We performed quantum mechanical calculations of electron scattering from four-membered heterocycles containing oxygen and sulfur, namely, oxetane (trimethylene oxide) and thietane (trimethylene sulfide), along with their isomers, focusing on the electron-impact energy range of 15–5000 eV. These compounds hold considerable significance in astrochemistry, atmospheric chemistry, and pharmaceutical science, as well as crucial roles in biological and industrial processes. We used the complex optical-potential model with screening correction to find the total, inelastic, and elastic cross sections. Ionization cross sections were derived through the semiempirical complex scattering potential-ionization contribution method from inelastic cross-sectional data. Our results exhibit strong agreement with the available theoretical predictions and the experimental data. This study marks the first analysis of most of the molecules investigated. Furthermore, a comparative analysis of isomeric forms and the heteroatom composition is reported to assess the impact of electronic-structural variations on scattering behavior.

Electron–molecule scattering studies are fundamental to the understanding of intermolecular interactions, energy transfer mechanisms, and also the dynamics of molecular systems under electron collision. Such investigations are crucial for applications in astrochemistry, atmospheric science, radiation biology, and industrial chemistry, where electron collisions are integral to processes such as chemical reactivity, ionization, dissociation, and the formation of transient molecular species.1 

Oxygen- and sulfur-containing chemical entities are of particular interest due to their widespread occurrence and significance across multiple scientific domains.2 The molecules considered in this study span isomers of molecular formulas C 3 H 6 O and C 3 H 6 S, exhibiting significant structural diversity, and are broadly classified as cyclic oxides (oxetane), cyclic sulfides (thietane), aliphatic carbonyls (acetone and propanal), thiocarbonyls (thioacetone), epoxides (propylene oxide), episulfides (methyl thiirane), ethers (methyl vinyl ether), thioethers (methyl vinyl sulfide), alcohols (cyclopropanol and allyl alcohol), and thiols (cyclopropanethiol and allyl thiol). This diversity makes them ideal candidates for investigating how structural variations, including the effect of heteroatoms and structural isomerism, influence electron scattering behavior. Most of these molecules have been extensively studied with significant focus on their structural and photochemical properties, including photodissociation, photoionization, ring-opening dynamics, spectroscopy, and chirality.3,4 Among these, four-membered heterocycles such as oxetanes and thietanes5 have garnered significant attention owing to their unique electronic configurations and strained ring systems. These molecules not only serve as privileged scaffolds in medicinal chemistry, aiding in the design of biologically active agents, but also play a crucial role in advancing materials science by providing tailored solubility, polarity, and hydrogen-bonding properties.6,7

Szmytkowski et al.8 measured total cross sections (TCSs) for oxetane (trimethylene oxide) experimentally from 1 to 400 eV. Additionally, elastic cross sections were calculated from 30 to 3000 eV using the Independent Atom Model (IAM) with additivity rules, and ionization cross sections were obtained from 9.342 to 3000 eV using the Binary-Encounter-Bethe (BEB) method. Theoretical estimates for TCSs were derived by summing elastic and ionization cross sections. However, as per the authors, the actual TCS could exceed these estimates by 3%–11%.

Propylene oxide is the first chiral molecule detected in the interstellar medium (ISM), and its use in electron microscopy for biological sample preparation has further stimulated interest in exploring molecular interactions in cold and low-density environments.9,10 As a prototypical chiral molecule, its detection has also reignited discussions about the role of chirality in the origins of homochirality in life and the underlying mechanisms that could explain such symmetry-breaking phenomena.11 Zhou et al.12 experimentally measured its electron-impact ionization cross sections over an energy range of 0–300 eV and performed BEB calculations to determine ionization cross sections.

