induced
by intense femtosecond-range X-ray pulses of FEL radiation. Specifically, we present examples on
how to extract detailed information about the nuclear, and also the related electron dynamics by
using coincident ion spectroscopy and momentum filtering analysis methods. The full results of these
experiments and their interpretation are published or submitted for publication elsewhere, in [12] for
CH3 I, in [13] for CH2 I2 , and in [14,15] for 5-iodouracil.
Appl. Sci. 2017, 7, 531; doi:10.3390/app7050531
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Appl. Sci. 2017, 7, 531
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In order to reconstruct the dissociation process, as much information as possible should be
gathered from each dissociation event; ideally this means detecting all atomic and molecular fragments
(of all charges), as well as emitted electrons, and measuring their momenta. In practice, it would be
a formidable task for all but the simplest systems and processes. Various experimental set-ups, as
well as analysis methods, have been developed towards this goal. Most usable at FEL sources so
far have been electron and ion time-of-flight (TOF) spectrometers and their various developments,
such as COLTRIMS for ion-electron coincidences [16,17], and magnetic bottle spectrometers for
electrons [18–23].
The results presented in this article are based on experiments performed at SACLA XFEL in
Japan, using momentum-resolving ion TOF spectrometers with multi-ion detection capabilities per FEL
pulse [24]. The multi-ion detection offers the opportunity for performing coincidence (specifically ion-ion
or multi-ion coincidence) analysis. In coincidence methods, each event is analyzed separately, tracing
back the detected ions to a single source—an ionized and subsequently dissociating molecule, cluster,
or nanoparticle. By its nature, it is one of the most accurate approaches in experimentally reconstructing
the quantum mechanical event [25–29].
Coincidence experiments at FEL sources also face major challenges. Firstly, the repetition rates of
FEL sources have been relatively low, even as low as 10 Hz for SACLA, which means that collecting
sufficient coincidence data is a lengthy process during the extremely valuable beamtime (once referred
to as a “heroic experiment” by a referee). This limitation is gradually becoming less severe with, for
example, the Linac Coherent Light Source (LCLS) operating at 120 Hz and the European XFEL shortly
starting operations at the planned 27,000 pulses per second. The second limitation is more fundamental,
namely that for efficient coincidence analysis it must be ensured that all detected fragment ions indeed
originate from the same event. Otherwise, the combinations of ions from different sources would be
meaningless and create erroneous data, often referred to as “false coincidences”. It can be a particularly
severe problem at FEL sources, since the pulses have very high photon density (often desirable
for a specific process to occur), creating many ionization events per pulse while, for a coincidence
experiment, the ideal would be a single ionized particle per pulse. As a simplified example, in an
(N+ , N+ ) coincidence analysis of the photodissociation of N2 , only 20% are proper (“true”) coincidences
if three molecules are ionized by the FEL pulse; and only 2% if 25 molecules are ionized. In the latter
regime (which is not uncommon in a FEL experiment), coincidence analysis would be overwhelmed
by the false coincidences, without additional means of distinguishing them from the true ones.
One solution to this predicament is to perform covariance analysis, in which statistically significant
relationships between various detected particles are looked for, not on an event-by event basis, but by
using statistical analysis methods [30–34]. Covariance analysis has been shown to extract useful
information even from datasets with high ionization rates per pulse. The second solution is to utilize
additional information in sorting the raw data into coincidence events. Modern ion TOF spectrometers
equipped with accurate position-sensitive detectors are capable of recording the data for complete
ion momentum reconstruction. On the same example of N2 above, one can confidently assume that
the true coincident ions should have the momentum vectors antiparallel and of equal length, as to
satisfy the momentum conservation. That condition can be used as a very efficient filter, dramatically
increasing the true/false coincidence ratio and making a coincidence analysis possible at seemingly
too high ionization rates. Naturally, the above example is trivial, but similar physically justified
momentum filtering (hereafter referred to as MF) conditions can often also be found in significantly
larger systems.
In the present paper, we present three systems of increasing complexity (Figure 1)—iodomethane
(CH3 I) possessing a three-fold symmetry axis, diiodomethane (CH2 I2 ) with two symmetry planes, and
a planar molecule 5-iodouracil (C4 H3 IN2 O2 ). We show how multi-ion coincidence analysis can be
applied in combination with the MF as a powerful tool for extracting information on femtosecond-scale
molecular dynamics.
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Figure 1. The molecules studied: (a) iodomethane, (b) diiodomethane, and (c) 5-iodouracil.
Figure
Figure 1. The
The molecules
molecules studied:
studied: (a)
(a)iodomethane,
iodomethane,(b)
(b) diiodomethane,
diiodomethane, and
and (c)
(c) 5-iodouracil.
5-iodouracil.
Pink—iodine, blue—nitrogen, red—oxygen, gray—carbon, and light gray—hydrogen.
Pink—iodine, blue—nitrogen,
blue—nitrogen, red—oxygen,
red—oxygen, gray—carbon,
gray—carbon, and light gray—hydrogen.
Pink—iodine,
2. Materials and Methods
2.
2. Materials
Materialsand
andMethods
Methods
The experiments were carried out at beam line 3 (BL3) of the SACLA X-ray free electron laser
The
experiments
were
carried out
at at
beam lineline
3 (BL3)
of the
X-ray free electron
laser
Thefacility
experiments
were
out
3 (BL3)
of SACLA
the
SACLA
free electron
(XFEL)
[35] and
arecarried
described
in beam
detail in [12–15].
The
XFEL
beamX-ray
is focused
by the
(XFEL)
facility
[35]
and
are
described
in
detail
in
[12–15].
The
XFEL
beam
is
focused
by
laser
(XFEL) facility
[35]
and are
described
in detail
in about
[12–15].
The(FWHM)
XFEL beam
is focused
by the
the
Kirkpatrick-Baez
(KB)
mirror
system
to a focal
size of
1 μm
diameter.
The photon
Kirkpatrick-Baez
(KB)
mirror
system
to
aa focal
size
of
about
11 μm
(FWHM)
diameter.
The
photon
Kirkpatrick-Baez
(KB)
mirror
system
to
focal
size
of
about
µm
(FWHM)
diameter.
The
photon
energy was set to 5.5 keV and the photon bandwidth was about 40 eV (FWHM). The repetition rate
energy
was
to
keV
and
the photon
bandwidth
energy
was set
set
to 5.5
5.5was
keV10
and
bandwidth was
was about
about 40
40 eV
eV (FWHM).
(FWHM). The
The repetition
repetition rate
rate
of the XFEL
pulses
(forthe
CHphoton
3I and 5-iodouracil) or 30 Hz (for CH2I2). The pulse duration was
2). The pulse duration was
of
the
XFEL
pulses
was
10
(for
CH
3
I
and
5-iodouracil)
or
30
Hz
(for
CH
2
I
of
the XFEL
was10
10 fs.
(forThe
CHpeak
5-iodouracil)
or 30 Hzto(for
I2 ). The
duration
2 inpulse
3 I and
estimated
topulses
be about
fluence
was estimated
be CH
26 2μJ/μm
the CH
3I and
2 2in the CH3I and
estimated
to betoabout
10 fs.
The
peak
fluence
was
estimated
to
be
26
μJ/μm
was
estimated
be
about
10
fs.
The
peak
fluence
was
estimated
to
be
26
µJ/µm
in
the
CH
3 I and
5-iodouracil experiment, and 26 μJ/μm2 in the CH2I2 experiment.
2 2in the CH2I2 experiment.
5-iodouracil
experiment, and
μJ/μm
5-iodouracil
and 26
26
µJ/µm
in the CH
I2 experiment.
