# Site-specific Interrogation of an Ionic Chiral Fragment During Photolysis
Using an X-ray Free-Electron Laser

Markus Ilchen<EMAIL_ADDRESS>Institut für Physik und CINSaT,
Universität Kassel, Heinrich-Plett-Straße 40, D-34132 Kassel, Germany
European XFEL GmbH, Holzkoppel 4, 22869 Schenefeld, Germany  Stanford PULSE
Institute, 2575 Sand Hill Road, Menlo Park, California 94025, USA  Philipp
Schmidt  Institut für Physik und CINSaT, Universität Kassel, Heinrich-Plett-
Straße 40, D-34132 Kassel, Germany  European XFEL GmbH, Holzkoppel 4, 22869
Schenefeld, Germany  Nikolay M. Novikovskiy  Institut für Physik und CINSaT,
Universität Kassel, Heinrich-Plett-Straße 40, D-34132 Kassel, Germany
Institute of Physics, Southern Federal University, 344090 Rostov-on-Don,
Russia  Gregor Hartmann  Institut für Physik und CINSaT, Universität Kassel,
Heinrich-Plett-Straße 40, D-34132 Kassel, Germany  Helmholtz-Zentrum Berlin
für Materialien und Energie, Albert-Einstein-Straße 15, 12489 Berlin, Germany
Patrick Rupprecht  Max-Planck-Institut für Kernphysik Heidelberg,
Saupfercheckweg 1, 69117 Heidelberg, Germany  Ryan N. Coffee  SLAC National
Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
Arno Ehresmann  Institut für Physik und CINSaT, Universität Kassel, Heinrich-
Plett-Straße 40, D-34132 Kassel, Germany  Andreas Galler  European XFEL GmbH,
Holzkoppel 4, 22869 Schenefeld, Germany  Nick Hartmann  SLAC National
Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
Wolfram Helml  Technische Universität Dortmund, Fakultät für Physik, Maria-
Göppert-Mayer-Straße, 44227 Dortmund, Germany  Zhirong Huang  SLAC National
Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
Ludger Inhester  Center for Free-Electron Laser Science (CFEL), Notkestraße
85, 22607 Hamburg, Germany  Deutsches Elektronen-Synchrotron DESY, Notkestraße
85, 22607 Hamburg, Germany  Alberto A. Lutman  SLAC National Accelerator
Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA  James P.
MacArthur  SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo
Park, California 94025, USA  Timothy Maxwell  SLAC National Accelerator
Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA  Michael
Meyer  European XFEL GmbH, Holzkoppel 4, 22869 Schenefeld, Germany  Valerija
Music  Institut für Physik und CINSaT, Universität Kassel, Heinrich-Plett-
Straße 40, D-34132 Kassel, Germany  European XFEL GmbH, Holzkoppel 4, 22869
Schenefeld, Germany  Heinz-Dieter Nuhn  SLAC National Accelerator Laboratory,
2575 Sand Hill Road, Menlo Park, California 94025, USA  Timur Osipov  SLAC
National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California
94025, USA  Dipanwita Ray  SLAC National Accelerator Laboratory, 2575 Sand
Hill Road, Menlo Park, California 94025, USA  Thomas J. A. Wolf  Stanford
PULSE Institute, 2575 Sand Hill Road, Menlo Park, California 94025, USA  SLAC
National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California
94025, USA  Sadia Bari  Deutsches Elektronen-Synchrotron DESY, Notkestraße 85,
22607 Hamburg, Germany  Peter Walter  SLAC National Accelerator Laboratory,
2575 Sand Hill Road, Menlo Park, California 94025, USA  Zheng Li  Center for
Free-Electron Laser Science (CFEL), Notkestraße 85, 22607 Hamburg, Germany
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking
University, Beijing 100871, China  Stefan Moeller  SLAC National Accelerator
Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA  André Knie
Institut für Physik und CINSaT, Universität Kassel, Heinrich-Plett-Straße 40,
D-34132 Kassel, Germany  Philipp V. Demekhin<EMAIL_ADDRESS>Institut für Physik und CINSaT, Universität Kassel, Heinrich-Plett-Straße 40,
D-34132 Kassel, Germany

###### Abstract

Short-wavelength free-electron lasers with their ultrashort pulses at high
intensities have originated new approaches for tracking molecular dynamics
from the vista of specific sites. X-ray pump X-ray probe schemes even allow to
address individual atomic constituents with a ‘trigger’-event that preludes
the subsequent molecular dynamics while being able to selectively probe the
evolving structure with a time-delayed second X-ray pulse. Here, we use a
linearly polarized X-ray photon to trigger the photolysis of a prototypical
chiral molecule, namely trifluoromethyloxirane (C3H3F3O), at the fluorine
K-edge at around 700 eV. The evolving fluorine-containing fragments are then
probed by a second, circularly polarized X-ray pulse of higher photon energy
in order to investigate the chemically shifted inner-shell electrons of the
ionic motherfragment for their stereochemical sensitivity. We experimentally
demonstrate and theoretically support how two-color X-ray pump X-ray probe
experiments with polarization control enable XFELs as tools for chiral
recognition.

###### pacs:

32.80 Fb, 32.60 Rm, 32.30 Rj, 33.55.+b, 81.05.Xj

Chirality is a fundamental phenomenon that determines everybody’s all-day-life
to a large extent. It is, for instance, responsible for odor perception,
taste, and the effect of most pharmaceutical drugs on any living organism. In
fact, the molecular building blocks of all known biological matter possess a
handedness. They are non-superimposable mirror images of themselves, called
enantiomers. It currently constitutes an interdisciplinary effort to find the
underlying reason for this and its origin. Determining and controlling the
conformation of chiral molecules is not only an important aspect of the
natural sciences but also an industrial, specifically, pharmaceutical research
subject. However, chiral molecules are identical in their stoichiometric
composition and they are practically only distinguishable via their
interaction with other chiral objects.

A versatile tool for investigating enantiomers in the gas phase in a
controlled and theoretically well accessible way is circularly polarized
light, since it possesses a handedness as well. The so-called circular
dichroism (CD) quantifies the absorption difference between left and right
circularly polarized light and is typically an effect accounting only for a
few per mille of the overall signal. This light–matter interaction is today
commonly used for chiral recognition and control. In 1976, Ritchie Ritchie76
predicted that circularly polarized light can imprint its enantio-selectivity
onto emitted photoelectrons. His groundbreaking idea can be visualized with a
picture of an electron driven by circularly polarized light which scatters on
the asymmetric potential of a chiral molecule like a nut on a thread, meaning
it either moves in forward or in backward direction with respect to the
propagation of the light, depending on the rotational direction of the
components. This so-called photoelectron circular dichroism (PECD) can be
orders of magnitude stronger than the respective absorption difference of
circularly polarized photons, since it emerges already in the electric-dipole
approximation.

At present, PECD has been exploited for chiral recognition using a variety of
light sources and photon energy ranges. Low photon energy has, for example,
been used for directly exploring the chiral chemical environment Nahon15 ;
Hadidi18 , and higher photon energies to address individual constituents of a
molecule and to explore how specific sites encounter the surrounding chiral
potential Hergenhahn04 ; Ilchen17 . Contrary to the case of outer-shell
photoionization with low photon energies where both, initial and final
electronic states contribute to the observed effect, the case of high photon
energy photoionization from an almost symmetric atomic-like inner shell allows
one to study an individual contribution of the final electron continuum state.
Furthermore, strong laser sources have been used to explore how a chiral
molecule interacts with multiple photon absorptions in the long-wavelength
regime Lux12 ; Lehmann13 . Finally, time-resolved investigations have recently
started to explore ultrafast processes in chiral compounds with femtosecond
optical laser pulses Beaulieu16 ; Comby16 . The versatility of PECD is
valuable but also a challenge to the differentiation of individual properties
and processes of chirality Wollenhauptreview .

