††thanks:

# Electron impact partial ionization cross sections: R-carvone, 2-butanol,
imidazole, and 2-nitroimidazole

Suriyaprasanth Shanmugasundaram  0000-0002-3939-1446 Department of Physics,
School of Advanced Sciences,
Vellore Institute of Technology, Katpadi,
Vellore - 632014, Tamil Nadu, India.  Rounak Agrawal  School of Computer
Science and Engineering,
Vellore Institute of Technology, Katpadi,
Vellore - 632014, Tamil Nadu, India.  Dhanoj Gupta∗111Corresponding author
Corresponding author: 0000-0001-6717-8194 Department of Physics, School of
Advanced Sciences,
Vellore Institute of Technology, Katpadi,
Vellore - 632014, Tamil Nadu, India<EMAIL_ADDRESS>
###### Abstract

We theoretically calculate the electron impact partial and total ionization
cross sections of R-carvone $(\mathrm{C_{10}H_{14}O})$, 2-butanol
$(\mathrm{C_{4}H_{10}O})$, imidazole $(\mathrm{C_{3}H_{4}N_{2}})$ and
2-nitroimidazole $(\mathrm{C_{3}H_{3}N_{3}O_{2}})$. We have used the Binary
Encounter Bethe (BEB) model to obtain the total electron impact ionization
cross sections (TICS). The modified BEB method in combination with mass
spectrum data of the molecules is used to calculate the PICS of the cationic
fragments dissociating from the parent molecule. Our PICS data for R-carvone
and 2-butanol are in good agreement with the experimental data for all the
cation fragments along with the TICS data. For imidazole and 2-nitroimidazole,
the estimates of the PICS are reported for the first time in the present
study. We have found that both the modified BEB method and the mass spectrum
dependence method work effectively to estimate PICS if we have information
about the appearance energies and relative abundance data of the target under
investigation.

††preprint: AIP/123-QED

##  I Introduction:

Electron impact total ionization cross section (TICS) and partial ionization
cross section (PICS) are important to many branches of sciences ranging from
plasma physics to astrophysics and biological sciences Itikawa (2017); Kim
_et al._ (2015); Boudaïffa  _et al._ (2000). In medical sciences, radiation
damage to DNA/RNA is a major concern, where it has been found that secondary
electrons play a crucial role in single and double-strand breaks of DNA/RNA
Boudaïffa  _et al._ (2000); Sanche (2002). The electron impact cross sections
data at low and intermediate energy are important inputs in Monte Carlo track
(MCT) analysis, which is used to study damage to living cells using ionizing
radiation Boudaïffa  _et al._ (2000). In recent times, electron collision with
biomolecules has geared up and many studies have been conducted both
experimentally Rehman and Krishnakumar (2022a, b) and theoretically Gupta and
Antony (2014); Gupta  _et al._ (2014, 2019); Vinodkumar  _et al._ (2006);
Scheer  _et al._ (2007) to provide more data for understanding the mechanism
of damages caused due to the electrons. While performing the MCT simulations,
only the single channel ionization is taken into account and the channels due
to the dissociative ionization processes are not considered in the model,
which may reduce the accuracy of the MCT analysis. Hence, the inclusion of
dissociative ionization processes is important and will help us to make the
MCT model more accurate. Hence, providing information on the PICS for the
cations that are different due to their mass-to-charge ratio originating from
their parent molecule is inevitable for accurate analysis Rehman and
Krishnakumar (2022b). Even with the rapid surge of electron-molecule
interaction studies, there are many important molecules for which data are
scarce in the literature both experimental and theoretical. In the present
study, we have investigated the PICS and TICS of R-carvone, 2-butanol,
imidazole, and 2-nitroimidazole. Our motivation has been to provide the
theoretical estimates of the PICS for all the cation fragments originating
from the parent molecules using the recently developed methods Graves  _et
al._ (2022); Goswami  _et al._ (2022). Here we will highlight the importance
and applications of each of these targets.

R-carvone is an organic molecule that belongs to the class of terpenoids and
has a wide variety of applications in the food industry, agriculture, and pest
control. R-carvone has a minty flavored odor, used in essential oils. A recent
study has found this compound can be used in anti-fungal wrapper Boonruang
_et al._ (2017); Soleimani  _et al._ (2022) for packaging fruits which
increases shelf life. Jones et al.performed an experimental and theoretical
study on electron (e,2e) impact ionization dynamics on R-carvone and its
enantiomer S-carvone Jones  _et al._ (2019), using three-body distorted wave
(3BDW) formalism for calculating the cross sections theoretically. There is a
three-part study performed on this molecule by Lopes et al.Lopes  _et al._
(2020a) and Amorim et al.Amorim  _et al._ (2021a, b). In the first part, Lopes
et al.Lopes  _et al._ (2020a) presented the appearance energies for 35 cations
and the electron impact mass spectrum in which they observed 103 peaks with
the incident electron energy of 70 eV at the mass range of 1 amu till 151 amu
and compared their findings with the data available at National Institute of
Standards and Technology (NIST) web book Linstrom and Mallard (2001) and
Spectral database for organic compounds (SDBS) SDB . Also, they have provided
the scheme for the ionic fragmentation pathways. The successive work of Amorim
et al.Amorim  _et al._ (2021a) presents the PICS for 78 cations from
ionization threshold to 100 eV, the PICS of the isotopologue was also
measured. The absolute values of PICS for all the cations presented are in the
range of 8 eV to 100 eV, only singly ionized fragments were assessed. The last
work from Amorim et al.Amorim  _et al._ (2021b) in this series of articles
contains the experimental TICS of the R-carvone compared with literature data
along with the theoretically predicted TICS, using the Binary encounter Bethe
(BEB) Amorim  _et al._ (2021b) model and the independent atom model (IAM) in
conjunction with the screening correction additive rule (SCAR) incorporating
the interference effects (I) also, which is colloquially called IAM+SCAR+I
method which can be used to calculate the TICS Blanco and García (2002);
Blanco and Garcıa (2003); Blanco and García (2003); Blanco  _et al._ (2016);
Chiari  _et al._ (2013). In all the studies, Lopes et al., used Hiden
analytical energy pulse ion counting (EPIC) quadrupole mass spectrometer (QMS
- EPIC 300) which can detect mass from 1 amu to 300 amu comprising a detector
resolution of 1 amu which was used at residual gas analyzing (RGA) mode.

2-butanol is a colorless organic solvent that also possesses chirality
Iwahashi  _et al._ (1999). Recently the compound has become a study of
interest for many researchers as it can be a potential replacement for
gasoline and can be directly used as a replacement without modifying the
engines Lopes  _et al._ (2020b) and references therein. Like other alcohols
2-butanol also belongs to the class of biofuels like methanol, ethanol,
1-proponol, and 1-butanol. Several experimental and theoretical investigations
are available for these molecules Pires  _et al._ (2018); Ghosh  _et al._
(2018); Goswami  _et al._ (2022) and references therein. Nirali et al.Bhavsar
_et al._ (2023) provided a recent study of electron collision dynamics with
n-butanol containing an extensive review of the available literature on
n-butanol. But studies on 2-butanol are scarce. Researchers are looking to
engineer microbes to produce fuels such as 1-butanol and 2-butanol and have
identified an engineered strain of L. diolivorans microbe, which can be used
to produce 2-butanol up to 10g/Litre from meso-2,3-butanediol through an
anaerobic fermentation process Russmayer  _et al._ (2019). Amorim et al.Amorim
_et al._ (2022) experimentally observed the mass spectrum for 51 cations and
the appearance energies for 38 cationic fragments of 2-butanol are provided in
their work. For their measurements, they used the same QMS EPIC - 300 operated
on residual gas analyzing (RGA) mode Nixon  _et al._ (2016); Pires  _et al._
(2018); Lopes  _et al._ (2020a). Lopes et al.have performed a comprehensive
review on the fragmentation of biofuels which contains all the literature till
the year 2019 for the methanol, ethanol, proponol, and butanol molecules Lopes
_et al._ (2020b). Bettega and co-workers performed low-energy electron
scattering studies on isomers of butanol including 2-butanol where they
presented the differential cross sections (DCS), momentum transfer cross
sections (MTCS), and integral cross sections (ICS) for an incident energy
range of 1 eV to 50 eV Bettega  _et al._ (2010). The preceding work of Amorim
et al.provided the experimental PICS for the fragments of 2-butanol along with
their experimental TICS and theoretical TICS using the BEB method and the
IAM+SCAR+I method Amorim  _et al._ (2023).