The gasexperiment,
phase samples
were
introduced
to 2the
focal point of the XFEL pulses as a pulsed
The
gas
phase
samples
were
introduced
to
the
focal
point
the XFEL
The
gas
phase
samples
were
introduced
to
the
focal
point of
of
XFEL pulses
pulses as
as arecoil
a pulsed
pulsed
supersonic gas jet seeded by helium gas. The ions were
detected
by the
a multi-coincidence
ion
supersonic
gas
jet
seeded
by
helium
gas.
The
ions
were
detected
by
aa multi-coincidence
multi-coincidence recoil
ion
supersonic
gas
jet
seeded
by
helium
gas.
The
ions
were
detected
by
recoil
momentum spectrometer to measure three-dimensional momenta of each fragment ion (see Figureion
2).
momentum
spectrometer
to
measure
three-dimensional
momenta
ofofeach
fragment
ion
(see
Figure
2).2).
momentum
spectrometer
to
measure
three-dimensional
momenta
each
fragment
ion
(see
Figure
The molecular beam was crossed with the focused XFEL beam at the reaction point and the
The
molecular
beam
crossed with
focused
XFEL
at
the
point
and
Theions
molecular
beam was
was
with the
the
focused
XFEL beam
beam
at (MCP)
the reaction
reaction
point
and the
thea
emitted
were projected
bycrossed
electric fields
onto
a microchannel
plate
detector
in front
of
emitted
ions
were
projected
by
electric
fields
onto
aa microchannel
plate
(MCP)
detector
in
front
of
aa
emitted
ions
were
projected
by
electric
fields
onto
microchannel
plate
(MCP)
detector
in
front
of
delay-line anode (Roentdek HEX80, by RoentDek Handels GmbH, Kelkheim, Germany). We used
delay-line
anode
(Roentdek
HEX80,
by
RoentDek
Handels
GmbH,
Kelkheim,
Germany).
We
used
delay-line
anode (Roentdek
RoentDek
Handels
GmbH,
Germany).
We used
velocity-map-imaging
(VMI)HEX80,
electricby
field
conditions.
Signals
from Kelkheim,
the delay-line
anode and
MCP
velocity-map-imaging
(VMI)
electric
field
conditions.
Signals
from
the
delay-line
anode
and
MCP
velocity-map-imaging
(VMI)
electric
field
conditions.
Signals
from
the
delay-line
anode
and
MCP
were recorded by a digitizer and analyzed by a software discriminator. The arrival time and
the
were
recorded by
byaadigitizer
digitizerand
and
analyzed
by
a software
discriminator.
The arrival
timethe
and
the
were
recorded
analyzed
by
a
software
discriminator.
The
arrival
time
and
arrival
arrival position of each ion were determined and allowed us to extract the three-dimensional
arrival
position
of each
ion were determined and allowed us to extract the three-dimensional
position
of each
ion
were
momentum
of each
ion. determined and allowed us to extract the three-dimensional momentum of
momentum
each ion. of each ion.
Figure 2. Sketch of the experimental setup at SPring-8 Angstrom Compact free electron LAser (SACLA).
Figure 2. Sketch of the experimental setup at SPring-8 Angstrom Compact free electron LAser (SACLA).
Figure 2. Sketch of the experimental setup at SPring-8 Angstrom Compact free electron LAser (SACLA).
An
An essential
essential element
element in
in interpreting
interpreting the
the observations
observations in
in all
all three
three cases
cases was
was aa comparison
comparison with
with aa
Ansimple
essential
elementexplosion
in interpreting
the
observations
in all threemomentum
cases was a vector
comparison
with a
rather
Coulomb
model,
predicting
the
fragments’
correlations,
rather simple Coulomb explosion model, predicting the fragments’ momentum vector correlations,
rather
simple Coulomb
explosion
model,
predicting
theproved
fragments’
momentum
correlations,
magnitudes
quick,
empirical
models
an invaluable
aid vector
in
analysis
and
magnitudesand
andgeometry.
geometry.Such
Such
quick,
empirical
models
proved
an invaluable
aiddata
in data
analysis
magnitudes
and
geometry.
Such
quick,
empirical
models
proved
an
invaluable
aid
in
data
analysis
we,
thus,
summarize
its
main
properties.
The
classical
point
charge
model
assumes
the
source
of
and we, thus, summarize its main properties. The classical point charge model assumes the sourcethe
of
and
we,
thus,creation
summarize
main properties.
Theiodine)
classical
point
charge
assumes
the source of
total
charge
to beits
the
(inheavy
this case
atom,
due
to atom,
its model
much
higher
photoionization
the total
charge creation
toheavy
be the
(in this case
iodine)
due
to its
much higher
the
total charge
creation
to be
the
heavy
(in this
case iodine)
atom, due
to its much
higher
cross-section
at around
5 keV.
The
charge
build-up
is described
statistically
as a smooth
function:
photoionization
cross-section
at around
5 keV. The
charge build-up
is described
statistically
as a
photoionization cross-section at around 5 keV. The
charge
build-up
is
described
statistically
as a
smooth function:
t
smooth function:
Qtot (t) = Qtot, f inal 1 − exp −
,
(1)
τ
( )=
1
−
exp(−
) ,
(1)
,
( )=
1 − exp(− ) ,
(1)
,
Appl. Sci. 2017, 7, 531
4 of 14
where τ is the empirical, adjustable charge build-up constant. In comparison with the experiments,
we found τ close to 10 fs in all cases. The positive charge is multiplied by additional absorption and by
Auger cascades, transferring charge from iodine (QI ) to the rest of the molecule (QX ):
dQ X (t)
= R × Q I ( t ),
dt
(2)
where R is the charge transfer rate—another empirical constant in the model. The fragment
momenta and their correlations is a sensitive function of the charge dynamics and the above-given
model parameters.
3. Results and Discussion
3.1. Iodomethane
CH3 I molecules were irradiated with ultrashort (∼ 10 fs) XFEL pulses of 5.5 keV energy.
The experimental results, as well as the Coulomb explosion modeling, was published in [12]; here we
summarize them as far as necessary for the coincidence analysis’ background.
The molecules absorb X-rays predominantly in the iodine atomic site, where electrons from inner
shells down to I 2p are emitted. Multiphoton absorption occurs during the pulse and the charge is
also further increased by Auger cascades, as demonstrated in the case of xenon—an atom with a
very similar electronic structure [36,37]. The Auger cascades are also the most likely mechanism of
transferring charge to the methyl group of the molecule. The highly-charged molecule undergoes
Coulomb explosion, producing the In+ , Cm+ , and H0,1+ fragments. Ion-ion coincidence analysis of
these fragments was detected by the momentum-resolving ion TOF spectrometer, which then provided
the data to reconstruct the dynamics of the dissociation events.
The ion count per XFEL pulse was quite high, with the average of 7.25 heavy (excluding H+ )
ions/pulse. Assuming an ion collection and detection efficiency of roughly 50% means that in average
of about 7 molecules/pulse were ionized; quite unfavorable conditions for coincidence analysis.
Under such conditions, the most informative approach was, mainly, to perform a two-particle ion-ion
coincidence (PIPICO) analysis with the help of MF.
A possible pitfall in the MF-enhanced PIPICO lies in carrying over the filtering conditions to the
result and erroneously interpreting the apparent correlations as coincidence information, while they
were just created by the filtering process. To avoid this, we used several strategies. First, the MF can
be performed using only two momentum vector components on the detector plane perpendicular
to the TOF spectrometer’s axis (See Figure 2). That leaves the third axial component undisturbed
and, if a clear PIPICO pattern emerges in the first ion’s TOF versus the second ion’s TOF plot, it is a
confirmation that true coincidence events were found. Second, the measured events can be “scrambled”
by redistributing the individual ions between the events. Scrambling ensures that there are no true
coincident ion pairs left in the data and, thus, all remaining apparent correlations, if any, must be
assigned to the MF action and discarded.
