|  Photoelectron circular dichroism in angle-resolved photoemission from
liquid fenchone†
---|---
|  Marvin Pohl,a,b,c,‡ Sebastian Malerz,a,‡ Florian Trinter,a,d Chin Lee,b,c
Claudia Kolbeck,a,§ Iain Wilkinson,e Stephan Thürmer,f Daniel M. Neumark,b,c
Laurent Nahon,g Ivan Powis,h Gerard Meijer,a Bernd Winter,a Uwe Hergenhahn∗a
|  We present an experimental X-ray photoelectron circular dichroism (PECD)
study of liquid fenchone at the C 1s edge. A novel setup to enable PECD
measurements on a liquid microjet [Malerz et al., Rev. Sci. Instrum., 2022,
93, 015101] was used. For the C 1s line assigned to fenchone’s carbonyl
carbon, a non-vanishing asymmetry is found in the intensity of photoelectron
spectra acquired under a fixed angle in the backward-scattering plane. This
experiment paves the way towards a novel probe of the chirality of
organic/biological molecules in aqueous solution.

##

††footnotetext: a Molecular Physics, Fritz-Haber-Institut der Max-Planck-
Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany. E-mail: hergenhahn@fhi-
berlin.mpg.de††footnotetext: b Department of Chemistry, University of
California, Berkeley, CA 94720, USA††footnotetext: c Chemical Sciences
Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720,
USA††footnotetext: d Institut für Kernphysik, Goethe-Universität Franfurt am
Main, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany††footnotetext: e
Department of Locally-Sensitive & Time-Resolved Spectroscopy, Helmholtz-
Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, 14109
Berlin, Germany††footnotetext: f Department of Chemistry, Graduate School of
Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502,
Japan††footnotetext: g Synchrotron SOLEIL, L’Orme des Merisiers, St. Aubin, BP
48, 91192 Gif sur Yvette, France††footnotetext: h School of Chemistry, The
University of Nottingham, University Park, Nottingham, UK††footnotetext: †
Electronic Supplementary Information (ESI) available: Raw data, further
details on peak-background separation. See DOI:
10.1039/cXCP00000x/††footnotetext: ‡ These authors contributed equally to this
work.††footnotetext: § Current address: sonUtec GmbH, Mittlere-Motsch-Straße
26, 96515 Sonneberg, Germany.

##  1 Introduction

Many of the molecules providing the basis of living matter are chiral, that is
they may exist in two different 3-D structural forms, which are mirror images
of each other. Due to steric effects, these two forms or enantionmers may
behave very differently when they interact with other chiral partners: this is
chiral recognition, a fundamental metabolic process. Furthermore, the chiral
molecular building blocks of terrestrial life, such as amino-acids and nucleic
acid sugars, are almost exclusively found as single enantiomers, a fascinating
property known as the homochirality of life.1 As a consequence, it is
immensely important to have the means to distinguish between enantiomers at
the molecular level, despite them possessing largely identical physico-
chemical properties such as mass, spectra, and energetics (apart from putative
tiny electroweak effects2). Therefore, chiral discrimination, or recognition,
requires interaction with another chiral entity. A common example is the
interaction with circularly polarized light (CPL), which gives rise to the
well-known circular dichroism (CD) effect in absorption.3, 4 Relatedly, chiral
(spin-polarized) electrons have also been shown to discriminate for the
molecular-level handedness of a sample.5, 6

It is of great appeal that elements of these two techniques are combined in
yet another effect that discriminates between different enantiomers of a
species, namely photoelectron circular dichroism (PECD). This term designates
an asymmetry in the angle-resolved photoelectron (PE) flux after ionization of
a sample of chiral molecules with circularly polarized light. The effect
requires a suitable geometry of the experiment, as it vanishes in the plane
perpendicular to the photon propagation direction (‘dipole plane’). It can be
observed as a difference of photoelectron intensity between two measurements,
in which either (1) the same sample is probed by left- vs. right-handed
circularly polarized light, or (2) the same sample is probed by any helicity
of the light, and electrons are collected under two different angles, one in
the forward and the other in the backward scattering direction, with the two
angles being mirror imaged at the dipole plane, or (3) by probing the two
different enantiomers of a substance with either helicity, at an angle outside
of the dipole plane. Historically, the potential existence of PECD was noted
in theoretical papers in the 1970s,7, 8 but only abstract model systems were
considered, and these works received only minor attention at that time. It was
over twenty years later that a dedicated numerical simulation on actual
molecules by I. Powis suggested that this effect could have an observable
magnitude.9 In fact, it was simulated to be significantly greater than that of
more conventional chiroptical methods, since PECD is already allowed in the
pure electric dipole approximation, in contrast to regular CD.10 Thereafter,
the first experimental observations of PECD were reported for valence
photoionization,11, 12, 13 and about two years later, a systematic
experimental and theoretical study of PECD in core-level photoionization of
gaseous camphor confirmed its existence and several features of its behaviour,
including its general manifestation within a few tens of eV of an ionization
threshold, where the generated photoelectrons are sensitive to the subtleties
of any local chiral potential.14 Since then, PECD has been studied in the case
of one-photon valence and core-level photoionization of gaseous chiral free
molecules15, 16, 17 and up to clusters and nanoparticles.18, 19, 20
Furthermore, its investigation has broadened to include multi-photon21, 22,
23, 24, 25 and time-dependent26, 27 ionization processes. Using charged
particle coincidence experiments, the underlying molecular-frame photoelectron
angular distributions (PADs) were also measured.28, 29 A profound analysis of
the symmetry principles underlying the original PECD mechanism and its
variants has appeared recently,30 and the mechanism underlying the build-up of
the asymmetric emission in one-photon PECD has been investigated from a
fundamental viewpoint.31, 32

