#
Elastic and Inelastic Cross Sections for Low-Energy Electron Collisions with ClF Molecule Using the **R**-Matrix Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. R-Matrix Method

## 3. Target Description and Computational Details

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BEB | Binary-encounter-Bethe |

HF | Hartree–Fock |

SE | Static-Exchange |

SEP | Static-Exchange-polarisation |

CI | Configuration Interaction |

CC | Close Coupling |

CASCI | Complete Active Space Configuration Interaction |

CSF | Configuration State Functions |

DCS | Differential Cross Sections |

TICS | Total Ionization Cross Sections |

MO | Molecular Orbitals |

eV | Electron Volt |

au | Atomic Unit |

SCF | Self-Consistent Field |

## References

- Ewig, C.S.; Sur, A.; Banna, M.S. A theoretical study of core and valence ionization in ClF. J. Chem. Phys.
**1981**, 75, 5002. [Google Scholar] [CrossRef] - Law, C.K.; Chien, S.H.; Li, W.K. Thermochemistry of Chlorine Fluorides ClF
_{n}, n = 1–7, and Their Singly Charged Cations and Anions: A Gaussian-3 and Gaussian-3X Study . J. Phys. Chem. A**2002**, 106, 11271. [Google Scholar] [CrossRef] - Eden, J.G.; Dlabal, M.L.; Hutchison, S.B. The interhalogens IF and ICl as Visible Oscillators or Amplifiers. IEEE J. Quantum Electron.
**1981**, 17, 1085. [Google Scholar] [CrossRef] - Diegelmann, M.; Hohla, K.; Rebentrost, F.; Kompa, K.L. Diatomic interhalogen laser molecules: Fluorescence spectroscopy and reaction kinetics. J. Chem. Phys.
**1982**, 76, 1233. [Google Scholar] [CrossRef] - Diegelmann, M.; Proch, D.; Zhensheng, Z. Discharge pumped ClF laser at 285 nm. Appl. Phys. B
**1986**, 40, 49. [Google Scholar] [CrossRef] - Naulin, C.; Bougon, R. Photochemistry of the chlorine monofluoride, ClF. Thermal and photochemical reactions with sulfur tetrafluoride SF
_{4}. J. Chem. Phys.**1980**, 72, 2155. [Google Scholar] [CrossRef] - Ibbotson, D.E.; Mucha, J.A.; Flamm, D.L. Plasmaless dry etching of silicon with fluorine-containing compounds. J. Appl. Phys.
**1984**, 56, 2939. [Google Scholar] [CrossRef] - Takahashi, Y.; Kato, K.; Habuka, H. Development of SiC Etching by Chlorine Fluoride Gas. Mater. Sci. Forum
**2020**, 1004, 731. [Google Scholar] [CrossRef] - Bargainer, M.; Dietrich, P.; Schwentner, N. Spectroscopy and photodissociation of ClF in rare gas solids. J. Chem. Phys.
**2001**, 115, 149. [Google Scholar] - Naulin, C.; Lambard, J.; Bougon, R. Vibrational spectra of the chlorine monofluoride ClF in cryogenic solutions. J. Chem. Phys.
**1982**, 76, 3371. [Google Scholar] [CrossRef] - Krogh, O.D.; Pimentel, G.C. Chemical Lasers from the Reactions of ClF and ClF
_{3}with H_{2}and CH_{4}: A Possible Chain-Branching Chemical Laser. J. Chem. Phys.**1972**, 56, 969. [Google Scholar] [CrossRef] - Krogh, O.D.; Pimentel, G.C. ClF
_{x}-H_{2}chemical lasers (x = 1, 3, 5): Vibration–rotation emission by HF from states with high rotational excitation. J. Chem. Phys.**1977**, 67, 2993. [Google Scholar] [CrossRef] - Cuellar, E.; Pimentel, G.C. Rotational laser emission by HF in the ClF-H
_{2}chemical laser. J. Chem. Phys.**1979**, 71, 1385. [Google Scholar] [CrossRef] - Pimentel, G.C.; Krogh, O.D. Vibrational emission by HCl from the ClF-H
_{2}chemical laser. J. Chem. Phys.**1980**, 73, 120. [Google Scholar] [CrossRef] - Alekseyev, A.B.; Liebermann, H.P.; Buenker, R.J.; Kokh, D.B. Relativistic configuration interaction study of the ClF molecule and its emission spectra from O
^{+}ion-pair states. J. Chem. Phys.**2000**, 112, 2274. [Google Scholar] [CrossRef] - Li, S.; Chen, S.J.; Zhu, D.S.; Wei, J.J. Structure and Potential Energy Function of ClF