We first present an example of the analysis of a coincident pair (I5+ , C2+ ) that has the best counting
statistics. At first, ion pairs are formed from all events with no filtering nor bias—if, for example,
one iodine and two carbon ions are detected in a pulse, a pair is formed by randomly choosing
one of the carbons. A momentum sum plot is then generated and is shown in Figure 3a, where the
direction of the iodine’s momentum is always pointing along the x-axis. It is seen from Figure 3a,
that there is a diffuse background of uncorrelated momenta and a bright spot that corresponds to
well-correlated momenta. However, the bright spot is not centered at zero; its shift indicates that the
iodine’s momentum is larger than the carbon’s. This is easily understood from the molecular geometry:
both the H+ and C2+ ions balance the momentum of I5+ , but the H+ momenta are not included in the
sum. This “dark” momentum is manifested as the shift of the correlated spot. However, it is also seen
that the spot is well defined in the y-direction, meaning that the three hydrogens carry a concerted
Appl. Sci. 2017, 7, 531
5 of 14
momentum that is directed closely along the C-I bond. In short, the momentum sharing between I and
C ions can be, based on Figure 3a, approximated by a two-body dissociation if the C momentum is
Appl. Sci. 2017, 7, 531
5 of 14
corrected by a dark momentum coefficient k:
Appl. Sci. 2017, 7, 531
5 of 14
1
, =
p I,x =
−(−pC,x ,++3p3H,x,) ==−− pC,x, . .
=− k , .
, =−
, +3
,
Figure 3. Momentum sum plots on the detector plane of the two ions in the (I5+, C2+) coincident pairs
Figure 3. Momentum sum plots on the detector plane of the two ions in5+the (I5+5+, C2+2+) coincident pairs of
Figure
3. Momentum
sum
plots
onrotated
the detector
plane
the two ions
thethe
(I x-direction.
, C ) coincident
pairs
(a) Applying
of iodomethane.
The
pairs
were
to point
theof
momentum
of Iin in
iodomethane. The pairs were rotated to point the momentum of I5+ 5+
in the x-direction. (a) Applying the
in the x-direction.
(a) Applying
of iodomethane.
pairs were
momentum
of I illustrates
the correctionThe
coefficient
k =rotated
1, (b) to
k =point
0.78.the
The
black circle
the strength
of the MF,
correction coefficient k = 1, (b) k = 0.78. The black circle illustrates the strength of the MF, applied later.
theapplied
correction
later.coefficient k = 1, (b) k = 0.78. The black circle illustrates the strength of the MF,
applied later.
As
Asthe
thenext
nextstep,
step,the
thecorrect
correctvalue
valueofofthis
thiscoefficient
coefficientisisdetermined
determinedbybyapplying
applyinga atwo-dimensional
two-dimensional
MF
and
restricting
the
momentum
sum
of
acceptable
pairs
on
the
detector
plane
totoa asmall
Asand
the restricting
next step, the
value of
thisof
coefficient
is determined
applying
a two-dimensional
MF
thecorrect
momentum
sum
acceptable
pairs on thebydetector
plane
smallcircle
circle
around
zero.
The
value
of
the
coefficient
k
is
scanned
and
the
filtered
coincident
pair
count
obtained
for
MF
and
restricting
the
momentum
sum
of
acceptable
pairs
on
the
detector
plane
to
a
small
circle
around zero. The value of the coefficient k is scanned and the filtered coincident pair count obtained
each
value,
with
the
result
shown
in
Figure
4.
It
shows
a
clear
maximum
at
k
=
0.78
±
0.02.
When
we
around
zero.
The
value
of
the
coefficient
k
is
scanned
and
the
filtered
coincident
pair
count
obtained
for each value, with the result shown in Figure 4. It shows a clear maximum at k = 0.78 ± 0.02. When
now
regenerate
the momentum
sum plot
withplot
this
coefficient,
but without
applying
theapplying
MF
(Figure
for
each
value,
with
thethe
result
shown
in sum
Figure
4. Itwith
shows
clear
maximum
at k = 0.78
± 0.02.
When
we
now
regenerate
momentum
thisa coefficient,
but
without
the3b),
MF
it(Figure
has
theregenerate
characteristics
of
a
two-body
process:
a
circular
diffuse
false
coincidence
background
and
the
we
now
the
momentum
sum
plot
with
this
coefficient,
but
without
applying
the
MF
3b), it has the characteristics of a two-body process: a circular diffuse false coincidence
true
coincidence
zero. Misleadingly,
spot
exactly
centered
at zero.
(Figure
3b), it has
the
characteristics
of spot
a two-body
aappears
circularnot
diffuse
false
coincidence
background
andspot
theclose
true to
coincidence
closethe
toprocess:
zero.still
Misleadingly,
the
spot
still
appears
not
This
is ancentered
artifact
of
rotation
point
pI always
the x-direction,
and
warrants
a brief
discussion
background
and the
true
coincidence
spot
close
toin
zero.
Misleadingly,
the
spot
still
appears
not
exactly
atthe
zero.
This istoan
artifact
of the
rotation
to point p
I always
in the
x-direction,
and
inwarrants
Appendix
A. at discussion
exactly
centered
zero. This in
is an
artifact A.
of the rotation to point pI always in the x-direction, and
a brief
Appendix
warrants a brief discussion in Appendix A.
2+ ) counts as a function of the dark momentum coefficient k.
Figure
4. 4.
Coincident
pair
(I5+
,C,C
2+) counts as a function of the dark momentum coefficient k.
Figure
Coincident
pair
(I5+
Figure 4. Coincident pair (I5+,C2+) counts as a function of the dark momentum coefficient k.
To verify that we have obtained true coincidences, a PIPICO plot is shown in Figure 5a, obtained
To the
verify
that wecoefficient
have obtained
true
coincidences,
PIPICO
shown
in Figure
5a,coincidences
obtained
with
correction
k = 0.78,
but
not applyinga MF.
Hereplot
oneiscan
see both
the true
with
the
correction
coefficient
k
=
0.78,
but
not
applying
MF.
Here
one
can
see
both
the
true
coincidences
as a tilted rectangular pattern and the false coincidence background as the fainter rectangle. The tilted
as pattern
a tilted rectangular
pattern
and the
coincidence
background
as the
rectangle.
tiltedcan
is the result of
correlation
in false
the axial
momentum
component,
notfainter
used for
MF. ThisThe
pattern
pattern
is the result
of correlation
in the
axialdetector
momentum
not
used for
This
patternsharper
can
be improved
by applying
the MF
to the
plane,component,
as shown in
Figure
5b, MF.
where
a much
Appl. Sci. 2017, 7, 531
6 of 14
To verify that we have obtained true coincidences, a PIPICO plot is shown in Figure 5a, obtained
with the correction coefficient k = 0.78, but not applying MF. Here one can see both the true coincidences
as a tilted rectangular pattern and the false coincidence background as the fainter rectangle. The tilted
Appl. Sci. 2017, 7, 531
6 of 14
pattern is the result of correlation in the axial momentum component, not used for MF. This pattern
can beAppl.
improved
Sci. 2017, 7,by
531 applying the MF to the detector plane, as shown in Figure 5b, where6 a
of much
14
PIPICO pattern with almost no background is seen. The strength of the MF is indicated in Figure 3 by
sharper PIPICO pattern with almost no background is seen. The strength of the MF is indicated in
the black circle,
althoughalmost
the events
were chosen
from
within
this
unrotated
image,
not in
pattern
no background
is seen.