Here, we present experimental results in the framework of single-photon
photoionization processes in a liquid. The primary question we aim to answer
is whether PECD can be observed from the photoionization of a liquid composed
of chiral constituents. Since the existence of PECD in the gas phase does not
require any local molecular ordering, from symmetry principles, this may well
be the case. On the other hand, we are not aware of any experiments trying to
directly address this question, although a first PECD valence-shell study on
pseudo-amorphous nanoparticles of the amino-acid serine revealed a reduced but
yet non-vanishing PECD.20 Some of the authors therefore have constructed a new
setup dedicated to PECD studies on a liquid microjet, as described
elsewhere.33 Here, we present a complete feasibility study of actual PECD
detection using a nearly-neat liquid microjet of fenchone. This work opens up
the perspective to study the handedness of chiral molecules in aqueous
solution, such as amino acids, their building blocks,34 or sugars.35

Fenchone (C10H16O, 1,3,3-Trimethylbicyclo[2.2.1]heptan-2-one) is a chiral
bicyclic mono-terpenoid built from a six-membered ring with a single-carbon
bridge connecting C1 and C4 and featuring several methyl ligands and a
carbonyl (C=O) group adjacent to one of the asymmetrically substituted chiral
centres. A structural diagram is shown below in Fig. 1. The (1R,4S)-fenchone
enantiomer naturally occurs in fennel. Importantly, the C=O carbonyl carbon
has a 1s core binding energy shift that allows it to be spectroscopically
distinguished from the remaining carbon atoms in a core-level photoelectron
spectrum (PES).33 Moreover, it has been shown to exhibit a sizeable PECD
effect in the gas phase.36, 33 Follow-on studies on this molecule also
examined PECD effects in its valence PES,37, 38 and subsequently targeted
multi-photon PECD processes21, 23, 39, 40 and complex electronic-structure
dynamics using ultrafast laser pulses.26, 41 The choice of fenchone for these
prototypical studies has been partially motivated by the relative rigidity of
its geometric structure, making conformational isomerism a lesser complication
in the interpretation of any associated results, in comparison to those from
other similarly-sized chiral systems. In this work, we will address single-
photon C 1s core-level PES of fenchone in its native, liquid form, as this
presents a clear-cut case for the demonstration of liquid-phase PECD. A small
subset of the data from this project was already used for illustrative
purposes in an apparatus paper that some of the authors have recently
published.33

##  2 Experimental

Photoionization experiments on a liquid microjet of fenchone were performed
using circularly polarized synchrotron radiation from an undulator, and a
hemispherical electron analyzer arranged in the backward-scattering plane.
Data were acquired over two measurement campaigns with a setup described
recently.33 Details of the experimental setup are as follows:

###  2.1 Synchrotron Radiation

The experiments used synchrotron radiation in the soft X-ray range provided by
the P04 beamline of the PETRA III storage ring at DESY, Hamburg (Germany).
This beamline is equipped with an APPLE-II-type undulator42 allowing
experiments with high-purity CPL.43 A VLS (variable line spacing)
monochromator’s planar grating of 400 l/mm spacing and 15 nm groove depth
(campaign 1) or 1200 l/mm spacing and 9 nm groove depth (campaign 2) was used
with typical exit-slit settings of 100-120 µm, yielding an energy resolution
of approximately 90 meV (400 l/mm) or 30 meV (1200 l/mm) at photon energies
slightly above the carbon K-edge. The minimum spot size of the beamline (using
smaller exit-slit openings than 30 µm) has been measured as (h x v) 10 x 10
µm2 in the nominal focus position of the optics.44, 45 For our experiment, due
to spatial constraints, the interaction region had to be placed approximately
220 mm downstream of that position, the vertical focus however was shifted
accordingly using a pair of Kirkpatrick-Baez mirrors.43 We correspondingly
estimate the beam spot size at the point of interaction to be (h $\times$ v)
180 $\times$ 35 µm2.

The photon-energy scale of the monochromator was calibrated by a standard
procedure that optimizes the pitch angle for specular reflection. We estimate
the residual error after this procedure as $\pm 0.2$ eV in the photon-energy
range used in this work.

Circularly polarized radiation of either helicity was produced by shifting the
magnet blocks of the APPLE-II undulator accordingly. In a separate experiment,
the polarization of the ensuing radiation has been analyzed by measuring the
photoelectron angular distributions (PADs) of various gases in the plane
perpendicular to the light propagation direction.46, 47 Measurements were
performed for both signs of the undulator geometric shift, corresponding to
both output radiation helicities. The shift was varied in small steps in the
spectral region of interest, preferentially yielding circularly polarized
light. Then the Stokes parameter for circular polarization was calculated as
the complement to the Stokes parameters for the residual amount of linear
polarization. Experiments were carried out with the 400 l/mm, 15 nm groove
depth grating and yielded absolute values for the circular Stokes parameter,
$S_{3}$, larger than 0.98 for photon energies between 550 and 1250 eV, and in
an interval of values of the undulator shift about 5 mm wide. The photon
energies of interest in this work are somewhat lower, however, namely in the
vicinity of the carbon K-ionization edges of fenchone, slightly below 300 eV.
In this energy region, some degradation of the purity of circular polarization
has been observed in experiments on another APPLE-II undulator beamline, and
was attributed to carbon contamination of the optical elements.48 In any case,
on that occasion $|S_{3}|$ was still found to be $>0.92$. Despite the lack of
direct measurements for our setup, we consider it fair to assume similar or
lesser circular polarization degradation here. Correspondingly, no further
normalization of the measured PECD magnitude has been applied.