imidazole acts as a base for several biomolecules. imidazole and
2-nitroimidazole are very good radiosensitizers used in cancer treatment and
also in the development of drugs in pharmaceutical chemistry Meissner (2019).
A brief review Shalini  _et al._ (2010); Zhang  _et al._ (2014) of their use
provides us with the importance of these targets for various applications.
Rebecca et al.Meissner  _et al._ (2019) studied the low-energy fragmentation
of imidazole and 2-nitroimidazole, and has provided us with the appearance
energies and mass spectrum for the cationic fragments. A recent study by Tejas
et al.Jani  _et al._ (2023) for imidazole has investigated the dissociative
electron attachment (DEA), excitation, and ionization processes by electron
impact.

In the present study, we have made use of the appearance energies and mass
spectrum data from the literature Lopes  _et al._ (2020a); Meissner  _et al._
(2019); Amorim  _et al._ (2022) for all the targets studied here. The
structure of the article is as follows: In section II, we have discussed the
BEB model for TICS and the computational method to calculate orbital energies
required as input in the BEB model. In sections
LABEL:sec:level2a,sec:2b,sec:2c, various methods to calculate the PICS using
the BEB model, appearance energies, and mass spectrum data are discussed. In
section III, we have shown the results and their discussions. In Section IV we
summarize our results and findings.

##  II  BEB Model

The BEB model Kim and Rudd (1994) is one of the most common and widely used
methods for predicting the TICS for atoms, molecules, radicals, and ions and
is being employed here with some modifications to calculate the PICS. The BEB
method calculates the electron impact ionization cross section for each
orbital and the sum of the ionization cross section for each orbital gives the
total ionization cross section [Eq. (1)] for a target under consideration. [Eq
(2)] gives the BEB formula for determining the TICS.

$\sigma_{TICS}(E)=\sum_{i}^{N}\sigma_{i}(E)$ (1)
$\sigma_{i}^{BEB}(E)=\frac{S}{(t_{i}+u_{i}+1)/n}\left[\frac{Q_{i}\ln
t_{i}}{2}\left(1-\frac{1}{t_{i}^{2}}\right)+(2-Q_{i})\left\\{\left(1-\frac{1}{t_{i}}\right)-\frac{\ln
t_{i}}{t_{i}+1}\right\\}\right]$ (2)

The reduced variables $t_{i},u_{i}$ and S are defined,

$S=4\pi
a_{0}^{2}N\left(\frac{R}{B}\right)^{2},~{}u_{i}=\frac{U}{B},~{}t_{i}=\frac{E}{B},~{}Q_{i}=1$
(3)

Here, $(n)$ is the principal quantum number, $(a_{0}=0.52918~{}A^{\circ})$ is
the Bohr radius, $(R=13.6057~{}\mathrm{eV})$ is Rydberg constant, $(B)$ is the
occupation number of the orbitals, $(U)$ is the orbital kinetic energies,
$(N)$ is the orbital occupation number, $(E)$ is the incident electron kinetic
energy and $(Q_{i})$ is differential oscillator strength which is set to unity
according to the simplified BEB model.

To calculate the orbital parameters that are required as input to the BEB
model we adopted the similar methodology that was applied in our recent work
Suriyaprasanth  _et al._ (2023), we first optimized the target molecules using
the density functional $\omega B97X-D$ with the aug-cc-PVTZ (aVTZ) basis set,
which calculates the energy minima at which the molecule is more stable. After
optimization, the orbital binding and kinetic energies are calculated using
the Hatree-Fock (HF) approximation that has been found to work efficiently
over the years within 10 % $\sim$ 15 % of experimental uncertaintyVukstich
_et al._ (2022). All the quantum chemistry calculations are performed using
the Gaussian-16 Frisch  _et al._ (2016) quantum chemistry software. The
structures of the target molecules studied are shown in Figure. 1. The main
aspect of this work is to calculate the branching ratios and PICS of the
possible fragments forming from the parent molecules which is described in the
sections to follow.

(a) R-Carvone
$(C_{10}H_{14}O)$

(b) 2-butanol
$(C_{4}H_{10}O)$

(c) imidazole
$(C_{3}H_{4}N_{2})$

(d) 2-nitroimidazole
$(C_{3}H_{3}N_{3}O_{2})$

Figure 1: Structure of molecular targets, for which the PICS were presented in
this manuscript.

###  II.1 Branching ratio (BR) and Partial ionization cross section (PICS)

When the molecular target undergoes dissociative ionization (DI) by an
electron or positron impact, there will be several reaction channels in which
DI takes place. The electron impact mass spectrum (EIMS) is a characterization
technique that can provide information about the various cations present,
along with their mass-to-charge ratio $(m/z)$, relative abundances, and
respective appearance energies. Here, the branching ratio plays an important
role, which describes the contribution of each reaction channel to the TICS.
There are different methods proposed to calculate the branching ratio (BR),
which in turn is used to compute the PICS. Karl Irikura Irikura (2017) used
the EIMS data from the NIST Linstrom and Mallard (2001) to calculate BR and
have used that to compute the PICS of many organic molecules at a single
electron impact energy. Hamilton et al.Hamilton  _et al._ (2017) used the
experimental EIMS to calculate the BR and hence the PICS, which is discussed
in more detail later. Huber et al.Huber  _et al._ (2019) proposed the way to
calculate the BR using the appearance energy of the fragments by electron
impact. The BR was combined with the TICS from the BEB method to obtain the
PICS for various fragments which is discussed in more detail below in Section.
II.2. Hamilton et al.Hamilton  _et al._ (2017) proposed a modification in the
reduced variable $t_{i}=E/B$, which is given in Eq. (4).