Today’s short-wavelength FELs provide photon pulses of very high brilliance,
i.e. they can exceed the brilliance of any other light source at the
accessible photon energies by more than a billion times. The high intensity
allows for very efficient time-resolved experiments that either use optical
lasers in order to trigger processes in the target of choice optXray  or even
X-ray pulses as so called ‘pump’ XrayXray1 ; XrayXray2 ; XrayXray3 ; XrayXray4
; XrayXray5 ; XrayXray6 , while in both cases, the dynamics are probed with a
second X-ray pulse. Their capability of enabling high-precision studies of
dichroic light–matter interaction in dilute species was initially demonstrated
in the vacuum ultraviolet regime at FERMI in Italy Allaria14 ; Mazza14 . The
first circularly polarized X-ray pulses that enabled high irradiation levels
were achieved at the LCLS Lutman16 ; Hartmann16 . Such polarization-controlled
(X)FELs naturally offer the possibility for ultrafast studies of chiroptically
sensitive targets from the perspective of element- and even site-specific
constituents during ultrafast structural changes or electron migration.

The present work reports the first investigation of a site-specific PECD in an
ionic chiral fragment of a dissociating chiral molecule by an XFEL. The
employed X-ray pump – X-ray probe scheme allows for addressing specific atoms
in the molecule in both pulses. In particular, an ultrashort X-ray pump pulse
triggers photolysis of the prototypical molecule trifluoromethyloxirane
(C3H3F3O) in a way that, predominantly, one singly-charged fluorine atom
dissociates and leaves the singly-charged mother-fragment behind. While the
distance between these two ionic systems increases in time, a second
ultrashort X-ray pulse probes the PECD of F 1s photoelectrons of the remaining
mother-fragment. This possible channel of dissociation is one out of many,
however, it can be energetically disentangled via electron VMI spectroscopy.
The static PECD of F 1s photoelectrons of neutral trifluoromethyloxirane
molecules was systematically studied both, experimentally and theoretically,
in our previous work Ilchen17 . This preliminary work uncovers which chiral
asymmetry can be expected in a broad interval of the photoelectron kinetic
energies and demonstrates that the presently used theoretical approach can
describe the measured PECD quantitatively. In the present work, we
theoretically demonstrate that the PECD of a fluorine core-photoelectron
emitted from the chiral mother-fragment can sense the dissociating fluorine
ion over a wide range of internuclear distances, far beyond chemical bond
dynamics. Averaging these dynamics in the predicted stereochemical sensitivity
of the mother-fragment over the individual fluorine ejection and ionization
channels, surprisingly, results in a slightly oscillating PECD of around 1% to
2$\%$. This finding is qualitatively supported by the experimental data.

##  I Results and discussion

###  I.1 The process

The presently studied process is schematically illustrated in Fig. 1. The
X-ray pump pulse with a photon energy of about 698 eV releases a 1s
photoelectron from one of the fluorine atoms in the neutral C3H3F3O molecule
with a kinetic energy of about 4 eV. This corresponds to a calculated F 1s
binding energy of about 694 eV. In the next step, the created core-ionized
state decays by an ultrafast Auger process (the presently calculated lifetime
is about 2.3 fs) and populates dicationic states in the molecule. The F 1s
binding energy of the doubly-charged but still intact molecule in the ground
state is calculated to be about 704.7 eV. After charge rearrangement, the
created dicationic states initiate a Coulomb explosion, predominantly into a
singly-charged fluorine ion F+, i.e. the one which was initially ionized, and
the also singly-charged mother-fragment C3H3F2O+. The F 1s binding energy of
the mother-fragment, after having undergone the full chemical shift due to a
missing fluorine ion, is estimated to be about 8 eV higher compared to that in
the neutral molecule, i.e. about 702 eV. Previous studies support that this
channel under investigation can indeed be expected to be prominent Iwayama13 .

Figure 1: Principal scheme of the process. The X-ray pump pulse ejects a 1s
photoelectron from one of the fluorine atoms of the neutral C3H3F3O molecule.
This step is represented by the upward transition from the ground state to the
core-ionized state of the molecule. In the second step, the core-ionized state
undergoes Auger decay which populates dicationic states of the molecule as
indicated by the downward transition pointing to the repulsive curve. The
doubly-charged molecule can Coulomb-explode into the fluorine ion and the
singly-charged mother-fragment. During this dissociation, a delayed,
circularly polarized X-ray pulse probes the asymmetric scattering of the 1s
photoelectron emitted from one of the remaining fluorine atoms attached to the
singly-charged mother-fragment. This second electron emission in an altered
Coulomb potential of the transient system is shown by the upward transition at
an enlarged distance between the ionic fragments. The present experiment
analyzes the PECD of this secondary F 1s photoelectron of C3H3F2O+ as a
function of the time delay between the pulses.

In the course of this fragmentation, a delayed, circularly-polarized X-ray
pulse with a photon energy of about 710 eV ionizes the 1s electron of one of
the fluorine atoms in the C3H3F2O+ at different distances to the ejected F+
ion. A second photoelectron with a kinetic energy of about 8 eV is emitted.
Those secondary photoelectrons can be energetically separated from the primary
photoelectrons and from other nonlinearly generated electronic contributions.
In fact, signals of the photoelectrons released from the charged system by the
probe pulse scale nonlinearly with the X-ray pulse energy, i.e. quadratic for
a two-photon absorption. Therefore, they can be discriminated from the
photoelectrons released from the neutral molecule, whose signals scale
linearly with the XFEL pulse intensity. Details on the data analysis and a
discussion of alternative possible processes to be taken into account can be
found in Sec. III.4. In the present experiment, the forward–backward
asymmetry, i.e. PECD, of the secondary F 1s photoelectrons released from the
singly-charged mother fragment C3H3F2O+ by the probe pulse is analyzed, while
the initially ionized fluorine atom increases its distance to the remaining
chiral structure along the respective C–F bond.

###  I.2 Theoretical estimates

For enabling access to the transient PECD of the F 1s photoelectrons ejected
from the singly-charged mother-fragment, we modeled the final step of the
process theoretically. It should be stressed, that a full theoretical
treatment of even this last photoionization step is currently almost
impossible. This is because the Auger decay of the initially core-ionized
F+(1s-1) in the trifluoromethyloxirane molecule populates a huge manifold of
different dicationic states, which leave the created F+ and C3H3F2O+ fragments
in a variety of different electronic configurations. As a consequence,
different channels generate different chiral potentials for the scattering of
the secondary F 1s photoelectron. In addition, the internuclear geometry of
the singly-charged mother-fragment relaxes dynamically in the course of the
fragmentation. Moreover, since the center of charge of the C3H3F2O+ fragment
does not necessarily coincide with the center of its mass, the mother-fragment
may rotate as a whole, alternating thereby the relative geometry of the two
species.

Because of these difficulties, we made a qualitative estimate of what can be
expected as outcome of such an experiment. In particular, the present
theoretical model implies the following restrictions. First of all, we used a
frozen internuclear geometry at the equilibrium of the neutral molecule in its
ground state. Secondly, we assumed straight dissociation of the F+ ion along
the respective C–F bond, without possible changes in the relative orientation
of the ions. Finally, we assumed that both, the F+ and C3H3F2O+ ions end up in
their electronic ground configurations after Auger decay. Under those
assumptions, the PECDs of the 1s photoelectrons of individual fluorine atoms
remaining bound to the mother-fragment were computed for the second ionization
step alone at different separations to the dissociating F+ ion in the
photoelectron energy range of 6–10 eV. These calculations were performed by
the single center (SC) method and code SC1 ; SC2 , as outlined in Sec. III.1.