By carrying out a PECD measurement on the fenchone gaseous phase evaporating
from the liquid jet, we established a correspondence of the geometric shift
with negative sign to left-handed circularly polarized light (l-CPL),
according to the ‘optical’ convention.49, 36, 33

###  2.2 Liquid Microjet

Both enantiomers of fenchone were obtained commercially (Sigma-Aldrich, purity
$\geq 98$%) and were used without further purification. A microjet was
produced by pushing the liquid through a glass capillary nozzle with an inner
diameter of 28 µm by a commercial HPLC pump (Shimadzu LC-20AD). A flow rate of
0.6-0.8 ml/min at pressures of 11-14 bar was typically used. The sample was
made conductive by addition of 75 mM tetrabutyl-ammonium nitrate salt (TBAN),
to prevent charging by the photoionization process. Our liquid-jet holder
features a cooling jacket that was stabilized to 10 ∘C. Since it, however,
does not extend up to the nozzle tip, a slightly higher temperature of the
injected liquid cannot be ruled out. The liquid stream was directed
horizontally, perpendicular to the light propagation axis. After passing the
interaction region, the jet was collected on a cold trap cooled by liquid
nitrogen, thus maintaining the interaction chamber pressure below 10-3 mbar. A
bias voltage could be applied to the liquid microjet via a gold wire brought
in contact with the liquid approximately 550 mm upstream of the expansion
nozzle;33, 50 this wire was connected to the chamber ground potential, unless
otherwise stated. Comparison measurements were performed using the same
equipment to produce a jet of high-purity liquid water, made conductive by the
addition of NaCl to 50 mM concentration.

###  2.3 Electron Detection

Photoelectrons produced from the liquid fenchone jet by circularly polarized
synchrotron radiation were detected in a backward-scattering geometry under an
angle of 130∘ with respect to the light propagation direction. Electrons were
detected by a near-ambient-pressure hemispherical electron analyzer (HEA,
Scienta-Omicron HiPP-3) with a lens mode adapted to specifically enable the
measurement of electrons at low kinetic energies (KEs, below 30 eV). For the
same purpose, $\mu$-metal shielding was added to the interaction chamber
housing the liquid jet. Electrons passed a first skimmer into the HEA with an
opening of 800 $\mu$m diameter and set to the ground potential of the setup,
and were accelerated immediately thereafter to diminish scattering losses at
the elevated background pressure produced by evaporation from the liquid jet.
The distance of the liquid jet to this opening was approximately equal to the
skimmer aperture diameter. Under these conditions, photoelectrons from a
liquid jet can be observed down to very low KEs, though they appear atop of an
intense background of low-energy electrons produced by scattering of
photoelectrons created inside the bulk liquid.51 This point will be further
discussed in detail below.

The slit restricting the entrance into the hemispheres was set to 800 $\mu$m,
adapted to the size of the skimmer opening. Electron spectra were measured
with a pass energy of 20 eV, and electrons were detected by a stack of two
microchannel plates and a fluorescence screen, read out by a CCD camera. The
so-called ADC (analog-to-digital conversion) mode of the control software was
used, in which the gray-scale camera image is interpreted to yield the
underlying electron detection rates.

Spectra were acquired in swept mode. In order to minimize loss of acquisition
time by shifting the undulator structure and switching the X-ray beam
helicity, spectral sweeps were typically repeated ten to thirty times for each
photon helicity, and several pairs of spectra were acquired for both
helicities at each photon energy. A set of individual sweeps that were
averaged to produce a spectrum are shown in Fig. S1 of the ESI.† Some amount
of sweep-to-sweep variation is seen, concerning both intensities and peak
energies. The typical extent and time-scale of intensity fluctuations is
further illustrated by Fig.s S2 and S3 of the ESI.† While the exact origin of
these effects is still under investigation, the occurrence of small variations
of the jet position (much smaller than the focus size, that is on a length
scale of one-two µm) likely contributes significantly to these observations.
Before analysing the intensity difference between l,r-CPL, the raw data were
checked for sweep-to-sweep variations of intensity or KE, and sweeps
identified as clear outliers were removed. Intensities were always determined
from sweep-averaged spectra, to make up for the fact that a different amount
of sweeps may pass the quality criterion for l\- vs. r-CPL. Between 3-30% of
sweeps were dropped. In some cases, small KE drifts over the course of data
acquisition (50 meV or less) were numerically corrected. Methods for peak-area
determination and peak-to-background separation were an essential part of the
data analysis and will be detailed below.

##  3 Results

Fig. 1: Electron spectra recorded after photoionization of
(1S,4R)-(+)-fenchone with l-CPL at photon energies of 301 eV, 302 eV, and 304
eV; dotted, dashed, and solid lines, respectively. Spectra averaged over a
number of sweeps performed at the respective photon energy are shown; no
further normalization has been performed. See text for details.

###  3.1 The C 1s photoelectron spectrum of liquid fenchone

Figure 1 shows typical C 1s photoemission spectra from liquid
(1S,4R)-fenchone, measured at 301 eV, 302 eV, and 304 eV photon energies with
l-CPL. Two features due to C 1s photoionization can be readily identified and
strongly resemble earlier results for gaseous fenchone.36 The less intense
peak at lower KE (higher binding energy) is correlated with ionization of the
single carbon from the C=O double-bond carbonyl group, while the larger peak
at higher energy arises from the cumulative ionization of the remaining nine
carbon atoms at the primary, secondary, and tertiary sites. This leads to
rather similar C 1s binding energies, which cannot be spectroscopically
separated.

