# Laser-induced Coulomb explosion imaging of (C6H5Br)2 and C6H5Br-I2 dimers in
helium nanodroplets using the Timepix3

Constant Schouder  Department of Chemistry, Aarhus University, 8000 Aarhus C,
Denmark  Adam S.Chatterley  Department of Chemistry, Aarhus University, 8000
Aarhus C, Denmark  Melby Johny  Center for Free-Electron Laser Science,
Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany  Flora
Hübschmann  Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
Ahmed F. Al-Refaie  Center for Free-Electron Laser Science, Deutsches
Elektronen-Synchrotron DESY, 22607 Hamburg, Germany  Florent Calvo  Université
Grenoble Alpes, LIPHY, F-38000 Grenoble, France  Jochen Küpper  Center for
Free-Electron Laser Science, Deutsches Elektronen-Synchrotron DESY, 22607
Hamburg, Germany  Center for Ultrafast Imaging, Universität Hamburg, Luruper
Chaussee 149, 22761 Hamburg, Germany  Department of Physics, Universität
Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany  Henrik Stapelfeldt
<EMAIL_ADDRESS>Department of Chemistry, Aarhus University, 8000 Aarhus C,
Denmark

###### Abstract

We have deduced the structure of the bromobenzene–I2 heterodimer and the
(bromobenzene)2 homodimer inside helium droplets using a combination of laser-
induced alignment, Coulomb explosion imaging, and three-dimensional ion
imaging. The complexes were fixed in a variety of orientations in the
laboratory frame, then in each case multiply ionized by an intense laser
pulse. A three dimensional ion imaging detector, including a Timepix3 detector
allowed us to measure the correlations between velocity vectors of different
fragments and, in conjunction with classical simulations, work backward to the
initial structure of the complex prior to explosion. For the heterodimer, we
find that the I2 molecular axis intersects the phenyl ring of the bromobenzene
approximately perpendicularly. The homodimer has a stacked parallel structure,
with the two bromine atoms pointing in opposite directions. These results
illustrate the ability of Coulomb explosion imaging to determine the structure
of large complexes, and point the way toward real-time measurements of
bimolecular reactions inside helium droplets.

###### pacs:

##  I Introduction

Helium nanodroplets offer a unique environment for the creation of weakly-bond
complexes [1, 2, 3, 4]. Helium nanodroplets can be, also sequentially, doped
with combinations of a broad range of guest molecules[1, 2, 3], and their
temperature (0.37 K) [1] is low enough to freeze molecules into complexes and
clusters that are difficult to achieve with traditional molecular beam
techniques. One particularly exciting possibility is the creation of
bimolecular complexes in a pre-reactive geometry[4], which could be made to
react by excitation with a fs laser pulse [5]. To study such a reaction, one
needs to first characterize the initial static structure of the complex, and
then, ideally, measure the structure as a function of time.

Most studies of molecular complexes in helium droplets have used frequency-
resolved spectroscopy to infer structure, in particular IR spectroscopy [6, 2,
7, 8]. This is possible because molecules and complexes in droplets tend to
show sharp vibrational spectral lines, despite the helium solvent. The
inherently limited time resolution of frequency-resolved spectroscopies make
them, however, inadequate for measuring how the structure of complexes changes
on the natural atomic time-scale. Such studies require structure-sensitive
techniques with ps or fs time-resolution.

Recently, we demonstrated that Coulomb explosion imaging (CEI), triggered by
intense fs laser pulses, combined with laser-induced alignment and covariance
analysis of fragment ion recoil directions, provide an alternative to IR
spectroscopy for determining the structure of molecular complexes embedded in
He nanodroplets. The method was applied to the homodimers of carbon disulfide
[9], carbonyl sulfide [10], and tetracene [11]. In the gas phase, laser-
induced CEI has been a fruitful technique for studying molecular structure
[12, 13], including measurements of the handedness of chiral molecules [14,
15], determinations of (time-dependent) internuclear wave functions of
diatomic molecules and atomic or molecular dimers [16, 17, 18, 19, 20], and
imaging of intramolecular motions and isomerization dynamics in real-time [21,
22, 23].

Conceptually, CEI is simple: an intense laser pulse multiply ionizes
molecules, which then break up into cationic fragments. Applying the axial
recoil approximation, the original molecular structure can then be
reconstructed from the velocity vectors of the fragments. Coincidence and
covariance techniques are essential here, as they allow the velocity vectors
from explosion of a single system to be related to each other [24, 25, 26,
27]. For the structural determination of carbon disulfide, carbonyl sulfide,
and tetracene dimers, we also used laser-induced alignment to fix the dimers
in the laboratory frame [10, 11] . Laser-induced alignment is the practice of
using moderately intense non-resonant laser pulses to fix a molecule’s spatial
orientation in the laboratory frame through the polarizability interaction
[28, 29, 30]. Alignment is key to CEI structural determination, because it
optimizes the information content about the molecular structure extractable
from the fragment velocity vectors. Also, it allows us to relate the velocity
vectors of different fragments to the most, second most, or least polarizable
axes of the complex. For instance, for the tetracene dimer we were able to
tell how the two monomers were oriented with respect to the polarizability
axes (which themselves are dependent on the dimer structure), and from this
deduced a parallel stacked structure [11].

The limitation of the technique introduced in [11] was that it was only
applicable to homodimers, because it depends on gating the imaging detector in
time to detect only ion species with similar mass-to-charge, $m/z$, values,
the tetracene+ ion in that case. However, if one uses a three-dimensional
imaging detector, which records the time as well as the position of each ion
hit, it is possible to correlate events between ion species with different
$m/z$ ratios. Such detectors have traditionally used either delay lines [24,
31, 32] or correlated photon counters [33, 34] to determine ion timings, with
the drawback that these detectors are limited to a few ion events per laser
shot, so data collection is rather laborious. Recently, a new generation of 3D
detectors has emerged in the form of ’cameras’ whose pixels record a time-
stamp of each ion event. Ion imaging experiments employing either the PImMS
[35, 36, 37] or Timepix [38, 39] devices are able to measure the time-stamp
and location of hundreds of events in every laser shot, significantly
enhancing data collection times and enabling statistical analysis of many
fragment correlations.

Here, we have used a Timepix3 camera to overcome the homodimer limitation, and
measure the structure of the bromobenzene – iodine (BrPh–I2) heterodimer
inside a helium droplet. We do this by measuring correlations between the
emission directions of Br+ and I+ fragments following Coulomb explosion, for
complexes fixed in space using laser-induced alignment. We find a structure
where the I2 molecule is nearly perpendicular to the BrPh aromatic ring very
similar to related gas phase complexes [40, 41, 42]. Additionally, we have
determined the structure of the (BrPh)2 homodimer ’for free’, as a number of
these complexes are also present in our helium droplets, and the detection
system simultaneously records their recoil data while the heterodimer CEI is
being recorded. We find a parallel displaced structure, with the two Br atoms
pointing away from each other. These experiments demonstrate the power of
combining alignment, 3D ion imaging, and CEI to simultaneously measure the
structures of multiple complexes, and point the way toward measurement of
real-time structural changes of loosely bound complexes.