The
strength
of circle
the
MFinisthe
indicated
3 by
FigurePIPICO
3 by the
blackwith
circle, although
the events
were
chosen
from
within
this
circleininFigure
the unrotated
the rotated
onecircle,
(see Appendix
A)events
(therewere
waschosen
a technical
problem
thisin
experiment
that
resulted
the black
although the
from within
thisin
circle
the unrotated
image,
not inin an
image, not in the rotated one (see Appendix A) (there was a technical problem in this experiment that
increased
ion source
sizeAppendix
along theA)TOF
axis.
strong filtering
applied
resulted that
alsoresulted
in ions in
accepted
the rotated
one (see
(there
wasThe
a technical
problem in
this experiment
an
resulted in an increased ion source size along the TOF axis. The strong filtering applied resulted also
increased
source
size along
the TOFaaxis.
The strong
applied resulted also in ions accepted
only from
part ion
of the
source
and created
narrower
tiltedfiltering
pattern).
in ionsonly
accepted
only
part and
of the
source
and created
narrower tilted pattern).
from part
of from
the source
created
a narrower
tilted apattern).
5+, C2+)5+
5. Photoion-photoioncoincidence
coincidence (PIPICO)
maps
of the
(a) without (a) without
FigureFigure
5. Photoion-photoion
(PIPICO)
maps
of(Ithe
(I coincidences,
, C2+ ) coincidences,
Figure 5. Photoion-photoion coincidence (PIPICO) maps of the (I5+, C2+) coincidences, (a) without
momentum
filtering
(MF),
and
(b)
with
two-dimensional
MF
applied.
momentum filtering (MF), and (b) with two-dimensional MF applied.
momentum filtering (MF), and (b) with two-dimensional MF applied.
We also demonstrate an application of the MF to a difficult case where no PIPICO pattern is initially
We
also
demonstrate
an
the
MF
to
difficult
casem/q
where
no PIPICO
pattern
is
We also
demonstrate
an application
of theof
MF
to
a difficult
case
no
PIPICO
pattern
is initially
discernible
at all—the
(I11+application
,C3+) coincidences.
Here,
theaI11+
ions where
(with
of 11.5)
are
completely
11+
3+
11+
11+
3+
11+
initially
discernible
at strong
all—the
,C C)+ coincidences.
the(with
I
ions
(with
m/q
11.5)
discernible
at
all—the
(I ,Cand
) (Icoincidences.
ITOFions
m/q
of 11.5)
are of
completely
buried
under
the
broad
peakHere,
in thethe
ion Here,
spectrum.
The initial
creation
of
the are
+ peak in the ion TOF spectrum. The initial creation of
completely
buried
the
strong
andunder
unbiased
ion
pairsand
produces
momentum
sum plot
in FigureThe
6a that
is dominated
buriedunfiltered
under
the
strong
and
broad
C+broad
peakaCin
the ion TOF
spectrum.
initial
creation by
of the
+ and C3+), but a weak coincident spot of I11+,C3+ is also seen as a
false
coincidences
(mostly
between
C
the
unfiltered
and
unbiased
ion
pairs
produces
a
momentum
sum
plot
in
Figure
6a
that
is
dominated
unfiltered and unbiased ion pairs produces a momentum sum plot in Figure 6a that is dominated by
+ and
3+the
11+
3+ is also seen
slight
enhancement
of the
intensity
just
right
position
in the plot.
11+I,C
3+,C
by
false
coincidences
(mostly
between
), but
a weak
coincident
spot
false
coincidences
(mostly
between
C+C
and
C3+C
),ofbut
a(0,0)
weak
coincident
spot
of Iof
is also
seen as a
as
a slight
enhancement
of intensity
the intensity
of (0,0)
the (0,0)
position
in plot.
the plot.
slight
enhancement
of the
just just
rightright
of the
position
in the
Figure 6. Momentum sum plots (a) and (b) and PIPICO plots (c) and (d) of (I11+, C3+) coincidences.
The PIPICO plot in Figure 6c does not show any typical tilted pattern. Repeating the procedure
described
before, we sum
first plots
obtain(a)the
correlation
coefficient, (c)
k = and
0.825,
and recreate
momentum
11+ , C3+ )the
Figure
6.6.Momentum
(b)
coincidences.
11+, C3+) coincidences.
Figure
Momentum
sumthis
plots
(a)and
and
(b)and
andPIPICO
PIPICOplots
plotsis(c)
and(d)
(d)ofof(I(Imomentum
sum
plot
(Figure
6b). For
plot,
the lowest-strength
MF
applied—the
sum is not
restricted to a certain maximum length, but a set of ion pairs was formed that gave the best
The PIPICO
plotcorrelation,
in Figure instead
6c doesofnot
showpairs
any randomly.
typical tilted
pattern.
the procedure
momentum
forming
Finally,
strongRepeating
MF is applied
on the
described before, we first obtain the correlation coefficient, k = 0.825, and recreate the momentum
sum plot (Figure 6b). For this plot, the lowest-strength MF is applied—the momentum sum is not
restricted to a certain maximum length, but a set of ion pairs was formed that gave the best
Appl. Sci. 2017, 7, 531
7 of 14
The PIPICO plot in Figure 6c does not show any typical tilted pattern. Repeating the procedure
described before, we first obtain the correlation coefficient, k = 0.825, and recreate the momentum
sum plot (Figure 6b). For this plot, the lowest-strength MF is applied—the momentum sum is not
Appl. Sci. 2017, 7, 531
7 of 14
restricted to a certain maximum length, but a set of ion pairs was formed that gave the best momentum
correlation,
instead
of forming
pairs
Finally,
strong MF
is applied
on circle
the detector
plane
detector plane
(eliminating
97.8%
of randomly.
the ion pairs),
as indicated
with
the black
in Figure
6b.
(eliminating
97.8% now
of theemerges
ion pairs),
as indicated
with
the black
A PIPICO pattern
clearly,
as seen in
Figure
6d. circle in Figure 6b. A PIPICO pattern
now emerges
as seenare
in Figure
6d. from the (I11+, C3+) pairs, let us attempt to also derive the
Since theclearly,
coincidences
extractable
Since
the coincidences
fromthis
themost
(I11+ , difficult
C3+ ) pairs,
letin
usour
attempt
to also
kinetic
energy
distributionsare
ofextractable
the ions from
case
dataset.
The derive
results the
are
kinetic
energy
distributions
of
the
ions
from
this
most
difficult
case
in
our
dataset.
The
results
are
shown in Figure 7, where first the curves were extracted for the (I11+, C3+) set using MF to remove false
3+ ) set using MF to remove false
shown
in Figure
7, where
firstthe
thefiltered
curvesdata
were
extracted
the (I11+of
, Cfalse
coincidences.
However,
even
still
containsfor
a number
coincidences from the diffuse
coincidences.
However,
even
filtered data
still to
contains
false coincidences
from to
thea
background (see
Figure 6b,
forthe
example).
In order
removea number
that, the of
filtering
was also applied
diffuse
background
(see
Figure
6b,
for
example).
In
order
to
remove
that,
the
filtering
was
also
applied
scrambled dataset, where iodine ions were always paired with carbon ions from a different event
to
a scrambled
dataset,
where
iodineonly
ionsfalse
werecoincidences.
always paired
with
carbon
fromdistributions
a different event
(XFEL
pulse) and
which
contained
The
final
kineticions
energy
were
(XFEL
pulse)
and which contained
only false
coincidences.
The
final
distributions
obtained
by subtracting
the scrambled
distributions.
In the
case
of kinetic
C3+, forenergy
example,
it is seen were
from
obtained
the scrambled
distributions.
C3+ , for
example,
it is
is since
seen from
Figure 7 by
thatsubtracting
the false coincidences
mostly
contribute In
to the
the case
lowerofkinetic
energies:
this
most
Figure
7
that
the
false
coincidences
mostly
contribute
to
the
lower
kinetic
energies:
this
is
since
most
of
the
3+
of the C ions come from other events with iodine charges lower than 11+ and, thus, with lower
3+ ions come from other events with iodine charges lower than 11+ and, thus, with lower energy release.