Acetone, a simple yet versatile ketone, is widely utilized in industrial and pharmaceutical processes and naturally occurs in human metabolism and environmental emissions. It has long been a molecule of extensive interest in electron scattering studies due to these wide-ranging applications and fundamental significance in various chemical and physical processes. It has also been identified in the interstellar medium,13 underscoring its significance in astrochemical studies. Similarly, propanal is an aliphatic aldehyde detected in interstellar clouds,14 and both have been the subject of various experimental and theoretical investigations. Recent research by Stachová et al.15 has explored the emission dynamics of acetone under low-energy electron impact, revealing hydrogen migration and the formation of OH groups—previously absent in the molecule—through detailed spectral and excitation-emission analysis. Theoretically, Gupta and Antony16 calculated ionization cross sections for both molecules, propanal (propionaldehyde) and acetone, from ionization threshold ( IE) to 2000 eV, followed by Gupta et al.17 calculating acetone’s elastic and total cross sections over 50–10 000 eV. Prajapati et al.18 expanded acetone’s theoretical analysis using R-matrix, spherical complex optical-potential (SCOP), and BEB methods, along with POLYDCS codes, to compute total, differential, elastic, and ionization cross sections over 0.1–5000 eV. Experimental measurements have also been reported, with Vacher et al.19 reporting acetone’s ionization cross sections experimentally and with BEB calculations over the 10–100 eV range. Bull and Harland20 provided ionization cross-sectional measurements for acetone and propanal between 10 and 300 eV, while Harrison et al.,21 Beran et al.22 and Otvos et al.23 reported specific values at 70 and 75 eV. For acetone, Szmytkowski et al.24 and Kimura et al.25 measured total cross sections, covering the energy range from 0.7–5000 eV, while Homem et al.26 and Pastega et al.27 extended these studies to include differential, elastic, and momentum-transfer cross sections using experimental and theoretical methods across 1–1000 eV.

This work is the first comprehensive investigation of electron scattering from these molecules. Even though a lot of progress has been made both theoretically and experimentally, the scattering data for most isomers, especially thietane, methyl thiirane, and cyclopropanethiol, are limited.

The primary goal of this study is to systematically investigate electron scattering dynamics for isomers of C 3 H 6 O and C 3 H 6 S. By employing optical-potential methods, we calculate elastic, inelastic, total, and ionization cross sections over an energy range of 15–5000 eV. Molecular properties, such as geometry and ionization energy, were determined using ORCA28 calculations and used where experimental data were unavailable. Additionally, the study explores the effects of heteroatom composition and isomeric variations, providing insights into molecular-level interactions and scattering behavior. The computational methodologies utilized in this study are detailed in Sec. II, while the results, including comparisons and analyses, are presented in Sec. III.

In molecular systems, most electron density is localized within compact regions—either individual atoms or tightly bonded groups. We treated the electron–molecule collisions based on the well-established complex optical-model potential approach. This method, initially formulated for single-center atomic targets, has been effectively extended to large molecules under multi-center approximation through the Group-Additivity Rule (GAR). This approach considers each group of atoms with strongly overlapping charge density—typically arising from covalent bonding—as a single spherically symmetric center. For many years, the spherical complex optical potential29 (SCOP) and complex scattering potential-ionization contribution30 (CSP-ic) formalisms have been extensively used on a variety of atomic and molecular targets. These methods have been proven to provide reasonable cross-sectional data over a wide electron-impact energy range, starting from intermediate ( 50 eV) to high energies. However, modeling of the scattering processes is challenging at the energies, starting from just below the ionization threshold (IE) to 50 eV, due to the aspherical nature of distribution functions and presence of multiple scattering channels (like vibrational and rotational excitations or ionization to the continuum levels) and inter-channel couplings. To extend the applicability of the methods employed, we adopted the model of screening correction31 that refines the cross-sectional data, especially near-threshold energy. We used the group-additivity rule with screening correction (GAR-SC) to overcome the aspherical and overlapping charge distributions.32,33 These corrections extend the accuracy of the methods down to energies as low as 15 eV. The splitting of the molecules into smaller groups enhances spherical symmetry, hence allowing the potentials to be assessed at equivalent levels of approximation.