$t^{\prime}_{i}=\left(\dfrac{E}{B-\varepsilon}\right)$ (4)

Here, $\varepsilon$ can either be the appearance energy (AE) or the
dissociation energy $(\varepsilon)$ for the specific fragment. The AE and
ionization energy (IE) or ionization potential (IP) aren’t the same, IP is the
minimum energy that is required to remove an electron from a molecule’s bound
state whereas the AE is the minimum energy required to induce fragmentation of
a molecule. After the modification of Eq.(4), the modified BEB formula given
in Eq.(5) can be used to calculate PICS,

$\sigma_{i}^{mBEB-A}(E)=\frac{S}{(t^{\prime}_{i}+u_{i}+1)/n}\left[\frac{Q_{i}\ln
t^{\prime}_{i}}{2}\left(1-\frac{1}{t_{i}^{{}^{\prime}2}}\right)+(2-Q_{i})\left\\{\left(1-\frac{1}{t^{\prime}_{i}}\right)-\frac{\ln
t^{\prime}_{i}}{t^{\prime}_{i}+1}\right\\}\right]$ (5)

Using Eq.(5) the PICS of each fragment can be calculated as,

$\sigma^{PICS}(E)=\Gamma_{i}(E_{r})\times\sigma_{i}^{mBEB-A}(E)$ (6)

Here, $\Gamma_{i}(E_{r})$ is the experimental BR obtained from the electron
impact mass spectrometry (EIMS). The EIMS is performed at the reference
incident electron energy $(E_{r})$ of 70 eV or 100 eV. The branching ratio of
the fragment is defined as,

(7)

$R(E_{r})$ denotes the relative intensity of the particular fragment and
$T(E_{r})$ is the total ion intensity which is the sum of all the relative
intensity of the fragments that are detected. In case of unavailability of
EIMS data for a molecule of interest, performing quantum chemical mass
spectrometry (QCxMS) Grimme (2013) can provide information on the fragments
along with their relative abundances and fragmentation pathways. The project
QCxMS is very well tested Koopman and Grimme (2019) and is actively under
development for more accurate prediction of the EIMS theoretically.

On the other hand Baluja et al.Goswami  _et al._ (2021) presented a similar
form of the Eq.(5), where they also call it a modified BEB method, we address
their model with the superscript B making it $\sigma^{mBEB-B}$. The key
assumption in the mBEB-B model is, that the cation that is dissociated from
the neutral parent molecule can be distinguished by their $\varepsilon$, which
is different from IE that corresponds to the neutral molecule. The vertical IE
is the energy of the highest occupied molecular orbital (HOMO). To make the
BEB model feasible across cations, a consistent alteration is made in the
values of occupied orbitals binding energies. The changes are accomplished by
adding the difference $(\delta)$ between IE of the neutral molecule and the
$\varepsilon$ of the cation $\delta=(IE-\varepsilon)$ to the all the values in
orbital binding energy (B) of the neutral molecule ($B^{\prime}=B+\delta$). As
a result, the HOMO of the particular cation becomes its appearance energy.

$\sigma_{i}^{mBEB-B}(E)=\frac{S^{*}}{(t^{*}_{i}+u^{*}_{i}+1)/n}\left[\frac{Q_{i}\ln
t^{*}_{i}}{2}\left(1-\frac{1}{t_{i}^{*2}}\right)+(2-Q_{i})\left\\{\left(1-\frac{1}{t^{*}_{i}}\right)-\frac{\ln
t^{*}_{i}}{t^{*}_{i}+1}\right\\}\right]$ (8)

The new reduced variables are,

$S^{*}=4\pi
a_{0}^{2}N\left(\frac{R}{B^{\prime}}\right)^{2},~{}t^{*}_{i}=\left(\dfrac{E}{B^{\prime}}\right),~{}u^{*}_{i}=\frac{U}{B^{\prime}},~{}Q_{i}=1$
(9)

The PICS is calculated using a similar approach used in Eq. (6)

$\sigma^{PICS}(E)=\Upsilon_{i}(E_{r})\times\sigma_{i}^{mBEB-B}(E)$ (10)

The PICS calculated from the mBEB-B model is then scaled using the factor
$\Upsilon_{i}(E)$, which is obtained from the experimental BR $\Gamma_{i}(E)$
Eq.(7) and the theoretical BR which is calculated from the PICS itself. The
theoretical BR for the fragment is calculated at the same incident energy as
the experimental BR $\Gamma_{i}(E)$,

$\Gamma_{i}^{Theo}(E_{r})=\frac{\sigma_{i}^{mBEB-B}(E_{r})}{\sigma_{i}^{BEB}(E_{r})}$
(11)

There are other ways to calculate the theoretical BR without the need for
PICS, which was introduced by Huber et al.Huber  _et al._ (2019) which will be
explained in the later part of this article. The scaling factor
$\Upsilon_{i}(E_{r})$ is obtained by

$\Upsilon_{i}(E_{r})=\frac{\Gamma_{i}(E_{r})}{\Gamma_{i}^{Theo}(E_{r})}$ (12)

This scaling factor implemented by Baluja et al.Goswami  _et al._ (2021) and
the structural factor incorporated by Huber et al.Huber  _et al._ (2019) and
Vincent et al.Graves  _et al._ (2022) are the same, details about structural
factor are discussed in the next section.

###  II.2 Huber’s method

To theoretically calculate the BR of the fragments we require the information
about the dissociation energies $(\varepsilon)$. $b_{i}$ is the branching
factor, which isn’t the same as BR.

$b_{i}=\left(\dfrac{1}{\varepsilon}\right)^{\alpha}~{}\mathrm{if}~{}E\geq\varepsilon$
(13)

$\alpha$ is a parameter that is used to make the $b_{i}$ slowly reach the
asymptotic region and if the incident energy is less than the $\varepsilon$
then $b_{i}$ is 0 as the dissociation never commences. In our case, we keep it
as 3 as proposed by Huber et al.Huber  _et al._ (2019). The theoretical BR
calculated by Huber’s method is given below and is denoted by the superscript
H.

$\Gamma_{i}^{H}(E_{r})=\begin{cases}\dfrac{b_{i}}{\sum^{n}_{i}b_{i}}&\text{ if
}E\geq\varepsilon\\\ 0&\text{ if }\mathrm{otherwise}\end{cases}$ (14)

It is provided that the additional structural factor $(\chi_{i})$ paves the
way for other processes within the threshold region.

$\Gamma(E_{r})=\Gamma_{i}^{H}(E_{r})\chi_{i}(E_{r})$ (15)

$\Gamma_{i}^{H}$ is the actual BR, and $\chi$ is determined from the
experimental BR $(\Gamma_{i})$ by taking the ratio of experimental BR to that
of theoretical BR calculated using Huber’s method at the reference energy,

$\chi_{i}(E_{r})=\dfrac{\Gamma_{i}(E_{r})}{\Gamma_{i}^{H}(E_{r})}$ (16)

The way this structural factor is calculated is the same as the scaling factor
$(\Upsilon_{i})$ which was discussed earlier. It is shown that for simple
dissociation of $C-H$ bonds, the $\chi_{i}$ is taken as, $\chi_{i}\leq 1$ and
for more complex dissociation it is suggested to be $\chi_{i}>1$ Huber  _et
al._ (2019). It was considered $\chi_{i}=1$ by Vincent et al.Graves  _et al._
(2022) for the ease of calculation of branching ratios and this could be
explored further in the future.

###  II.3 Mass spectrum dependence (MSD) method

In all the above methods the BR is calculated at a single energy, this method
was proposed to make the branching ratio dependent on the incident energy of
the electron. The BR calculated using this method will be denoted with the
superscript (MSD), continuous data for all energy ranges.

$\Gamma_{i}^{MSD}(E)=\begin{cases}0&\text{ if }E<\varepsilon\\\
\Gamma_{i}(E_{r})\left[1-\left(\dfrac{\varepsilon}{E}\right)^{\nu}\right]&\text{if}~{}E\geq\varepsilon\end{cases}$
(17)

Here, we would also need a BR at the reference energy, which can either be
theoretical BR or experimental BR. Suppose, there are no experimental EIMS
data present for the target then we can use the theoretical BR calculated from
Huber’s method, referred to as the hybrid method by Vincent et al.Graves  _et
al._ (2022). This assumption is true only if we strictly interpret that the
already computed branching ratios are asymptotic when the incident energy is
infinity, the branching ratio reaches the known branching ratio which gives
rise to the assumption that reference energy is at infinity. Also, this method
does not give the same reference branching ratio at the reference incident
energy Graves  _et al._ (2022). The control parameter $\nu$ was taken as
$1.5\pm 0.2$ by Janev et al.Janev and Reiter (2004), it was taken as 1.5 in
this work as an average value. As we have discussed several methods to
calculate the branching ratios, we should also remember that the sum of all
the branching ratios of the fragments should sum up to give unity
$\sum_{i}\Gamma_{i}=1$, irrespective of the methods employed. However, this
condition may not be satisfied if we do not have information on all the
fragmentation or dissociation pathways for a target molecule.