C
energy release.
3+
11+
Figure
(I11+
Figure 7.7.Kinetic
Kineticenergy
energydistributions
distributionsofofions
ionsininthe
the
(I11+, ,CC3+))coincidences.
coincidences. Top
Toppanel:
panel:I I11+,, bottom
bottom
3+
panel:
panel: C
C3+..
Briefly, the
the complete
complete analysis
analysis similar
similar to
to the
the procedures
procedures described
described here
here allowed
allowed us
us to
to draw
draw
Briefly,
importantconclusions
conclusionsonon
interplay
of the
electron
and nuclear
dynamics
shortpulses.
XFEL
important
thethe
interplay
of the
electron
and nuclear
dynamics
duringduring
short XFEL
pulses.
Wethat
found
the C-I
bond
only
to elongate
only
even
less during
thepulse,
10 fs
We
found
the that
C-I bond
has
onlyhas
time
to time
elongate
only 10%
or 10%
evenorless
during
the 10 fs
pulse, whereas
the
C-H distances
are nearly
[12]. These
are rather
different
from
the
whereas
the C-H
distances
are nearly
tripledtripled
[12]. These
resultsresults
are rather
different
from the
ones
ones predicted
by instantaneous
creation
and redistribution.
predicted
by instantaneous
chargecharge
creation
and redistribution.
3.2.
3.2. Diiodomethane
Diiodomethane
In
In diiodomethane
diiodomethane that
that contains
contains three
three heavier
heavier atoms,
atoms, one does
does not
not expect
expect to
to find
find two-ion
two-ion
coincidences
that
can
be
well-approximated
by
a
two-body
dissociation
process.
However,
coincidences that can be well-approximated by a two-body dissociation process. However, the
the
geometry
geometry suggests
suggests that,
that, at least
least in
in the
the cases
cases where
where the
the charge
charge distribution
distribution between
between the
the two
two iodine
iodine
atoms
unbalanced,
a similar
approach
than than
for CH
could
be useful.
We, therefore,
assume
atoms isisnot
notvery
very
unbalanced,
a similar
approach
for
3I could
be useful.
We, therefore,
3 I CH
that
the C
ionthe
is well
correlated
with the with
combined
momentamomenta
of the two
ions,
but
that
assume
that
C ionmomentum
is well momentum
correlated
the combined
of Ithe
two
I ions,
some
momentum
is removed
by the hydrogens
along the
direction
of the carbon
This is
but that
some momentum
is removed
by the hydrogens
along
the direction
of the momentum.
carbon momentum.
supported
by point-charge
Coulomb
explosion
simulations.
This is supported
by point-charge
Coulomb
explosion
simulations.
A test of this approach is presented on the example of a triple-coincidence set, (I3+, I3+, C2+). In a
dark momentum coefficient scan, such as in CH3I, the triple coincident count reaches maximum at
around k = 0.75, although in this case the maximum is not as sharply defined as in CH3I. The triple
momentum sum plot, after applying the correction coefficient to the carbon momentum, is shown in
Figure 8. An alternative would be to apply the dark momentum correction to the combined
Appl. Sci. 2017, 7, 531
8 of 14
A test of this approach is presented on the example of a triple-coincidence set, (I3+ , I3+ , C2+ ). In a
dark momentum coefficient scan, such as in CH3 I, the triple coincident count reaches maximum at
around k = 0.75, although in this case the maximum is not as sharply defined as in CH3 I. The triple
momentum sum plot, after applying the correction coefficient to the carbon momentum, is shown in
Figure 8. An alternative would be to apply the dark momentum correction to the combined momentum
of the two iodine atoms, reducing it instead of increasing the carbon momentum. Both approaches gave
very similar results. In Figure 8 one can see a rather well defined true coincidence region (again there
is a slight displacement of it from the origin, for the same reason as discussed above).
Appl. Sci. 2017, 7, 531
8 of 14
For triple coincidences, a more informative representation than PIPICO plots is, for example,
a Newtonapproaches
plot, as shown
Figure
9. The
plot 8was
obtained
by applying
the strength as
gave veryinsimilar
results.
In Figure
one can
see a rather
well definedMF
truewith
coincidence
region
(again
there
is
a
slight
displacement
of
it
from
the
origin,
for
the
same
reason
as
discussed
above).
indicated by the circle in Figure 9, but in order to further reduce the false coincidence contributions,
the filter was applied in all three dimensions (restricting the full vector sum to within a sphere
around zero). The MF, itself, does not define any structures in the Newton plot, as it only restricts the
three-vector sum values not, for example, the angle between the iodine ions. In generating Figure 9,
all momenta of the first I3+ ion in the set were rescaled to 1 × 10−21 kg·m/s and rotated onto the
x-axis. The red spot is the distribution of the second iodine ion’s momenta and the blue spot shows the
momenta of carbon ions. The black dots are the calculated momentum vectors from a point-charge
Coulomb explosion simulation. For the simulation, the initial positions of the charges were fixed
according to the ground state equilibrium geometry of diiodomethane, full charges were assigned
instantaneously to the atoms and then their classical trajectories were followed. The comparison
Figure 8. Momentum sum plot of (I3+, I3+, C2+) triple coincidences. The circle illustrates the strength
with the experimental
momentum islands in Figure 9 shows a very good agreement in the angular
of the three-dimensional MF applied afterwards. The sum of the iodine momenta is directed along
distribution, but
a
clearly
shorter vector length for the carbon ions, indicating that in the Coulomb
the
x-axis.
Appl. Sci.
2017,
7, 531
8 of 14
explosion they obtain a lesser share of the kinetic energy release than predicted by the simplest model.
For triple
a more In
informative
representation
than
PIPICO
plots
is,
for example,
gavecoincidences,
very
similar
results.
Figure 8 one
can see a rather
well
true
coincidence
Detailed approaches
investigations
of the
Coulomb
explosion’s
dynamics
in CH
found
in [13].
2 Idefined
2 can be
a Newton
Figure 9. The
was
MF as
with
the strength
region
(againplot,
thereasisshown
a slightin
displacement
of itplot
from
theobtained
origin, forby
theapplying
same reason
discussed
above).as
indicated by the circle in Figure 9, but in order to further reduce the false coincidence contributions,
the filter was applied in all three dimensions (restricting the full vector sum to within a sphere around
zero). The MF, itself, does not define any structures in the Newton plot, as it only restricts the
three-vector sum values not, for example, the angle between the iodine ions. In generating Figure 9,
all momenta of the first I3+ ion in the set were rescaled to 1 × 10−21 kg·m/s and rotated onto the x-axis.
The red spot is the distribution of the second iodine ion’s momenta and the blue spot shows the
momenta of carbon ions. The black dots are the calculated momentum vectors from a point-charge
Coulomb explosion simulation. For the simulation, the initial positions of the charges were fixed
according to the ground state equilibrium geometry of diiodomethane, full charges were assigned
instantaneously to the atoms and then their classical trajectories were followed. The comparison with
the experimental momentum islands in Figure 9 shows a very good agreement in the angular
distribution, but a clearly shorter vector length for the carbon ions, indicating that in the Coulomb
2+) triple coincidences. The circle illustrates the strength
Figure 8. Momentum sum plot of3+(I3+,3+
I3+, C2+
explosion
they obtain
lesser
release than
predicted
by the the
simplest
Figure
8. Momentum
sumaplot
of share
(I , I of, the
C kinetic
) tripleenergy
coincidences.
The circle
illustrates
strength of
of the three-dimensional MF applied afterwards. The sum of the iodine momenta is directed along
model.
Detailed
investigations
of
the
Coulomb
explosion’s
dynamics
in
CH
2I2 can be found in [13].
the three-dimensional MF applied afterwards. The sum of the iodine momenta is directed along the x-axis.
the x-axis.
