# Ion-pair dissociation dynamics in electron collision with carbon dioxide
probed by velocity slice imaging

Narayan Kundu  Sumit Naskar  Irina Jana  Anirban Paul  Dhananjay Nandi
<EMAIL_ADDRESS>Indian Institute of Science Education and Research
Kolkata, Mohanpur 741246, India

###### Abstract

Ion-pair dissociation (IPD) to gas phase carbon dioxide molecule has been
studied using time of flight (TOF) based mass spectroscopy in combination with
the highly differential velocity slice imaging (VSI) technique. The appearance
energy of the fragmented $O^{-}$ ion provides the experimental threshold
energy value for the ion-pair production. The kinetic energy (KE)
distributions and angular distributions (AD) of the fragment anion dispense
the detailed insight to the IPD dynamics. The KE distribution clearly reveals
that the IPD dynamics may be due to the direct access to the ion-pair states.
However, indirect mechanism can’t be ruled out at higher incident electron
energies. The angular distribution data unambiguously identified the
involvement of ion-pair state associated with $\Sigma$ symmetry and minor
contribution from $\Pi$ symmetric states. Computational calculations using
density functional theory (DFT) strongly support the experimental
observations.

##  I Introduction

In recent years dynamics study with anion fragments has marked a new realm in
the field of electron induced chemistry Nikjoo  _et al._ (1997); Boamah  _et
al._ (2014). Dissociative electron attachment (DEA) and ion-pair dissociation
(IPD) are the two well established inelastic scattering phenomena to probe
such anion dynamics in low (0 - 15 eV) and intermediate (15 - 50 eV) electron
molecule collisions, respectively. In DEA, resonances occur at some particular
energies (less than ionization energy of that particular molecule) whereon the
colliding particles generate quasi-bound temporary negative ion (TNI)
complexes Whelan and Mason (2006); resulting in rapid variations in the energy
dependence of the inelastic scattering cross sections. Contrastingly, IPD is a
non-resonant post-DEA phenomenon in ionization continuum. In general, ion-pair
dissociation originates via. some well defined Rydberg states, even if direct
dissociation to an ion-pair states provides a finite probabilistic value for
some cases Suits and Hepburn (2006); Chakraborty  _et al._ (2016). However,
the energetically higher (greater than ionization potential energy of that
particular molecule) neutral states in ionization continuum are responsible
for such ion-pair generation. These well defined high energetic Rydberg states
are commonly known as super-excited states Kouchi (2013); Kouchi  _et al._
(1997); Hao  _et al._ (2017). During the study of interaction process between
ionizing radiation and matter, Platzman first gives the importance of the
super-excited states Platzman (1962). The dissociation dynamics obtained from
these super-excited states varies greatly with that of obtained from the
ordinary Rydberg states excited below ionization thresholds Hatano (2001).
Suitable amount of energy transferred to the target molecule using electron or
photon collisions reveals this type of states to play with. IPD often occurs
when the incident electron partially transfers its kinetic energy to the
molecule and leaves the molecule to one of its neutral super-excited states or
neutral ion-pair states. Suppose, the molecule AB inelastically scatters due
to electron molecule interaction and reaches the states beyond its ionization.
Then the future of this energy pick up by the molecule will be the reason for
achieving one of the following processes.

$\displaystyle\rm{AB}+\ energy\ $
$\displaystyle\longrightarrow\rm{AB}^{+}+e^{-}\ :\ direct\ \ ionization$ (1)
$\displaystyle\longrightarrow\rm{AB}^{**}\ :\ super\ excitation$ (2)

Finally, the super excitation gives us phenomena like:-

$\displaystyle\rm{AB}^{**}$ $\displaystyle\longrightarrow\rm{AB}^{+}+e^{-}:\
\rm{autoionization}$ (3) $\displaystyle\longrightarrow\rm{A}^{+}+\rm{B}^{-}:\
\rm{ion-pair\ dissociation}$ (4) $\displaystyle\longrightarrow\rm{A}+\rm{B}\
:\ \rm{neutral\ dissociation}$ (5) $\displaystyle\longrightarrow\
\rm{fluorescence\ and\ other\ processes}$ (6)

The ion-pair threshold not only depends on geometry of that ion-pair states
but also on the geometry of the target and products as well; resulting in the
threshold energy value to be channel specific.