The SCOP method, incorporating the screening corrections, provides a convenient way to determine the elastic ( Q e l) and inelastic ( Q i n e l) contributions in the total ( Q t o t a l) cross section for spherically symmetric systems. From optical analogy, the interaction of the projectile and neutral target system can be considered as V o p t ( r , E i ) = V R ( E i ) + i V I ( r , E i ). The real part accounts for elastic scattering, including static ( V s t),34 exchange ( V e x),35 and polarization ( V p o l)36 effects, while the imaginary part ( V a b s)37 models energy loss processes like excitation and ionization. Since molecular cross sections are computed group-wise, with each group treated as a single unit, the method retains the computational advantages of atomic models while incorporating essential molecular features, including bonding interactions, geometry, polarizability, and ionization potentials. The static potentials and electronic charge densities are obtained by analytic expressions of Cox and Bonham.34 The polarization potential, constructed by Zhang et al.,36 is used to capture short-range correlation effects38 specific to the group, while at long range, it smoothly transitions to an asymptotic form governed by the molecular polarizability. The exchange potential is modeled using Hara’s free electron gas approximation,35 which relies on the molecular ionization potential and local electron density of the molecular fragment. This ensures that both local and collective molecular responses are consistently represented, maintaining Hara’s original assumption that both the incident and target electrons experience the same effective potential.

For this spherical model potential of each scattering center, the radial Schrödinger equation is solved using the conventional partial wave approximation. The numerical solution of the resulting differential equation using the Numerov method yields the associated complex phase shifts ( δ ), leading to the elastic, inelastic, and total scattering cross sections given by
(1)
(2)
and
(3)
where η = exp ( 2 [ δ ] ) is the inelasticity factor.

Based on the methods employed here, ionization energies (IEs), electric dipole polarizability ( α d), molecular charge density [ ρ ( r )], and the geometry are the primary inputs for the interaction potentials. The ground-state molecular geometry optimization was performed in the ORCA 6.0.0 program package39,40 with the time-dependent density functional theory (TD-DFT), employing a dispersion-corrected41, ω B 97 X D 3 functional,42 and aug c c p V T Z basis set. The input files for the same were prepared using the Avogadro43 software. The obtained parameters are compared with the available dataset on the NIST CCCBDB Database,44 listed in Table I. We preferred the NIST database-recommended values over the current calculations.

TABLE I.

Target properties.

TargetIonization energy (eV)HOMO (eV)Polarizability (Å3)
NISTa44 PresentbNIST44 Presentb
Allyl alcohol 9.67 (10.22) 9.749 6.67c 6.654 
Cyclopropanol 9.1 9.801 6.048c 6.029 
Propanal 9.96 (9.96) 9.623 6.35a 6.206 
Acetone 9.703 (9.8) 9.458 6.27a 6.171 
(E) 1-propen-1-ol … 8.578 … 6.644 
(Z) 1-propen-1-ol … 8.612 … 6.593 
Acetone enol 8.48 8.771 6.668c 6.656 
Methyl vinyl ether 8.9 8.684 … 6.888 
Oxetane 9.65 (9.679) 9.387 5.885c 5.870 
Propylene oxide 10.22 (10.44) 10.048 6.001c 5.983 
Allyl thiol … 9.071 … 9.081 
Thietane 8.61 8.459 8.24c 8.183 
Thioacetone 8.6 8.461 9.039c 8.988 
Propylene sulfide 8.85 (8.88) 8.677 8.456c 8.387 
Cyclopropanethiol … 9.002 … 8.343 
Methyl vinyl sulfide … 8.182 … 9.207 
TargetIonization energy (eV)HOMO (eV)Polarizability (Å3)
NISTa44 PresentbNIST44 Presentb
Allyl alcohol 9.67 (10.22) 9.749 6.67c 6.654 
Cyclopropanol 9.1 9.801 6.048c 6.029 
Propanal 9.96 (9.96) 9.623 6.35a 6.206 
Acetone 9.703 (9.8) 9.458 6.27a 6.171 
(E) 1-propen-1-ol … 8.578 … 6.644 
(Z) 1-propen-1-ol … 8.612 … 6.593 
Acetone enol 8.48 8.771 6.668c 6.656 
Methyl vinyl ether 8.9 8.684 … 6.888 
Oxetane 9.65 (9.679) 9.387 5.885c 5.870 
Propylene oxide 10.22 (10.44) 10.048 6.001c 5.983 
Allyl thiol … 9.071 … 9.081 
Thietane 8.61 8.459 8.24c 8.183 
Thioacetone 8.6 8.461 9.039c 8.988 
Propylene sulfide 8.85 (8.88) 8.677 8.456c 8.387 
Cyclopropanethiol … 9.002 … 8.343 
Methyl vinyl sulfide … 8.182 … 9.207 
a