For triple coincidences, a more informative representation than PIPICO plots is, for example,
a Newton plot, as shown in Figure 9. The plot was obtained by applying MF with the strength as
indicated by the circle in Figure 9, but in order to further reduce the false coincidence contributions,
the filter was applied in all three dimensions (restricting the full vector sum to within a sphere around
zero). The MF, itself, does not define any structures in the Newton plot, as it only restricts the
three-vector sum values not, for example, the angle between the iodine ions. In generating Figure 9,
all momenta of the first I3+ ion in the set were rescaled to 1 × 10−21 kg·m/s and rotated onto the x-axis.
The red spot is the distribution of the second iodine ion’s momenta and the blue spot shows the
momenta of carbon ions. The black dots are the calculated momentum vectors from a point-charge
Coulomb explosion simulation. For the simulation, the initial positions of the charges were fixed
according to the ground state equilibrium geometry of diiodomethane, full charges were assigned
instantaneously to the atoms and then their classical trajectories were followed. The comparison with
3+,I3+,C
2+) triple
3+islands
the 9.experimental
momentum
Figure
9 shows awith
very
in the
Figure
9. Newton
coincidences,
thegood
first
ion’sI3+
momentum
inangular
the
Figure
Newton
plot
ofplot
theof(Ithe
,I(I3+
,C2+in
) triple
coincidences,
with
theI3+agreement
first
ion’s
momentum
in the
−21
distribution,
but
a
clearly
shorter
length
for
the
carbon
ions,
indicating
that
in
the
x-direction
and
normalized
to vector
1 ×−10
kg·m/s.
The
red-coloured
area
marks the
second
I3+Coulomb
ion’s
21
3+
x-direction and normalized to 1 × 10
kg·m/s. The red-coloured area marks the second I ion’s
momenta.
dots are
from
point-charge
Coulomb
momenta
the blue-colored
area of
the2+
C2+ ion’s
explosion
theyand
obtain
a lesser share
the
kinetic
energyBlack
release
than
predicted
by the
simplest
momenta explosion
and the blue-colored
area
the
C
ion’s momenta. Black dots are from point-charge Coulomb
model. Detailedsimulation.
investigations of the Coulomb explosion’s dynamics in CH2I2 can be found in [13].
explosion simulation.
Appl.
Sci.
2017,
531
Appl.
Sci.
2017,
7, 7,
531
9 of
9 of
1414
Finally, Figure 10 displays an ion-ion coincidence plot between the C2+ and I3+ ions in the
Finally,
Figure
10 displays
ion-ion
coincidence
plot
theNewton
C2+ and
I3+ The
ionsemission
in the
(I ,I ,C2+) triple
coincidence
set,anafter
applying
the same
MFbetween
as for the
plot.
3+
3+
2+
(I angle
,I ,C
)
triple
coincidence
set,
after
applying
the
same
MF
as
for
the
Newton
plot.
The
emission
of about 107° between the two ions (see Figure 9) results in an elliptical PIPICO island, which
◦
angle
of about
the two
(see Figure
9) results
in an elliptical
PIPICOwith
island,
is
is also
quite 107
wellbetween
represented
by ions
a simple
modeling
of isotropic
dissociation
thewhich
angular
also
quite
well
represented
by
a
simple
modeling
of
isotropic
dissociation
with
the
angular
correlation
correlation of 107° between the two ions, and using a simple linear dependency of the ion TOF from
◦ between the two ions, and using a simple linear dependency of the ion TOF from the axial
ofthe
107axial
velocity component. The shape of the PIPICO island is also affected by the “dark”
velocity
component.
The shape
thenonlinearity
PIPICO island
also affected
“dark”
momentum
of
momentum of hydrogens
and byofthe
of theisdependency
ofby
ionthe
TOF
from the
axial velocity.
hydrogens and by the nonlinearity of the dependency of ion TOF from the axial velocity.
3+ 3+
2+ I3+ ) PIPICO plot from the (I3+ , I3+ , C2+ ) coincidence set in CH I . Color map:
Figure
2
Figure10.
10. (C
(C2+,, I3+
) PIPICO plot from the (I3+, I3+, C2+) coincidence set in CH2I2. Color2map:
experiment,
experiment,
red
dots:
model.
red dots: model.
3.3.
3.3.5-Iodouracil
5-Iodouracil
The
Thelast
lastmolecule
moleculeininthe
theseries
seriesstudied
studiedatatSACLA
SACLAisis5-iodouracil,
5-iodouracil,a acyclic
cyclicplanar
planarmolecule.
molecule.
Extracting
high-quality
coincidence
datasets
by
MF
is,
on
one
hand,
more
difficult
in
this
case
Extracting high-quality coincidence datasets by MF is, on one hand, more difficult in this casebecause
because
nonoclear
ofof
ions.
clearaxis
axisofofmomentum
momentumdistribution
distributionexists
existsand
andit itis isshared
sharedbybya number
a number
ions.On
Onthe
theother
other
hand,
the
ionization
rate/pulse
was
relatively
low
in
this
experiment
[14,15].
Here,
again,
preliminary
hand, the ionization rate/pulse was relatively low in this experiment [14,15]. Here, again, preliminary
Coulomb
Coulombexplosion
explosionsimulations
simulationsare
arevaluable
valuableinindeciding
decidingthe
thestrategy
strategyofofapplying
applyingMF.
MF.Modeling
Modeling
suggested,
suggested,first,
first,that
thatthe
theion
iontrajectories
trajectoriesare
aresignificantly
significantlyaffected
affectedbybytheir
theirinitial
initialvibrational
vibrationalmotion,
motion,
which
should,
therefore,
be
added
to
the
model.
Second,
the
ion
momenta
are
not
expected
to
which should, therefore, be added to the model. Second, the ion momenta are not expected to remain
remain
to vibrations)
butdeviations
strong deviations
occur. is,
Planarity
is,not
therefore,
the
planarplanar
(due to(due
vibrations)
but strong
can occur.can
Planarity
therefore,
the bestnot
criterion
best
the MF.
carbon
ions,
being surrounded
by heavier
elements,
have
very
for criterion
the MF. for
Third,
the Third,
carbonthe
ions,
being
surrounded
by heavier
elements,
have very
variable
variable
trajectories
thatlittle
bearresemblance
little resemblance
the original
geometry
therefore,
trajectories
that bear
to thetooriginal
geometry
and, and,
therefore,
are are
not not
the the
best
best
candidates
to included
be included
in MF.
other
hand,
oxygen
ions,
being
on outer
the outer
positions,
candidates
to be
in MF.
On On
the the
other
hand,
oxygen
ions,
being
on the
positions,
have
have
trajectories
reflect
geometry
of the
ring
and
also
have
sufficiently
high
momenta
trajectories
thatthat
reflect
wellwell
the the
geometry
of the
ring
and
also
have
sufficiently
high
momenta
for
for
efficient
filtering.
However,
lack
of axial
symmetry
means
the filtering
should
be done
efficient
filtering.
However,
thethe
lack
of axial
symmetry
means
thatthat
the filtering
should
be done
based
based
onangle
the angle
between
the momenta,
rather
the length
of their
We will
demonstrate
on the
between
the momenta,
rather
thanthan
the length
of their
sum.sum.
We will
demonstrate
thisthis
type
type
of
MF
on
the
cases
of
triple
coincidence
sets
containing
the
two
oxygen
ions.