In case of collision between photon and isolated molecules, coherent vacuum
ultraviolet laser sources play a crucial role for obtaining the IPD dynamics
in a similar fashion like photoelectron spectroscopy. Threshold ion pair
production spectroscopy (TIPPS) Shiell  _et al._ (2000); Martin and Hepburn
(1998) and ion pair imaging spectroscopy (IPIS) Yang  _et al._ (2005); Suto
_et al._ (1997) are the two traditionalistic approaches to probe such ion-pair
states. TIPPS is focused at around the dissociation threshold where as IPIS is
based on ion imaging of the energetic fragments. Although IPD process is most
studied using photon impact, the electron collision with isolated molecules
can provide us similar types of results as obtained from the techniques
mentioned below. Thus, the super-excitation as well as direct excitation to
the ion pair states can be investigated by the electron collision. During the
dynamics studies of DEA or IPD products, this VSI probing technique has
satisfactorily provided us adequate information over the last two decades
Nandi  _et al._ (2005); Ram and Krishnakumar (2012); Chakraborty  _et al._
(2016).

In the present work, we apply the VSI technique in a TOF based mass
spectrometry to obtain the IPD pathway for a triatomic molecule: carbon
dioxide (CO2). Here, the energetic and dynamic informations are reported for
the wide range of incident electron-energy spanning roughly from 20 to 40 eV.
Till today, there is no experimental report about the threshold energy value
of incident electron to kick off ion-pair origination in CO2. Kinetic energy
(KE) and angular distributions (AD) of the fragmented anion are also unknown
to the scientific community for the so-called molecule. In this article, our
work have been focused on the study of both KE and AD for produced O- channel
along with ion-pair threshold behaviour using the high resolution VSI
spectroscopy.

##  II Instrumentation

The experimental set up used for this study is based on crossed-collision
between electron and molecular beam and has already been discussed in details
elsewhere Nag and Nandi (2015). The measurements are done by the highly
differential time sliced velocity map imaging (VMI) spectrometer specially
built to study low energy electron-molecule interactions. The experimental
set-up is made of with a magnetically collimated and pulsed electron beam, a
Faraday cup, effusive molecular beam, a three field time-of-flight velocity
map imaging electrode system, and a two-dimensional position sensitive (PSD)
detector with linked data acquisition system. The experiment is carried out in
a vacuum chamber, which is pumped down up-to $10^{-10}$ mbar using a turbo
molecular vacuum pump and scroll pump arrangement. In this experiment, the
pulsed electron beam interacts with an effusive molecular beam formed by a
capillary tube. After finite time delay, the fragmented anions (O-)are
extracted into a time-of-flight mass spectrometer using a suitable extraction
pulse.

Thermionic emission process is applied successfully to generate our electron
beams whereon a programmable power supply (Instek PSM-6003) controls the beam
energy. The energy resolution of this electron beam is about 0.6 to 0.7 eV.
The electron beams used here are pulsed in nature. The typical pulse width is
about 200 nanosecond with 10 kHz repetition rate. A Faraday cup measures the
time averaged current using the collected electrons. Our TOF based three field
configuration spectrometer capable of mapping the fragmented anions on the two
dimensional position sensitive detector. All the anions created with a
particular velocity vector are mapped onto a single point on the 2D PSD,
consisting of three microchannel plates (MCP) with Z-stack configuration. A
three-layer delay line hexanode is used to encode position information
Jagutzki  _et al._ (2002) for the detected anions. The TOF of the detected
ions are calculated from the back-MCP signals. The position informations (x
and y) for the detected ions are redeemed using the hexanode placed behind the
MCPs. The flight time (t) and the redeemed position (x, y) of each detected
ion is saved in a list-mode format (LMF) generated through CoboldPC software
Ullmann-Pfleger  _et al._ (1999). The experiments are performed under ultra-
high vacuum conditions having pressure $10^{-7}$ mbar. $99.9\%$ pure
commercially available CO2 gas is used to perform this experiment. Only the
MCP output is used to obtain the ion yield curve. In this case, a fast
amplifier amplifies the MCP signal and then sent to a constant fraction
discriminator (CFD). CFD output signal act as a STOP signal for nuclear
instrumentation module (NIM) that converts the time signal to a corresponding
amplitude, commonly known as time to amplitude converter (TAC). A master pulse
generator used to generate the START pulse synchronized with the electron gun
pulse. The TOF of the detected O- ion is nothing but time difference between
this START and STOP signals. The TAC output signal is connected to a
multichannel analyzer (MCA, Ortec model ASPEC-927). Using USB 2.0 port, MCA
output signal is transferred to a computer for further analysis. Lastly, the
mass spectra and the ion yields for the fragments are measured using LABVIEW
based data acquisation system.

When the electrons with intermediate energy (15 to 50 eV) interact with the
molecule, each ion-pair dissociation event yields two partner fragments flying
with equal momentum in opposite directions in the centre of mass frame. When
we repeat the same event for many times, spherical distributions of fragments
will be build up in velocity space. These spherical distributions of fragments
are the so called ‘Newton (velocity) Sphere’s. The size of this Newton Sphere
tells us about the balance of internal and translational energy in the
reaction Whitaker (2003). One can extract the kinetic energy and angular
distribution statistics of the fragments from the projection of the Newton
Sphere onto a position sensitive detector. Here the radius of a particular
Newton Sphere is proportional to the kinetic energy of that particular
fragment. Thus, the fragmented ions with higher momentum must fall onto the
PSD with bigger diameter.