The present theoretical results are collected in Fig. 2. This figure depicts
the PECD (upper panel) as twice the dichroic parameter $\beta_{1}$ and the
angular distribution parameter $\beta_{2}$ (lower panel), computed for all
possible combinations of the dissociating fluorine ion F${}^{+}_{\mathrm{j}}$
and the ionized fluorine atom Fi, as a function of the internuclear separation
$R_{\mathrm{C-F}}=R_{\mathrm{eq}}+\Delta R$. Each depicted point represents a
value averaged over the studied kinetic energy interval to account for the
experimental photon energy bandwidth of $\approx 3.5$ eV. As one can see for
the combination of the F2 atom and the F${}_{1}^{+}$ ion, the computed PECD
grows almost monotonically from a small value of about +2% at
$R_{\mathrm{C-F}}=R_{\mathrm{eq}}$, i.e. at $\Delta R=0$, to a large value of
about +17% at $\Delta R=14$ a.u. For the second remaining fluorine atom F3 and
the same dissociating ion F${}_{1}^{+}$, the computed PECD exhibits an
opposite behaviour, i.e. it monotonically decreases from a similar positive
value of about +2% at $\Delta R=0$ to a large negative value of about –12% at
$\Delta R=14$ a.u., changing thereby its sign around $\Delta R=2$ a.u.

Figure 2: PECD (upper panel) and angular distribution parameter (lower panel)
of 1s photoelectrons of the individual fluorine atoms Fi (as enumerated in the
inset-picture) remaining bound to the singly-charged C3H3F2O+ mother-fragment
and the respective averaged quantities, computed for the
R-trifluoromethyloxirane at different distances
$R_{\mathrm{C-F}}=R_{\mathrm{eq}}+\Delta R$ between the C atom of the
CF2-group and the individual F${}^{+}_{\mathrm{j}}$ fluorine ions dissociating
along the bond (see legend for details).

For the dissociation of the second F${}_{2}^{+}$ ion and ionization of the two
remaining atoms F1 and F3, as well as of the third F${}_{3}^{+}$ ion and the
F1 and F2 atoms, changes of the computed PECDs as functions of the
internuclear separation $\Delta R$ are not as strong, i.e. well within $\pm
6$%. Those PECDs possess distinct oscillations, which are comparable to the
whole variation range, and can change their sign (even multiply as can be seen
for the F${}_{3}^{+}$/F1-combination). Such oscillations might be a result of
interference effects in the multiple scattering of the photoelectron waves
emitted from the mother-fragment on the dissociating fluorine ions. It is
interesting to note that, for a given dissociating F${}^{+}_{\mathrm{j}}$ ion,
PECDs of the two remaining Fi atoms exhibit qualitatively ‘opposite’ trends.
On the contrary, the computed individual angular distribution parameters
$\beta_{2}$ possess very similar trends: They fall monotonically with an
increase of the internuclear separation from a value in between 1.15–1.21 to a
value in between 0.70–0.92. As can also be seen from Fig. 2, the computed
individual PECDs and $\beta_{2}$-parameters are almost saturated to their
asymptotic (non-zero) values at the largest considered internuclear distance
of $\Delta R=14$ a.u.

The black solid curves in Fig. 2 represents the total PECD and
$\beta_{2}$-parameter, averaged over all individual contributions, since
photoelectrons released in different F${}_{\mathrm{j}}^{+}$/Fi-combinations
cannot be distinguished in the present experiment. Because of almost opposite
behaviors of the chiral asymmetries computed for individual combinations,
their strong changes and oscillations as functions of the internuclear
separation cancel out, resulting in a moderate total chiral asymmetry which
varies in between +1.2% and +1.9%. Although these theoretical results should
be considered as a qualitative estimate of the effect, Fig. 2 allows to draw a
few important conclusions. For the considered photoelectron kinetic energy
interval, the PECD computed for the individual F${}_{\mathrm{j}}^{+}$/Fi-
combinations can change as a function of the internuclear separation between
the two fragments by almost an order of magnitude. Those individual chiral
asymmetries can distinctly oscillate with the internuclear separation, and can
even change their sign. The described variations and changes persist for a
rather large internuclear separation beyond the chemical bond breaking, where
the $R_{\mathrm{C-F}}$ bond is extended beyond $\Delta R=10$ a.u. The latter
observation can be related to the long-range impact of the Coulomb repulsion
between the two ionic fragments.

###  I.3 Experimental results and discussion

The present experiment was carried out at the AMO beamline of the LCLS at the
SLAC National Accelerator Laboratory in the USA LCLS_AMO . Both intense pump
and probe X-ray pulses had a similar duration of about 10$\pm$3 fs. To be able
to energetically distinguish the primary and secondary photoelectrons and to
specifically address the F 1s electrons of the singly-charged C3H3F2O+ mother-
fragment at an enantio-sensitive kinetic energy, the photon energies of the
pump and probe pulses were set to 698$\pm$2 eV and 710$\pm$2 eV, respectively.
In order to minimize a possible influence of the pump pulse on the studied
PECD effect, we used a linearly polarized pump pulse, while the time-delayed
probe pulse was circularly polarized. The emitted photoelectrons were detected
with a VMI spectrometer, which provided access to their laboratory-frame
angular emission patterns. The measurements were performed for four time
delays between the pulses at $\tau$=0, 60, 125, and 250 fs. More details on
the beamline operation, experimental setup, and data analysis are provided in
the Secs. III.2–III.4.

In the obtained VMI-spectrum, we observe different photoelectron signals. The
photoelectrons from the neutral molecules ejected by the linearly-polarized
pump pulse emerge in the low kinetic energy range at around 4 eV and cannot
exhibit any chiral asymmetry. Photoelectrons released by the circularly-
polarized probe pulse from the neutral molecules, at around 16 eV, are not
found to possess any significant PECD, presumably because of their rather high
kinetic energy. These observations are consistent with our previous study of
the F 1s photoionization of trifluoromethyloxirane Ilchen17 . As also
expected, photoelectrons released by the circularly-polarized probe pulse from
the neutrally ejected fluorine atoms, at around 12.5 eV kinetic energy,
exhibit no chiral asymmetry. On the contrary, we observe an enantio-selective
chiral asymmetry for the secondary F 1s photoelectrons from the singly-charged
mother-fragment C3H3F2O+ with a kinetic energy of 8 eV. For the time delay
$\tau$=0 fs, i.e. when the two pulses overlap, a variety of processes occurs
within the duration of the pulses, such as Auger decay, charge-migration
dynamics, restructuring before the actual bond-breaking, and rapid change of
the Coulomb potential. All these processes significantly alter the observed F
1s photoelectron signal from C3H3F2O+, and its respective PECD which can,
therefore, not be decisively extracted. For longer delays, when most ultrafast
relaxation processes are essentially completed, the present data analysis
could be performed in a more consistent way. In particular, for the time
delays of $\tau$=60, 125 and 250 fs and the R-enantiomer, we observe PECDs of
$+2.7\%(+1.0\%/-2.0\%)$, $+0.3\%(\pm 2.6\%)$, and $+0.9\%(\pm 3.0\%)$,
respectively. The PECD of $-2.5\%(-1.0\%/+2.0\%)$ measured for the
S-enantiomer and $\tau$=60 fs time delay confirms a chiral origin of the
observed asymmetry.