No discernible features can be attributed to gas-phase contributions to the
spectrum. This is unusual compared to photoelectron spectra of other
substances probed in liquid microjet experiments, most notably water,52 but
also, e.g., methanol,53 acetic-acid solutions54, and liquid ammonia55. In
principle, two explanations are conceivable: The gas-phase contributions are
too low in intensity to become apparent, or they overlap—in this case—with the
features stemming from the liquid phase. The vapour pressure of fenchone in
the temperature range relevant for this experiment is 0.33 mbar at 10 ∘C, more
than a factor of ten lower than that of liquid water.56 Typical gas-phase
contributions in O 1s spectra of liquid water with the EASI setup at beamline
P04 amount to 5-20% of the signal in the O 1s liquid core level peak,
depending on the conditions. Hence, a small gas-phase contribution to the
fenchone spectra can be expected. In our previous work, we deduced an upper
limit for the gas-phase contribution of 14%, based on spectra recorded with a
small negative bias applied to the jet in order to separate the gas- and
liquid-phase features.33 From the same analysis, we concluded that gas- and
liquid-phase C 1s features indeed energetically overlap in the current case.
This is a rather non-trivial result, as even in the valence spectrum of liquid
fenchone (unpublished data from our own work), or of other non-polar, liquid
solvents,57, 58 ionization energies are typically lower in the liquid in
comparison to the gas phase. In a crude manner, the gas-liquid shift was
rationalized by considering the Born free energy of solvation of a positive
charge (the vacancy created by photoionization) in the bulk liquid, described
by its polarizability, $\varepsilon$, at optical frequencies.59 The quantity
$\varepsilon$, taken as the square of the refractive index, does not differ
qualitatively between fenchone and liquid water.60 Therefore, we suggest that
the small or vanishing gas-liquid shift for the inner-shell levels of fenchone
is coincidental; it may result from a cancellation of various factors, e.g.
electronic charge redistribution following ionization versus electronic
structure changes due to nuclear rearrangement. In this study, we additionally
append the previously-determined gas-phase binding energies of 292.6 eV (C=O
site) and 290.3 eV (CH site) to the analogous liquid phase peaks.36

In addition to the C 1s main lines, an unstructured background of low-KE
electrons can be seen (low KE tail, LET). This phenomenon is well known from
photoemission studies on bulk solid samples61 and has recently been described
in detail for a liquid water jet by some of the authors.51 Briefly, in our
study on aqueous solutions, an intense LET was found, atop of which no
discernible structures could be resolved in electron spectra below kinetic
energies of approximately 10 eV. This is a general result, valid not only for
emission out of water’s orbitals, but also for features resulting, e.g., from
electronic levels of solutes.51 While its exact nature is not fully understood
at this moment, it is attributed to a strong increase of the importance of
quasi-elastic, e.g. vibrational scattering channels, particularly at electron
kinetic energies for which electron-impact ionization channels are closed.
Adding to that is an influence of excitation into neutral resonant states
lying above the nominal ionization potential.51

Strictly speaking, the nature of the LET and the phenomenon of diminishing
peak intensities may very well be of a different nature in fenchone, e.g.,
less or more intense and with a different energetic threshold, since in
liquids little is known about the LET dependence on the ionized substance.
Fig. 1 suggests that peak features are observable with acceptable spectral
distortion down to KEs of 8 eV in liquid fenchone, which is similar or
slightly lower compared to water. This result is of great importance for our
work, as in gas-phase studies it has been learned that PECD only leads to
significant asymmetries in the threshold region, i.e., at photoelectron
kinetic energies below 20 eV. Notably, a comparison of the results on low-KE
electron emission from liquid water in Ref. 51, giving a lower KE bound at
which liquid-phase photoemission peaks from aqueous solutions are discernible,
with the gas-phase data by Ulrich et al.,36 giving an upper KE bound at which
PECD is still sizeable, suggests that the energy window shown in Fig. 1 spans
a range offering good prospects for the identification of PECD in a liquid.

###  3.2 Observed dichroism in the angle-resolved spectra

In order to demonstrate the functionality of our apparatus the PECD of gas-
phase fenchone, as sampled by lowering the liquid jet out of the synchrotron-
radiation focus, was recorded and the literature results of Ulrich et al.36
were successfully reproduced with an improved energy resolution and a shorter
acquisition time. These tests are described in our recent apparatus
description and characterization paper.33

Fig. 2: Background-corrected photoemission spectra of (1S,4R)-(+)-fenchone
measured at 301 eV with l\- and r-CPL. Panels (A) to (C) show the results of
various models by which to subtract the background contribution from a pair of
spectra; spectra in Fig. 1 were instead displayed as measured for l-CPL.
Background contributions were calculated by (A) fitting an exponential
function to the high kinetic end of the spectrum, and subtracting an
additional linear background (‘roi’-approach); or (B) by fitting a linear
combination of an exponential and a linear function to the high- and low-KE
ends of the spectra (‘exp’-approach). For (C), an exponential function has
been fitted and subtracted from the raw data. Then, the ‘total background’
function62 is applied to the remaining spectrum (‘sum’-approach). Blue points
in panel (A) indicate the experimental asymmetries,
$A_{\text{corr}}(130^{\circ})$ (plotted versus the left y-axis) for the peaks
originating from C=O and C-H K-edge photoionization, obtained as the
difference divided by two times the mean of r\- and l-CPL (eqn (2)), together
with associated error bars. The areas marked with dashed lines in panels (B)
and (C) indicate the width of the C=O peak, which is used for the asymmetry
calculations. Expanded ($\times 4$) views of these peaks are drawn above the
full spectra to get a clearer view on the magnitudes of the l-r asymmetry.

We now turn to an analysis of the differences in photoemission spectra
recorded with different helicities of the ionizing photons. Conceptually, we
will distill an intensity asymmetry due to PECD from pairs of spectra recorded
in the energy range shown in Fig. 1 by taking the following three steps:

  1. 1.

peak-to-background separation and background subtraction,

  2. 2.

calculation of the asymmetry from a pair of spectra at equal KE, and

  3. 3.

correction of this raw value for any apparatus asymmetry.

As the first step, quantifying the amount of background present underneath the
two C 1s peaks turned out to be the most problematic as obviously the C 1s
signal is outweighed by the background contribution. Representing it by an
analytic procedure recommended for UPS data62 did not yield a satisfactory
representation. We therefore tested several ad hoc approaches to background
subtraction, and compare them in detail below.

An exemplary background-corrected pair of sweep-averaged spectra of
(1S,4R)-fenchone measured at 301 eV with l\- and r-CPL is shown in Fig. 2, for
all three background models used. Before we detail the various background-
subtraction methods further, we would like to discuss dichroic properties of
these two spectra and our approach to apparatus asymmetry correction.