In this present experiment, 4 micro-seconds extraction pulse is used. This
extraction pulse is functionally active in such a time scale that fragments
get enough time to construct the Newton sphere. Usually we have taken 100
nanosecond delay with respect to electron gun pulse for starting the
extraction pulse. This approach not only allow to achieve better resolution
for time sliced images but also restrict the incident electrons to fall onto
the position sensitive detector. One can obtain the slice images from the
detected Newton Sphere using suitable time window. The CoboldPC from RoentDek
is used to slice the raw data. The central is more informative due to its
biggest diameter as well as formed in electron beam plane territory. Thus, the
central time slice images are taken into consideration to analyse angular
distribution (AD) for the fragmented ions (usually anions). So, the fragmented
ions for central slice are roughly parallel to the detector. Generally, the
fragmented O- ions detected by 2D PSD lie within the full with half maximum
(FWHM) about 500 nanoseconds. To determine to kinetic energy of the fragmented
ions, Kinetic energy calibration is performed using the well known DEA
resonant peaks for O- ions produced due to electron collision with gas phase
oxygen moledcule.

##  III Results and Discussions

If we consider the collision between gas phase CO2 and electrons with
intermediate energy, then produced intermediate super-excited state may decay
through the channels as discussed below.

$\rm{CO}_{2}+e^{-}\longrightarrow
CO_{2}^{**}+e^{-}\longrightarrow\begin{cases}\rm{CO}^{+}+O^{-}+e^{-}\\\
\rm{CO}^{-}+O^{+}+e^{-}\end{cases}$ (7)

Though CO2 is a non-polar molecule because of the symmetry of its bonding, the
double covalent bond attached with each oxygen atom is polar in nature. When
the bond dissociation of CO2 comes into picture, the charge cloud generated
through this molecule’s electrons and nuclei can serve as fate to ingress the
molecule’s reactivity towards ion-pair formation. Thus, three dimensional
visualization of molecular charge distribution i.e. electrostatic potential
(ESP) map will play a key role to rationalize the most probabilistic ion-pair
generation channel. Considering B3LYP functional with 6-31G(d,p) basis set, an
$ab\ \ initio$ electronic structure calculation is performed using density-
functional theory (DFT) to optimize the geometry of this molecule. The
optimized systemic framework is used to plot the ESP map at the ground state
of CO2 as shown in Fig. 1.

Figure 1: Electrostatic potential map at 0.004 electron/Bohr3 iso-density
surface of CO2 molecule. The red in the color spectrum denotes lowest
electrostatic potential value while the blue denotes the highest. The red
spheres represent the O-atoms and the blue sphere represents the C-atom.

From the Fig. 1, it is obvious to state that the C$=$O bond is strongly
polarised towards oxygen due to higher electro-negativity of oxygen atom as
compared to carbon atom. So, we can easily vindicate that the IPD of CO2 is
more likely via. first channel i.e. the formation of O- and CO+. Again, the
variation in the number of ion-pair formations is plotted as the function of
incident electron beam energy, conventionalised ion yield curve as shown in
Fig. 2. The most conspicuous influences on the ion yield characteristic are
electron affinity for negative ions and ionization potential energy for
positive ion. This ion yield curve is in good agreement with the DEA-
resonances at 4.4 and 8.2 eV incident electron energy as previously reported
by Cicman et al. Cicman  _et al._ (1998).

The channel specific threshold energy value due to IPD process of CO2 can also
be determined with the help of known thermochemical parameters associated with
the channel. Applying energy conservation principle all over the IPD process,
we can write the following equation,

Figure 2: The data points in blue color represent the number of produced anion
(O-) as a function of electron beam energy. Both DEA and IPD region are shown
by red arrows. Black arrows represents the incident beam energies accounted
for studying IPD dynamics.

$\rm{V}_{e}=(E_{i}+D-A+IP)+E_{1}+E_{2}$ (8)

where Ve is accounted for the energy transferred from the incident electron to
the molecule, $E_{i}$’s are the energy associated with the possible excited
states for the cation, D stands for the bond energy for the process;
CO${}_{2}\longrightarrow$ CO + O, IP denotes the ionization potential energy
for CO molecule and lastly A implies the electron affinity for oxygen atom. E1
and E2 denote the kinetic energies of the fragmented cation and anion,
respectively. Again, E1 and E2 are restricted to zero at IPD threshold
(V${}_{e}=$ Eth). If we consider that both CO- and O- ions are produced on
their corresponding accessible ground state i.e. E${}_{i}=$0, then the
threshold energy value of O- formation will obey the equation as below

$\rm{(V_{e})}_{threshold}=E_{th}=(D-A+IP)$ (9)

Figure 3: The data points in blue color represent the number of produced anion
(O-) as a function of electron beam energy, fitted using Fiegele et al.
Fiegele  _et al._ (2000) model. The arrow in black color is used to point out
the threshold energy for anion formation. Figure 4: Time slices images taken
with 50 ns time window of O- ions created due to the ion-pair formation
process of CO2 for five different incident electron energy. The arrow in red
denotes the incident electron direction.