Figure 3: Average PECD of all combinations of remaining and dissociating
fluorine atoms in singly-charged C3H3F2O+ in its R-enantiomeric form, measured
at different time delays between the pump and probe X-ray pulses (shown by
circles with error bars; refers to the upper horizontal scale), together with
the corresponding average theoretical PECD (solid curve), computed at
different internuclear separations $R_{\mathrm{C-F}}=R_{\mathrm{eq}}+\Delta R$
between the C atom on the CF2-group of the mother-fragment and the
dissociating F+ ion along the respective C–F bond (refers to the lower
horizontal scale). The two horizontal scales are adjusted via a classical
Coulomb explosion model (see text for details). The theoretical value at the
largest shown separations represents an asymptotic PECD for
$R_{\mathrm{C-F}}=\infty$. Experimental PECD measured for S-enantiomer at the
delay of 60 fs is shown by solid square with error bars (refers to the upper
horizontal scale).

These experimental results are collected in Fig. 3 as a function of the time
delay (upper horizontal scale). Owing to the large experimental uncertainties
(see Sec. III.4 for details), an unambiguous PECD can only be observed for the
time delay of $\tau$=60 fs. The red curve in Fig. 3 depicts the average
theoretical PECD from Fig. 2 (black solid curve) as a function of the
internuclear separation $R_{\mathrm{C-F}}=R_{\mathrm{eq}}+\Delta R$ (lower
horizontal scale; note also the axis breaking). In order to interrelate the
internuclear separation with the pump-probe time delay, we used a simplified
classical Coulomb-explosion model. In the model, we considered two point
charges, one localized on the dissociating fluorine and another on the oxirane
ring, being initially separated by 5.5 a.u. The model yields, that the
considered time delays of 60, 125, and 250 fs correspond to the internuclear
separations of about $\Delta R\approx$ 4, 10 and 26 a.u.

It should be stressed, however, that the used Coulomb-explosion model is by
far oversimplified. Indeed, as the F+ fragment moves apart, the positive
charge of the double-hole instantly delocalizes over the molecular skeleton in
order to reduce the Coulomb-repulsion force. Owing to this dynamical charge
delocalization and additional geometry relaxation, the realistic fragmentation
dynamics does not follow an expected $1/R$ repulsion law. In addition, a part
of the repulsion energy can be transferred to the remaining manifold of
internal nuclear degrees of freedom of the whole system, and owing to this
energy dissipation, the overall separation should proceed on a slower
timescale. Nevertheless, since the calculated average chiral asymmetry changes
only moderately over the whole internuclear distance range, we rely in the
further discussion on the implied Coulomb-explosion model.

As one can see from Fig. 3, the average theoretical and experimental PECDs
exhibit a similar value for $\tau$=60 fs and $\Delta R\approx 4$ a.u., whereas
the measured asymmetry is somewhat stronger (note that the large experimental
uncertainties do not allow for a more decisive interpretation). The computed
PECD becomes almost constant ($\approx$+1.5%) at the internuclear separations
of about $\Delta R\approx 10$ a.u. (corresponding to a time delay of about
$\tau$=125 fs). Further on, it saturates very slowly to its asymptotic value
of about +1.2% (shown by the red horizontal bar at the internuclear
separations of around $\Delta R\approx 26$ a.u. after the axis break). These
theoretical predictions agree with the experimental results within the
respective uncertainties, which reveals a PECD on the targeted singly-charged
chiral fragment created via an X-ray photon. A decisive confirmation that the
experimental PECD indeed drops down at 125 fs requires more accurate
calculations of the complicated fragmentation dynamics as well as advanced
experimental methods to reduce the present uncertainties.

##  II Conclusions and outlook

In the present work, we fragment enantiomerically pure trifluoromethyloxirane
and study the specific channel that creates a singly-charged chiral mother-
fragment C3H3F2O+ and a singly-charged fluorine atom. The PECD of the F 1s
photoelectrons of the ionic mother-fragment is the subject of the present
investigation. We employ an X-ray pump – X-ray probe scheme enabled by the
LCLS-XFEL at SLAC in the USA. For the F 1s photoionization of C3H3F2O+ in the
vicinity of a dissociating F+ ion via a circularly polarized X-ray pulse, we
theoretically predict a highly-dynamical chiral asymmetry that differs
enormously for different emitter-site perspectives. The absolute values of the
individual channels’ PECD can grow as high as 17$\%$. It is remarkable that
the PECD provides a dynamical screening of the chirality of the mother-
fragment even at very large internuclear distances to the ejected fluorine
ion. This indicates, that the chiral potential of the mother-fragment is still
influenced by the presence of the dissociating fluorine ion, similar to
findings of a recent time-resolve study of an ordinary circular dichroism (CD)
of a chiral molecule Woerner19 . The prediction of a persisting average PECD
of about 1% agrees qualitatively with the experimental results within the
present experimental uncertainties and quantitatively for the time delay at
$\tau$=60 fs.

It should be noted that the quality of the presently performed experiment to
access time-resolved PECD is compromised by the complexity of the nuclear and
electron dynamics accompanying the process. The advantages of the inner-shell
ionization of the atomic fragment, which allows an unambiguous assignment of
the origin of the secondary photoelectrons, can potentially be utilized in a
more controlled way if e.g. (neutral) dissociation of a specific (unique)
element is governing the fragmentation dynamics. This can in principle be
achieved, e.g., by an optical laser pulse preceding an ionizing XFEL pulse.
There are cases where both, a dissociating atom and its mother-fragment, could
mainly stay in their neutral ground states and no significant charge and bond
rearrangements, as well as rotations of the fragments with respect to each
other would be expected. Very importantly, neutral dissociation evolves on a
much slower time scale, enabling higher resolution in the time domain.

The present work is the first step on a road map that is set to pave the way
for future investigations of chirality with free-electron lasers. Tackling the
underlying challenges effectively requires robust understanding of ultrafast,
nonlinear and polarization dependent physics that in several cases lies at the
very limit of today’s technical capabilities and insights. All of the
mentioned topics entail independent and vital fields of state-of-the-art
science. However, only in combination, a reasonably broad basis can be
established to allow for the site-specific study of fundamental and applied
dynamics in complex chiral systems. Besides further establishing the
fundamentals of nonlinear and ultrafast light–matter interaction in chiral
systems, future studies of dynamics in, e.g., partially chiral peptides and
larger complexes, transiently chiral systems, and nonlinear chirality in the
X-ray regime can be enabled by XFELs. With seeded XFELs, high repetition rate,
few-femtosecond time resolution and advanced detection schemes, studies of
ultrafast dynamics in chiral systems with site specificity yield promising
potential for new perspectives on exploring chiral dynamics.

##  III Methods

###  III.1 Theoretical model

The molecular structure, i.e. assignment of states, their potential energy
curves, and the respective vertical ionization potentials were modeled with
the recently developed toolkit XMOLECULE Inhester16 ; Yajiang19 ; Inhester19 .
To identify the signal from various fragmentation channels, we have computed
core-ionization potentials for the neutral molecule and a number of plausible
atomic and molecular fragments of different charge. The calculations are based
on the $\Delta$-SCF method, where the binding energy is obtained from
independent self-consistent-field (SCF) calculation for the initial and final
electronic states. We have employed the Hartree-Fock or restricted open-shell
Hartree-Fock method, respectively. Specific open-shell electronic
configurations, as for example in atomic fluorine, have been taken into
account via respective multi-configuration self-consistent-field (MCSCF)
calculations. All calculations have been performed with the 6-311G(d,p) basis
set Krishnan80 . Auger decay rates and core-hole lifetimes have been
calculated using the method described in earlier work Inhester16 . The
presently estimated binding energies of the F 1s electrons of different
species are in a reasonable agreement with the present observation, providing
reliable estimates for the photoelectron energies in Fig. 5.