##  II Experimental setup

The general experimental setup has been described in detail before[43, 11];
the two key differences here are the use of two separate doping cells for
creation of heterodimers in He droplets, and the replacement of the CCD camera
by a Timepix3 detector. The helium nanodroplets are produced by expanding 25
bar He into vacuum through a $5\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$
nozzle, cooled to 14 K. This produces liquid helium droplets with a mean size
of 5000 He atoms [1]. Molecular dimers are formed by sending the droplets
through two doping cells, the first containing BrPh vapor and the second I2
vapor. The vapor pressure inside the two doping cells is controlled by needle
valves connected to external room temperature reservoirs, and is set to
optimize signal from BrPh-I2 heterodimers, while minimizing signal from
unsolvated gas phase molecules. In practice, this amounts to turning both
vapor pressures as low as possible, while still observing dimer signals.

The doped helium droplets enter the target region, where they are intersected
at $90\text{\,}\mathrm{\SIUnitSymbolDegree}$ by two pulsed laser beams. The
pulses in the first beam are used to adiabatically align the dimers. Each
pulse turned on in $\sim$$120\text{\,}\mathrm{p}\mathrm{s}$ and off in
$\sim$$10\text{\,}\mathrm{p}\mathrm{s}$. The asymmetric shape is obtained by
spectral truncation of the uncompressed pulses from a regenerative amplified
fs laser system [44, 45]. The alignment pulse parameters are:
$\lambda_{\textrm{align}}=$800\text{\,}\mathrm{n}\mathrm{m}$$,
$\omega_{0}=$40\text{\,}\mu\mathrm{m}$$, and peak intensity
I${}_{\textrm{align}}\sim$3\text{\times}{10}^{11}\text{\,}\mathrm{W}\mathrm{/}\mathrm{c}\mathrm{m}^{2}$$.
The second laser beam contains the probe pulses used to multiply ionize the
molecules in the droplets and thereby trigger Coulomb explosion of the dimers.
The probe pulse parameters are:
$\lambda_{\textrm{probe}}=$400\text{\,}\mathrm{n}\mathrm{m}$$,
$\tau_{\textrm{probe}}=$40\text{\,}\mathrm{f}\mathrm{s}$$ (FWHM),
$\omega_{0}=$25\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$, and
I${}_{\textrm{probe}}\sim$2\text{\times}{10}^{14}\text{\,}\mathrm{W}\mathrm{/}\mathrm{c}\mathrm{m}^{2}$$.
Each probe pulse is sent $\sim$$5\text{\,}\mathrm{p}\mathrm{s}$ after the
truncation of the alignment pulse. This timing is chosen such that the dimers
are both well-aligned and that the alignment field is negligible at the time
of probing [46]. The spot size of the probe beam is considerably smaller than
the spot size of the alignment beam to minimize focal volume effects. The
polarization of the probe laser pulse is linear and orthogonal to the detector
plane, while the ellipticity and plane of polarization of the alignment pulse
is varied to control how the dimers are aligned. In all cases, the effect of
the alignment pulse is to coerce the most polarizable axis (MPA) of the dimers
to coincide with its major polarization axis. If the alignment pulse is
linearly polarized, then the complex rotates freely around the polarization
axis. When elliptically polarized laser pulses are used, the second most
polarizable axis of the dimers is constrained to the minor polarization axis,
and the complex is 3D aligned [47, 48].

Following fragmentation, the velocities of the resulting ions are projected
onto a 2D detector by a velocity map imaging spectrometer. Usually, such
apparatus is temporally gated to only accept ions with one specific $m/z$
value at the time. With the TimePix3 detector [38] and its SPIDR read out
[49], both the spatial coordinates of each ion impact event, and its time-of-
flight with a temporal resolution of a few ns are measured. Each ion impact
results in a small cluster of pixels registering events containing the pixel
coordinates and the time of the hits. This data is recorded and clusters of
pixels are separated and centroided in time and space using the Pymepix
software to give a list of ion hits [50]. The time of each hit is used to
differentiate fragments with different $m/z$, values, while the spatial
coordinates give the projected velocities of the ionic fragments.

The detector is gated to ignore all events with $m/z<63$ u, firstly to avoid
damage to the detector from the very significant number of light ions,
including He+ ions and residual water in the chamber, and secondly to ensure
that the centroiding system could keep up with the incoming data rate for
online data analysis.

The outcome of these experiments is a set of 3D data with two polar
coordinates $r$ and $\theta$ (transformed from the Cartesian pixels), and one
time coordinate, $t$. For each ion event, $r$ and $\theta$ give the projection
of the velocity vector, $v$, onto the 2D detector, and $t$ gives the time-of-
flight and thereby the $m/z$ value. Throughout the manuscript, $r$ will be
given in relative units of pixels, as read-off from the camera, and $\theta$
in degrees with respect to a space-fixed axis (the laser propagation axis).
The ion species detected will be denoted by a lower index, e.g., $r_{\rm
Br^{+}}$.

Our primary analytical tool is covariance analysis, which gives the likelihood
of two events being correlated as a function of one of their coordinates
($r,\theta$ or $t$) [25]. Formally, the covariance is defined as
$C_{UV}=\langle UV\rangle-\langle U\rangle\langle V\rangle$, where $U$ and $V$
are the histograms of the coordinates for events of the two ion species being
considered, and angle brackets denote expectation values. For the mass
spectrum covariance, subsection III.1, $U=V$ and is the transformed time-of-
flight of every ion event. For the angular and radial covariance of a single
species, $U$ and $V$ are each histograms of the respective coordinate, but
only for events whose $m/z$ value is equal to the ion species of interest.

##  III Results and analysis

###  III.1 Mass spectra

Figure 1: The mass spectrum and mass spectrum covariance map of helium
droplets doped with both BrPh and I2 molecules, following Coulomb explosion.
(a) and (b) show the 1D mass spectrum, while (c) shows the covariance of these
spectra. Positive peaks in the covariance indicate fragments that arrive
alongside each other. Four regions of interest, I, II, III, and IV, are
highlighted and expanded, see text for details.

The time axis of our 3D dataset is the mass spectrum after laser ionization
when both doping cells are opened, and the covariance map of these data shows
which fragments appear in conjunction with each other [51]. We shall focus
only on the mass region of 70–160 u (Fig. 1), which spans Ph+, Br+ and BrPh+
fragment ions from BrPh molecules, and I+ ions from I2 molecules, as these are
the most useful for structural determination. The full mass spectrum is shown
in Fig. A1. Although alignment has little effect on the yield of the mass
spectra, we note for completeness that the data in Fig. 1 are recorded with
the alignment pulse linearly polarized parallel to the detector plane.