##  III Results and Discussions

We have theoretically calculated the PICS for all the molecular targets which
we have shown in Figure. 1 using the mBEB-B method and the MSD method. Here we
did not employ Huber’s method Huber  _et al._ (2019) and the mBEB-A Hamilton
_et al._ (2017) method as the magnitude of their cross sections was not as
accurate as the MSD method Graves  _et al._ (2022) or the mBEB-B method
Goswami  _et al._ (2021) as compared to experimental results. More details can
be found in the upcoming subsections.

###  III.1 R-Carvone

In the series of articles published by Lopes et al.Lopes  _et al._ (2020a) and
Amorim et al.Amorim  _et al._ (2021a, b) have extensively studied the
fragmentation of R-carvone by electron impact and provided the absolute PICS
and TICS along with the mass spectrum and appearance energies and the Wannier
exponents for 35 cations. We have calculated the theoretical PICS for these
fragments using the MSD method [Eq. (17)], and mBEB-B method [Eq. (8)] based
on the data presented by Lopes et al.Lopes  _et al._ (2020a) and Amorim et
al.Amorim  _et al._ (2021a, b). The most stable cations were found to have
masses of 39 amu $[C_{3}H_{3}^{+}]$, 54 amu $[C_{4}H_{6}]^{+}$, and 82 amu
$[C_{5}H_{6}O]^{+}$, as their relative abundances contribute 40% to the total
ion intensity. Owing to higher contribution in the mass spectrum, their PICS
also tend to have higher magnitudes than other cations which can be seen from
the Table. 1. In the MSD method the BR is scaled for the incident energy
whereas in the mBEB-B method, the binding energies of the molecular orbitals
are scaled to the appearance energy of the cations. Although they seem
different from one another, but work the same when it comes to calculating the
PICS. In Table.1, we have shown all the important data that we have obtained
while performing our calculations. It consists of the BR obtained using
Huber’s method $(\Gamma_{i}^{H})$ [Eq. (14)], theoretical BR
$(\Gamma_{i}^{Theo})$ which is calculated while performing the mBEB-B method
[Eq. (11)], the experimental BR $(\Gamma_{i})$ which is obtained from the EIMS
data presented by Lopes et al.Lopes  _et al._ (2020a) [Eq. (7)], the
structural factor $(\chi_{i})$ [Eq. (16)], the scaling factor $(\Upsilon_{i})$
[Eq. (12)] and the PICS max from the MSD method and the mBEB-B method compared
with the experimental PICS max Amorim  _et al._ (2021a). The mBEB-B PICS
presented in the table are scaled using the $(\Upsilon_{i})$. We have also
calculated the mean squared error (MSE) for the PICS, assuming that the
experimental values are true values and the PICS we obtained as predicted
values. The MSE for MSD-PICS was 0.1327 and the MSE for mBEB-B was 0.1038
giving almost similar PICS.

Figure 2: Comparison of TICS of R-carvone with the literature. The blue line
represents our present TICS calculated using the BEB method, the orange line
represents the sum of all the PICS calculated for the various cations using
the mBEB-B method, and the green line represents the PICS calculated using the
MSD method. The red upright triangle represents the TICS presented by Amorim
et al.Amorim  _et al._ (2021b), the purple left triangle represents the TICS
which was calculated using IAM+SCAR+I by Amorim et al.Amorim  _et al._ (2021b)
and the black dotted lines represents the TICS calculated using the BEB model
by Amorim et al.Amorim  _et al._ (2021b)

In the Figure.3, It is seen that for most of the fragments, the PICS
calculated using both methods shows good agreement with the experimental PICS.
Some discrepancies of the present data with the experiment are seen for
cations $[CH_{2}]^{+}$, $[C_{3}H_{3}]^{+}$, $[C_{7}H_{6}O]^{+}$ and
$[C_{3}H_{5}]^{+}$ where our data are found to underestimate the experimental
results, the reason for the discrepancy may be due to the appearance energies
and the relative abundance which are smaller in our case compared to
experimental values. Also, there were two isomers detected in the mass
spectrum $[C_{2}H_{5}]^{+}/[CHO]^{+}$ and $[C_{2}HO]^{+}/[C_{3}H_{5}]+$ which
had two distinct AEs that are mentioned in square brackets in the Figure. 3.
However, for a few cations like
$[O]^{+},~{}[C_{2}H_{2}]^{+},~{}[C_{3}H_{4}]^{+},~{}[C_{4}H_{5}]^{+},~{}$ the
PICS calculated using the MSD shows a very good agreement with the
experimental data of Amorim et al.Amorim  _et al._ (2021a), whereas for
several other cations both the MSD method and the mBEB-B method predicts the
PICS within the experimental uncertainty as shown Figure.3. In Figure. 2,
shows the TICS obtained using the BEB model, MSD, and mBEB-B methods which is
the sum of the PICS of all the fragments. Our results are compared with the
existing experimental and theoretical data Amorim  _et al._ (2021a, b), and
the present results using the mBEB-B method are found to be in excellent
agreement with the experimental data. Our TICS using the MSD method is found
to underestimate all other data because the appearance energies were not
provided for all the fragments. In the series of articles Lopes  _et al._
(2020a); Amorim  _et al._ (2021a, b) they have presented the experimental PICS
at 100 eV for 78 cationic fragments but have only provided the AE for 35
prominent cations. We believe if we could calculate the PICS for other
remaining fragments and sum it then it might give a better comparison with the
experimental TICS and the TICS calculated using the BEB model.