Experimental data. (Note: Values in parentheses represent the vertical ionization potentials.)

b

Present ( ω B 97 X D 3 / a u g c c p V T Z).

c

Calculated ( ω B 97 X D / a u g c c p V T Z).

Furthermore, the inelastic cross section is the sum of all energy-altering processes, including electronic excitation and ionization. However, in the present case, rotational and vibrational channels are not considered in the theory. Hence, Q i n e l given in Eq. (2) is composed of two channels: ionization and excitation. That is,
(4)
The semiempirical CSP-ic method was used to estimate the electron-impact ionization contribution from the inelastic cross section. It offers a straightforward approach to represent their relationship as an energy-dependent ratio, generalized into the following analytical form:45 
(5)
where U ( = E i / I . E . ) is a dimensionless variable. This method relies on fitting the unknown parameters C 1, C 2, and a using boundary conditions obtained from the analysis of various measurements and theoretical predictions:
(6)
The ratio R ( E i ) approaches unity at higher energies when the dipole-allowed electronic excitations fall off as ln ( E i ) / E i. The first term inside the square bracket of Eq. (5) is included to best represent the ratio R ( E i ) at low and intermediate energy. Near the energy of the peak inelastic cross section ( E p), ionization typically contributes 70%–80% to the total inelastic process, i.e., R p varies from 0.7 to 0.8. We have considered R p = 0.7 for our calculations. This is because the lower limit is found to be true for most of the molecules having an ionization threshold of 10 eV, which is true for all the targets studied here. However, using a constant R p makes the method reproducible.
The molecules studied here are quite complex in terms of their structure. Hence, a straightforward use of the group-additivity rule to find cross section will overestimate the true value due to the overlapping charge densities as seen by the incoming projectile. Hence, we implemented the screened group-additivity rule to account for geometry-shielding effects due to overlapping charge distributions, which can be written as
(7)
where Q G A R is the cross section from the group-additivity rule, and Q O L is the overlapping cross section summed over all scattering groups. The overlapping cross section for an atom A surrounded by N neighboring atoms is calculated by31,33,46
(8)
where Q a is the cross section of atom A, and Q i is the cross section of ith atom at a distance r i.

This section provides an overview of the electron scattering calculations for molecules with formulas C 3 H 6 O and C 3 H 6 S. Scattering cross sections, elastic ( Q el), inelastic ( Q inel), and total ( Q total), were computed across an energy range of 15–5000 eV in a fine grid using the SCOP method, with ionization contributions ( Q ion) extracted through the CSP-ic approach. The subsequent subsections provide a detailed comparative analysis of these results with existing data, highlighting the reliability of the methodology, including the effects of heteroatom composition and isomeric variations on electron scattering dynamics.