Laser-induced ionization results in a variety of fragment ions, but for
structural determination purposes we are only interested in fragments that
appear in conjunction with another fragment. These appear as positive peaks in
the mass spectrum covariance map in Fig. 1. Peaks along the diagonal
correspond to fragments correlated with an identical partner, while off-
diagonal peaks reveal fragments correlated with a different partner. Four
groups of peaks are visible in the covariance map, labeled I–IV in Fig. 1.
Note that the covariance map is symmetric about the diagonal. Region I is a
cluster of peaks originating at (127,127) with weaker peaks shifted
periodically by 4 u either horizontally or vertically. These peaks correspond
to Coulomb explosion of an I2 molecule in a single He droplet into two I+ ions
each of which may pick up one or more He atoms as it escapes the droplet [52].
This effect of helium ’snowball’ formation is consistently observed when I+
ions are produced from laser-induced Coulomb explosion or photodissociation of
molecules inside helium droplets [53, 52].

Region II is also a cluster of evenly spaced peaks extending beyond the
diagonal. The main peaks at (79,79), (81,79) and (81,81), correspond to
correlated pairs of ^79Br+ and ^81Br+ ions (the natural abundances of ^79Br
and ^81Br are almost the same) produced by Coulomb explosion of BrPh
molecules, with the possibility for He atom pickup in the same manner as for
the I+ ions. An additional peak at (77,77) corresponds to a correlated pair of
Ph+ ions. As each BrPh molecule contains only one Br atom and one Ph fragment,
the covariance peaks in region II must stem from He droplets doped with a
(BrPh)_n oligomer with n $\geq 2$, created when a droplet picks up multiple
BrPh molecules. Further confirmation of the formation of (BrPh)_n comes from
the two peaks in region III, which correspond to a Ph+ ion detected in
coincidence with a ^79BrPh+ or ^81BrPh+ parent ion. We consider that the major
contribution of the correlation signal originated from (BrPh)2 as the doping
cell pressure was kept as low as possible to minimize the contribution of
larger oligomers.

The peaks in region IV show Br+ ions arriving in conjunction with I+ ions.
Such a correlation must originate from ionization of a complex containing at
least one I2 and one BrPh molecule, the simplest of which is the BrPh-I2
heterodimer. The mass spectrum covariance map leads us to conclude that we
have produced both (BrPh)2 homodimers and BrPh-I2 heterodimers. In principle,
parts of the correlation signals could also come from larger oligomers, but
the doping cell pressure was kept as low as possible to minimize this
contribution.

###  III.2 Heterodimer

Figure 2: (a1)-(b1): Radial covariance map between I+ and Br+ ions. (a2)-(b2):
Angular covariance map for the I+ and Br+ ions detected in the ovals shown in
(a1) and (b1), the black crosses mark the position of the islands’ center
listed in Table 1. (a3)-(b3): Simulated angular covariance map (see text). In
the left (right) column the MPA is aligned perpendicular (parallel) to the
detector plane.

The mass spectrum covariance map shows that we form BrPh-I2 heterodimers, but
does not give much information about their structure. For this, we turn to the
velocity vector covariance between I+ and Br+ fragments, in particular the
radial and the angular covariance maps [52]. The radial covariance map allows
us to identify correlation regions that are related to the ionization of the
heterodimer. The angular covariance map is then computed for ions in these
correlation regions and analyzed to identify the recoil angle of the
correlated fragments under study. We choose to study the correlations between
the I+ and Br+ fragment ions because they offer the most direct insight into
the complex structure: if we assume axial recoil then the I+ velocity reveals
the I–I bond axis, while the Br+ velocity reveals the orientation of the C–Br
axis of the BrPh molecule. For these measurements, it is essential to fix the
alignment of the dimer in the laboratory frame for two reasons. Firstly,
alignment restricts the range of laboratory recoil angles of the fragments,
which sharpens the peaks in the covariance maps and simplifies analysis.
Second, the direction in which the dimer aligns is determined by its
polarizability tensor, which in turn is determined by the dimer structure.
Thus, observing how the dimer aligns for a given polarization state of the
alignment field reveals information about the structure of the complex [10,
11]. For the measurements presented in Fig. 2, we use one-dimensional
alignment with the major polarizability axis (MPA) aligned either
perpendicular (left column) or parallel (right column) to the detector plane.
Fig. 2(a1)-(b1) shows the radial covariance map and Fig. 2(a2)-(b2) the
angular covariance map of (I+, Br+) ion pairs obtained from the ion images
recorded. Furthermore, to reduce the contribution from oligomers larger than
the heterodimer, we discard the ion images from those laser shots where more
than one Br+ ion is detected. For example, in the case of an alignment laser
parallel to the detector plane (see Fig. 2 panels (b1) and (b2)), there are
535757 lasershots that lead to the detection of at least one Br+ ion, out of
which 393088 contained only one.

For each of the I+ – Br+ covariance maps we shall now consider what insights
they give us about the structure of the complex. The radial covariance map
with the MPA aligned perpendicular to the detector, displayed in Fig. 2(a1),
shows that high-velocity Br+ ions, detected at radii between 40 and 110
pixels, are correlated with lower velocity I+ ions detected at radii between
10-50 pixels. This indicates that the velocity vector of the Br+ ions, and
thus the C–Br axis of the parent BrPh molecule, is in or close to the detector
plane while the velocity vector of the I+ ions, and thus the I–I axis, is
close to perpendicular to the detector plane. The radial covariance map thus
points to a dimer structure where the MPA is along the I–I axis and
perpendicular to the C–Br axis. We also determined the angular covariance map
for the events with radial covariance contained in the white oval in Fig.
2(a1). Fig. 2(a2) shows two broad stripes of positive covariance signal,
showing correlation for (I+,Br+) ion pairs where $\theta_{\rm
Br^{+}}=\theta_{\rm I^{+}}+180^{\circ}$, i.e. the two fragments recoil back-
to-back. This is consistent with the dimer structure tentatively suggested
from the radial covariance map but does not add any further insight.