Now, if we use the known thermochemical values 5.51 eV (127 kcal/mol)
B.deB.Darwent (1970), 1.46 eV Blondel  _et al._ (2001) and 14.014 eV Erman
_et al._ (1993) for the parameters D, A and IP, respectively; thermochemically
obtained threshold energy value for the IPD process of CO2 becomes 18.06 eV.
Near threshold the experimental data points of the ion-yield curve are shaped
using the model given by Fiegele et al. Fiegele  _et al._ (2000) and recently
used by Nag et al. Nag and Nandi (2018).

$\displaystyle\rm{f(E)}$ $\displaystyle=\rm{b\ \ \ \ for\ E<E_{th}}$ (10)
$\displaystyle=\rm{b\ +a(E-E_{th})^{n}\ \ \ for\ E>E_{th}}$ (11)

Here, the parameter b is a constant appearing due to background correction.
Eth stands for the threshold energy value. The parameter a is the scaling
factor that constraint to zero beneath the threshold. Lastly, n is the
exponent which measures the slope of fitted curve after the threshold. Thus, n
value is an indirect measurement of incident beam resolution. Due to finite
energy resolution of incident electron beam the ion-yield curve increases
slowly instead of sharp variation near the apparent threshold. To lessen this
effect on threshold energy value estimation, we have fitted the data point
12.0 to 32.2 eV of incident electron energy using Eqn. 11 and the fit (best)
gives it back more or less straight slope beyond the calculated threshold. The
extrapolated straight line up-to threshold is nothing but the mean of
background counts (parameter: b). The best fit shown by solid line in Fig. 3
is plotted using the values of different parameters as : a = 29.55715, b =
26.06994 and n = 1.549. Thus, we can say that our obtained threshold energy
value (18.13 eV) supports to a great extend in thermochemical view point.

During extraction of slice images, we have taken suitable ion-TOF (typically
50 nanoseconds) from the raw data in order to obtain central slice. Extracted
time sliced velocity map images for fragmented anion (O-) at 25 eV, 29 eV, 31
eV, 35 eV and 39 eV incident electron energies are shown in Fig. 4. The
extracted slice-images are equivalent to that obtained by conventional methods
using the inverse Abel transform, however, the artificial noise introduced by
Abel transform can be avoided. The red arrow attached with each slice image
indicates the direction of incident electron beam.

If we notice at the Fig. 4 consisting with different slice images, it is clear
to state that the maximum intensity of O-/CO2 strikes near the centre part of
sliced images and decreasing gradually with the increment the radius of 3D
‘Newton Sphere’ i.e. most of the produced O- fragments are low energetic.
Honestly, this type of two dimensional velocity slicing technique using time
gate would take into account a larger fraction of the total solid angle for
ions with lower momentum and a smaller fraction of solid angle for ions with
larger momentum. In order to preserve the fraction of governed solid angle for
any momentum to achieve better statistics, Moradmand et al. Moradmand  _et
al._ (2013a) defines a conical gate through wedge slicing technique instead of
flat time gate; resulting the data restricts by angle in a spherical momentum-
space, rather than in one Cartesian coordinate Wu  _et al._ (2012); Slaughter
_et al._ (2011). As a counter response for this over-estimation in 2D time
gated flat slicing technique, in a very recent article Nag  _et al._ (2019)
Nag et al. reported a new technique to study the characteristic of very low-
energy ions. They have shown that an entire Newton sphere analysis brings the
same results as canonical gated wedged slicing technique providing the similar
nature of a single 0 eV peak in the kinetic energy distribution. However,
during the study of sulfur dioxide using time gated velocity slice imaging
technique Jana et al. Jana and Nandi (2019) point out that although the 2D
flat slicing method exaggerate the ions with lower momentum, the over-
estimated part roughly consist of $\leavevmode\nobreak\ 10^{-3}$ eV to the
kinetic energy distribution. Thus, this does not change the underlying science
qualitatively. In our case, we have taken the ‘Half Newton Sphere’ to study
the kinetic energy distribution instead of considering entire ’Newton Sphere’
as the ‘Half Newton Sphere’ also accounts equal fraction of solid angle for
ions with all momenta.

Figure 5: This plot shows the normalised kinetic energy distributions of the
fragmented anion (O-) for the five different beam energies. O- ions with lower
momentum are shown in zoomed view at upper right corner of this plot.