Calculations of the photoelectron angular distributions were carried out by
the single center (SC) method and code SC1 ; SC2 , as described in detail in
our previous work on trifluoromethyloxirane Ilchen17 . In particular,
calculations were performed in the frozen-core Hartree-Fock approximation at
different internuclear geometries between the F+ and C3H3F2O+ ionic fragments.
For numerical convenience, the molecular center was chosen on the carbon atom
of the CF2-group of the mother-fragment, to enable an accurate SC-
representation of the 1s orbitals of the remaining fluorine atoms. In the
calculations, we ignored the 1s core electrons of a dissociating fluorine ion
and reduced its nuclear charges accordingly by 2. This allowed us to use
shorter SC expansions. In particular, using $\ell_{c},|m_{c}|<80$ was
sufficient to accurately describe the included 2s and 2p orbitals of a
dissociating fluorine ion at the largest considered separation of $\Delta
R=14$ a.u. For the photoelectron in the continuum, we used shorter SC
expansions with $\ell_{\varepsilon},|m_{\varepsilon}|<30$. The working
equations required to compute the dichroic parameter are reported in Refs.
Ilchen17 ; Knie14 .

###  III.2 LCLS machine operation

The LCLS provided ultraintense, circularly polarized femtosecond pulses via a
periodic, magnetic dipole structure, the so-called Delta undulator, at 120 Hz
repetition rate Lutman16 ; Hartmann16 . In general, the radiation from an FEL
is generated via relativistically moving electrons that are periodically
displaced by magnetic chicane arrays, so-called undulators. In contrast to
undulators used in storage-ring synchrotron radiation sources, segmented FEL
undulators are longer and provide sufficient interaction of the electrons with
the emitted light in order to form regions of minimal and maximal localization
probability within the electron bunch (coherent microbunching). The light
emitted from these fs-substructures is exponentially amplified in subsequent
undulator segments.

For the present experiment, the LCLS was set up to generate two-color X-ray
pulses, one linearly polarized and one circularly polarized. Each pulse was
produced in the undulator line by a different electron bunch slice by using
the fresh-slice technique Lutman16b . This technique is based on impressing a
temporal-transverse correlation to the electron bunch upstream of the
undulator line and controlling the electron bunch trajectory in two
consecutive undulator sections. The linearly polarized X-ray pulse was
produced in the first 8 undulator segments from the bunch tail, while the
circularly polarized pulse was produced in the variable-polarization Delta
undulator from the bunch head, microbunched in the preceding last 8 regular
undulator segments and the beam diverting technique Lutman16 ; MacArthur18 .

In the second section, the first 7 undulator segments were used to microbunch
the electrons while the Delta undulator was set to produce circularly
polarized X-rays from the microbunched beam. The section used to microbunch
the electron beam was pointed downwards, so that the unwanted linearly
polarized light generated by the first 7 undulator segments was pointed off
the experiment and collimated by a photon collimator. The electron bunch orbit
corrector located just upstream of the Delta undulator integrated in a
quadrupole magnet was used to kick the bunch upwards MacArthur18 , to direct
the circularly polarized beam to the same location of the first X-ray pulse.

Downstream of the first undulator section, a magnetic chicane was used to
delay the electrons, thus granting control on the delay between the X-ray
photon pulses. When the chicane was turned off, the circularly polarized pulse
had a time advance of about 10 to 20 fs on the linearly polarized one, which
would correspond to a negative time-delay. By activating the chicane, the
circularly polarized pulse could be delayed by up to 1 ps with a resolution of
single femtoseconds. The photon energy of each pulse was controlled
independently by setting the magnetic strength, K, of the undulator segments
in the first and the second section at two different values. Switching between
right- and left-handed circular polarization is routinely possible within a
few minutes by setting the magnetic-pole phase shift of the Delta undulator
segment accordingly. The anticipated degree of polarization for these pulses
is $>95\%$.

Figure 4: Scheme of the experiment. A linearly polarized X-ray pulse triggers
the photolysis of C3H3F3O, while a circularly polarized X-ray pulse probes the
PECD of 1s electrons emitted from the remaining fluorine-site in the C3H3F2O+
fragment. A VMI spectrometer measures the electrons from the effusively
injected molecules with angular resolution. The depicted electron VMI images
show one exemplary raw single shot in quadrant 3 (a), an inverted averaged raw
image containing information from 150.000 shots in quadrant 2 (b) which is
dominated by one-photon processes and basically just reflects the ionization
of the neutral molecule by the pump and the probe pulse, and in the upper half
(c) the nonlinear signal from the probe pulse, see also Fig. 5 for a
corresponding angle integrated view. The signal from the singly charged
C3H3F2O+ fragment [see contribution c) in Fig. 5] is in the inner one of the
two visible rings, the outer one stems from neutral fluorine atoms
[contribution b) in Fig. 5]. All data corresponds to $\tau$=60 fs.

###  III.3 Experimental parameters and setup

Fig. 4 illustrates the principal scheme of the experiment. The first-arriving,
linearly polarized, pump pulse with h$\nu$=698$\pm$2 eV provided an average
pulse energy of $\approx$150 $\mu$J, whereas the second, circularly polarized,
probe pulse with h$\nu$=710$\pm$2 eV provided $\approx$50 $\mu$J. The photon
energy bandwidth as well as its jitter broaden the linear pump signal to about
5 eV and to about 3.5 eV for the probe pulse. Both pulses had a duration of
10$\pm$3 fs and were focused to 20$\pm$5 $\mu$m FWHM via Kirkpatrick-Baez
optics into the LAMP endstation at the AMO beamline of the LCLS Bozek09 ;
Ferguson15 ; Osipov18 . With a beamline transmission of 60$\%$ at the chosen
photon energies, the irradiation from these pulses in the interaction region
with the randomly aligned molecular target was about 2$\times 10^{15}$ W/cm2
and 7$\times 10^{14}$ W/cm2, respectively, for the pump and probe pulses. This
level of irradiation yields a non-negligible level of multiple ionizations
within each of these pulses, which complicates the data interpretation and
requires a comparison between high and low irradiation levels (see Sec III.4).

(R)-(+)+3,3,3-Trifluoro-1,2-methyloxirane and its enantiomeric partner
(S)-(–)+3,3,3-Trifluoro-1,2-methyloxirane, each with a purity of 97$\%$ (Sigma
Aldrich), were chosen to provide a molecular compound that yields observer
sites that are located outside of the stereocenter of the molecule, i.e. the
fluorine atoms (see molecular representation in Fig. 4). It is experimentally
simple to handle in terms of effusive gas-phase delivery due to its vapor
pressure of $\approx$530 hPa at room temperature. The three fluorine atoms
increase the absolute photoionization cross section at the chosen photon
energy to a total of 1.2 Mb which is beneficial for a proof-of-principal
experiment, however, it further complicates the differentiation of the
expected PECD, since electrons ionized from the individual fluorine atoms have
previously been shown to yield very different scattering properties in the
molecule Ilchen17 . This is further substantiated by the theoretical results
of Sec. I.2. For a detailed interpretation of the data, it furthermore needs
to be taken into account that the cross sections of the other elements of the
molecule are non-negligible at the chosen photon energies. In particular, the
three carbon atoms as well as the single oxygen atom are accounting for
$\approx$350 kbarn each, whereas the three hydrogen atoms only contribute
$\approx$0.1 kbarn in total. All of these constituents may also undergo
multiple photon absorptions at high intensities.