More detailed information comes from the radial and angular covariance maps
when the dimer is aligned with the MPA, which we now believe to be close to
the I–I axis, parallel to the detector plane. Fig. 2 (b1) shows the radial
covariance map for this alignment. The most prominent feature is a positive
region centered around $(r_{\rm Br^{+}}=60,r_{\rm I^{+}}=75)$ pixels. When
compared to Fig. 2(a1), it shows a decrease and an increase of the kinetic
energy release in the detector plane for the Br+ and I+ fragments
respectively. Hence similar arguments apply and we conclude that for this
alignment geometry $v_{\rm I^{+}}$ is more in the plane of the detector than
$v_{\rm Br^{+}}$, which is consistent with the assessment that the I–I axis
coincides with the MPA. However, the angle between the I–I and C–Br axes is
still unclear. The angular covariance in this alignment geometry Fig. 2(b2),
contains most of the information on this parameter. Here, we see four separate
islands (note that the axes wrap around), at locations close to
($90\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$180\text{\,}\mathrm{\SIUnitSymbolDegree}$),
($90\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$0\text{\,}\mathrm{\SIUnitSymbolDegree}$),
($270\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$180\text{\,}\mathrm{\SIUnitSymbolDegree}$) and
($270\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$0\text{\,}\mathrm{\SIUnitSymbolDegree}$), although not centered exactly on
these spots. The positions of the islands indicate that the I+ fragment is
flying in a direction close to the alignment laser polarization
($90\text{\,}\mathrm{\SIUnitSymbolDegree}$ or, equivalently,
$270\text{\,}\mathrm{\SIUnitSymbolDegree}$), while the Br+ fragment flies
nearly perpendicular to it, confirming the previous observations. Putting all
the covariance observations together, we arrive at a qualitative structure
with the I–I axis perpendicular to the C–Br axis. In panel (b1) of Fig. 2, a
fainter contribution appears for lower radius $(r_{\rm Br^{+}}=60,r_{\rm
I^{+}}=25)$ which is interpreted as originating from the I+ ion pointing
toward the phenyl ring. The angular covariance map of this region is
featureless and does not show a confined distribution. which can be expected
from the large scattering that this fragment can undergo compared to the outer
one.

Island | ($\mu_{\theta_{\textrm{I}^{+}}}\pm\sigma_{\theta_{\textrm{I}^{+}}}$ , $\mu_{\theta_{\textrm{Br}^{+}}}\pm\sigma_{\theta_{\textrm{Br}^{+}}}$)
---|---
(1) | ($96.2\pm 1.1$ , $349.2\pm 3.2$)
(2) | ($262.8\pm 1.3$ , $5.8\pm 3.1$)
(3) | ($82.7\pm 1.5$ , $189.9\pm 4.6$)
(4) | ($275.0\pm 0.9$ , $170.0\pm 3.8$)
Table 1: The center positions of the four islands in Fig. 2(b2), determined
using a clustering algorithm detailed in Appendix B.

Quantitative details of the structure come from comparison of the angular
covariance with simulations. The first step is to precisely identify the
center of each island in Fig. 2(b2), ($\mu_{\theta_{\rm I^{+}}}$ and
$\mu_{\theta_{\rm Br^{+}}}$), using a clustering algorithm detailed in the
Appendix B and shown in Fig. A2. The centers, and their uncertainties, are
shown in Table 1. Next, we construct trial structures, simulate their angular
covariance matrices, and then extract the center position of the islands as in
the experimental data. We then use an optimization algorithm to minimize the
difference between the island centers of the experimental and simulated
covariance maps by varying the trial structure. For each trial structure we
first assign a charge distribution to each atom (see below), then classically
simulate the atomic motion, assuming only Coulombic forces are significant.
The resultant velocity vectors are then transformed into an ensemble
distributed around the alignment polarization vector, taking into account the
imperfect alignment of the experiment. To account for scattering of the
fragment ions as they move out of the helium droplet [54, 43] we convolute the
final velocities of the Br+ and I+ ions with a Gaussian function. The angular
covariance maps are then computed, and compared to the experimental results.
The structure of the dimer is then varied until the simulated angular
covariance matches the experiment.

Figure 3: The starting structure for the optimization of the BrPh-I2 complex,
along with the structural parameters that were optimized.

There are 6 parameters to describe the structure for optimization,
(highlighted in Fig. 3: (1) An angle $\theta$ gives the the angle between the
I2 axis and the lab-frame major polarization axis of the alignment laser
($Y_{LF}$); and rotates the whole dimer around the $Z_{LF}$ axis of the
laboratory frame; (2-3) the I2 molecule is allowed to move in the $X-Z$ plane
of the molecular frame with parameters $\delta x_{I_{2}}$ and $\delta
z_{I_{2}}$ while the distance between the benzene ring and the closest iodine
atom is initially set to $3.5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$; (4-6) a
set of three Proper Euler angles ($\alpha,\beta,\gamma$) associated
respectively with the sequence of rotation axes
$\left(x_{Br}-z_{Br}-x_{Br}\right)$ permits free rotation of the bromobenzene
molecule in the laboratory frame. Each monomer of the complex is kept rigid in
its equilibrium geometry (computed with the $\omega$B97X-D method [55] with
aug-cc-pVTZ basis [56] set using Gaussian09 [57]). The starting geometry for
the optimization is the experimentally deduced qualitative structure, with the
I2 molecule perpendicular to the phenyl ring. The exact starting geometry is
given in Table A1 in the appendix.

The simulations also depend on the distribution of charges within the complex,
following Coulomb explosion. Unfortunately, we do not know precisely how the
ionization and fragmentation occur. However, as we only focus experimentally
on the I+ and Br+ fragments, we can select specific ionization and
fragmentation cases that must fulfill: (i) the double ionization of the I2
molecule fragmenting into two single charged I+ ions. (ii) the fragmentation
of BrPh leading to a single Br+ ion, along with some other ionic fragments. We
consider the following feasible fragmentation pathways for the BrPh molecule,
these channels are chosen such that the mass and the charges of the ionic
fragments are sufficiently different to lead to a broader distribution of the
plausible Coulomb explosion dynamics:

For each of the molecular fragments from these five pathways we assign the
charge on each atom by fitting an electrostatic potential using the
fluctuating charge method ($\omega$B97X-D method [55] with aug-pcseg-n basis
set [58]). For each fragmentation pathway, we now have a charge assigned to
each atom, which are listed in Table A2 in the appendix. The use of partial
charges and Coulombic force to simulate the dynamics will likely
underestimate/overestimate the interaction between each ionic fragment as the
non-Coulombic part of the interaction will not be taken into account[59].
However, its directionality should not be too affected by the inclusion of
these effects thanks to the use of partial charges to reproduce the
electrostatic potential.

Figure 4: Structures fulfilling experimental velocity recoil for several
charge and fragmentation schemes,label is associated to a particular
fragmentation pattern and a specific charge distribution detailed in the text.
The full parameters are given in Table A2 in the appendix. The angle on top of
each panel is the relative angle between the I2 axis and the C-Br axis.