In panel (A) of Fig. 2, we show a pair of spectra, averaged over two equally
long sets of sweeps for each helicity after deletion of outlier traces and
correction of (small) energy drifts. A visible apparatus asymmetry due to a
small mismatch in photon intensities produced by the undulator in its two
opposite settings has been corrected for in the figure as detailed below. The
deviation of the intensity ratio from unity by this effect is practically
invariant over the narrow photon-energy interval targeted in this paper, and
is constant over a measurement campaign. Uncorrected spectra are shown in Fig.
S4 of the ESI; the intensity mismatch can also be seen in the general trend of
the per-sweep total intensities in Fig. S2 of the ESI.† In order to correct
for this apparatus-induced effect, we have used the helicity-dependent
intensity of the C-H peaks in the spectra as an internal light-intensity
monitor. This follows a practice from gas-phase studies of PECD in several
terpenoids featuring a single C=O double bond, where it was noted that an
asymmetry associated with the sum of overlapping hydrocarbon site signals in
the more intense C-H peak can reasonably be assumed to cancel out.14 It was
therefore postulated that the asymmetry of the latter peak vanishes exactly,
and the C=O asymmetry was correspondingly measured relative to it.14 While
this started out as an ad hoc assumption, this tenet was experimentally
verified after work on the data-acquisition methodology allowed the
measurement of gas-phase PECD free from a baseline error.48, 36 We have,
therefore, determined the asymmetry of the C-H peak as explained below. For
the purpose of illustration, we have used this information to normalize the
pair of traces shown in Fig. 2 such that they correspond to the outcome of a
measurement that is free from apparatus-induced asymmetry. Here and in the
following we use the ratio:

$A=\frac{L-R}{L+R}=\frac{r-1}{r+1}\quad\hbox{with}\quad r\equiv\frac{L}{R}$
(1)

to calculate the asymmetry, $A$, from the intensities $L$ and $R$ recorded
with l-CPL and r-CPL, respectively. If we include a correction for the
apparatus asymmetry, the corrected asymmetry $A_{\text{corr}}$, determined
from a measured intensity ratio $r^{\prime}$ and a correction factor $\gamma$
is then:

$A_{\text{corr}}=\frac{r^{\prime}\gamma-1}{r^{\prime}\gamma+1},$ (2)

where $\gamma$ can be determined from the measured asymmetry $A_{0}^{\prime}$
of an isotropically emitted line (intensities $L_{0}^{\prime},R_{0}^{\prime}$)
by:

$\gamma=\frac{1-A_{0}^{\prime}}{1+A_{0}^{\prime}}=\frac{R_{0}^{\prime}}{L_{0}^{\prime}}.$
(3)

In that terminology, panel (A) of Fig. 2 shows the traces $L\gamma$ and $R$.
An exponential function fitted only to the part of the spectrum at higher KE
than the C-H main line has also been subtracted from the data.

An intensity difference in the traces corrected for apparatus asymmetry, shown
in Fig. 2A, can be seen in the region of the C=O C 1s line at a KE of
$\sim$8.5 eV. In order to exclusively analyse the intensity that can be
attributed to C 1s photoemission, we have subtracted a further, linear
background, as indicated by the dashed lines. Within the main C 1s peaks, we
have then calculated the corrected asymmetry $A_{\text{corr},i}$ for every KE
channel $i$. The resulting values are shown in Fig. 2A, plotted against the
left-hand axis in a blue color. The error bars were derived as follows: We
arranged all sweeps made with l\- and with r-CPL into pairs. Labelling the
pairs with the index $k$, we then calculated the distribution
$A_{\text{corr},i}^{k}$, and give the standard deviation of its mean as an
error to the data point $A_{\text{corr},i}$. More details of the data
processing steps are provided in ESI† Section 1.3 and Supplementary Fig.s
S4,S5.

Trivially, channel-wise asymmetries $A_{i}$ are equal or very near to zero in
the range of the major C-H peak (showing the consistency of the baseline
correction). Whether the rising trend of the asymmetry data pointing from
slightly negative to slightly positive values in going towards smaller KEs is
significant cannot be definitively ascertained at this moment. A word of
caution is needed about its interpretation, as minute differences in the peak
profile as a function of KE may occur e.g. due to small pointing differences
for the left-handed versus right-handed undulator radiation, and can readily
produce the apparent trend. On the contrary, asymmetry values for the C=O peak
clearly show an asymmetry which is significantly different from zero. Still,
with the current data and uncertainty limits, we refrain from
(over-)interpreting the trend of the C=O asymmetry data across the low KE C 1s
peak.

###  3.3 Analysis of the C 1s peak areas

No clear-cut approach to peak-to-background separation is applicable to our
spectra (see Fig. 1), to the best of our knowledge. As this point is
nevertheless essential, we used different methods in parallel and will compare
their results in subsection 3.5. Panels (A)-(C) in Fig. 2 serve to illustrate
these methods.

As explained above, an exponential background was subtracted in Fig. 2A.
Subsequently, peak areas were determined as integrated counts between the
range marked with the vertical dashed lines, minus a linear background as
indicated by the approximately horizontal dashed lines. Using the term ‘region
of interest’ for these ranges, we term this the ‘roi’ method.

The spectra in Panel (B) were constructed by selectively fitting a linear
combination of an exponential and a linear function to the data points
containing the LET contribution only, specifically at the low- and high-KE
ends of the spectra. After subtraction of the estimated background, the
spectra were normalized to the C-H peak maximum. Asymmetries have then been
calculated from the integrated PE intensities in a 1.4 eV energy range around
the C=O peak, as indicated by the areas enclosed by the dashed lines in Panel
(B) of Fig. 2. We use the label ‘exp’ for this method.