We have aggregated all the time gated flat slices (each of 20 ns) extracted
from the entire flight time for a particular ion where the average flight time
of a slice act as bin-time of the corresponding slice. Then proper scaling of
time-bin transfers the ellipsoidal shaped ion’s packet into Newton sphere.
Half Newton sphere is taken to consideration to obtain the kinetic energy
distributions of the fragmented anion (O-). The Fig. 5 shows the normalised
kinetic energy distributions for the five different beam energies. The KE
distribution shows maximum number of O- ions are low energetic instead of zero
in nature.

Figure 6: The most probable kinetic energy of the fragmented O- ions as a
function of the incident beam energy. The most probable values are extracted
using the Gaussian fit near the peak values.

From the variation of most probable KE with incident electron energy as shown
in Fig. 6, it is prominent that the ion kinetic energy first increases with
the incident electron energy and then becomes locked. From previous reports
Chakraborty  _et al._ (2016); Nag and Nandi (2018), the formation of ion-pair
dissociation can be explained due to presence of mainly two types of
processes: direct and indirect process. In a direct process, the energy of the
incident electron is transferred to the target molecule resulting in direct
excitation of that neutral target to an ion-pair state. Such direct excitation
dynamics are mainly governed by the Frank-Condon factor along with the
valance-Rydberg mixing characteristics. Our obtained results in an increase in
the anion kinetic energy (most probable value) with an increase incident
electron energy; an irrefutable experimental indication of the direct
transitions to the ion-pair state. However, In case of directly access ion-
pair states, the variation of most probable kinetic energy of the fragmented
ion-pair may governed by the partial energy transfer to the dissociation
products. During the study of electron impact dissociative ionization of
ethylene Wang et al. Wang  _et al._ (2015) obtains similar kind of mass
depending average kinetic energy saturation phenomenon for different
fragmented ions as a function of beam energies. on the other hand, in an
indirect excitation the molecule may first get excited to a well defined
Rydberg states (superexcited states) within the Frank-Condon region followed
by transition to an ion-pair state through a predissociative cross-over; often
occurs in case of excitation of molecules using photon. Such indirect
excitation may result in a ‘locking’ of the anion kinetic energy with increase
in incident beam energy provided, the Rydberg and ion-pair states have same
symmetry. Considering the kinetic energy distribution (Fig. 5) of this present
work, it can be seen that the ion KE first increases for incident electron
energies 25, 29 and 33 eV; then becomes almost constant for 37 eV incident
energy onward. The same can be noted from the most probable anion KE plot as
shown in Fig. 6. It clearly noticeable that KE variations of the fragmented
anion is small with respect to the variation of incident beam energies. Ion-
pair state achieved directly via. electron collision may transfer its energy
partially to dissociate the molecule; could be a rationale for such KE
variation of fragmented anion. Beyond 33 eV incident electron energy, the most
probable anion KE becomes saturated due to unavailability for accessing the
ion-pair state directly. However, ion-pair generation via. direct access to
the ion-pair state is strongly depends on molecular geometry; where as
indirectly produced ion-pair is a generalization for all target molecules.

Table 1: state specific characteristics of CO2 molecule obtained from DFT and TDDFT calucations. Energy eigenvalue |  Total energy in eV |  Symmetry attached |  Oscillatory strength
---|---|---|---
Ground | 00.00 | $\Sigma_{g}$ | NA
9th | 11.31 | $\Sigma_{u}$ | 0.343
17th | 16.33 | $\Sigma_{u}$ | 1.498
30th | 24.19 | $\Sigma_{u}$ | 0.207

However, considering the quantum chemistry computation calculated using the
above mention framework, the 17th excited state seem to have the maximum
contribution followed by the 30th excited state (as guided by the decreasing
non-zero oscillatory strength values). Again, we may conclude that significant
amount of the ion-pair dissociation results from a direct transition to the
ion-pair excited state. To give a clear idea of the above mentioned processes,
we have given a schematic of the potential energy curves for CO2 as shown in
Fig. 7. A firm conclusion delineating the direct and indirect excitations
would require a nuclear dynamics calculation which is beyond the scope of this
work. Also, we have calculated total ground states energies of CO+ and O- ions
using same level of theory. The minimum energy required for transition
directly from CO2’s ground to these ionic ground states is about 19.98 eV, not
distinctly far away from our experimental observation in appearance of O- ion.

Figure 7: Potential energy curves of CO2 along with ion-pair state in red line
are shown schematically. Among the calculated nonzero oscillatory strength,
$\Psi_{17}$ and $\Psi_{30}$ states positioned above the ionization potential
energy of CO2 i.e. superexcited states shown in blue line. The ordinary
Rydberg state ($\Psi_{9}$) in pink line lies well below the ionization
potential Tanaka  _et al._ (1960). Red vertical arrow using solid line
indicates the direct transition to the ion-pair state. Figure 8: Figure shows
the angular distribution of the fragmented anions (O-) due to the IPD process
for CO2. The solid lines in different color are fit to the data for $\Sigma$
final state only. Figure 9: Figure shows the angular distribution of the
fragmented anions (O-) due to the IPD process for CO2. The solid lines in
different color are fit to the data for $\Sigma+\Pi$ final states.