Energy (eV)PICS $(10^{-16}cm^{2})$ Figure 3: Comparison of PICS calculated for the cations of R-carvone. The X-axis represents the incident kinetic energy range in (eV), and the Y-axis represents the PICS in $(10^{-16}cm^{2})$. The green line represents the PICS calculated using the mBEB-B method, the red line represents the PICS calculated using the MSD method, and the blue Rhombus represents the experimental PICS presented by Amorim et al. Amorim  _et al._ (2021a), along with their error bars for each energy value. Table 1: Absolute values of branching ratio $(\Gamma)$ structural factor $(\chi_{i})$, scaling factor $(\Upsilon)$ and maximum PICS calculated using MSD and mBEB-B method compared with experimental PICS Amorim  _et al._ (2021a) for R-carvone $m/z$ | Cations222The forward slash denotes ”or” added for the cations with same $m/z$ values |  $\varepsilon$ (eV) Lopes  _et al._ (2020a) | $\Gamma_{i}^{H}$ | $\Gamma_{i}^{Theo}$ |  $\Gamma_{i}$Lopes  _et al._ (2020a) | $\chi_{i}$ | $\Upsilon_{i}$ | $\sigma_{max}^{MSD}$ | $\sigma_{max}^{mBEB-B}$ |  $\sigma_{max}^{exp}$Amorim  _et al._ (2021a)
---|---|---|---|---|---|---|---|---|---|---
14 | $CH_{2}$ | 15.34 | 0.033333 | 0.540558 | 0.001539 | 0.046171 | 0.002847 | 0.03263 | 0.037382 | 0.04474
16 | O | 14.16 | 0.030769 | 0.608827 | 0.002601 | 0.084534 | 0.004271 | 0.055578 | 0.062124 | 0.05242
26 | $C_{2}H_{2}$ | 11.67 | 0.025358 | 0.794778 | 0.004087 | 0.161172 | 0.005142 | 0.08878 | 0.094934 | 0.08685
28 | $C_{2}H_{4}/CO$ | 12.3 | 0.026727 | 0.741232 | 0.032002 | 1.197369 | 0.043174 | 0.692441 | 0.748003 | 0.64644
28 | $C_{2}H_{4}/CO$ | 14.58 | 0.031681 | 0.583319 | 0.032002 | 1.010126 | 0.054862 | 0.682016 | 0.768848 | 0.64644
29 | $C_{2}H_{5}/CHO$ | 12.04 | 0.026162 | 0.762717 | 0.014356 | 0.548735 | 0.018822 | 0.311144 | 0.334674 | 0.37457
29 | $C_{2}H_{5}/CHO$ | 14.93 | 0.032442 | 0.563107 | 0.014356 | 0.442517 | 0.025494 | 0.305212 | 0.346601 | 0.37457
31 | $CH_{3}O$ | 11.97 | 0.026010 | 0.768646 | 0.000531 | 0.020415 | 0.000690 | 0.011508 | 0.012364 | 0.01021
39 | $C_{3}H_{3}$ | 10.83 | 0.023533 | 0.874773 | 0.074061 | 3.147148 | 0.084663 | 1.617523 | 1.708448 | 2.61851
39 | $C_{3}H_{3}$ | 15.61 | 0.033919 | 0.526334 | 0.074061 | 2.183447 | 0.140712 | 1.567225 | 1.806174 | 2.61851
40 | $C_{3}H_{4}$ | 10.63 | 0.023098 | 0.895457 | 0.010667 | 0.461812 | 0.011913 | 0.233269 | 0.245712 | 0.2041
41 | $C_{2}HO/C_{3}H_{5}$ | 12.56 | 0.027292 | 0.720556 | 0.046743 | 1.712707 | 0.06487 | 1.009673 | 1.095517 | 2.15466
41 | $C_{2}HO/C_{3}H_{5}$ | 14.82 | 0.032203 | 0.569361 | 0.046743 | 1.451525 | 0.082097 | 0.994528 | 1.126763 | 2.15466
42 | $C_{2}H_{2}O$ | 10.32 | 0.022425 | 0.928897 | 0.005758 | 0.256772 | 0.006199 | 0.126158 | 0.132352 | 0.11159
43 | $C_{2}H_{3}O$ | 11.99 | 0.026053 | 0.766946 | 0.007496 | 0.287718 | 0.009774 | 0.162525 | 0.174674 | 0.15451
45 | $C_{2}H_{5}O$ | 11.99 | 0.026053 | 0.766946 | 0.000756 | 0.029017 | 0.000986 | 0.016396 | 0.017622 | 0.01444
52 | $C_{4}H_{4}$ | 10.68 | 0.023207 | 0.890223 | 0.005387 | 0.232130 | 0.006051 | 0.117758 | 0.124124 | 0.10637
53 | $C_{4}H_{5}$ | 12.52 | 0.027205 | 0.723686 | 0.024386 | 0.896380 | 0.033697 | 0.526899 | 0.571304 | 0.50587
54 | $C_{4}H_{6}$ | 13.81 | 0.030008 | 0.631203 | 0.093897 | 3.129061 | 0.148758 | 2.011533 | 2.233011 | 2.43499
55 | $C_{4}H_{7}$ | 12.67 | 0.027531 | 0.712042 | 0.009911 | 0.359995 | 0.013919 | 0.213932 | 0.232561 | 0.19521
58 | $C_{3}H_{6}O$ | 10.01 | 0.021751 | 0.964127 | 0.029481 | 1.355390 | 0.030578 | 0.647126 | 0.676302 | 0.56612
60 | $C_{3}H_{8}O$ | 10.62 | 0.023076 | 0.896510 | 0.000836 | 0.036227 | 0.000932 | 0.01828 | 0.019252 | 0.01595
65 | $C_{5}H_{5}$ | 15.31 | 0.033267 | 0.542169 | 0.006979 | 0.209785 | 0.012872 | 0.147989 | 0.169430 | 0.1409
67 | $C_{5}H_{7}$ | 12.16 | 0.026423 | 0.867692 | 0.012153 | 0.459945 | 0.016146 | 0.263205 | 0.283664 | 0.24021
69 | $C_{5}H_{9}$ | 10.94 | 0.023772 | 0.863681 | 0.007894 | 0.332075 | 0.00914 | 0.172297 | 0.182264 | 0.15821
77 | $C_{6}H_{5}$ | 13.12 | 0.028509 | 0.678578 | 0.010561 | 0.370448 | 0.015564 | 0.227293 | 0.249071 | 0.2091
79 | $C_{6}H_{7}$ | 11.13 | 0.024185 | 0.844976 | 0.016200 | 0.669847 | 0.019172 | 0.353152 | 0.374592 | 0.32259
80 | $C_{5}H_{4}O$ | 9.63 | 0.020925 | 1.009962 | 0.007271 | 0.347475 | 0.007199 | 0.159963 | 0.16644 | 0.14366
82 | $C_{5}H_{6}O$ | 10.85 | 0.023576 | 0.872742 | 0.132679 | 5.627668 | 0.152025 | 2.897386 | 3.061113 | 2.71195
83 | $C_{5}H_{7}O$ | 10.9 | 0.023685 | 0.867692 | 0.007231 | 0.305301 | 0.008334 | 0.157858 | 0.166896 | 0.13467
91 | $C_{7}H_{7}/C_{6}H_{3}O$ | 10.83 | 0.023533 | 0.874773 | 0.012047 | 0.511925 | 0.013772 | 0.263116 | 0.277906 | 0.23679
92 | $C_{7}H_{8}/C_{6}H_{4}O$ | 9.87 | 0.021447 | 0.980661 | 0.00743 | 0.346440 | 0.007577 | 0.163231 | 0.170305 | 0.14487
93 | $C_{6}H_{5}O$ | 10.83 | 0.023533 | 0.874773 | 0.036261 | 1.540875 | 0.041452 | 0.791954 | 0.836472 | 0.73009
94 | $C_{6}H_{6}O$ | 9.72 | 0.021121 | 0.998829 | 0.007258 | 0.343642 | 0.007266 | 0.159585 | 0.166215 | 0.13833
106 | $C_{7}H_{6}O$ | 9.56 | 0.020773 | 1.018745 | 0.007258 | 0.349394 | 0.007124 | 0.159737 | 0.166078 | 0.3352
107 | $C_{7}H_{7}O$ | 9.35 | 0.020317 | 1.045762 | 0.01815 | 0.893349 | 0.017356 | 0.399984 | 0.414931 | 0.35451
108 | $C_{7}H_{8}O$ | 10.2 | 0.022164 | 0.942315 | 0.034881 | 1.573783 | 0.037017 | 0.764773 | 0.801114 | 0.69171
135 | $C_{9}H_{11}O$ | 10.27 | 0.022316 | 0.934455 | 0.003728 | 0.167056 | 0.003990 | 0.081708 | 0.085665 | 0.07175