^{−}Molecular Ion. Acta Phys.-Chim. Sin.**2013**, 29, 737. [Google Scholar] - Horny, L.; Sattelmeyer, K.W.; Schaefer, H.L. Elusive electron affinity of ClF. J. Chem. Phys.
**2003**, 119, 11615. [Google Scholar] [CrossRef] - Nguyen, M.T.; Ha, T.K. Abinttio calculation of the ionization potentials and hyperfine splitting constants of the radical anions FCl
^{XXX}and Cl${}_{2}^{XXX}$. Chem. Phys. Lett.**1987**, 136, 413. [Google Scholar] [CrossRef] - Van Huis, T.J.; Galbraith, J.M.; Schaefer, H.F. The monochlorine fluorides (ClF
_{n}) and their anions (ClF${}_{n}^{-}$) n = 1–7: Structures and energetics. Mol. Phys.**1996**, 89, 607. [Google Scholar] [CrossRef] - McDermid, I.S. Potential-energy curves, Franck-Condon factors and laser excitation spectrum for the B
^{3}Π(O^{+})-X^{1}Σ^{+}system of chlorine monofluoride. J. Chem. Soc. Faraday Trans. II**1981**, 77, 519. [Google Scholar] [CrossRef] - de Jong, W.A.; Styszynski, J.; Visscher, L.; Nieuwpoort, W.C. Relativistic and correlation effects on molecular properties: The interhalogens ClF, BrF, BrCl, IF, ICl, and IBr. J. Chem. Phys.
**1998**, 108, 5177. [Google Scholar] [CrossRef] [Green Version] - Kaur, S.; Baluja, K.L.; Tennyson, J. Electron-impact study of NeF using the R-matrix method. Phys. Rev. A
**2008**, 77, 032718. [Google Scholar] [CrossRef] - Wang, F.; Liu, J.B.; Sinibaldi, J.; Brophy, C.; Kuthi, A.; Jiang, C.; Ronney, P.; Gundersen, M.A. Transient plasma ignition of quiescent and flowing air/fuel mixtures. IEEE Trans. Plasma Sci.
**2005**, 33, 844. [Google Scholar] [CrossRef] - Nguyen-Kuok, S. Theory of Low-Temperature Plasma Physics; Springer International Publishing: Cham, Switzerland, 2017. [Google Scholar]
- Chu, P.K.; Lu, X.P. (Eds.) Low Temperature Plasma Technology: Methods and Applications; CRC Press: Boca Raton, FL, USA, 2014. [Google Scholar]
- Wiens, J.P.; Sawyer, J.C.; Miller, T.M.; Shuman, N.S.; Viggiano, A.A.; Khamesian, M.; Kokoouline, V.; Fabrikant, I.I. Electron attachment to the interhalogen compounds ClF, ICl, and IBr. Phys. Rev. A
**2016**, 93, 032706. [Google Scholar] [CrossRef] [Green Version] - Tennyson, J. Electron–molecule collision calculations using the R-matrix method. Phys. Rep.
**2010**, 491, 29. [Google Scholar] [CrossRef] - Burke, P.G. R-Matrix Theory of Atomic Collisions; Springer: Berlin/Heidelberg, Germany, 2011. [Google Scholar]
- Baluja, K.L.; Burke, P.G.; Morgan, L.A. R-matrix propagation program for solving coupled second-order differential equations. Comput. Phys. Commun.
**1982**, 27, 299. [Google Scholar] [CrossRef] - Masin, Z.; Benda, J.; Harvey, A.G.; Gorfinkiel, J.D.; Tennyson, J. UKRmol+: A suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method. Comp. Phys. Commun.
**2020**, 249, 107092. [Google Scholar] [CrossRef] [Green Version] - Masin, Z.; Benda, J.; Harvey, A.G.; Al-Refaie, A.; Gorfinkiel, J.D.; Tennyson, J. UKRmol+: UKRMol-in (Version 3.0); Zenodo: Genève, Switzerland, 2019. [Google Scholar] [CrossRef]
- Johnson, R.D., III (Ed.) Computational Chemistry Comparison and Benchmark Database, Number 101, Release 21, August 2020. Available online: http://cccbdb.nist.gov (accessed on 21 December 2021).
- Faure, A.; Gorfinkiel, J.D.; Morgan, L.A.; Tennyson, J. GTOBAS: Fitting continuum functions with Gaussian-type orbitals. Comput. Phys. Commun.
**2002**, 144, 224. [Google Scholar] [CrossRef] [Green Version] - Fabrikant, I.I. Long-range effects in electron scattering by polar molecules. J. Phys. B At. Mol. Opt. Phys.
**2016**, 49, 222005. [Google Scholar] [CrossRef] - Bassi, M.; Bharadvaja, A.; Baluja, K.L. A study of electron scattering from 1-1 C
_{2}H_{2}F_{2}from 0.1 eV to 5 keV. Eur. Phys. J. D**2020**, 74, 232. [Google Scholar] [CrossRef] - Ewing, J.J.; Tigelaar, H.L.; Flygare, W.H. Molecular Zeeman Effect, Magnetic Properties, and Electric Quadrupole Moments in ClF, BrF, ClCN, BrCN, and ICN J. Chem. Phys.