Angular distributions study of the fragmented ion-pairs contributes a
significant determinant to gauge the molecular symmetry associated with the
ion pair state. The angular distributions of produced O- ions as shown in Fig.
8 and Fig. 9, have been analysed for anion kinetic energy from 0 to 2.5 eV.
During the AD study, 50 nanoseconds slices of O-/CO2 have been taken into
account. Due to experimental difficulties of determine simultaneously both the
distribution of the fragments and the scattering angles of the electrons, we
have set the direction of electron beam as a convenient reference system for
reporting the form of angular distribution. All the data points have been
normalised at 90∘. In Fig. 8 and Fig. 9 symbols represents the experimentally
obtained data points and the solid curves are the fit-to data using the
expression given by Van Brunt Van Brunt (1974).

Table 2: The model parameters reported here for the O-/CO2 angular distribution as a function of electron energies with contributions from $\Sigma$ final state only. The am’s are the relative strengths of various partial waves for contributing to the $\Sigma$ final states. The $\delta_{l}$’s expressed in radian signify the phase differences with respect to the lowest order partial wave responsible for the transition. $\beta_{1}$’s are the product of the momentum transfer vector and the distance of closest approach between the incident electron and the centre of mass of the molecule for $\Sigma$ final state only. Lastly, each m used in this caption is nothing but the whole numbers. Incident electron energy (eV) |  Weighting ratio of the different partial waves $\hskip 22.76219pta_{0}:a_{1}:a_{2}:a_{3}$ |  Phase differences in radian $\delta_{s-p}$, $\delta_{s-d}$, $\delta_{s-f}$ |  $\beta$ parameter $\beta_{1}$ |  $R^{2}$ value
---|---|---|---|---
25 | 1.94 : 1.16 : 2.17 : 8.65 | 2.99, 1.75, 3.14 | 1.00 | 0.940
29 | 1.65 : 1.74 : 3$\times 10^{-9}$ : 9.71 | 0.16, 3.14, 0.21 | 0.79 | 0.897
33 | 1.54 : 1.59 : 2$\times 10^{-5}$ : 9.08 | 0.02, 0.71, 0.50 | 0.58 | 0.904
37 | 1.59 : 0.02 : 2.44 : 7.83 | 1.66, 2.07, 2.67 | 0.60 | 0.964
41 | 1.52 : 0.26 : 2.29 : 4.88 | 0.02, 3.14, 1.93 | 0.44 | 0.938
Table 3: The model parameters reported here for the O-/CO2 angular distribution as a function of electron energies with contributions from $\Sigma+\Pi$ final states. The am’s and bm’s are the relative strengths of various partial waves for contributing to the $\Sigma$ and $\Pi$ final states, respectively. The $\delta_{l}$’s expressed in radian signify the phase differences with respect to the lowest order partial wave responsible for the transition. $\beta_{1}$’s and $\beta_{2}$’sare the product of the momentum transfer vector and the distance of closest approach between the incident electron and the centre of mass of the molecule for $\Sigma$ and $\Pi$ final states, respectively. Lastly, each m used in this caption is nothing but the whole numbers. Incident electron energy (eV) |  Weighting ratio of the different partial waves $\hskip 28.45274pta_{0}:a_{1}:a_{2}:a_{3}$ $\hskip 28.45274ptb_{1}:b_{2}:b_{3}:b_{4}$ |  Phase differences in radian $\delta_{s-p}$, $\delta_{s-d}$, $\delta_{s-f}$ $\delta_{p-d}$, $\delta_{p-f}$, $\delta_{p-g}$ |  $\beta$ parameter $\beta_{1}$ $\beta_{2}$ |  $R^{2}$ value
---|---|---|---|---
25 | 1.37 : 2.50 : 3.08 : 6.54 | 4.8$\times 10^{-4}$, 4.3$\times 10^{-14}$, 0.75 | 1.081 | 0.943
0.03 : 0.62 : 0.72 : 1.25 | 0.20, 1.25, 1.24 | 0.058
29 | 1.15 : 0.10 : 10.88 :7.48 | 0.06, 3.14, 1.38 | 0.409 | 0.975
1.87 : 0.01 : 5.13 : 8.73 | 0.20, 2.01, 2.55 | 1.418
33 | 1.51 : 1.48 : 0.18 : 3.04 | 0.01, 0.20, 1.00 | 0.685 | 0.985
0.27 : 1.21 : 4.21 : 2.73 | 0.38, 0.08, 2.40 | 1.450
37 | 1.64 : 0.03 : 1.75 : 4.95 | 0.50, 2.08, 2.66 | 0.702 | 0.964
0.006 : 0.047 : 0.15 : 4.839 | 0.035, 2.365, 1.98 | 0.008
41 | 1.56 : 0.075 : 5.42 : 4.70 | 0.005, 1.75, 2.28 | 0.559 | 0.978
0.126 : 5.84 : 0.27 : 0.274 | 1.89, 2.31, 0.236 | 0.059