###  III.2 2-butanol

The PICS that we have theoretically determined for the fragments of 2-butanol
are based on the EIMS data presented by Amorim et al.Amorim  _et al._ (2022),
their experimentally provided EIMS, AEs for 51 cations. Pires et al.Pires  _et
al._ (2018) and Gosh et al.Ghosh  _et al._ (2018) provided the EIMS, AEs, and
the experimental PICS for the fragments of 1-butanol. Goswami et al.Goswami
_et al._ (2022) have theoretically calculated the PICS using the mBEB-B method
[Eq.(8)], which has good agreement with the existing experimental PICS
presented by Pires et al.Pires  _et al._ (2018) and the experimental TICS
presented by Gosh et al.Ghosh  _et al._ (2018). Owing to a good comparison of
the mBEB-B model with the literature data in 1-butanol, we proceed to
calculate the PICS theoretically applying both the mBEB-B model and the MSD
model that requires the experimental EIMS data. In Table. 2, all the relevant
data required for calculating the PICS using the mBEB-B and MSD are given
similarly to R-carvone. The maximum cross sections are also provided in the
table using the two methods and are compared with the experimental maximum
cross section. In Figure. 5, we have compared our PICS data with the
experimental PICS presented by Amorim et al.Amorim  _et al._ (2023) in the
entire energy range. The MSD method and mBEB-B method for 2-butanol show
excellent comparison with the experimental data of Amorim et al.Amorim  _et
al._ (2023) for most of the cationic fragments. However, for a few fragments
such as $[CH]^{+}$, $[C_{2}H_{2}]^{+}$, $[C_{3}H_{2}]^{+}$, and
$[C_{3}H_{3}]^{+}$, there were slight discrepancies when comparing our data
with the experimental PICS which can be seen in Figure. 5. The PICS that we
calculated are consistent for all cations from their AE threshold to 5000 eV,
magnitudes of the PICS of the cations differ concerning their RI and AE.

Figure 4: Comparison of TICS of 2-butanol. The blue solid line represents the
TICS calculated using the BEB method, the orange solid line represents the sum
of all the PICS calculated by us using the mBEB-B method, the green solid
lines represent the sum of all the PICS calculated by us using the MSD method.
The back dashed-dotted lines represent the BEB TICS presented by Amorim et
al.Amorim  _et al._ (2023), the red upright triangle represents the
experimental TICS presented by Amorim et al.Amorim  _et al._ (2023) and their
error bars are shown in pale pink colors, they have also provided the TICS
calculated using the IAM+SCAR+I model which is shown by purple left triangle,
the green dashed-dotted line represents the TICS presented by Bull et al.Bull
_et al._ (2012) and the brown bowtie represents the experimental TICS
presented by Hudson et al.Hudson  _et al._ (2003).

Figure. 4, shows the comparison of our TICS with the existing data available
in the literature for 2-butanol. The present TICS calculated using the BEB
method, compares very well with the experimental data and lies within the
uncertainty of the experimental TICS. Also the TICS (obtained after summing
all the PICS of the fragments) from the mBEB-B and MSD methods compare well
with the experiment and are within the range of uncertainty of the
experimental TICS. The average experimental uncertainty is $19\%$ and all our
present data lies within that limit.

Energy (eV)PICS $(10^{-16}cm^{2})$ Figure 5: Comparison of PICS calculated using various methods for 2-butanol. The X-axis represents the incident kinetic energy range in (eV), and the Y-axis represents the PICS in $(10^{-16}cm^{2})$. The green line represents the PICS calculated using the mBEB-B method, the red line represents the PICS calculated using the MSD method, and the blue Rhombus represents the experimental PICS presented by Amorim et al. Amorim  _et al._ (2023), along with their error bars for each energy value. Table 2: Absolute values of branching ratio $(\Gamma)$, structural factor $(\chi_{i})$, scaling factor $(\Upsilon)$ and maximum PICS calculated using MSD and mBEB-B method compared with experimental PICS Amorim  _et al._ (2023) for 2-butanol. $m/z$ | Cations333The forward slash denotes ”or” added for the cations with same $m/z$ values |  $\varepsilon$ (eV) Amorim  _et al._ (2022) | $\Gamma_{i}^{H}$ | $\Gamma_{i}^{Theo}$ |  $\Gamma_{i}$Amorim  _et al._ (2022) | $\chi_{i}$ | $\Upsilon_{i}$ | $\sigma_{max}^{MSD}$ | $\sigma^{mBEB-B}_{max}$ |  $\sigma_{max}^{Exp}$ Amorim  _et al._ (2023)
---|---|---|---|---|---|---|---|---|---|---
1 | $H$ | 13.45 | 0.015970 | 0.826677 | 0.029448 | 1.843945 | 0.035623 | 0.328767 | 0.354294 | 0.0929
2 | $H_{2}$ | 15.52 | 0.010394 | 0.662681 | 0.033981 | 3.269164 | 0.051278 | 0.374218 | 0.417960 | 0.0997
13 | $CH$ | 15.38 | 0.010681 | 0.672343 | 0.033674 | 3.152747 | 0.050085 | 0.371191 | 0.413481 | 0.0254
14 | $CH_{2}$ | 14.84 | 0.011890 | 0.711384 | 0.032492 | 2.732773 | 0.045674 | 0.359453 | 0.396460 | 0.1330
15 | $CH_{3}$ | 9.99 | 0.038974 | 1.251373 | 0.021873 | 0.561216 | 0.017479 | 0.249473 | 0.257970 | 0.594
16 | $O/CH_{4}$ | 13.3 | 0.016517 | 0.840578 | 0.02912 | 1.763079 | 0.034643 | 0.325416 | 0.349881 | 0.0459
17 | $OH$ | 10.91 | 0.029923 | 1.113007 | 0.023887 | 0.798291 | 0.021462 | 0.270959 | 0.282552 | 0.0655
19 | $H_{3}O$ | 13.56 | 0.015585 | 0.816679 | 0.029689 | 1.905022 | 0.036354 | 0.331219 | 0.357553 | 0.772
26 | $C_{2}H_{2}$ | 11.5 | 0.025549 | 1.035467 | 0.025179 | 0.985502 | 0.024317 | 0.284586 | 0.298677 | 0.188
27 | $C_{2}H_{3}$ | 13.87 | 0.014563 | 0.789364 | 0.030368 | 2.085312 | 0.038472 | 0.338110 | 0.366797 | 0.964
28 | $C_{2}H_{4}/CO$ | 11.59 | 0.024959 | 1.024311 | 0.025376 | 1.016714 | 0.024774 | 0.286654 | 0.301163 | 0.279
29 | $C_{2}H_{5}/CHO$ | 13.62 | 0.015380 | 0.811294 | 0.029821 | 1.939005 | 0.036757 | 0.332554 | 0.359333 | 0.834
30 | $CH_{2}O/C_{2}H_{6}$ | 11.46 | 0.025818 | 1.040480 | 0.025091 | 0.971845 | 0.024115 | 0.283665 | 0.297576 | 0.0392
31 | $CH_{3}O$ | 12.91 | 0.018059 | 0.878236 | 0.028266 | 1.565195 | 0.032185 | 0.316662 | 0.338509 | 1.27
32 | $CH_{4}O$ | 12.5 | 0.019895 | 0.920350 | 0.027368 | 1.375620 | 0.029737 | 0.307408 | 0.326724 | 0.015
38 | $C_{3}H_{2}$ | 13.11 | 0.017245 | 0.858645 | 0.028704 | 1.664470 | 0.033429 | 0.321159 | 0.344321 | 0.0289
39 | $C_{3}H_{3}$ | 10.52 | 0.033375 | 1.168847 | 0.023033 | 0.690118 | 0.019706 | 0.261885 | 0.272052 | 0.198
40 | $C_{2}O/C_{3}H_{4}$ | 10.35 | 0.035047 | 1.194444 | 0.022661 | 0.646585 | 0.018972 | 0.257912 | 0.267511 | 0.0317
41 | $C_{2}HO/C_{3}H_{5}$ | 12.34 | 0.020679 | 0.937536 | 0.027018 | 1.306544 | 0.028818 | 0.303780 | 0.322175 | 0.801
42 | $C_{2}H_{2}O/C_{3}H_{6}$ | 10.66 | 0.032078 | 1.148352 | 0.02334 | 0.727609 | 0.020325 | 0.265148 | 0.275806 | 0.0805
43 | $C_{2}H_{3}O/C_{3}H_{7}$ | 11.77 | 0.023831 | 1.002498 | 0.02577 | 1.081357 | 0.025706 | 0.290782 | 0.306157 | 0.566
44 | $C_{2}H_{4}O/C_{3}H_{8}$ | 10.35 | 0.035047 | 1.194444 | 0.022661 | 0.646585 | 0.018972 | 0.257912 | 0.267511 | 0.546
45 | $C_{2}H_{5}O$ | 10.93 | 0.029759 | 1.110246 | 0.023931 | 0.804168 | 0.021555 | 0.271423 | 0.283094 | 2.53
46 | $C_{2}H_{6}O$ | 10.67 | 0.031988 | 1.146908 | 0.023362 | 0.730346 | 0.020369 | 0.265381 | 0.276075 | 0.0629
51 | $C_{4}H_{3}$ | 12.33 | 0.020729 | 0.938625 | 0.026996 | 1.302309 | 0.028761 | 0.303552 | 0.321891 | 0.0118
53 | $C_{4}H_{5}/C_{3}HO$ | 12.01 | 0.022431 | 0.974409 | 0.026296 | 1.172314 | 0.026986 | 0.296266 | 0.312863 | 0.0198
54 | $C_{4}H_{6}/C_{3}H_{2}O$ | 9.75 | 0.041924 | 1.291528 | 0.021347 | 0.509186 | 0.016529 | 0.243820 | 0.251661 | 0.0192
55 | $C_{4}H_{7}/C_{3}H_{3}O$ | 12.34 | 0.020679 | 0.937536 | 0.027018 | 1.306544 | 0.028818 | 0.303780 | 0.322175 | 0.102
56 | $C_{4}H_{8}/C_{3}H_{4}O$ | 9.45 | 0.046045 | 1.344407 | 0.020691 | 0.449368 | 0.01539 | 0.236726 | 0.243829 | 0.0483
57 | $C_{3}H_{5}O/C_{4}H_{9}$ | 11.38 | 0.026366 | 1.050608 | 0.024916 | 0.944997 | 0.023716 | 0.281823 | 0.295374 | 0.0974
58 | $C_{3}H_{6}O$ | 10.04 | 0.038395 | 1.243236 | 0.021982 | 0.572524 | 0.017682 | 0.250648 | 0.259290 | 0.0313
59 | $C_{3}H_{7}O$ | 10.99 | 0.029274 | 1.102023 | 0.024062 | 0.821959 | 0.021835 | 0.272813 | 0.284722 | 0.84
60 | $C_{3}H_{8}O$ | 10.66 | 0.032078 | 1.148352 | 0.02334 | 0.727609 | 0.020325 | 0.265148 | 0.275806 | 0.0298
72 | $C_{4}H_{8}O$ | 9.66 | 0.043107 | 1.307068 | 0.02115 | 0.490645 | 0.016182 | 0.241695 | 0.249305 | 0.014
73 | $C_{4}H_{9}O$ | 11.45 | 0.025886 | 1.041738 | 0.02507 | 0.968492 | 0.024065 | 0.283435 | 0.297300 | 0.0588
74 | $C_{4}H_{10}O$ | 9.98 | 0.039092 | 1.253010 | 0.021851 | 0.558970 | 0.017439 | 0.249238 | 0.257706 | 0.0196
75 | ${}^{13}C^{12}C_{3}H_{10}O$ | 9.79 | 0.041412 | 1.284707 | 0.021435 | 0.517603 | 0.016685 | 0.244764 | 0.252710 | 0.00111