The approach adopted to produce Panel (C) follows a similar procedure to that
used to produce Panel (B), with the exception that the background was
constructed by first fitting an exponential function to the high-KE side of
the spectra and then applying the ‘total background’ function62 (also known as
non-iterative Shirley method 63) in order to estimate the LET background. This
procedure iterates from the high- to the low-KE end of the spectra while
aggregating (‘summing’) spectral intensity and is thus referred to as
‘sum’-approach.

More detail on the various background-signal separation methods is provided in
the ESI.†

###  3.4 Parametrization of the measured results

In order to connect our results to other experiments and to calculations, it
is important to resort to parametrized forms of the differential
photoionization cross section, which is the quantity measured here. Building
on the earlier work of Ritchie,7, 8 Ivan Powis showed that within the
electric-dipole approximation, for chiral molecules the differential
photoionization cross-section can be cast in the following form:9, 10

$I^{p}(\theta)=\frac{\sigma}{4\pi}\left[1+b_{1}^{p}\cos(\theta)+b_{2}^{p}P_{2}(\theta)\right].$
(4)

Here, the intensity has been written as a function of the angle $\theta$
measured from the photon propagation vector to the electron emission vector,
for the left-handed circular ($p=1$) or right-handed circular ($p=-1$) pure
polarization states. $P_{2}$ denotes the second Legendre polynomial. The
second-order coefficient $b_{2}$ turns out to be independent of the handedness
of circular polarization, and can be expressed via the more familiar
$\beta$-parameter as $b_{2}^{+1}=b_{2}^{-1}=-\beta/2$. A similar equation can
be written for linearly polarized ($p=0$) light, with the understanding that
the angular coordinate in this case refers to the major axis of the
polarization ellipse. In the latter case, the first-order coefficients vanish
($b_{1}^{0}=0$) and the second-order coefficient becomes $b_{2}^{0}=\beta$.
Higher-order and magnetic terms in the interaction of the radiation field with
the molecule or liquid have been presented,8 but based on experimental
results, they seem to have been unimportant in earlier gas-phase work.14 The
first-order coefficient $b_{1}$ vanishes for non-chiral molecules, and
undergoes a sign change upon changing the chiral handedness of the molecule or
swapping the light helicity; it is therefore the chiroptical parameter
defining the PECD-induced asymmetry. Correspondingly, we can identify the
corrected asymmetry (2) as follows:

$A_{\text{corr}}=\frac{I^{+1}(\theta)-I^{-1}(\theta)}{I^{+1}(\theta)+I^{-1}(\theta)}=\frac{b_{1}^{+1}\cos\theta}{1-(\beta/2)\,P_{2}(\cos\theta)}.$
(5)

Here, the symmetry relation $b_{1}^{+1}=-b_{1}^{-1}$ has been used.7, 9 It is
interesting that, in the general case, $A_{\text{corr}}$ depends on both the
chiral parameter $b_{1}$ and the conventional angular distribution. In earlier
gas-phase PECD experiments based on measurements performed at a single
electron collection angle,14 or a pair of angles mirrored in the dipole
plane,64 the so-called magic angle-geometry of $\theta=54.7^{\circ}$ was used.
This geometry was adopted to ensure that the denominator in eqn (5) becomes
identical to unity and the dependence on $\beta$ ceases. Another option is to
use imaging techniques collecting electrons over the full 4$\pi$ sr emission
solid angle, directly allowing the cosine dependence of the asymmetry to be
extracted.12, 65

In our case, a rigorous determination of $b_{1}$ from our experiment would
require a separate measurement of $\beta$, which however was outside the scope
of this work. In the following, we will therefore estimate the potential
influence of the deviation of our setup from the magic-angle geometry.
Similarly, an estimate of the potential influence of non-complete circular
polarization is in order. Inserting the limiting values of $\beta$ ($-$1 and
+2) into $[1-(\beta/2)\,P_{2}(\cos\theta)]^{-1}$, we find that this factor may
range from 0.94 to 1.14 for our $\theta=130^{\circ}$ detection geometry. In
the few works on the angular distribution parameter in photoemission from
liquids, however, a trend towards small absolute $\beta$ values has been found
at low kinetic energies.66 Given the results of that study on the O 1s orbital
of water, a $\beta\sim 0.5$ might be a plausible but conservative estimate for
our case of C 1s emission, which would lead to a factor of 1.03, resulting
from the denominator in eqn (5).

Further, consideration of polarization impurities requires a look at the full
angular-distribution function, which can be written as:

$\displaystyle I(S,\theta,\phi)=$
$\displaystyle\frac{\sigma}{4\pi}\left[1-S_{3}\,b_{1}^{+1}\cos\theta-\frac{\beta}{2}\,\bigl{(}P_{2}(\cos\theta)-\frac{3}{2}(S_{1}\cos
2\phi+S_{2}\sin 2\phi)\sin^{2}\theta\bigr{)}\right],$ (6)

with the understanding that the first $\theta$-dependent term is only present
for chiral molecules.67, 9 The polarization state of the radiation is now
represented by the three-component Stokes vector $S$, with $S_{1}$ and $S_{2}$
representing linear polarization measured with horizontal and vertical, or 45∘
and 135∘ polarizers, and $S_{3}$ defining the degree and type of circular
polarization. The angle $\phi$ is measured from the horizontal axis in the
dipole plane to the electron spectrometer, and amounts to 90∘ in our
experiment. As explained in the experimental section, polarimetry results in
the photon-energy range of interest are not available for the P04 beamline
yet. However, the degree of linear polarization and the direction of the
polarization ellipse were measured between 550 and 1250 eV, as a function of
the undulator shift.47 The complement of the linear polarization degree was
attributed to circular polarization, neglecting the presence of an unpolarized
fraction of radiation. This is supported by full polarimetry results
associated with another APPLE-II undulator beamline.68 In all data sets
recorded, when the circular component was maximized, a remaining Stokes
parameter of linear polarization with magnitude 0.04 or smaller was found,
which almost exclusively had $S_{2}$ character. As, from eqn (6),
$S_{2}$-dependent terms cannot play a role in our geometry, we will neglect
the residual linear components entirely, although this is not fully rigorous.
Including a finite angular acceptance of our electron analyzer (see Ref. 33)
in a discussion of eqn (6) leads to corrections that vanish, to first order,
and are essentially independent of the enantiomer and helicity of the light.
We therefore deem it safe to assume that the impact of such effects is much
smaller than the others we have explicitly considered above