**1972**, 56, 1957. [Google Scholar] [CrossRef] - Vassilakis, A.A.; Kalemos, A.; Mavridis, A. Accurate first principles calculations on chlorine fluoride ClF and its ions ClF
^{±}. Theor. Chem. Acc.**2014**, 133, 1436. [Google Scholar] [CrossRef] - Quintero-Monsebaiz, R.; Perea-Ram<i>ι</i>rez, L.I.; Piris, M.; Vela, A. Spectroscopic properties of open shell diatomic molecules using Piris natural orbital functionals. Phys. Chem. Chem. Phys.
**2021**, 23, 2953. [Google Scholar] [CrossRef] [PubMed] - Darvesh, K.V.; Boyd, R.J.; Peyerimhoff, S.D. Electronically excited states of chlorine monofluoride: A multi-reference configuration interaction study. Chem. Phys.
**1988**, 121, 361. [Google Scholar] [CrossRef] - Tennyson, J.; Noble, C.J. RESON-A program for the detection and fitting of Breit-Wigner resonances. Comput. Phys. Commun.
**1984**, 33, 421. [Google Scholar] [CrossRef] - Sahgal, V.; Bharadvaja, A.; Baluja, K.L. Positron-induced scattering of acetone from 0.1 eV to 5 keV. J. Phys. B At. Mol. Opt. Phys.
**2021**, 54, 075202. [Google Scholar] [CrossRef] - Cooper, B.; Tudorovskaya, M.; Mohr, S.; O’Hare, A.; Hanicinec, M.; Dzarasova, A.; Gorfinkiel, J.D.; Benda, J.; Mašín, Z.; Al-Refaie, A.F.; et al. Quantemol Electron Collision: An expert system for performing UKRmol+ electron molecule collision calculations. Atoms
**2019**, 7, 97. [Google Scholar] [CrossRef] [Green Version] - Itikawa, Y. Molecular Processes in Plasmas; Springer: Berlin/Heidelberg, Germany, 2007. [Google Scholar]
- Bharadvaja, A.; Kaur, S.; Baluja, K.L. Electron-impact cross sections of SiH
_{2}using the R-matrix method at low energy. Phys. Rev. A**2015**, 91, 032701. [Google Scholar] [CrossRef] - Bharadvaja, A.; Kaur, S.; Baluja, K.L. Low-energy electron impact cross-sections and rate constants of NH
_{2}. Pramana-J. Phys.**2017**, 89, 30. [Google Scholar] [CrossRef] - Gianturco, F.A.; Jain, A. The theory of electron scattering from polyatomic molecules. Phys. Rep.
**1986**, 143, 347. [Google Scholar] [CrossRef] - Sanna, N.; Gianturco, F.A. Differential cross sections for electron/positron scattering from polyatomic molecules. Comput. Phys. Commun.
**1998**, 114, 142. [Google Scholar] [CrossRef] - Sarma, G.; Saha, A.K.; Bishwakarma, C.K.; Scheidsbach, R.; Yang, C.H.; Parker, D.; Wiesenfeld, L.; Buck, U.; Mavridis, L.; Marinakis, S. Collision energy dependence of state-to-state differential cross sections for rotationally inelastic scattering of H
_{2}O by He. Phys. Chem. Chem. Phys.**2017**, 19, 4678. [Google Scholar] [CrossRef] - Kaur, S.; Bharadvaja, A.; Baluja, K.L. Electron-impact study of S
_{3}using the R-matrix method. Phys. Rev. A**2011**, 27, 062707. [Google Scholar] [CrossRef] - Itikawa, Y. Effective collision frequency of electrons in atmospheric gases. Planet. Space Sci.
**1971**, 19, 993. [Google Scholar] [CrossRef] - Baille, P.; Chang, J.S.; Claude, A.; Hobson, R.M.; Ogram, G.L.; Yau, A.W. Effective collision frequency of electrons in noble gases. J. Phys B At. Mol. Phys.
**1981**, 14, 1485. [Google Scholar] [CrossRef] - Kim, Y.-K.; Rudd, M.E. Binary-encounter-dipole model for electron-impact ionization. Phys. Rev. A
**1994**, 50, 3954. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Eigenphase sum for the scattering symmetry ${}^{2}{A}_{1}$ as a function of bond length in 12-states CC model (