###  III.3 imidazole (IMI) and 2-nitroimidazole (2NI)

The PICS that we present here for IMI and 2NI are based on the mass spectrum
and AEs presented by Rebecca et al.Meissner  _et al._ (2019). In Table 3, and
Table. 4, we have presented the BRs calculated using Huber’s method [Eq.(14)],
the theoretical BRs [Eq.(11)], the experimental BRs calculated from the EIMS
data [Eq.(7)] and the structural factor [Eq.(16)] and the scaling factor
[(12)] along with the maximum cross sections calculated using the MSD and the
mBEB-B methods. The PICS for $[HCNH]^{+}$, $[HCCNH]^{+}$, $[HCNCH]^{+}$ and
$[CHCHNH]^{+}$ cationic fragments of IMI is shown in Figure. 6(a), which were
observed in the experiment of Rebecca et al.Meissner  _et al._ (2019).
$[HCNH]^{+}$ is the cation with the lowest m/z having the second highest AE of
11.74 eV, $[HCCNH]^{+}$ and $[HCNCH]^{+}$ fragments have m/z value of 40 and
same AE, $[CH_{2}NCH]^{+}$ & $[CH_{2}CNH]^{+}$ also share their AEs and their
m/z value are same 41, $[CHCHNH]^{+}$ fragment has the same m/z value of 41
but has a different AE and $[IMI-H]^{+}$ is the de-hydrogenated IMI which was
also observed in the EIMS experiment. For fragments which has the same m/z
values and AEs, the calculated PICS will be the same and is presented in one
figure for both fragments. From the Figure. 6(a), it can be seen that for
almost all the fragments the magnitude of the PICS from the MSD method is
slightly smaller than the PICS calculated using the mBEB-B method. Both
methods match very well from the ionization threshold to 70 eV after which the
cross sections show slight variation for all the fragments.

In Figure 6(b), we have compared all the TICS from the existing literature
along with our data. Our BEB TICS compares very well with the BEB TICS
presented by Tejas et al.Jani  _et al._ (2023), albeit their TICS calculated
using the csp-ic method has a higher magnitude in comparison to BEB data,
especially at higher energies after the peak. The magnitudes of the sums of
the PICS calculated using both the MSD and the mBEB-B methods are lower than
the TICS due to the lack of information on all the fragments and the AEs as
our methods are dependent on the AEs and mass spectrum data of the fragments
of the parent molecule.

The PICS of 2NI is shown in Figure. 7(a), which contains the PICS of 8
fragments. The smallest fragment is $[HCNH]^{+}$ of m/z of 28 which has an AE
of 11.44 eV and the biggest fragment is $[C_{3}H_{3}N_{3}O]^{+}$ having the
m/z of 97. The $[C_{3}H_{3}N_{2}]^{+}$ cation has two AEs. Like the PICS of
IMI a similar trend is seen here, both the MSD PICS and the mBEB-B PICS show a
good agreement from the ionization threshold to 100 eV, after which the PICS
of the MSD method falls short on comparison with the mBEB-B PICS, but their
magnitudes remain similar.