To summarize this discussion, we find that optical polarimetry at the carbon
edge, to determine the on-target radiation state, and a photoelectron angular-
distribution measurement on liquid fenchone would be desirable for a
quantitatively accurate determination of the $b_{1}$-parameter in our
experiment. However, for the moment we will retain the simple relation,
$b_{1}^{+1}=A_{\text{corr}}/\cos\theta$, and will make an appropriate
adjustment to the error bar with respect to the influence of $\beta$ and any
residual non-circular soft X-ray beam polarization.

Fig. 3: The corrected asymmetry, $A_{\text{corr}}$, and the resulting chiral
angular-distribution parameter $b_{1}^{+1}$ as a function of photon energy. We
use black symbols for the (1S,4R)- and colored symbols for the
(1R,4S)-enantiomer. For the latter, the results from three data sets, acquired
in two different measurement campaigns, are shown to indicate the stability of
our experiment. Different approaches to subtract the LET and, possibly, a
residual background are differentiated by the symbol shape, with diamonds
referring to the ‘total background’ approach (Fig. 2C, ‘sum’), circles to the
linear-exponential approach (Fig. 2B, ‘exp’) and triangles to the region-of-
interest (‘roi’) approach (Fig. 2A). To guide the eye we indicate the averaged
values detailed in Table 1 by dashed lines. Values in the figure are not
corrected for any possible gas-phase contributions and angular-anisotropy
effects (see Table 1).

###  3.5 Averaged and corrected results

A compilation of the $b_{1}^{+1}$ values as obtained from the described
analysis procedure is provided in Fig. 3. The results in the figure have a
rather large spread between different data sets and different analysis
methods. Nevertheless, for most photon energy values, the chiral asymmetry
parameter $b_{1}^{+1}$ is clearly different from zero, with the $b_{1}^{+1}$
values having an opposite sign for the two different enantiomers. This
expected mirroring of the chiroptical data attests that we are indeed
measuring, with a reasonable error bar, an enantio-specific observable.

Table 1:  Recommended $b_{1}^{+1}$ values calculated as the averages of the values shown in Fig. 3. In round brackets, the standard deviation of all values pertaining to the same enantiomer and photon energy is shown. The rows labelled ‘measured’ are not corrected for the possible presence of gaseous fenchone nor the $\beta$-dependence of the relationship between measured asymmetry and chiral parameter, $b_{1}$ (see eqn (5)). In rows labelled ‘corrected’, the expected maximum correction of the $b_{1}$ values has been applied for both factors. See the main body of the text for details. | 301 eV | 302 eV | 303 eV | 304 eV | 305 eV | 307 eV
---|---|---|---|---|---|---
measured |  |  |  |  |  |
(1R,4S)-fenchone | 0.023(11) | 0.017(5) | 0.014(7) | - | 0.014(6) | 0.014(5)
(1S,4R)-fenchone | -0.017(6) | -0.015(7) | - | -0.011(2) | - | -
corrected |  |  |  |  |  |
(1R,4S)-fenchone | 0.014(12) | 0.010(5) | 0.010(7) | - | 0.011(6) | 0.012(6)
(1S,4R)-fenchone | -0.008(6) | -0.009(7) | - | -0.008(2) | - | -

If we scrutinize the data points in Fig. 3, we find that they neither group by
analysis method nor by data set. We therefore believe that the scatter between
points does not result from a systematic effect leading to preferentially
higher or lower asymmetry values as a function of time or associated with
peak-background separation method. In order to arrive at consolidated values,
we performed a simple average over all data points for the same photon energy
and enantiomer. The results are compiled in Table 1. The scatter in our data
points, perceived as rather coming from fluctuations in the signal and
background of the spectra than from the data treatment, is represented by the
standard deviation of the individual data points leading to each table entry.
In the table, we also include two potentially important $b_{1}^{+1}$
corrections, namely one for the presence of gaseous components in the C 1s
spectra and another for the potential influence of a non-zero
$\beta$-parameter, which would affect the connection between the measured
anisotropy and $b_{1}$ values (eqn (5)). As explained above, although no
visible presence of a gaseous component has been observed in the PECD
measurements, a separate experiment with a biased jet, albeit at slightly
different conditions, suggested that this might result from an inconvenient
overlap of liquid-phase and gas-phase C 1s peak features; these results have
been discussed in an earlier paper.33 Referring to that work, we estimate a
gas-phase fraction $g$ between negligible, which is expected from the low
vapour pressure of fenchone, and $g=0.14$, which is the finding of the
aforementioned biased jet experiment. As the gas-phase contribution has a
$b_{1}$-parameter of larger magnitude, correction for the gas-phase
contribution would reduce the liquid phase parameter $b^{p}_{1,l}$ according
to:

$b^{p}_{1,l}=\frac{b^{p}_{1,m}-gb^{p}_{1,g}}{1-g},$ (7)

where subscripts $m$ and $g$ designate the measured and gas-phase values of
$b_{1}^{p}$, the latter being taken from Ref. 36 with interpolation where
necessary. For the correction due to the $\beta$-dependent denominator in eqn
(5), we expect a value between unity (no correction), for a $\beta=0$, and
multiplication by 0.94, for a $\beta=1$. Accordingly, the table contains two
lines for each parameter stating the averaged, but uncorrected value, and the
values corrected downwards by the factors quantified above, which we believe
gives the maximum plausible extent of the gas-phase contribution and $\beta$
parameter effects.