Quantum chemistry calculations, including geometry optimization, ionization energy (approximated using HOMO energies), and dipole polarizability, were performed using the ORCA package at the TD D F T / ω B 97 X D 3 / a u g c c p V T Z level theory. The results, summarized in Table I, show excellent agreement with available data sourced from the NIST CCCBDB database,44 with minimal variations. These minor inconsistencies likely arise from differences in the DFT functionals used: the reference calculations employed ω B 97 X D, while the present study utilized the dispersion-corrected ω B 97 X D 3, leading to improved accuracy for polarizability and geometry-dependent properties. We expect slight variations in the scattering calculations because we use HOMO energies as an approximation for ionization energies, which inherently differ from experimental ionization values due to limitations in capturing electron correlation and system polarization effects. This approach was adopted due to the unavailability of experimental data for all molecules. However, experimental values were used wherever available.

Figure 1 illustrates a comparison of present cross-sectional data for the oxetane ring with the only available experimental and theoretical results from Szmytkowski et al.8 along with the uncorrected Q t o t a l for reference. Szmytkowski et al. measured the total cross section experimentally in the 1–400 eV range using the linear electron-transmission method. In addition to experimental TCSs, they calculated integral elastic and ionization cross sections using the additivity rule with independent atom model approximation and BEB method, extending up to 3000 eV. They also estimated the theoretical TCS by summing elastic and ionization contributions.

FIG. 1.

Electron scattering cross sections for oxetane. Solid and dashed lines: present corrected and uncorrected Q t o t a l; dash-dotted, dotted, and dash-dot-dotted lines: present Q e l, Q i n e l, and Q i o n, respectively; star, short-dashed, short-dash-dotted, and short-dotted lines: Q t o t a l, estimated Q t o t a l( = Q e l + Q i n e l), Q i o n(IAM), and Q i o n(BEB), respectively, from Szmytkowski et al.8 

FIG. 1.

Electron scattering cross sections for oxetane. Solid and dashed lines: present corrected and uncorrected Q t o t a l; dash-dotted, dotted, and dash-dot-dotted lines: present Q e l, Q i n e l, and Q i o n, respectively; star, short-dashed, short-dash-dotted, and short-dotted lines: Q t o t a l, estimated Q t o t a l( = Q e l + Q i n e l), Q i o n(IAM), and Q i o n(BEB), respectively, from Szmytkowski et al.8 

Close modal

When compared to available experimental data, the uncorrected TCS shows an overestimation at low energies due to overlap effects, which is significantly refined by screening correction, resulting in excellent agreement with experimental data. However, the partial agreement of the estimated TCS, obtained by neglecting electronic excitation, with the present results highlights that the independent atom model likely overestimates the elastic cross section compensating for the absence of the excitation contribution. Furthermore, while comparing the ionization cross section, a mismatch is observed in the energy value corresponding to the peak ionization, where the CSP-ic method slightly underestimates the energy of the peak ionization cross section. Moreover, the difference in the set of model potentials and additivity rules used by each approach contributes to the discrepancy in Q e l. The IAM treats each atom as an independent scatterer, neglecting molecular geometry, bonding effects, and interatomic interactions, and parameters like polarizability and ionization potential are assigned on a per-atom basis. This often leads to an overestimation of total cross sections. Although GAR introduces an approximation, the SCOP-GAR model has demonstrated strong agreement with experimental observations, particularly in low- and intermediate-energy electron scattering, where molecular geometry and bonding effects are important.

Importantly, our method also includes geometrical screening correction, following the classical procedure introduced by Blanco and García,31 which further refines the cross sections by accounting for the overlapping scattering contribution of atomic regions. These corrections are especially relevant at low incident energies, where the elastic contribution peaks, leading to a cross-sectional overlap among adjacent atoms.