We find that the optimization converges well on the experimental angular
covariance for all five fragmentation pathways. Figure 2 (a3) and (b3) show
the simulated angular covariance for the case of fragmentation pathway (a),
although the covariance plots simulated for the other four fragmentation
channels look essentially the same. The agreement is excellent, although we
note that the shape of the islands is controlled mostly by the assumptions of
imperfect alignment and non-axial recoil. However, the island centers, which
are the target for the optimization, depend solely on the initial structure
and fragmentation pathway. The geometries that the optimization finds do not
deviate far from our initial input, with the main change being that the angle
between the I–I and C–Br axes now varies from 70∘to 95∘, depending on the
fragmentation pathway choice. The five resultant structures, and this angle,
are shown in Fig. 4. These structures are local minimum in the optimization
landscape and should not be considered as trustworthy predictions of the real
geometry. The optimization algorithm can lead to an almost perfect replica of
the experimental data over a broad distribution of initial geometry limiting
the accuracy of the prediction and the interpretation of the final given
structures found. In order to improve the modeling and to reduce the
optimization landscape, more observables would be needed such as C+ and H+.
Nevertheless, it provides a starting guess for further inquiries.

To test these classical predictions, we calculate the polarizability tensor of
each structure, shown in Table A3 in the appendix. We use the $\omega$B97X-D
method [55] with Def2QZVPP [60] as a basis set. The largest component of the
polarizability tensor identifies the axis of the complex that aligns along the
alignment laser polarization axis. It is then possible to extract the relative
angles between the I–I and C–Br axes using the alignment laser polarization as
a reference. These angles can then be compared with the prediction from
classical simulations. The results are displayed in Table A4 in the appendix
and allow us to discard structures (a) and (e), because they show a large
offset in the predicted angles between the classical calculations and the
quantum approach. The most likely explanation is that the classical
calculations are not able to predict correctly the initial structure from
these two charge/fragment distributions.As only structures (b), (c) and (d)
show a consistent behavior between classical and quantum mechanics, we believe
it provides the best estimate for the angle. Nevertheless, the large spread
used to reproduce the island shape makes the estimation of its spread
difficult. Therefore, we use the upper value of the experimental noise used in
the simulations, $20^{\circ}$, and give an estimate of $85\pm 20^{\circ}$ for
the angles between the I–I and C–Br axes.

Regarding the position of the I2 molecule relative to the molecular plane of
BrPh, we find that the agreement between the simulations and the experiment is
roughly equal whether the I2 is located above the center of the phenyl ring,
above a carbon atom, or above a C–C bond. As such, the current experimental
observables only allows us to estimate the angle between the I2 molecule and
the C–Br axis, but not the spatial location of the I2 molecule above the BrPh
molecular plane. Insight into the latter are obtained by theoretical
calculations of the stable structures of the heterodimer in the gas phase, see
Appendix G for details. Four stable structures are identified as shown in Fig.
A5. For the two most stables structures, the angle between the I–I and C–Br
axes is $81.8^{\circ}$ and $93.0^{\circ}$ and the I–I axis lies above one
carbon atom. The two others structures are higher in energy by about 70 meV
and the I–I axis is parallel to the molecular plane of BrPh. Therefore, the
experimentally found result is in good agreement with the two most stable
structures predicted by the gas phase geometry optimization.

###  III.3 Homodimer

Figure 5: Angular covariance maps of BrPh+ parent ions (left column) and Br+
ions (right column), after Coulomb explosion of aligned (BrPh)2 dimers. The
alignment geometry is indicated on the left of each row. In all cases, only
ions with significant kinetic energy were considered.

In addition to the BrPh-I2 heterodimer, we have also determined the structure
of the (BrPh)2 homodimer, using a similar methodology. Most of the structural
information comes from the angular covariance maps of either BrPh+ or Br+
fragments with themselves. First, the parent ion covariance maps are
consistent with four different dimer configurations. The parent ion covariance
is calculated by only considering the energetic ions originating from Coulomb
explosion of the dimer, similar to the approach used for the CS2 [10] and the
tetracene dimer [11]. In practice, we implement this by selecting parent ions
with a radius larger than 11 pixels. The Br+ fragments allow us to directly
observe the relative orientation of the two monomers, and hence deduce the
final structure.

The BrPh+ – BrPh+ angular covariance map is given in Fig. 5 (a1)–(a3), for the
three different alignment polarization geometries. In all cases, the two
fragments recoil with a $180^{\circ}$ angle between them, as expected for a
two-body breakup. However, different alignment geometries result in different
localizations of the angles, which tells us where the MPA is relative to the
two monomers. When the MPA is aligned perpendicular to the detector [Fig. 5
(a1)] shows an isotropic distribution. However, alignment of the MPA parallel
to the detector [Fig. 5 (a2)] shows confinement to two islands centered at
(0∘, 180∘) and equivalently (180∘, 360∘). Alignment with an elliptically
polarized laser pulse, which also confines the second most polarizable axis
perpendicular to the detector, shows an angular covariance map [Fig. 5 (a3)]
almost identical to the one in Fig. 5 (a2). In analogy with the analysis in
recent studies on the dimer of tetracene [11], also a planar molecule, we
identify four possible dimer structures that are consistent with the observed
angular covariance maps. Three of them have a stacked parallel displaced
geometry (1,2,3), and one has a T-shaped geometry (4), as shown in Fig. 6.

We can distinguish between these four plausible structures with the help of
the Br+ – Br+ angular covariance, shown in Fig. 5(b1)–(b3) for the three
different alignment polarizations. In all cases, the two Br+ ions recoil in
opposite directions with a $180^{\circ}$ relative angle. In the two cases
where the MPA is parallel to the detector [Fig. 5 (b2)–(b3)], the Br+ ions are
localized at $90^{\circ}$ and 270∘, i.e. along the polarization direction of
the alignment pulse. This means that the MPA in the dimer is parallel to the C
– Br axes. Inspecting the four structures in Fig. 6, the immediate impression
is that this is only the case for structure 1. Simulating the recoil direction
from Coulomb explosion of the four different structures corroborates that only
conformation 1 leads to recoiling Br+ ions that reproduce the observed
experimental covariance maps as shown in Fig. A4. Again, we compare our
experimental findings with predictions from quantum chemistry as discussed in
Appendix G. Three displaced parallel structures are found, the lowest one
shows a parallel displaced structure with the bromine opposing to one another
while the other two, also parallel displaced, show an angle of 120∘ and 30∘
between the two C–Br axes and have an energy respectively of 15 and 39 meV
above in energy. Therefore, only the first one seems to be consistent with our
experimental data.

Figure 6: Conformations of the BrPh2 consistent with the experimental angular
covariance maps from Fig. 5. The angle difference between the directions of
the C–Br axes is 1: 180∘, 2: 120∘, 3: 30∘ and 4: 180∘.