We note two further effects that we cannot quantify at this moment, but could
be present to some extent. The exact enantiomeric excess (e.e.) of the samples
supplied was not specified and we were unable to have this independently
checked, but previous reports have found commercial samples of
(1R,4S)-($-$)-fenchone to have a lower e.e. than (1S,4R)-(+)-fenchone samples.
In principle, the measured PECD asymmetry should scale linearly with e.e.
values when these are known. However, such adjustments are here expected to be
within the current error bars, and so have not been applied. The same applies
to a correction for an unpolarized fraction of radiation at our sample, which
could be slightly increased at the photon energies used in this experiment
because of an influence of carbon contamination on the beamline optics. If
present, both factors would lead to a correction of the values of $b_{1}$
extracted from the measured asymmetry towards larger absolute values.

##  4 Discussion

It is interesting to discuss the reduction in $b_{1}^{+1}$ relative to gas-
phase experiments. In the case of fenchone, the reduction in $b_{1}^{+1}$
amounts to roughly a factor of five. This reduction can be compared to results
on the conventional angular distribution, represented by the $\beta$
parameter. A few experiments for the $\beta$ parameter of photoemission peaks
from liquids are available.69, 66, 70, 71 In comparison with gas-phase water,
a general reduction of $\beta$ has been observed,66, 71 but only the study on
the O 1s $\beta$ parameter of water by Thürmer et al. extended down to the KEs
of interest here. For their lowest data point at about 12 eV KE, the measured
$\beta$-values are approximately $\beta_{g}=0.92$ and $\beta_{l}=0.28$, which
implies a reduction by a factor of 3.3 (with subscripts $g$ and $l$
designating the gas and liquid phase, respectively).66 Fully consistent with
that, the onset of the reduction in $\beta$ upon aggregation of individual
molecules was also observed in an experiment on water clusters.72 A plausible
explanation for the reduction in $\beta$ is the elastic or quasi-elastic
scattering of photoelectrons in the liquid bulk, before traversing the liquid-
vacuum interface. Due to the random nature of the associated collisions, this
would tend to produce an isotropic angular distribution, and the explanation
would equally hold for the reduction in $b_{1}$. It could not be shown in Ref.
66, however, that this is the sole explanation for the $\beta$ reduction, due
to a lack of accurate knowledge of the elastic and inelastic mean free paths
of electrons in water. Note that electron scattering was also pointed out as
the main source of PECD reduction (by about a factor of five) between
nanoparticles and gas phase serine.20 This effect may be partly compensated by
an increased local order in the nanoparticles or fewer associated conformers
in the aggregated state. The former explanation may also be applicable to the
case of liquid fenchone. Elastic electron scattering on the water or fenchone
vapour surrounding the liquid jets may additionally contribute to the more
isotropic angular distributions from liquids, as the cross-sections for
elastic scattering for low-KE electrons on gas-phase water are considerable.73
As these cross-sections are also strongly peaked at low scattering angles,
this will likely be a smaller effect, though. A redistribution of intensity
from the forward- into the backward-scattering plane, which would be necessary
for a reduction of $b_{1}$, is not fully excluded for a cylindrical jet, but
seems relatively implausible.

##  5 Conclusions

A full report on an experiment to measure PECD from the chiral liquid fenchone
has been presented. We have shown a non-vanishing effect of opposite sign for
the two enantiomers, with a convincing mirroring attesting the overall quality
of the data. Akin to studies on the angular-distribution parameter $\beta$
from liquids, and to PECD from homochiral nanoparticles, a substantial
reduction of the chiral parameter, $b_{1}$, has been found relative to the
gas-phase sample. This can be explained to a large or full degree by elastic
scattering of the outgoing photoelectrons inside the liquid. Our study opens
up prospects to investigate the solution-phase chemistry of chiral substances
in their native environment. The in vivo study of biomolecules in water with
simultaneous site- and chemical-specificity, via an analysis of core-level
shifts,35 and the chiral handedness, via PECD measurements, is an especially
exciting and important example.

## Data Availability

Data relevant for this study are available at DOI: 10.5281/zenodo.5996526.

## Author Contributions

Conceptualization: BW, UH, LN, IP; Methodology: SM, IW, ST, BW; Investigation
(including data acquisition): MP, SM, FT, CL, CK, LN, IP, IW, BW; Data
analysis (formal analysis): MP, ST, UH; Visualization, Writing – original
draft: UH, MP; Writing – review & editing: All authors; Supervision: BW;
Funding acquisition: BW, UH, SM, DN.

## Conflicts of interest

There are no conflicts to declare.

## Acknowledgements

The authors would like to acknowledge help from Sebastian Kray and Stefan
Schlichting in setting up the experiment, and from Dana Bloss in data
acquisition. We would like to thank André Knie for his contributions in the
early stages of this work. B.W. acknowledges funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
investigation programme (grant agreement No. 883759). F.T. and B.W.
acknowledge support by the MaxWater initiative of the Max-Planck-Gesellschaft.
S.T. acknowledges support from the JSPS KAKENHI Grant No. JP20K15229. D.M.N.,
M.P., and C.L. were supported by the Director, Office of Basic Energy Science,
Chemical Sciences Division of the U.S. Department of Energy under Contract No.
DE-AC02-05CH11231 and by the Alexander von Humboldt Foundation. We acknowledge
DESY (Hamburg, Germany), a member of the Helmholtz Association (HGF), for the
provision of experimental facilities. Parts of this research were carried out
at PETRA III and we would like to thank Moritz Hoesch in particular, as well
as the whole beamline staff, the PETRA III chemistry laboratory and crane
operators for their assistance in using the P04 soft X-ray beamline. The
beamtime that enabled this work was allocated for proposal II-20180012 (LTP).

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