Figure
11
shows
the
of MF on the cases of triple coincidence sets containing the
oxygen ions. Figure 11 shows the
+ )+ triple coincidence set and
2+,H
angular
the
momenta
of of
thethe
ions
in the
(O+(O
,O+2+
angularcorrelations
correlationsbetween
between
the
momenta
ions
in the
,O,H
) triple coincidence set and
+
2+
+,O2+angle
confirms
ofof
thethe
simulations:
the
O O,O
confirmsthe
thepredictions
predictions
simulations:
the
anglehas
hasa astrong
strongcorrelation
correlationmaximum
maximumatat
◦ , while the planarity of the three vectors is not sharply defined (although the dissociation
around
115
around 115°, while the planarity of the three vectors is not sharply defined (although the dissociation
isispreferentially
planar).
preferentially
planar).
Next, we extract triple coincidence sets with angular correlation MF for the two oxygen ions.
Figure 12 shows a Newton plot for the (O+ , O+ , N+ ) dataset. There are two possible origins for the
oxygen defining the x-axis; these molecular orientations are depicted next to the figure. Then there
are four initial positions for the N+ ions, two of them degenerate. Indeed, the N+ island in the figure
corresponding to the degenerate position shows approximately twice the intensity of the other two.
In extracting this plot, the background was slightly improved by subtracting a Newton plot generated
from a scrambled coincidence set (not showing any defined islands). The conical sharp limits of the
O2+ island is the result of applying the angular MF.
Appl.
Sci.
2017,
531
Appl.
Sci.
2017,
7,7,
531
1010
ofof
1414
Figure 11. Distribution of angles between the momentum vectors in the (O+,O2+,H+) coincidence
dataset in 5-iodouracil. Blue curve with filled circles: cos(p(O+), p(O2+)); red curve with open circles:
cosine of p(H+) from the (O+,O2+) momentum plane.
Next, we extract triple coincidence sets with angular correlation MF for the two oxygen ions.
Figure 12 shows a Newton plot for the (O+, O+, N+) dataset. There are two possible origins for the
oxygen defining the x-axis; these molecular orientations are depicted next to the figure. Then there
are four initial positions for the N+ ions, two of them degenerate. Indeed, the N+ island in the figure
corresponding to the degenerate position shows approximately twice the intensity of the other two.
In extracting this plot, the background was slightly improved by subtracting a Newton plot generated
+ ,O2+ ,H+ ) coincidence
11. Distribution
of angles
between
the momentum
in the
from Figure
a scrambled
coincidence
set (not
showing
any definedvectors
islands).
The(Oconical
sharp limits of the
Figure 11. Distribution of angles between the momentum+ vectors
in
the
(O+,O2+,H+) coincidence
2+ )); red curve with open circles:
2+
dataset
in
5-iodouracil.
Blue
curve
with
filled
circles:
cos(p(O
),
p(O
O island
is the result of applying the angular MF.
dataset in 5-iodouracil. Blue curve with filled circles: cos(p(O+), p(O2+)); red curve with open circles:
2+ ) momentum plane.
cosine of p(H+ )+ from the (O+ ,O
cosine of p(H ) from the (O+,O2+) momentum plane.
Next, we extract triple coincidence sets with angular correlation MF for the two oxygen ions.
Figure 12 shows a Newton plot for the (O+, O+, N+) dataset. There are two possible origins for the
oxygen defining the x-axis; these molecular orientations are depicted next to the figure. Then there
are four initial positions for the N+ ions, two of them degenerate. Indeed, the N+ island in the figure
corresponding to the degenerate position shows approximately twice the intensity of the other two.
In extracting this plot, the background was slightly improved by subtracting a Newton plot generated
from a scrambled coincidence set (not showing any defined islands). The conical sharp limits of the
O2+ island is the result of applying the angular MF.
Figure 12. Newton plot of the (O+ ,O+ ,N+ ) coincidences in 5-iodouracil, with the first O+ ion’s
+,O+,N+) coincidences
+ ion’s
momentum
in the x-direction
and(Onormalized
to 1 × 10−21
·m/s, the red-colored
area O
marking
Figure
12. Newton
plot of the
in kg
5-iodouracil,
with the first
+
+
−21
the second O
ion’s
momentaand
andnormalized
the blue-colored
thered-colored
N ion’s momenta.
Possible
momentum
in the
x-direction
to 1 × area
10 marking
kg·m/s, the
area marking
the
molecular
and labeling
the nitrogen atoms
and islands
the right.Possible
ion’s momenta
and theofblue-colored
area marking
theare
N+shown
ion’s to
momenta.
second
O+ orientations
molecular orientations and labeling of the nitrogen atoms and islands are shown to the right.
The second example is the (O+ , O+ , H+ ) dataset. Due to the relatively low total charge in this
+, O+, H+) dataset. Due to the relatively low
The
second
example
theof(O
total
charge
in this
experiment
and the
largerissize
the
molecule, the kinetic energies of the H+ ions
were
sufficiently
+
experiment
and the
larger size
of thewith
molecule,
the kinetic
of the Hangular
ions were
sufficiently
low for efficient
detection
together
the heavier
ions. energies
After applying
MF for
the two
low
for
efficient
detection
together
with
the
heavier
ions.
After
applying
angular
MF
for
the two
oxygens and subtracting the scrambled coincidence background, again a clear island structure emerges
oxygens
and (H
subtracting
thedataset,
scrambled
coincidence
background,
again
a clear island
structure
+ ) ion in the
for the third
as shown
in Figure
13. Indeed,
all different
initial positions
+) ion in the dataset, as shown in Figure 13. Indeed, all different initial
emerges
for
the
third
(H
of the hydrogens are discernible, indicating that the Coulomb explosion involving these ions has a
positions
of the of
hydrogens
discernible,
indicating
that the we
Coulomb
explosionNewton
involving
these
+
+
+
+ plots for
common center
force in aare
good
approximation.
In contrast,
also generated
Figure 12. Newton plot of the (O ,O ,N ) coincidences in 5-iodouracil, with the first O ion’s
(O+ ,O+momentum
,C+ ) datasets,
which
showed
nonormalized
visible island
for the
ions,area
in agreement
with
in the
x-direction
and
to 1structures
× 10−21 kg·m/s,
the carbon
red-colored
marking the
the simulations.
second O+ ion’s momenta and the blue-colored area marking the N+ ion’s momenta. Possible
Interestingly,
hydrogens
directions
1,4 and
appear
to have
larger
molecular orientations
andemitted
labeling to
of the
the nitrogen
atoms
islands
are shown
to momenta
the right. than the
rest. Unfortunately, the number of events are not high enough to perform useful quantitative analysis
+, O+, H+) dataset. Due to the relatively low total charge in this
second
example of
is the
of the The
energy
distributions
ions(O
originating
from specific positions in a molecule in a particular
experiment
and
the
larger
size
of
the
molecule,
kinetic
energies
of the
H+high
ions repetition
were sufficiently
triple coincidence dataset. Such analysis would the
await
for FEL
sources
with
rates.
low for efficient
together
with
heavier ions.
After applying
angular sites
MF for
the two
Additionally,
theredetection
are indications
that
thethe
probability
of hydrogens
from different
acquiring
oxygens
andsomewhat,
subtracting
scrambled
coincidence
again a clear island structure
charge
varies
butthe
with
insufficient
statistics forbackground,
firm conclusions.
emerges for the third (H+) ion in the dataset, as shown in Figure 13. Indeed, all different initial
positions of the hydrogens are discernible, indicating that the Coulomb explosion involving these
Appl. Sci. 2017, 7, 531
11 of 14
ions has a common center of force in a good approximation. In contrast, we also generated Newton
plots for (O+,O+,C+) datasets, which showed no visible island structures for the carbon ions, in
Appl.
Sci. 2017,with
7, 531the simulations.
11 of 14
agreement
Figure 13. Newton plot of the (O+ , O+ , H+ ) coincidences in 5-iodouracil. The image is slightly smoothed
Figure 13. Newton plot of the (O+, O+, H+) coincidences in 5-iodouracil.