Figure 2(a) presents the total cross section for acetone, comparing screening-corrected and uncorrected results with available experimental and theoretical data. As expected, the uncorrected results show slight overestimation at low energies, while refined effectively in the screening-corrected results, which align well with experimental data from Szmytkowski24 and Kimura et al.25 Among theoretical approaches, Pastega et al.’s27 results exhibit consistent overestimation, attributed to their IAM-SCAR method, while Prajapati et al.’s18 TCS results using the single-center expansion approach in the SCOP method shows deviations at low and high energies. TCS calculated by Gupta et al.,17 employing SCOP with the group-additivity rule, provides closer agreement but is reported only for energies above 50 eV. The present study extends these calculations to lower energies using an improved approach.

FIG. 2.

Total, elastic, inelastic, and ionization cross sections for electron-acetone scattering. Solid line and dash-dotted lines: present corrected and uncorrected; dashed line: Gupta et al.;16,17 short-dashed and dotted lines: Prajapati et al.18’s SCOP and BEB results; short-dotted line: Pastega et al.;27 short-dash-dotted line and inverted-triangle: Vacher et al.;19 dash-dot-dotted line and square: Homem et al.;26 star: Szmytkowski et al.;24 sphere: Kimura et al.;25 right-triangle: Harrison et al.;21 left-triangle: Beran et al.;22 diamond: Otvos et al.;23 triangle: Bull et al.20 

FIG. 2.

Total, elastic, inelastic, and ionization cross sections for electron-acetone scattering. Solid line and dash-dotted lines: present corrected and uncorrected; dashed line: Gupta et al.;16,17 short-dashed and dotted lines: Prajapati et al.18’s SCOP and BEB results; short-dotted line: Pastega et al.;27 short-dash-dotted line and inverted-triangle: Vacher et al.;19 dash-dot-dotted line and square: Homem et al.;26 star: Szmytkowski et al.;24 sphere: Kimura et al.;25 right-triangle: Harrison et al.;21 left-triangle: Beran et al.;22 diamond: Otvos et al.;23 triangle: Bull et al.20 

Close modal

In Fig. 2(b), present Q e l results are in good accord with the findings of Gupta et al. (SCOP-GAR), and Homem et al.’s experimental elastic cross sections, particularly at intermediate energies, while Pastega et al.’s IAM-SCAR and Homem et al.’s molecular complex optical potential (MCOP) method overestimate in the high-energy region, diverging from the experimental results due to differences in theoretical frameworks. The present Q e l results are well aligned within the error bars of experimental data. In Fig. 2(c), Q i n e l has been compared against Gupta et al.’s and Homem et al.’s total absorption cross section. In Fig. 2(d), the present Q i o n shows excellent alignment with the available data for higher energies, while slight overestimations are observed in the intermediate energy range. The relatively closer agreement of the CSP-ic results from Gupta et al. and Prajapati et al. with experimental data may be attributed to their consideration of the excitation threshold as a slowly varying function of energy and single-center expansion, respectively. We considered the excitation threshold, which serves as one of the inputs to absorption potential, to be equal to the ionization threshold.

In Fig. 3, similar deviations in ionization cross sections are observed for propanal and propylene oxide at the mid-energy range, with better agreement at near-threshold and higher energy regimes. Notably, both the Q i n e l and Q i o n exhibit a peak at lower electron-impact energies compared to the experimental findings, with mid-energy overestimations likely resulting from nearly the same values of ionization potentials in the approximate range of 8–10 eV. This trend in the Q i o n and Q i n e l data highlights the need for further refinement of the absorption potential employed in the current theoretical framework. While some researchers, discussed by Staszewska et al.,48 have proposed some semiempirical scaling parameters, and Blanco and García49 have introduced a parameter-free screening-corrected model, none of these approaches have achieved consistently high accuracy across the whole energy range. This underscores the need for a more advanced and comprehensive theoretical model to address these limitations.

FIG. 3.