**a**) 1.4812 Å: dotted dashed curve; this work, dotted dashed curve with star, Wiens et al. [26], 1.5076 Å: dashed dotted curve; this work, dashed dotted curve with star; Wiens et al., 1.5341 Å: dashed curve; this work, dashed curve with star, Wiens et al. (

**b**) 1.5605 Å: dashed curve; this work, dashed curve with star, Wiens et al., 1.587 Å: dashed dotted curve; this work, dashed dotted curve with star; Wiens et al., 1.61 Å: line curve; this work, line curve with star, Wiens et al.

**Figure 2.**Resonance position and width for 12-states CC model: Resonance position—line curve; this work, line curve with circles; Wiens et al. [26]. Resonance width—dashed curve; this work, dashed curve with triangles; Wiens et al.

**Figure 3.**(

**a**) Symmetry wise elastic cross sections in the SE and the 12-states CC model. (

**b**) Elastic cross sections obtained in different scattering models to highlight the effect of polarisation on scattering. These results do not include the long-range effects.

**Figure 4.**Elastic cross sections in the 12-states CC model. Born-corrected elastic cross sections, line curve; Born correction, dashed dotted curve; elastic cross sections without Born correction, dashed curve.

**Figure 5.**Electronic-excitation cross sections in 12-states CC model (

**a**) ground to spin-forbidden transition transition ${}^{1}X\to $${}^{3}\Pi $ and (

**b**) ground to dipole-allowed transition transition ${}^{1}X\to $${}^{1}\Pi $, line curve; Born approximation, dashed curve.

**Figure 7.**(

**a**) Rotationally summed DCS at different incident energies obtained using 12-states CC model. 1 eV; dashed curve, 3 eV; dotted dashed curve, big dashed curve; 6 eV and 8 eV; double dotted dashed curve, 9 eV; line curve (

**b**) Rotationally resolved and summed DCS at 2 eV: 0 → 0 transition, dashed curve; 0 → 1 transition, dotted curve with star; 0 → 2 transition, dotted dashed curve; 0 → 3 transition, double dotted dashed curve; 0 → 4 transition, dashed dotted curve; circles, summed (0 → J); circle with dotted line curve, Born approximation; dots.

**Figure 9.**Effective collision frequencies: line curve, $\u2329\nu \u232a$; dashed curve, ${\overline{\nu}}^{-1}$.

**Figure 10.**BEB ionization cross section using all electron models by considering different free numbers of electrons: dashed dotted curve, only 3$\pi $ molecular orbitals (MO); dotted dashed curve, 10 free electrons; double dashed curve, 12 free electrons; dotted curve, from total 26 electrons.

Model | Energy | Dipole Moment | Quadrupole Moment |
---|---|---|---|

(au) | (au) | (Q${}_{20}$) (au) | |

HF | −558.8667 | 0.5545 | 0.9398 |

12-states CI | −558.9011 | 0.4363 (0.353 * [32]) | 1.0045 (1.0 * [36]) |

**Table 2.**Vertical Excitation Energies (in eV) of the excited states for the target states in ${\mathit{C}}_{\infty v}$ and ${\mathit{C}}_{2v}$ symmetries.