Once ejected from the chiral target, the photoelectrons are projected onto a
position-sensitive micro-channel-plate (MCP) detector via electrostatic
electrodes, i.e. a VMI-spectrometer Eppink97  (see a schematic representation
in Fig. 4). The current from the MCPs illuminates a fast phosphorescent
screen, i.e. type P47, that is read out by a 1 Megapixel low-noise camera. The
kinetic energy window defined by the electrostatic field was set to 0–20 eV in
order to provide maximum resolution for low kinetic electron energies. The
resolution is estimated to be in the order of E/$\Delta$E$>100$. Due to these
settings, no Auger electrons were recorded since their kinetic energies lie
mainly in between 570 and 650 eV, as calculated by the XMOLECULE toolkit
Inhester16 . Exemplary VMI images for a single shot, an average image as well
as the derived nonlinear spectral contributions are depicted in Fig. 4.

###  III.4 Data interpretation and analysis

For each combination of polarization, target, and delay, we acquired in
average 150,000 images. Resulting from the above described experimental
conditions and present theoretical estimates for the F 1s binding energies of
the neutral molecule, electrons from one-photon absorption arrived with
kinetic energies of about 4 eV, if ionized by the pump pulse, and about 16 eV,
if ionized by the probe pulse (see upper panel of Fig. 5). Those correspond to
an F 1s binding energy in the C3H3F3O molecule of $E_{\mathrm{bind}}=694$ eV
and are indicated in the upper panel as signals a). As discussed above and in
agreement with the experimental data, neither of them are expected to yield a
significant PECD. Since only a small fraction of the target ionized by the
probe pulse corresponds to the ‘pumped’ target, the one-photon contribution a)
was subtracted by filtering the nonlinear pulse-energy progression via sorting
for high contributions in the region of interest (more details below). The
quadratic progression for the signal over the FEL pulse energy was cross
checked, and clearly supports the nonlinear character of the spectrum
highlighted in red in the lower panel of Fig. 5.

As indicated in the upper panel of Fig. 5 with a red arrow, absorption of the
first photon followed by the Auger decay and Coulomb explosion of the doubly-
ionized molecule results in a shift of the F 1s binding energy for the
C3H3F2O+ mother-fragment by about 8 eV, i.e. it has a binding energy of
$E_{\mathrm{bind}}=702$ eV. The partner-fragment of this dissociation channel,
i.e. the F+ ion, has a calculated 1s binding energy of 726.6 eV and can
therefore not be ionized by any of the pulses. The probe-pulse will not only
release the desired F 1s photoelectrons from the singly-charged mother-
fragment C3H3F2O+ [contribution c) in the lower panel of Fig. 5]. The lower
panel of Fig. 5 indicates the presence of further prominent fragments in the
‘pumped’ target, namely: b) the ionization of neutral F atoms by the probe
pulse ($E_{\mathrm{bind}}=697.6$ eV), as well as residuals from non-optimal
background subtraction of a); d) ionization of the doubly-charged (intact)
molecules C3H3F3O2+ by the probe pulse ($E_{\mathrm{bind}}=704.7$ eV); and e)
signal stemming from sequential ionization by the pump pulse of all neutral
fluorine-containing fragments with binding energies in between the neutral
molecule and neutral atomic fluorine. Further (unmarked) nonlinear
contributions from the probe-pulse could be originated by CF${}_{3}^{+}$
($E_{\mathrm{bind}}=704.5$ eV), CF${}_{2}^{+}$ ($E_{\mathrm{bind}}=704.9$ eV),
CF+ ($E_{\mathrm{bind}}=706.4$ eV) and C3H3F2O2+ ($E_{\mathrm{bind}}=707.8$
eV). As mentioned in the previous section, about one third of all fragmenting
channels can be originated by the photon-absorption of other atoms in the
molecule, which yields very different dynamics and dissociation products that
cannot be accounted for in the current experiment.

Figure 5: Illustration of energy distributions of the total (upper panel) and
nonlinear (lower panel) electron emission yields for the exemplary case of
$\tau$=60 fs. The former is dominated by the one-photon absorption signals,
while the latter by the two-photon absorption signals (as indicated in each
panel). The calculated contributions of core electrons of fluorine under
different conditions are indicated by letters a)–e) and, for the subject of
this study c), an arrow further illustrates the shift. Those linear and
nonlinear contributions correspond to: a) one photon ionization of the neutral
molecule with the pump or probe pulse, and b)–e) ionization of F 1s in
different fragments, as indicated in the panel (see also text for details). An
inset to the lower panel illustrates the theoretically predicted kinetic-
energy-dependence of the total PECD, computed for the respective internuclear
separation of $\Delta R=4$ a.u.

The F 1s photoelectrons of dissociated neutral fluorine atoms account for a
significant nonlinear pump-probe signal at a kinetic energy of 12.4 eV. It is
interesting to note that despite the large photon energy deposited in the
molecule, a significant amount of neutral fluorine atoms is apparently
created. This channel is in competition with c) since the underlying processes
exclude each other. This signal was analyzed for PECD but, as anticipated due
to the large kinetic energy, no sizable PECD was found. Contribution d)
represents the ionization of the doubly-charged intact molecule that can stem
mainly from sequential ionization via the probe-pulse, or at time-overlap, it
could occur as combination of photons from the pump and probe pulse. A small
contribution from sequential two-photon absorption from the linearly polarized
pump pulse of neutral fragments could explain the signal shifted towards lower
kinetic energies $<3$ eV. In the case of a fast dissociation, neutral fluorine
atoms can also be ionized by the pump pulse (calculated kinetic energy is
about 0.4 eV). Given its bandwidth of about 5 eV, this could in principle
contribute to the kinetic energy region below 3 eV.

The photon energy jitter can be corrected in the analysis, however, the broad
bandwidth inevitably leads to an averaging over the highly energy-dependent
PECD. The spatial and timing jitter are negligible due to the chosen operation
mode as described in Sec. III.2. A relative pixel-to-energy calibration of the
VMI images was performed by shifting the photon energy of the pump pulse
between 690 eV and 715 eV. The absolute photon energy is derived from the
calculated binding energy of the neutral molecule. Due to the complex machine
setup and a resulting lack of time, a common transmission-normalization to the
racemic target was only done for 60 fs delay. However, due to the subtraction
of normalized images from different targets and different polarizations under
otherwise similar conditions, the PECD determination for the other time delays
was still possible.

After normalization and calibration of the VMI-images, they are sorted into
different intensity regimes of the incoming light as well as signal strength
in the ROI (see Fig. 5). This is feasible due to the stochastic nature of the
photon generation, which causes a large variation of the pulse energy from
shot to shot. It can be regarded as intrinsic intensity scan. The images were
subsequently Abel-inverted Vrakking01  in order to recover the original three-
dimensional distribution of the electron emission. Due to a small damaged area
on the detector in one quadrant, only data from one half of the detector was
taken into account. Subtracting the average of the lower half of the intensity
contributions in the ROI from the average of the highest ten percent, as
identified to be the best trade-off between strong pump-probe signal and low
contributions from sequential ionization, allowed for self-referencing of the
individual spectra. This was cross checked for consistency with a dedicated
background subtraction of individual runs containing no circular color. In
Fig. 4, the pump-probe data is furthermore illustrated as VMI image (upper
half). As reference, also averaged data from the highest 10% of the recorded
pulse energies (lower right) as well as an exemplary single shot are depicted.