$\rm{I}(\theta)=K^{-n}\left\lvert\sum_{l=\mid\mu\mid}^{\infty}i^{l}\sqrt{\frac{(2l+1)(l-\mu)!}{(l+\mu)!}}j_{l}(\beta)Y_{l,\mu}(\theta,\phi)\right\rvert^{2}$
(12)

Here, K is the momentum transfer vector between the incident and scattered
electron, jl’s are the spherical Bessel function, $\beta$ denotes the product
of the momentum transfer vector and the distance of closest approach between
the incident electron and the centre of mass of the molecule, Yl,μ’s are the
spherical harmonics, l is the angular momentum of the electron and
$\mu=\mid\Lambda_{f}-\Lambda_{i}\mid$, where $\Lambda_{i}$ and $\Lambda_{f}$
are the projection of angular momentum along the molecular axis for the
initial and final states, respectively. Here, the summation over l is
responsible for the attachment of different partial waves. However, the
transition occurs between two specified states for a particular incident
electron’s energy then values K and n would be fixed and can be treated as
parameters. So, the AD data due to the inclusion of one or more than one final
states must be fitted using the expression

$\rm{I}(\theta)=\sum_{\mid\mu\mid}\left\lvert\sum_{l=\mid\mu\mid}^{\infty}a_{l}i^{l}\sqrt{\frac{(2l+1)(l-\mu)!}{(l+\mu)!}}j_{l}(\beta)Y_{l,\mu}(\theta,\phi)e^{i\delta_{l}}\right\lvert^{2}$
(13)

Where al’s are the energy dependent weight factors for different partial waves
and $\delta_{l}$’s are considered to calculate the phase difference of that
particular transitional partial wave with respect to the lowest order possible
partial wave. The summation over $\mu$ signifies the contribution of more than
one ion-pair states to this process. During the AD fitting, we have considered
possible lowest four partial waves for both $\Sigma$ to $\Sigma$ and $\Sigma$
to $\Sigma+\Pi$ transitions.

Being attached with the electron, temporary negative ion (TNI) of CO2 departs
from linear geometry before dissociation Moradmand  _et al._ (2013b); Jana
_et al._ (2019) and declines to obey axial recoil approximation. In case of
ion-pair dissociation, electron attachment to the molecule is no longer a
valid statement. Thus, considering axial recoil as a valid statement we can
demand the symmetry attached to the super-excited states would preserve in
ion-pair states also. We have already tabulated the symmetry and transition
probability of different states of CO2 while demonstrating the KE distribution
of the fragmented anions. Here the ground state symmetry of CO2 i.e. $\Sigma$
is considered as initial one for all of the involved transitions. In Fig. 8
and Fig. 9 the solid lines in the AD distribution represent the IPD dynamics
with symmetry $\Sigma$ and $\Sigma+\Pi$, respectively, for all of the final
states. However, the goodness (R2 value) for curve fitting to $\Sigma+\Pi$
final states is slightly better than $\Sigma$ final states. Theoretically, we
have not obtained any $\Pi$ symmetry involvement in the super-excited states.

In Fig. 8 and Fig. 9 it is clearly noticeable that number of scattered O- ions
in forward direction is slightly greater than scattered in backward direction.
Misakian et al. Misakian  _et al._ (1972) reported that this lack of symmetry
about $\theta=$90∘ aries due to the linear momentum transfer effect
consideration during the laboratory frame angular distribution measurement;
whereas thermal molecular motions alone are found to have no effect on the
center of mass angular distribution. Though, this asymmetry in lab frame
angular distribution is prominent near threshold for lighter molecules. During
the study of H2O through DEA resonance Haxton et al. Haxton  _et al._ (2006)
and Ram et al. Ram  _et al._ (2009) point out that forward backward asymmetry
in AD of dissociative products aries due to the contribution of partial waves
in different weight with different phase. Moreover, the momentum transfer
(either linear or angular) plays a crucial role to design such maintained
asymmetry.

Figure 10: This schematic represents the possible orientation of
${(\vec{\rm{k_{o}}})}$, $(\vec{\rm{k_{n}}})$ and $(\vec{\rm{k}})$ as
previously discussed by Zare Zare (1967), (a) although
$\rm{(\theta^{{}^{\prime}})}$ and $(\vec{\rm{k}})$ are small near IPD
threshold, contribute heavily to the form of $\rm{I}(\theta)$, (b) bigger
angle of $\rm{(\theta^{{}^{\prime}})}$ at far from IPD threshold, makes
$(\vec{\rm{k}})$ to weight loosely in $\rm{I}(\theta)$.