##  IV Discussion and Outlook

###  IV.1 Structure

The structure that we arrive at for the BrPh-I2 complex inside a helium
droplet is one where the I2 molecule is nearly perpendicular in the phenyl
ring. To our knowledge, there has been no previous investigations into this
complex. However, the related I2 - C6H6 complex has been rather well studied,
because it serves as a model system for charge transfer processes[40, 41, 42,
61, 62, 63, 64]. Matrix isolation spectroscopy found that the I2 molecule is
exactly perpendicular to the benzene plane, and lies directly above one of the
C–C bonds [42], in agreement with previous theoretical calculations [41]. From
our measurements of BrPh-I2 in He droplets, it appears that the angle between
the two molecules is slightly less than perpendicular, at around 85∘[65]. This
is perhaps not surprising; we can imagine that there will be dispersion forces
between the large halogen atoms and indeed our gas-phase calculations of the
bare heterodimer predict a deviation to perpendicular orientation by a few
degrees, which may be attractive enough to bend the complex. Another
possibility is that the helium environment may be responsible for this
structural change, although this is perhaps less likely as the interaction
strength with helium is much lower than that between the molecules [66, 67].
Alternatively, an unlikely but possible explanation is that the global minimum
energy structure is perfectly perpendicular, however the bent structure forms
a local minimum that the complex is trapped in at the 0.37 K temperature of
the droplets. We can imagine that as the two molecules approach each other, it
is rather infeasible that they do so with a precisely perpendicular angle. If
a local minimum does indeed exist, the complex will likely end up trapped
there. Frozen local minima of complexes in helium droplets have previously
been seen, for example in chains of HCN molecules [6] and in Br-HCCCN-Br [68].

###  IV.2 Coulomb Explosion imaging for structure determination

How useful is CEI of aligned molecules as a tool for structural determination
of loosely bound complexes? Compared to spectroscopic techniques, the
structural accuracy for CEI is still much lower. Frequency-resolved
spectroscopic tools can provide bond lengths and angles with sub-pm precision,
while CEI is restricted to a more qualitative overview of the complex
structure. Clearly, if high-resolution spectroscopy is available, then it is
the best tool for determining static structures. However, for more complex
molecules and complexes, high-resolution spectroscopy is not an option, and
often dynamics are more interesting than static structures. It is for these
cases where CEI holds the advantage.

Spectroscopic structural determination of complexes is usually accomplished by
studying some combination of vibrational and rotational lines, using (for
example) ultraviolet, infrared, microwave or rotational coherence
spectroscopies [69]. However, the applicability of these techniques is often
limited. If vibrational transitions are to be used, then the spectrum must be
sufficiently uncongested for clear assignment of the spectral lines. This
tends to rule out all but simple or highly symmetric complexes. Rotational
spectroscopy tends to have clearer assignments for isolated molecules, but
inside helium droplets the spectra, and thus the rotational constants, are
dominated by interactions with the helium solvent, rendering attempt to
extract structural information infeasible [70].

CEI is not the only non-spectroscopic structural tool: recently, the
alternative approaches of electron or x-ray diffraction have shown potential
for solving helium embedded structures [71, 72, 73, 74, 75, 76, 77]. These
diffraction experiments (which would also benefit from alignment) have the
possibility of directly reporting atomic positions. This can be achieved with
free electron lasers [78, 79, 80, 81], laser-induced electron diffraction
(LIED) [82] and laser-assisted electron diffraction (LAED)[83], which all
permit a time resolution comparable to that of the current work but with a
much higher structural resolution. However, LIED and LAED have so far only
been particularly successful on small molecules [82, 84, 83, 85] and have to
our knowledge not yet been applied in helium droplets. The presence of the
helium solvent can also be problematic as many events may originate from the
helium itself instead of the molecules of interest [86] making the scattering
diffraction profile of the molecules harder to resolve. The latter will also
increase in complexity as larger molecules are being studied which could also
limit the technique.

However, neither issue is an inherent limitation for CEI. Molecular complexity
certainly hampers CEI, but addition of ’tracer’ atoms, such as the Br atoms in
this work, allow us to narrow in on only small segments of the molecular
structure. Often, a few key parameters are the most interesting for telling
the story of a complex structure, and it is in these cases that CEI may be
useful. When performed inside a helium droplet, the helium blurs the recoil of
fragments as they leave the droplet, but it does not otherwise affect the
measurement, unlike it does for rotational spectroscopies [54]. Hence, CEI may
be the correct choice for measuring gross structure of complexes inside helium
droplets. Additionally, as demonstrated here, CEI with a 3D detector is able
to measure multiple structures simultaneously [87]. For helium droplets, this
is a particularly powerful feature as the statistical nature of the pickup
process naturally means that a mixture of complexes is created when one works
under conditions of moderately high signal.

The greatest promise of laser-induced CEI for structure determination
undoubtedly lies in femtosecond dynamics. As the duration of the probe laser
pulse is tens of femtoseconds, it interacts on a timescale where most
molecular motions are frozen. Intramolecular motions of molecules could be
observed, as was previously demonstrated for watching the torsion motion of
gas phase biphenyl molecules [27]. Even more exciting, one could in principle
use femtosecond CEI to watch a bimolecular reaction inside a helium droplet.
If one created a complex with a pre-reactive geometry that undergoes
bimolecular photoreaction, CEI could be used to study formation of chemical
bonds in real-time. In this instance, the lack of spatial resolution may be of
little concern if the amplitude of the motion is large enough during the
creation of bonds between the molecules. Such a study would represent a huge
leap in the ability to monitor chemical reactions.

The primary drawback of CEI is that the fragmentation pattern when the complex
undergoes Coulomb explosion radically affects the interpretation. If one would
know the fragmentation pathway, the uncertainty we quote could be lowered as
we could more reliably know how much angular spread could be expected from the
Coulomb explosion. This pathway choice can theoretically be overcome: in the
limit of extremely high charge states, cations are reduced entirely into
atomic fragments, and hence only one fragmentation pattern is possible [88].
For large systems, this requires 10s of positive charges in total, which is
not easily obtained with a standard femtosecond laser system. However, x-ray
free electron lasers can produce intensities high enough to reach these charge
states [89], and can be synchronized with an optical alignment laser, hence
XFEL facilities may be where the next generation of these experiments are
performed. In principle, these could even be combined with x-ray diffraction
experiments, for a very comprehensive view of dimer structures.

##  V Acknowledgments

We acknowledge support from the following three funding sources: the European
Union’s Horizon 2020 research and innovation programme under the Marie
Sklodowska-Curie Grant Agreement No 674960 "Angular Studies of Photoelectron
in Innovative Research Environments" (ASPIRE) and No 641789 "Molecular
Electron Dynamics investigated by Intense Fields and Attosecond Pulses"
(MEDEA), a Villum Experiment Grant (No. 23177) and a Villum Investigator grant
(No. 25886) from The Villum Foundation.

##  Appendix A Mass spectrum

The full mass spectrum is shown in Fig. A1 with the labeling of relevant ionic
fragments. Masses below 60 u were not recorded due to detector gating, and no
significant peaks lie above 320 u with the doping conditions used.

##  Appendix B Determination of peak centers in covariance maps

Figure A1: Mass spectrum of He droplets doped with both I2 and BrPh molecules,
shown for (a) 60–200 u and (b) 200–350 u. Masses below 60 u were not recorded
due to the choice of detector gating.