Electron scattering cross sections for propanal and propylene oxide. Solid line: present Q t o t a l; short-dashed line: present Q e l; dotted line: present Q i n e l; dash-dotted line: present Q i o n, short-dashed and short-dotted line: Q i n e l and Q i o n from Gupta et al.,16,17 diamond, sphere, star, and inverted-triangle: Q i o n from Beran et al.,22 Bull et al.,20 Harrison et al.,21 and Bobeldijk et al.,47 respectively, for propanal; solid square and short-dash-dotted line: experimental and calculated Q i o n for propylene oxide from Zhou et al.12 

FIG. 3.

Electron scattering cross sections for propanal and propylene oxide. Solid line: present Q t o t a l; short-dashed line: present Q e l; dotted line: present Q i n e l; dash-dotted line: present Q i o n, short-dashed and short-dotted line: Q i n e l and Q i o n from Gupta et al.,16,17 diamond, sphere, star, and inverted-triangle: Q i o n from Beran et al.,22 Bull et al.,20 Harrison et al.,21 and Bobeldijk et al.,47 respectively, for propanal; solid square and short-dash-dotted line: experimental and calculated Q i o n for propylene oxide from Zhou et al.12 

Close modal

Sulfur-containing molecules, such as C 3 H 6 S, exhibit distinct scattering characteristics compared to their oxygen-containing counterparts, like C 3 H 6 O. For instance, C 3 H 6 S is expected to have higher cross sections due to sulfur’s larger atomic radius, greater polarizability, and lower ionization potential (cf. Table I). Figure 4 presents a comparative analysis of the cross sections for C 3 H 6 O and C 3 H 6 S. Across a wide energy range, the total cross section of C 3 H 6 S consistently exceeds that of C 3 H 6 O. This is largely attributed to the increased molecular size and spatial distribution of C 3 H 6 S, which enhance the likelihood of electron interactions.

FIG. 4.

Comparison of electron scattering from C 3 H 6 O and C 3 H 6 S.

FIG. 4.

Comparison of electron scattering from C 3 H 6 O and C 3 H 6 S.

Close modal

At lower energies, the contribution of resonant processes and inelastic channels, such as electronic and vibrational excitations, is particularly prominent, leading to a more substantial enhancement in the total cross section for C 3 H 6 S. The relatively higher total cross section compared to the elastic cross section at intermediate energies, such as 15 eV, highlights the significant role of these inelastic contributions.

Furthermore, the ionization cross section for C 3 H 6 S is higher than that for C 3 H 6 O, attributed to the enhanced polarizability and lower ionization threshold characteristic of sulfur-containing molecules. These observations underscore the importance of molecular size, electronic properties, and excitation channels in determining the scattering dynamics of sulfur- and oxygen-containing molecules. This comparative study provides valuable insights into how molecular composition and structural factors influence electron–molecule interactions.

Figure 5 presents a comprehensive analysis of electron scattering data across a range of molecular isomers. At intermediate energies, below 100 eV, molecular isomerism, encompassing differences in molecular geometry, bonding arrangements, dipole moment, polarizability, ionization energy, and electronic charge distribution, profoundly influences electron scattering, as evident in the total and elastic cross sections of these molecular systems (cf. Fig. 5).

FIG. 5.

Electron collision cross sections for isomers of C 3 H 6 O (left) and C 3 H 6 S (right).

FIG. 5.

Electron collision cross sections for isomers of C 3 H 6 O (left) and C 3 H 6 S (right).

Close modal

The correlation between ionization threshold, polarizability, and ionization cross section has been previously observed and extensively studied for a wide range of molecules by many researchers.50 For Q i o n, this effect is evident across the entire energy range, with lower ionization potentials yielding higher ionization cross sections due to the ease of electron removal. The energy transferred during scattering interacts differently with these forms, revealing a nuanced interplay of structural and electronic factors tied to their molecular geometry.

Tautomeric forms further illustrate the dynamic impact of structural isomerism, as seen in acetone and its enol form. The enol tautomer, with its conjugated C=C and –OH groups, displays stronger inelastic scattering and ionization due to its higher polarizability and electron delocalization compared to the keto form, which is more compact and features a higher dipole moment. Similarly, open-chain isomers, such as methyl vinyl ether and (E/Z)–1–propen–1–ol, generally exhibit higher ionization cross sections than their cyclic counterparts (e.g., oxetane and propylene oxide) due to their larger spatial distribution, higher polarizability, and lower geometric constraints, which enhance their ability to polarize and interact with incident electrons.