Target State | Present Work | Other Works |
---|---|---|

${1}^{3}\Pi {(}^{3}{\mathit{B}}_{1}{,}^{3}{\mathit{B}}_{2})$ | 3.84 | 2.33 (Expt) [37] |

3.10 (CASSCF) [38] | ||

${1}^{1}\Pi {(}^{1}{\mathit{B}}_{1}{,}^{1}{\mathit{B}}_{2})$ | 5.10 | 4.63 (MRD-CI) [39] |

4.34 (CI) [39] | ||

${2}^{3}\Pi {(}^{3}{\mathit{B}}_{1}{,}^{3}{\mathit{B}}_{2})$ | 8.33 | - |

${1}^{3}{\Sigma}^{+}{(}^{3}{\mathit{A}}_{1}$) | 8.64 | - |

${1}^{3}{\Delta}_{2}{(}^{3}{\mathit{A}}_{2}$) | 8.80 | - |

${2}^{1}\Pi {(}^{1}{\mathit{B}}_{1}{,}^{1}{\mathit{B}}_{2})$ | 9.01 | 9.08 (MRD-CI) [39] |

8.19 (CI) [39] | ||

${1}^{1}{\Delta}_{2}{(}^{1}{\mathit{A}}_{2}$) | 9.45 | 10.54 (MRD-CI) [39] |

10.27 (CI) [39] |

**Table 3.**${E}^{res}$ and ${\Gamma}^{res}$ values in different scattering models for ${}^{2}{A}_{1}$ scattering symmetry.

Scattering | ${\mathit{E}}^{\mathit{res}}$ | ${\mathsf{\Gamma}}^{\mathit{res}}$ |
---|---|---|

Model | (eV) | (eV) |

SE | 0.94 | 0.75 |

SEP | 0.31 | 0.18 |

1-state | 0.79 | 0.62 |

5-states | 0.40 | 0.24 |

12-states | Bound | - |

**Table 4.**Molecular orbital binding energies, average kinetic energies, and occupation number of occupied molecular orbitals obtained at equilibrium geometry at the HF level using a 6-311G* basis set. The orbitals given in the parentheses correspond to ${\mathit{C}}_{2v}$ point group.

Molecular Orbital | |B| ( eV) | U ( eV) | N |
---|---|---|---|

1σ ($1{\mathit{a}}_{1}$) | 2855.47 | 3731.21 | 2 |

2σ ($2{\mathit{a}}_{1}$) | 717.01 | 1013.66 | 2 |

3σ ($3{\mathit{a}}_{1}$) | 289.97 | 593.89 | 2 |

1π ($1{\mathit{b}}_{1},1{\mathit{b}}_{2}$) | 221.94 | 562.46 | 4 (2,2) |

4σ ($4\mathit{a}1$) | 221.10 | 560.52 | 2 |

5σ ($5{\mathit{a}}_{1}$) | 44.69 | 101.877 | 2 |

6σ ($6{\mathit{a}}_{1}$) | 30.14 | 91.28 | 2 |

2π ($2{\mathit{b}}_{1},2{\mathit{b}}_{2}$) | 19.76 | 81.61 | 4 (2,2) |

7σ ($7{\mathit{a}}_{1}$) | 19.00 | 79.52 | 2 |

3$\pi $ ($3{b}_{1},3{b}_{2}$) | 13.44 | 72.43 | 4 (2,2) |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bassi, M.; Bharadvaja, A.; Baluja, K.L.
Elastic and Inelastic Cross Sections for Low-Energy Electron Collisions with ClF Molecule Using the * R*-Matrix Method.

*Atoms*

**2022**,

*10*, 8. https://doi.org/10.3390/atoms10010008

**AMA Style**

Bassi M, Bharadvaja A, Baluja KL.
Elastic and Inelastic Cross Sections for Low-Energy Electron Collisions with ClF Molecule Using the * R*-Matrix Method.

*Atoms*. 2022; 10(1):8. https://doi.org/10.3390/atoms10010008

**Chicago/Turabian Style**

Bassi, Monika, Anand Bharadvaja, and Kasturi Lal Baluja.
2022. "Elastic and Inelastic Cross Sections for Low-Energy Electron Collisions with ClF Molecule Using the * R*-Matrix Method"

*Atoms*10, no. 1: 8. https://doi.org/10.3390/atoms10010008