Figure A2: The method used to determine the centers of islands in the
$\theta_{I}$–$\theta_{\rm Br}$ covariance map. The raw image (a) is
interpolated (b), binned (c), and then the center is determined by weighted
centroid (d). See text for details.

The procedure for the center retrieval of the islands in the
($\theta_{I},\theta_{Br}$) covariance map, Fig. 2(b2), is highlighted in Fig.
A2. Panel (a) shows one island from Fig. 2(b2) in the main text. First, the
image is interpolated to smooth its shape and facilitate the clustering
procedure, using a sampling of 2500 points divided by the initial number of
points on each axis. This gives the interpolated image shown in panel (b).
Next, a k-means clustering procedure is applied on the interpolated image to
generate multiple clusters according to its intensity. It results into a
binning of the image into multiple intensity bins, resulting in the image in
panel (c). The binned image is then sent into the Matlab regionprops function.
The function will only use the points weighted by their intensity bins
belonging to the clusters associated to the island (here from 3 to 5) to
determine the center and bounding ellipse. The output is the red ellipse
displayed with a dot at its center, shown in panel (d). Each island is treated
separately to facilitate the clustering since the intensity might vary from
one island to another. This methodology has been applied for three different
angular binsizes, $2^{\circ}$, $3^{\circ}$, $4^{\circ}$ and for 3 different
island selection shown in Fig. A3. The centers given in Table 1 are the mean
positions of each island over all possible configurations.

Figure A3: Different island selections labeled (a), (b), (c) for an angular
binsize of $4^{\circ}$. On the $\theta_{\textrm{I}^{+}}$, the thresholds
points are ($340^{\circ}$ \- $20^{\circ}$) and ($160^{\circ}$ \-
$200^{\circ}$) for all panels. On the $\theta_{\textrm{Br}^{+}}$ axis, the
threshold points are, (a): ($70^{\circ}$ \- $110^{\circ}$) and
($0/360^{\circ}$), (b): ($70^{\circ}$ \- $110^{\circ}$) and ($250^{\circ}$ \-
$290^{\circ}$), (c): ($50^{\circ}$ \- $130^{\circ}$) and ($230^{\circ}$ \-
$310^{\circ})$. The axis $\theta_{\textrm{Br}^{+}}$ has been shifted by
$-90^{\circ}$ to facilitate the perception of all four islands.

##  Appendix C Structures of the BrPh–I2 heterodimer

The starting geometry for the five potential dimer structures is listed in
Table A1.

Atoms | X | Y | Z
---|---|---|---
Br | 0.0000 | 0.0000 | 1.7947
C | 0.0000 | 0.0000 | -0.1006
C | 1.2067 | 0.0000 | -0.7771
C | -1.2067 | 0.0000 | -0.7771
C | 1.1982 | 0.0000 | -2.1627
C | -1.1982 | 0.0000 | -2.1627
C | 0.0000 | 0.0000 | -2.8569
H | 2.1375 | 0.0000 | -0.2299
H | -2.1375 | 0.0000 | -0.2299
H | 2.1372 | 0.0000 | -2.6985
H | -2.1372 | 0.0000 | -2.6985
H | 0.0000 | 0.0000 | -3.9376
I | 0.0000 | 3.5000 | -1.4728
I | 0.0000 | 6.2000 | -1.4728
Table A1: Starting geometry for the classical simulations in the laboratory
frame, where Y is the alignment laser polarization axis and Z the laser
propagation axis

For each structure, a charge and a fragment distribution is assumed. The
values used in this work are shown in Table A2. The charges refer to the
electrical charge (in units of $e$) on each atom while the index indicates
which atoms belong to the same fragment. Each fragment is considered as a
rigid body, such that the distance between its atomic components is fixed
throughout the simulation.

The velocity of the iodine ion furthest from the benzene plane and of the
bromine ion are determined after 10 ps. A distribution of velocity vectors in
the laboratory frame is then generated taking into account the free rotation
of the dimer around the alignment laser polarization axis (1D alignment) and
the reflection symmetry in a plane orthogonal to this axis (no orientation). A
Gaussian spread is applied to the velocity vectors of both the Br+ and I+ ions
to simulate the finite degree of alignment of the dimer. The result is a blur
of the diagonal line in the
($\theta_{\textrm{Br}^{+}}$,$\theta_{\textrm{I}^{+}}$) covariance map. The
effect of the non-axial recoil of the fragment ions is accounted for in a
similar manner leading to further blurring of the diagonal line in the
covariance map. The observed angular covariance maps shown in Fig. 2(b2), are
best reproduced by Gaussian distributions with widths (standard deviations) of
20∘, 17.5∘ and 12.5∘, for the non-perfect alignment and non-axial recoil of
the Br+ and I+ ions, respectively.

The velocities vectors of the Br+ and I+ fragments are then projected onto a
2D plane, that either contains the alignment polarization axis or is
orthogonal to it in order to represent the two cases shown in Fig. 2. The
covariance maps were simulated for a set of $2\times 10^{6}$ events.

Atoms | (a) | (b) | (c) | (d) | (e)
---|---|---|---|---|---
| Index | Charge | Index | Charge | Index | Charge | Index | Charge | Index | Charge
Br | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
C | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 0.870700 | 2 | 1.071778
C | 3 | 0.190321 | 3 | 0.651576 | 3 | 0.615844 | 2 | -0.664491 | 2 | -0.594518
C | 4 | 0.190321 | 4 | 0.651576 | 4 | 0.615844 | 2 | -0.664491 | 2 | -0.594518
C | 3 | 0.190321 | 3 | 0.651576 | 5 | 0.615844 | 2 | 0.258182 | 2 | 0.294991
C | 4 | 0.190321 | 4 | 0.651576 | 6 | 0.615844 | 2 | 0.258182 | 2 | 0.294991
C | 5 | 0.615844 | 5 | 0.615844 | 7 | 0.615844 | 2 | -0.362198 | 2 | 0.022590
H | 3 | 0.309679 | 3 | 0.348424 | 3 | 0.384156 | 2 | 0.361166 | 2 | 0.410356
H | 4 | 0.309679 | 4 | 0.348424 | 4 | 0.384156 | 2 | 0.361166 | 2 | 0.410356
H | 3 | 0.309679 | 3 | 0.348424 | 5 | 0.384156 | 2 | 0.168724 | 2 | 0.218702
H | 4 | 0.309679 | 4 | 0.348424 | 6 | 0.384156 | 2 | 0.168724 | 2 | 0.218702
H | 5 | 0.384156 | 5 | 0.384156 | 7 | 0.384156 | 2 | 0.244336 | 2 | 0.246571
I | 6 | 1 | 6 | 1 | 8 | 1 | 3 | 1 | 3 | 1
I | 7 | 1 | 7 | 1 | 9 | 1 | 4 | 1 | 4 | 1
Table A2: Charge (in units of $e$) and index parameters used in the
simulations

##  Appendix D Polarizability tensors and final structures of the BrPh–I2
heterodimer

Conformation | Polarizability tensors
---|---
(a) | $\begin{pmatrix}138.95\\\ 185.38\\\ 166.99\end{pmatrix}$
(b) | $\begin{pmatrix}132.45\\\ 179.64\\\ 164.06\end{pmatrix}$
(c) | $\begin{pmatrix}132.71\\\ 177.63\\\ 163.94\end{pmatrix}$
(d) | $\begin{pmatrix}132.77\\\ 178.26\\\ 163.79\end{pmatrix}$
(e) | $\begin{pmatrix}131.6\\\ 188.03\\\ 158.3\\\ \end{pmatrix}$
Table A3:  Table listing polarizability tensors for each trial structures
presented in Fig. 4 . The polarizability components are expressed in
$a_{0}^{3}$ and are listed in the (x,y,z) order.