The image is slightly smoothed for
for better visibility. Blue-colored islands correspond to the H+ momenta. The red circle is a guide for
better visibility. Blue-colored islands correspond to the H+ momenta. The red circle is a guide for the eye.
the eye.
Interestingly, hydrogens emitted to the directions 1,4 appear to have larger momenta than the
4. Conclusions
rest.
Unfortunately, the number of events are not high enough to perform useful quantitative analysis
of theWe
energy
distributions
of ions
originating extraction
from specific
molecule in information
a particular
presented
three cases
of successful
andpositions
analysis in
ofacoincidence
triple
coincidence
dataset. studies
Such analysis
would await
FEL sources
high facility
repetition
rates.
in molecular
dissociation
with ultrashort
XFELfor
pulses
from thewith
SACLA
in Japan.
Additionally,
there
are
indications
that
the
probability
of
hydrogens
from
different
sites
acquiring
The molecular samples possessed quite different symmetry properties, and also an increasing number
charge
varies
but with insufficient
statistics for
firm
conclusions.
of atoms
fromsomewhat,
five in iodomethane
to 12 in 5-iodouracil.
We
showed
how efficient extraction of true
coincidence data is achieved by applying ion momentum filtering. The exact implementation of these
4.
Conclusions
techniques
must be flexible and adapted to the particular geometries of the samples, but is seen to
workWe
efficiently
even
in the
caseof
of successful
complete atomization
of a analysis
12-atom of
molecule.
presented
three
cases
extraction and
coincidence information in
Coincidence
techniques,
proven
to
be
powerful
methods
for
extracting
detailed
information
on
molecular dissociation studies with ultrashort XFEL pulses from the SACLA
facility
in Japan.
molecular
dynamics
frompossessed
experiments
conducted
more conventional
equally
The
molecular
samples
quite
different atsymmetry
properties,light
andsources,
also an are
increasing
valuable
in
FEL-based
experiments.
Their
full
potential
is
likely
to
be
realized
with
high
repetition
rate
number of atoms from five in iodomethane to 12 in 5-iodouracil. We showed how efficient extraction
sources,
where the required
long collection
time becomes
less of afiltering.
restriction.
of
true coincidence
data is achieved
by applying
ion momentum
The exact implementation
of these techniques must be flexible and adapted to the particular geometries of the samples, but is
Acknowledgments: First and foremost, we are most grateful for all of the co-authors of [11,12,14,15] for their
seen
to workin
efficiently
evendemanding
in the caseexperiments
of complete
atomization
of a 12-atom
molecule.
contributions
making these
a success.
The experiments
were
performed at SACLA
with the
approval oftechniques,
JASRI and the
program
committee.
They for
wereextracting
supporteddetailed
by the X-ray
Free Electron
Coincidence
proven
to review
be powerful
methods
information
on
Laser Utilization Research Project and the X-ray Free Electron Laser Priority Strategy Program of the Ministry of
molecular dynamics from experiments conducted at more conventional light sources, are equally
Education, Culture, Sports, Science, and Technology of Japan (MEXT), by the Japan Society for the Promotion of
valuable
in FEL-based
experiments.
Their
fullExperimental
potential is Instruments
likely to beofrealized
repetition
Science (JSPS),
by the Proposal
Program of
SACLA
RIKEN, with
by thehigh
IMRAM
project
and
by
the
Cooperative
Research
Program
of
“Network
Joint
Research
Center
for
Materials
and
Devices:
Dynamic
rate sources, where the required long collection time becomes less of a restriction.
Alliance for Open Innovation Bridging Human, Environment and Materials”. E.K. acknowledges financial support
Acknowledgments:
First and foremost, we are most grateful for all of the co-authors of [11,12,14,15] for their
by the Academy of Finland.
contributions in making these demanding experiments a success. The experiments were performed at SACLA
Author Contributions: E.K. participated in the experiments, performed the analysis reported here and wrote the
with
the approval
of JASRI and
program review
committee. They
were supported
by planned,
the X-ray prepared
Free Electron
manuscript,
K.M. prepared
andthe
participated
in the experiments
and analyzed
data, H.F.
and
Laser Utilization
Project
the X-ray
ElectronK.N.
Laser
Priorityand
Strategy
Program
of the
Ministry
participated
in theResearch
experiments
andand
contributed
to Free
the analysis,
prepared
participated
in the
experiments
and
analyzed Culture,
the 5-iodouracil
data, K.U.
supervised
theofexperimental
program,
experiments
and
of
Education,
Sports, Science,
and
Technology
Japan (MEXT),
by the participated
Japan Societyinfor
the Promotion
in the
preparation
of the
of
Science
(JSPS), by
themanuscript.
Proposal Program of SACLA Experimental Instruments of RIKEN, by the IMRAM
project
and
the Cooperative
Research
of “Network
Conflicts
ofby
Interest:
The authors
declareProgram
no conflict
of interest.Joint Research Center for Materials and Devices:
Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials”. E.K. acknowledges
Appendix
A. Two-Dimensional
Momentum Sum Plots
financial
support
by the Academy of Ion
Finland.
Let us first assume a perfect measurement of a two-body dissociation, with pC = −pI . Then, before,
as well as after, the rotation, psum is exactly zero. However, the imperfect measurement adds an
uncertainty ∆pI and ∆pC to both vectors. We can make a gedankenexperiment where we first choose the
x-axis according to the accurate vector pI and then add the uncertainty ∆pI . (see Figure A1). For the
sake of simplicity we do not add the uncertainty ∆pC . This uncertainly is directly transferred to psum :
Appendix A. Two-Dimensional Ion Momentum Sum Plots
Let us first assume a perfect measurement of a two-body dissociation, with pC = −pI. Then, before,
as well as after, the rotation, psum is exactly zero. However, the imperfect measurement adds an
uncertainty ∆pI and ∆pC to both vectors. We can make a gedankenexperiment where we first choose the
Appl. Sci.
2017, 7, 531to the accurate vector pI and then add the uncertainty ∆pI. (see Figure A1). For
12 of
14
x-axis
according
the
sake of simplicity we do not add the uncertainty ∆pC. This uncertainly is directly transferred to psum:
psum = ∆pI. and moves in a circle of radius ∆pI around the origin. In order to bring the vector pI back
p
= ∆pI . and moves in a circle of radius ∆pI around the origin. In order to bring the vector pI
onsum
the x-axis,
a rotation by an angle α relative to the x-axis needs to be performed, and with a
back on the x-axis, a rotation by an angle α relative to the x-axis needs to be performed, and with a
reasonable assumption that ∆pI < pI, |α| < 90°.◦ The vector pC and the sum vector psum are naturally
reasonable assumption that ∆p < pI , |α| < 90 . The vector pC and the sum vector psum are naturally
rotated by α as well and, thus, pIsum always
shifts in the direction of the x-axis in rotation as a consequence
rotated by α as well and, thus, psum always shifts in the direction of the x-axis in rotation as a consequence
of random uncertainty in the vector defining the x-axis. Thus, although the rotated sum momentum
of random uncertainty in the vector defining the x-axis. Thus, although the rotated sum momentum
plots give a good visualization of the correlations and quality in the coincident dataset, they should
plots give a good visualization of the correlations and quality in the coincident dataset, they should
not be used to find the correction coefficient by shifting the center of the true coincidence spot to
not be used to find the correction coefficient by shifting the center of the true coincidence spot to
zero—therefore, the scans, such as in Figure 4, for example, always operated on the unrotated momenta.
zero—therefore, the scans, such as in Figure 4, for example, always operated on the unrotated momenta.
Figure
pII on
FigureA1.
A1.Sketch
Sketchof
ofthe
theeffect
effect of
of the
the measurement
measurement error
error of
of p
on the
the P
Psum
plot,with
withtwo
twochoices
choicesa,a,bbof
of
sumplot,
the
measurement
error
vector.
the measurement error vector.
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