For deriving the PECD, the such processed normalized images acquired for left-
and right-handed circular polarizations for the same enantiomer are subtracted
from each other. The resulting asymmetric signal in the full three-dimensional
angular distribution for the observed F 1s region of C3H3F2O+ was then
quantified for its forward–backward asymmetry percentage. Contributions b),
c), and d) were fit with Gaussian curves in order to extract the individual
contribution of c). Due to this angle and energy integration of signal c) for
individual quadrants, it is not feasible to derive an energy-resolved PECD.
For 60 fs, we have additionally confirmed the anticipated sign-change of the
forward–backward asymmetry with swapping from R(+) to S(-) enantiomers. For
250 fs delay, this method of enantiomer-change was the only available data
set, which is part of the reason for the largest of the uncertainties. We have
partly encountered a slight energy and bandwidth shift after swapping
helicities of the photons, which also results in a larger uncertainty due to
slightly different kinetic energy contributions to the PECD. Combining these
imperfections with the estimated additional uncertainties of the manifold
processes after inner-shell ionization by the pump pulse, the complex machine
conditions, the partly damaged detector and therefore reduced statistics, the
broad bandwidth of the photons and their jitter as well as the challenging
derivation of the nonlinear signal and its angular distribution, causes the
overall experimental uncertainty to be large (see Fig. 3). Therefore, only the
60 fs delay reveals an unambiguous PECD. It should, however, be stressed that
the robust probe signal of the circularly polarized pulse, as shown in the
lower part of Fig. 5, is a significant outcome of the experiment in itself.
The present experimental procedure does not provide access to the energy-
resolved PECD of signal c). An inset to the lower panel of Fig. 5 illustrates
that the averaged total PECD, computed for the internuclear separation of
$\Delta R=4$ a.u. corresponding to the time delay of 60 fs, increases smoothly
from about 0.8% to 1.9% in the kinetic energy range of 6–10 eV, yielding the
energy-averaged value of about 1.4%.

###### Acknowledgements.

We gratefully acknowledge the fruitful discussions with M. Larsson (University
of Stockholm, Sweden), V. Zhaunerchyk (University of Gothenburg, Sweden), B.
Erk (DESY, Germany), L. Nahon (SOLEIL, France), and R. Boll (European XFEL,
Germany). Use of the Linac Coherent Light Source (LCLS), SLAC National
Accelerator Laboratory, is supported by the U.S. Department of Energy, Office
of Science, Office of Basic Energy Sciences under Contract No. DE-
AC02-76SF00515. The authors acknowledge the invaluable support of the
technical and scientific staff of the LCLS at SLAC National Accelerator
Laboratory. This work was funded in part by the Deutsche
Forschungsgemeinschaft (DFG) – Projektnummer 328961117 – SFB 1319 ELCH
(Extreme light for sensing and driving molecular chirality). M.I., P.S., V.M.,
and Z.L. acknowledge funding from the Volkswagen Foundation within a Peter
Paul Ewald-Fellowship. G.H. and A.K. acknowledge funding from the BMBF
(05K16RKA) and A.O.L. from the Knut and Alice Wallenberg Foundation. P.R.
acknowledges funding from the Studienstiftung des deutschen Volkes and from
the German Academic Exchange Service DAAD. S.B. was supported by the Helmholtz
Initiative and Networking Fund through the Young Investigators Group Program
and acknowledges support from the Deutsche Forschungsgemeinschaft, project
B03/SFB755. T.J.A.W. is supported by the U.S. Department of Energy, Office of
Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and
Biosciences Division.

Author contributions
M.I., A.K., and S.M. have conceived the experiment. The experiment was
performed by M.I., Ph.S., G.H., P.R., R.N.C., A.G., N.H., W.H., T.O., D.R.,
P.W., T.W., S.B., A.K., and S.M. Machine operation and diagnostics were
conducted by A.A.L., J.P.M., T.M., H.-D.N., and Z.H. P.S., G.H., and M.I. have
analyzed the data. N.M.N., L.I., Z.L., and Ph.V.D. performed the theoretical
calculations. M.I. and Ph.V.D. have written the paper with dedicated
contributions by Z.L., L.I., A.A.L., and further contributions from all co-
authors.

## References

  * (1) B. Ritchie, Theory of the Angular Distribution of Photoelectrons Ejected from Optically Active Molecules and Molecular Negative Ions, Phys. Rev. A 13, 1411 (1976).
  * (2) L. Nahon, G. A. Garcia, and I. Powis, Valence Shell One-Photon Photoelectron Circular Dichroism in Chiral Systems, J. Electron Spectrosc. Relat. Phenom. 204, 322 (2015).
  * (3) R. Hadidi, D. K. Bozanic, G. A. Garcia, and L. Nahon, Electron Asymmetries in the Photoionization of Chiral Molecules: Possible Astrophysical Implications, Adv. Phys. X 3, 1477530 (2018).
  * (4) U. Hergenhahn, E. E. Rennie, O. Kugeler, S. Marburger, T. Lischke, I. Powis, and G. Garcia, Photoelectron Circular Dichroism in Core Level Ionization of Randomly Oriented Pure Enantiomers of the Chiral Molecule Camphor, J. Chem. Phys. 120, 4553 (2004).
  * (5) M. Ilchen, G. Hartmann, P. Rupprecht, A. N. Artemyev, R. N. Coffee, Z. Li, H. Ohldag, H. Ogasawara, T. Osipov, D. Ray, et al., Emitter-Site-Selective Photoelectron Circular Dichroism of Trifluoromethyloxirane, Phys. Rev. A 95, 053423 (2017).
  * (6) C. Lux, M. Wollenhaupt, T. Bolze, Q. Liang, J. Kohler, C. Sarpe, and T. Baumert, Circular Dichroism in the Photoelectron Angular Distributions of Camphor and Fenchone from Multiphoton Ionization with Femtosecond Laser Pulses, Angew. Chem. Int. Ed. 51, 5001 (2012).
  * (7) C. S. Lehmann, N. B. Ram, I. Powis, and M. H. M. Janssen, Imaging Photoelectron Circular Dichroism of Chiral Molecules by Femtosecond Multiphoton Coincidence Detection, J. Chem. Phys. 139, 234307 (2013).
  * (8) S. Beaulieu, S. Comby, B. Fabre, D. Descamps, A. Ferré, G. Garcia, R. Géneaux, F. Légaré, L. Nahon, S. Petit, et al., Probing Ultrafast Dynamics of Chiral Molecules Using Time-Resolved Photoelectron Circular Dichroism, Faraday Discuss. 194, 325 (2016).
  * (9) A. Comby, S. Beaulieu, M. Boggio-Pasqua, D. Descamps, F. Légareé, L. Nahon, S. Petit, B. Pons, B. Fabre, Y. Mairesse, et al., Relaxation Dynamics in Photoexcited Chiral Molecules Studied by Time-Resolved Photoelectron Circular Dichroism: Toward Chiral Femtochemistry, J. Phys. Chem. Lett. 7, 4514 (2016).
  * (10) M. Wollenhaupt, Universality of Photoelectron Circular Dichroism in the Photoionization of Chiral Molecules, New J. Phys. 18, 102002 (2016).
  * (11) B. Erk, R. Boll, S. Trippel, D. Anielski, L. Foucar, B. Rudek, S. W. Epp, R. Coffee, S. Carron, S. Schorb, et al., Imaging Charge Transfer in Iodomethane Upon X-Ray Photoabsorption, Science 345, 288 (2014).
  * (12) K. Schnorr, A. Senftleben, M. Kurka, A. Rudenko, G. Schmid, T. Pfeifer, K. Meyer, M. Kübel, M. F. Kling, Y. H. Jiang, et al., Electron Rearrangement Dynamics in Dissociating I${}_{2}^{n+}$ Molecules Accessed by Extreme Ultraviolet Pump-Probe Experiments, Phys. Rev. Lett. 113, 073001 (2014).
  * (13) C. E. Liekhus-Schmaltz, I. Tenney, T, Osipov, A. Sanchez-Gonzalez, N. Berrah, R. Boll, C. Bomme, C. Bostedt, J. D. Bozek, S. Carron, et al., Ultrafast Isomerization Initiated by X-Ray Core Ionization, Nat. Commun. 6, 8199 (2015).
  * (14) K. R. Ferguson, M. Bucher, T. Gorkhover, S. Boutet, H. Fukuzawa, J. E. Koglin, Y. Kumagai, A. A. Lutman, A. Marinelli, M. Messerschmidt, et al., Transient Lattice Contraction in the Solid-to-Plasma Transition, Sci. Adv. 2, e1500837 (2016).
  * (15) C. S. Lehmann, A. Picón, C. Bostedt, A. Rudenko, A. Marinelli, D. Moonshiram, T. Osipov, D. Rolles, N. Berrah, C. Bomme, et al., Ultrafast X-Ray-Induced Nuclear Dynamics in Diatomic Molecules Using Femtosecond X-Ray-Pump-X-Ray-Probe Spectroscopy, Phys. Rev. A 94, 013426 (2016).
  * (16) A. Picón, C. S. Lehmann, C. Bostedt, A. Rudenko, A. Marinelli, T. Osipov, D. Rolles, N. Berrah, C. Bomme, M. Bucher, et al., Hetero-Site-Specific X-Ray Pump-Probe Spectroscopy for Femtosecond Intramolecular Dynamics, Nat. Commun. 7, 11652 (2016).
  * (17) N. L. Opara, I. Mohacsi, M. Makita, D. Castano-Diez, A. Diaz, P. Juranić, M. Marsh, A. Meents, C. J. Milne, A. Mozzanica, et al., Demonstration of Femtosecond X-Ray Pump X-Ray Probe Diffraction on Protein Crystals, Struct. Dynam. 5, 054303 (2018).
  * (18) E. Allaria, B. Diviacco, C. Callegari, P. Finetti, B. Mahieu, J. Viefhaus, M. Zangrando, G. De Ninno, G. Lambert, E. Ferrari, et al., Control of the Polarization of a Vacuum-Ultraviolet, High-Gain, Free-Electron Laser, Phys. Rev. X 4, 041040 (2014).
  * (19) T. Mazza, M. Ilchen, A. J. Rafipoor, C. Callegari, P. Finetti, O. Plekan, K. C. Prince, R. Richter, M. B. Danailov, A. Demidovich, et al., Determining the Polarization State of an Extreme Ultraviolet Free-Electron Laser Beam Using Atomic Circular Dichroism, Nat. Commun. 5, 4648 (2014).
  * (20) A. A. Lutman, J. P. MacArthur, M. Ilchen, A. O. Lindahl, J. Buck, R. N. Coffee, G. L. Dakovski, L. Dammann, Y. Ding, H. A. Dürr, et al., Polarization Control in an X-Ray Free-Electron Laser, Nat. Photon. 10, 468 (2016).
  * (21) G. Hartmann, A. O. Lindahl, A. Knie, N. Hartmann, A. A. Lutman, J. P. MacArthur, I. Shevchuk, J. Buck, A. Galler, J. M. Glownia, et al., Circular Dichroism Measurements at an X-Ray Free-Electron Laser With Polarization Control, Rev. Sci. Instrum. 87, 083113 (2016).
  * (22) H. Iwayama, N. Sisourat, P. Lablanquie, F. Penent, J. Palaudoux, L. Andric, J. H. D. Eland, K. Bučar, M. Žitnik, Y. Velkov, et al., A Local Chemical Environment Effect in Site-Specific Auger Spectra of Ethyl Trifluoroacetate, J. Chem. Phys. 138, 024306 (2013).
  * (23) Ph. V. Demekhin, A. Ehresmann, V. L. Sukhorukov, Single Center Method: A Computational Tool for Ionization and Electronic Excitation Studies of Molecules, J. Chem. Phys. 134, 024113 (2011).
  * (24) S. A. Galitskiy, A. N. Artemyev, K. Jänkälä, B. M. Lagutin, and Ph. V. Demekhin, Hartree-Fock Calculation of the Differential Photoionization Cross Sections of Small Li Clusters, J. Chem. Phys. 142, 034306 (2015).
  * (25) Webpage of the LCLS Beamline AMO:
https://lcls.slac.stanford.edu/instruments/amo