The TICS of 2NI is shown in Figure. 7(b), with the BEB model is compared with
the TICS obtained after summing the cross sections of all the available
fragments in the MSD and mBEB-B methods. The TICS do not match very well with
the BEB TICS, as we don’t have information on the AEs of all the fragments
that appeared in the EIMS. All the details of the parameters required to
compute PICS are given in the Table. 4, which contains the theoretical BRs,
the experimental BRs, the scaling factors, and the structural factors along
with the maximum CS.

Table 3: Absolute values of branching ratio $(\Gamma)$, structural factor $(\chi_{i})$, scaling factor $(\Upsilon_{i})$ and maximum PICS calculated using MSD and mBEB-B method compared for imidazole. $m/z$ | Cations |  $\varepsilon$ (eV) Meissner  _et al._ (2019) | $\Gamma_{i}^{H}$ | $\Gamma_{i}^{Theo}$ |  $\Gamma_{i}$ Meissner  _et al._ (2019) | $\chi_{i}$ | $\Upsilon_{i}$ | $\sigma_{max}^{MSD}$ | $\sigma_{max}^{mBEB-B}$
---|---|---|---|---|---|---|---|---|---
28 | $HCNH$ | 11.74 | 0.125833 | 0.700872 | 0.112307 | 0.892509 | 0.160239 | 1.043251 | 1.128965
40 | $HCCNH$ | 14.96 | 0.060814 | 0.498982 | 0.246460 | 4.052667 | 0.493925 | 2.240973 | 2.592455
40 | $HCNCH$ | 14.96 | 0.060814 | 0.498982 | 0.246460 | 4.052667 | 0.493925 | 2.240973 | 2.592455
41 | $CH_{2}NCH$ | 11.68 | 0.127782 | 0.705604 | 0.025329 | 0.198219 | 0.035897 | 0.235377 | 0.254443
41 | $CH_{2}CNH$ | 11.68 | 0.127782 | 0.705604 | 0.025329 | 0.198219 | 0.035897 | 0.235377 | 0.254443
41 | $CHCHNH$ | 14.06 | 0.073256 | 0.546657 | 0.025329 | 0.345758 | 0.046334 | 0.231722 | 0.262657
67 | $IMI-H$ | 8.76 | 0.302892 | 0.688466 | 0.007728 | 0.025516 | 0.054560 | 0.073110 | 0.378300

Energy (eV)PICS $(10^{-16}cm^{2})$ (a)

(b)

Figure 6: a) Comparison of PICS calculated using various methods for
imidazole. The green line represents the PICS calculated using the mBEB-B
method, and the red line represents the PICS calculated using the MSD method,
b) Comparison of TICS for imidazole, the blue line indicates the present BEB
data, the orange line indicates the sum of PICS calculated using the mBEB-B
method, the green line represents the sum of the PICS calculated using the MSD
method, the red line, and the purple line represents the BEB TICS and the csp-
ic TICS data presented by Tejas et al.Jani  _et al._ (2023).

Energy (eV)PICS $(10^{-16}cm^{2})$ (a)

(b)

Figure 7: a) Comparison of PICS calculated using various methods for 2-nitroimidazole. The green line represents the PICS calculated using the mBEB-B method, and the red line represents the PICS calculated using the MSD method. b) Comparison of TICS for 2-nitroimidazole, the blue line presents our BEB-TICS, the green line shows the sum of PICS of MSD, and the orange line shows the sum of the PICS of the mBEB-B. Table 4: Absolute values of branching ratio $(\Gamma)$ structural factor $(\chi_{i})$, scaling factor $(\Upsilon)$ and maximum PICS calculated using MSD and mBEB-B method compared for 2-nitroimidazole. $m/z$ | Cations |  $\varepsilon$ (eV) Meissner  _et al._ (2019) | $\Gamma_{i}^{H}$ | $\Gamma_{i}^{Theo}$ | $\Gamma_{i}$ | $\chi_{i}$ | $\Upsilon_{i}$ | $\sigma_{max}^{MSD}$ | $\sigma_{max}^{mBEB-B}$
---|---|---|---|---|---|---|---|---|---
28 | $HCNH$ | 11.44 | 0.124877 | 0.836333 | 0.112307 | 0.134285 | 0.134285 | 1.306890 | 1.388680
30 | $NO$ | 11.11 | 0.136339 | 0.867858 | 0.070544 | 0.081285 | 0.081285 | 0.822306 | 0.868480
40 | $HCCNH$ | 13.74 | 0.072078 | 0.654551 | 0.246460 | 0.376533 | 0.376533 | 2.832763 | 3.155850
56 | $HNCHCO$ | 11.34 | 0.128210 | 0.845716 | 0.032927 | 0.038934 | 0.038934 | 0.383366 | 0.406602
67 | $C_{3}H_{3}N_{2}$ | 13.00 | 0.085100 | 0.508922 | 0.037563 | 0.073808 | 0.073808 | 0.433492 | 0.475207
67 | $C_{3}H_{3}N_{2}$ | 16.29 | 0.043251 | 0.508922 | 0.037563 | 0.073808 | 0.073808 | 0.425538 | 0.504195
83 | $C_{3}H_{3}N_{2}O$ | 11.12 | 0.135971 | 0.866878 | 0.038764 | 0.044717 | 0.044717 | 0.451837 | 0.477295
97 | $C_{3}H_{3}N_{3}O$ | 13.92 | 0.069318 | 0.642637 | 0.016542 | 0.025741 | 0.025741 | 0.189945 | 0.212466

##  IV Conclusion

In the present work, we have theoretically computed the partial and total
ionization cross sections of R-carvone, 2-butanol, imidazole, and
2-nitroimidazole using the MSD and mBEB-B methods in combination with the BEB
model. We obtained a fairly good agreement of our theoretical PICS data of
various fragments with the experimental PICS for R-carvone and 2-butanol.
Also, the TICS which is obtained as the sum of all the PICS of the fragments
in the MSD and mBEB-B method gives good agreement with TICS computed using the
BEB model. For imidazole and 2-nitroimidazole, we could not find any
experimental PICS study, and hence are computed in the present study for the
first time. Hence, more investigation both theoretical and experimental is
needed for these molecules. The appearance energies and relative abundances of
the fragments were the key parameters for the determination of the PICS, which
were all taken from the experimental papers for our calculations. All other
parameters such as the experimental and theoretical BRs, scaling factors, and
structural factors employed for the determination of PICS were computed and
are presented in Tables. 1, 2, 3 and 4 respectively. The TICS data obtained
after summing all the PICS of the fragments in the MSD and mBEB-B method
underestimates the TICS data computed using the BEB model for imidazole and
2-nitroimidazole. The discrepancy is due to the lack of complete information
on the fragmentation of the parent molecule, where only the major dissociation
fragments are given for imidazole and 2-nitroimidazole.

###### Acknowledgements.

S.S. acknowledges Vellore Institute of Technology for providing a research
fellowship; D.G. acknowledges Science and Engineering Research Board (SERB),
Department of Science and Technology (DST), Government of India (Grant No.
SRG/2022/000394) for providing the financial support and computational
facility.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## Author Contributions

S. Suriyaprasanth: Conceptualization (lead), Data curation (lead),
Investigation (lead), Methodology (Supporting), Resources (Supporting),
Validation (lead), Writing – original draft (lead), Writing – review & editing
(equal); Rounak Agrawal: Data curation (supporting), Methodology (Supporting),
Investigation (Supporting); Dhanoj Gupta: Conceptualization (equal), Data
curation (equal), Investigation (equal), Methodology (lead), Resources (lead),
Validation (equal), Writing – original draft (equal), Writing – review &
editing (lead), Supervision (lead).

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