The classical simulations of the angular covariance maps identified the
structure of the dimer relative to the aligned axis, i.e. the MPA. Thus, these
simulations allow us to determine the angle, $\theta_{1}$, between the I–I
axis and the alignment pulse polarization, as well as the angle, $\theta_{2}$
between the C–Br axis and the alignment pulse polarization. These angles are
listed in Table A4 for each of the five dimer structures in the columns
labeled ’classical’.

For comparison, we calculated the polarizability tensor of the five dimer
structures with the $\omega$B97X-D method [55] with Def2QZVPP [60] as a basis
set. The results, expressed in the frame where the tensor is diagonal, are
given in Table A3. These calculations enable a determination of $\theta_{1}$
and $\theta_{2}$ and these values are listed in Table A4 in the columns
labeled ’quantum’. It can be seen that the classical simulation only agrees
with the result from the quantum chemistry calculation for structures (b), (c)
and (d).

Angle | (a) | (b) | (c) | (d) | (e)
---|---|---|---|---|---
| Quantum | Classical | Quantum | Classical | Quantum | Classical | Quantum | Classical | Quantum | Classical
$\theta_{1}$ | 14.0∘ | 4.2∘ | $\bm{5.1^{\circ}}$ | $\bm{3.7^{\circ}}$ | $\bm{4.7^{\circ}}$ | $\bm{3.3^{\circ}}$ | $\bm{6.4^{\circ}}$ | $\bm{3.6^{\circ}}$ | 23∘ | 5.6∘
$\theta_{2}$ | 66.6∘ | 66∘ | $\bm{91.9^{\circ}}$ | $\bm{83.0^{\circ}}$ | $\bm{79.2^{\circ}}$ | $\bm{80.6^{\circ}}$ | $\bm{77.0^{\circ}}$ | $\bm{79.8^{\circ}}$ | 118.2∘ | 89.6∘
Table A4: Predicted angles between the I–I axis and the C–Br axis with the
alignment laser polarization axis for quantum chemical calculations through
the polarizability tensor and classical calculations from the recoil of the
charged ionic fragments. Bold values refer to conformations that show similar
angles between the polarizability calculation and the least square fitting
procedure.

##  Appendix E Structures of the (BrPh)_2 homodimer

We simulated Coulomb explosion of the four structures of the homodimer shown
in Fig. 6. For each structure we calculated the polarizability tensor and
determined the recoil velocity of the Br+ ions (at 10 ps after the probe pulse
where the recoil velocity has reached its final direction). The simulations
were done using fragmentation pathways (a), (b) and (c) of BrPh listed in
subsection III.2 in the main text. Only dimer structure 1 leads to Br+ recoil
directions that are consistent with the experimentally observed back-to-back
recoil. The other three structures lead to recoil patterns that deviate
significantly from the experimental findings when the alignment laser
polarization is either parallel or perpendicular to the detector plane.

Figure A4: Angular covariance for Br+ ions for different conformations and
charge distributions. The letter labels are associated to the fragmentation of
the C6H5Br presented in the main text while the numbers refer to each
conformation shown in Fig. 6 and represented on top of the figure. The
parallel and the perpendicular sign indicate the relative angle between the
polarization of the alignment laser and the detector plane. The standard
deviation used for misalignment and non axial recoil is respectively 10∘ and
10∘.

##  Appendix F Polarizability tensors and structures of the (BrPh)_2 homodimer

Conformation | Polarizability tensors
---|---
1 | $\begin{pmatrix}223.77\\\ 172.13\\\ 125.14\end{pmatrix}$
2 | $\begin{pmatrix}206.77\\\ 182.57\\\ 128.18\end{pmatrix}$
3 | $\begin{pmatrix}217.62\\\ 178.41\\\ 124.67\end{pmatrix}$
4 | $\begin{pmatrix}224.32\\\ 170.42\\\ 141.16\end{pmatrix}$
Table A5:  Table listing the polarizability tensors for each conformation
presented in Fig. 6. The polarizability components are expressed in
$a_{0}^{3}$.

The polarizability tensors of each final structure are shown in Table A5. The
tensors are expressed in the principal axes of polarizability frame.

##  Appendix G Predicted structures from geometry optimization

Stable structures for the heterodimer and homodimer were also theoretically
investigated, independently from any experimental input, from a combination of
computational methods. A force field exploration of the energy landscapes was
first conducted using the Amber ff99 molecular mechanics framework, and
replica-exchange molecular dynamics. The partial charges on the bromobenzene
molecule were taken from a density-functional theory calculation at the M06-2X
level with aug-cc-pvDZ basis set using the restrained electrostatic potential
fitting procedure. The candidate structures were then reoptimized at the DFT
level, using the same hybrid functional but with the DGDZVP basis set that is
appropriate for the iodine molecule. The DFT reoptimizations were conducted
using the Gaussian09 quantum chemistry package [57].

For the heterodimer, four local-minimum structures were found, as depicted in
Fig. A5. Their relative stability can be compared from the binding energy,
defined as the total electronic energy minus twice the monomer energy taken in
its equilibrium geometry. The binding energies thus obtained for the four
heterodimers are (A) 185; (B) 193; (C) 171; and (D) 146 meV, respectively,
confirming that perpendicular configurations for the iodine molecule are much
more stable energetically.

Figure A5: The resultant structures from the geometry optimization of the
dimer structure in the gas phase using M06-2x[90] with DGDZVP[91]. The angle
on top of each panel is the relative angle between the I–I axis and the Br–C
axis.

For the homodimer, a similar exploration predicts 3 locally stable geometries
all having the aromatic planes parallel to each other in shifted and rotated
fashions, corresponding to the structures 1, 2, and 3 in Fig. 6. Structure 4
with a T shape is not a local minimum at the present DFT level. The binding
energies obtained for structures 1, 2, and 3 were found to be 332.2, 318.9,
and 292.3 meV, respectively. The prediction that structure 1 is the most
stable agrees with the CEI experiment.

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