However, the molecules with higher dipole moments, such as acetone (2.88 D) and propanal (2.52 D), exhibit higher total cross sections due to long-range polarization interactions, which are critical at lower electron energies. Conversely, less polar isomers, such as allyl alcohol (1.6 D) and cyclopropanol (1.46 D), scatter electrons less effectively, as reflected in their lower total and ionization cross sections. Subtle differences between two conformers E- and Z-stereoisomers of 1-propen-1-ol demonstrate how changes in dipole orientation and molecular geometry modulate scattering probabilities despite similar electronic properties.

At higher electron energies, however, the influence of isomeric effects diminishes as the reduced interaction time between the electron and molecule minimizes sensitivity to detailed molecular geometry and charge distribution. Consequently, the cross-sectional curves for C 3 H 6 O and C 3 H 6 S merge with minimal differences in their isomeric forms. Additionally, resonant enhancements in the TCS, often attributed to temporary anion formation and other quasi-bound states, are more prominent in open-chain isomers. A similar isomeric effect is expected for C 3 H 6 S isomers, as their structural and electronic variations would similarly influence cross sections, mirroring the trends observed in C 3 H 6 O isomers.

In summary, this study provides a comprehensive theoretical analysis of electron scattering for the isomers of C 3 H 6 O and C 3 H 6 S using complex optical-potential methods, offering detailed cross-sectional datasets spanning elastic, inelastic, and ionization processes over a wide energy range (15–5000 eV). The findings emphasize the role of molecular structure, electronic properties, isomeric variations, and the presence of different heteroatoms in shaping scattering behavior, addressing critical gaps in our understanding of electron interactions with complex organic molecules found in interstellar and planetary environments. Molecular parameters were determined using dispersion-corrected DFT methods and validated against experimental data, ensuring high accuracy in the calculated results.

Our findings reveal that sulfur-containing molecules exhibit consistently higher cross sections than their oxygen-containing counterparts due to sulfur’s larger atomic radius, greater polarizability, and lower ionization potential. Isomeric effects emerge prominently at low and intermediate energies (<100 eV). Open-chain isomers exhibit higher cross sections than their cyclic counterparts, attributable to their larger spatial distribution, fewer geometric constraints, and lower ionization thresholds. Tautomeric forms, such as acetone and its enol variant, further emphasize the role of delocalized electrons in amplifying scattering, a phenomenon relevant to complex organic chemistry. The role of dipole moments is highlighted in enhancing long-range interactions, with more polar molecules such as acetone exhibiting higher total cross sections compared to less polar isomers like allyl alcohol. At higher electron energies, structural variations have a diminished influence due to reduced interaction times. These findings emphasize the interplay between molecular composition, geometry, and electronic properties in shaping scattering dynamics.

Our methodology, incorporating screening corrections and CSP-ic models, effectively aligns theoretical results with available experimental data, overcoming limitations in prior low-energy scattering calculations. This study advances the understanding of electron-induced processes across diverse fields, including astrochemistry, atmospheric science, and industrial applications, while emphasizing the need for further theoretical and experimental research.

See the supplementary material for molecular geometries, and corresponding electron impact scattering cross-section data for oxetane and thietane and their isomers.

The authors have no conflicts to disclose.

Sudhanshu Arya: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (lead); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (supporting). Bobby Antony: Conceptualization (equal); Formal analysis (equal); Investigation (supporting); Methodology (equal); Project administration (lead); Software (lead); Supervision (lead); Validation (equal); Visualization (equal); Writing – review & editing (lead).

The data that support the findings of this study are available within the article and its supplementary material.

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