  * (26) D. Baykusheva, D. Zindel, V. Svoboda, E. Bommeli, M. Ochsner, A. Tehlar, H. J. Wörner, Real-Time Probing of Chirality During a Chemical Reaction, Proc. Natl. Acad. Sci. USA, 116, 23923 (2019).
  * (27) L. Inhester, K. Hanasaki, Y. Hao, S.-K. Son, and R. Santra, X-Ray Multiphoton Ionization Dynamics of a Water Molecule Irradiated by an x-Ray Free-Electron Laser Pulse, Phys. Rev. A 94, 023422 (2016).
  * (28) Y. Hao, L. Inhester, S.-K. Son, and R. Santra, Theoretical Evidence for the Sensitivity of Charge-Rearrangement-Enhanced x-Ray Ionization to Molecular Size, Phys. Rev. A 100, 013402 (2019).
  * (29) L. Inhester, Z. Li, X. Zhu, N. Medvedev, and T. J. A. Wolf, Spectroscopic Signature of Chemical Bond Dissociation Revealed by Calculated Core-Electron Spectra, J. Phys. Chem. Lett. 10 6536 (2019).
  * (30) R. Krishnan, J.S. Binkley, R. Seeger, and J. A. Pople, Self‐consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions, J. Chem. Phys. 72, 650 (1980).
  * (31) A. Knie, M. Ilchen, P. Schmidt, P. Reiß, C. Ozga, B. Kambs, A. Hans, N. Müglich, S. A. Galitskiy, L. Glaser, et al., Angle-Resolved Study of Resonant Auger Decay and Fluorescence Emission Processes After Core Excitations of the Terminal and Central Nitrogen Atoms in $N_{2}O$, Phys. Rev. A 90, 013416 (2014).
  * (32) A. A. Lutman, T. J. Maxwell, J. P. MacArthur, M. W. Guetg, N. Berrah, R. N. Coffee, Y. Ding, Z. Huang, A. Marinelli, S. Moeller, et al., Fresh-Slice Multicolour X-Ray Free-Electron Lasers, Nat. Photon. 10, 745 (2016).
  * (33) J. P. MacArthur, A. A. Lutman, J. Krzywinski, and Z. Huang, Microbunch Rotation and Coherent Undulator Radiation from a Kicked Electron Beam, Phys. Rev. X 8, 041036 (2018).
  * (34) J. D. Bozek, AMO Instrumentation for the LCLS X-Ray FEL, Eur. Phys. J. - Special Topics 169, 129 (2009).
  * (35) K. R. Ferguson, M. Bucher, J. D. Bozek, S. Carron, J.-C. Castagna, R. Coffee, G. I. Curiel, M. Holmes, J. Krzywinski, M. Messerschmidt, et al., The Atomic, Molecular and Optical Science Instrument at the Linac Coherent Light Source, J. Synchr. Rad. 22, 492 (2015).
  * (36) T. Osipov, C. Bostedt, J.-C. Castagna, K. R. Ferguson, M. Bucher, S. C. Montero, M. L. Swiggers, R. Obaid, D. Rolles, A. Rudenko, et al., The LAMP Instrument at the Linac Coherent Light Source Free-Electron Laser, Rev. Sci. Instrum. 89, 035112 (2018).
  * (37) A. T. J. B. Eppink and D. H. Parker, Velocity Map Imaging of Ions and Electrons Using Electrostatic Lenses: Application in Photoelectron and Photofragment Ion Imaging of Molecular Oxygen, Rev. Sci. Instrum. 68, 347 (1997).
  * (38) M. J. J. Vrakking, An Iterative Procedure for the Inversion of Two-Dimensional Ion/Photoelectron Imaging Experiments, Rev. Sci. Instrum. 72, 4084 (2001).