Interestingly, at higher incident electron energies the angular distribution
gradually losses it’s anisotropic nature. This reduction of anisotropy in IPD
dynamics could be explained by much the same argument given by Zare Zare
(1967). During the theoretical study of angular distribution of the
H${}^{+}_{2}$ ions from electron impact dissociation Zare reported that the
nature of AD of dissociation product, calculated with respect to the electron
beam direction, depends on the angle $\rm{(\theta^{{}^{\prime}})}$ generated
by wave vector ${(\vec{\rm{k_{o}}})}$ along the incident electron beam
direction and the direction of wave vector $(\vec{\rm{k}})$ responsible for
the momentum transfer to the molecule. Near threshold this angle
$(\theta^{{}^{\prime}})$ is restricted to small and increases gradually with
the increment of incident beam energies as shown in Fig. 10; resulting the lab
frame distribution disfigures from a cosine-squared dependence for
$(\vec{\rm{k}})$ parallel to $(\vec{\rm{k_{o}}})$ to a sine squared dependence
for $(\vec{\rm{k}})$ perpendicular to $(\vec{\rm{k_{o}}})$. Here,
$(\vec{\rm{k_{n}}})$ denotes the wave vector corresponding to the nth
transitional state of that molecule. Thus, it is not like that the absolute
value of momentum transfer vector is decreasing with the increment of incident
beam energies, it is due to the decreasing nature of the momentum transfer
weight factor to the intensity distribution. If we focus on the $\beta$
parametric values for $\Sigma$ final states, it is clear that cosine-squared
dependency to AD is diminishing gradually as a function incident beam
energies. Thus, in IPD dynamics of CO2, the momentum transfer vector weights
strongly to the differential cross section for lower beam energies. Under the
restriction imposed for contributing from the higher order partial waves
$(l>1)$ to the angular distribution, Zare also predicts that if the
measurements of Dunn and Kieffer Dunn and Kieffer (1963) were extended towards
threshold, the fragment distribution would not approach a "pure" cosine-
squared anisotropy, but would resemble like our obtained angular distribution
shown in Fig. 8 and Fig. 9.

##  IV Conclusions

Here, a quite similar process of ion-pair imaging spectroscopy (IPIS) has been
sucessfully applied in case of low energy electron-molecule interaction.
Determination of the threshold energy value to initiate the ion-pair formation
matches well with the thermochemically obtained value. Here, the dissociation
dynamics as well as the product of dissociation reported through out this
analysis is based on the fragmented anion characteristic only; coincidentally
measurement of both the anion and cation products can overstoke our findings.
Detail calculations for the ion-pair generation may provide an explanation for
the surprisingly strong direct process; a difficult job to the scientific
community. However, Krauss  et al. Krauss and Neumann (1975) have reported
this valance-Rydberg mixing is relatively small in case of oxygen. We have
assigned the symmetries to the ion-pair states based on the angular
distribution fit using equation given by Van Brunt Van Brunt (1974). Ion-pair
states associated with $\Sigma$ and $\Pi$ symmetry have been identified
throughout the entire kinetic energy range (0 - 2.5 eV) of produced anion;
where as the contribution from $\Pi$ symmetry is notably low in comparison
with $\Sigma$ symmetry. Too much cosine-squared dependency in AD could be a
rationale for the dominance of such $\Sigma$ symmetric ion-pair states.
Interestingly, we have still hearken with two dimensional time gated flat
slicing technique to analyse the AD instead of three dimensional method; as
slices out of the incident electron beam plane territory will make an angle
with the incident beam, resulting diversion from the in general anisotropic
nature of dissociation products. Thus, our referencing direction (electron
beam direction) for obtaining AD should be redefined for considering three
dimensional Newton sphere (either half or full) analysis. Due to
unavailability of complete theoretical demonstration of IPD dynamics, state
forward determination of the symmetry associated with a particular ion-pair
state is a challenging job to the theoretical science community. However, our
density functional theory (DFT) calculations for CO2 Rydberg states enable us
to define its super excited states and also provide the symmetries associated
with the ion-pair states. Nevertheless, in case of IPD dynamics induced by
electron impact on carbon dioxide, straightforward dipole interpretation is no
longer carried out during angular distribution measurement of produced anions.

##  V Acknowledgements

N. K. gratefully acknowledges the financial support from ‘DST of India’ for
"INSPIRE Fellowship" program. A. P. express deep appreciation to "Council of
Scientific and Industrial Research (CSIR)" for the financial assistance. We
gratefully acknowledge financial support from the Science and Engineering
Research Board (SERB) for supporting this research under Project No. “
EMR/2014/000457 ”.

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